diff --git a/00 Home/01 Home/01 Home.html b/00 Home/01 Home/01 Home.html index 845cb8b..ff41ca3 100644 --- a/00 Home/01 Home/01 Home.html +++ b/00 Home/01 Home/01 Home.html @@ -1,5 +1,5 @@ -
We choose 4 factors: FCFYield, PriceChange1M, BookValuePerShare and RevenueGrowth.
diff --git "a/04 Strategy Library/09 Stock Selection Strategy Based on Fundamental Factors/02 \350\246\201\347\264\240\351\200\211\346\213\251.cn.html" "b/04 Strategy Library/09 Stock Selection Strategy Based on Fundamental Factors/02 \350\246\201\347\264\240\351\200\211\346\213\251.cn.html" new file mode 100644 index 0000000..b8cefb8 --- /dev/null +++ "b/04 Strategy Library/09 Stock Selection Strategy Based on Fundamental Factors/02 \350\246\201\347\264\240\351\200\211\346\213\251.cn.html" @@ -0,0 +1,236 @@ ++ QuantConnect为美国股市提供了晨星基本面数据。估值比率是每日数据。对于其他项目,如营业比率和财务报表,可以根据不同的属性获得不同时期的数据。详细的可用要素请参阅Data Library。 +
++ 该算法的设计是为了每次测试一个要素的重要性。 +
+ +def Initialize(self):
+ self.SetStartDate(2005,01,01) # 设置开始日期
+ self.SetEndDate(2012,03,01) # 设置结束日期
+ self.SetCash(50000) # 设置策略现金
+ self.UniverseSettings.Resolution = Resolution.Daily
+ self.AddUniverse(self.CoarseSelectionFunction, self.FineSelectionFunction)
+ self.AddEquity("SPY") # add benchmark
+ self.numOfCourseSymbols = 200
+ self.numOfPortfolio = 5
+ self._changes = None
+ self.flag1 = 1 # 控制粗选和精选函数每月重新平衡的变量
+ self.flag2 = 0 # 控制OnData函数每月重新平衡的变量
+ self.flag3 = 0 # 记录重新平衡次数的变量
+ # 将不同投资组合的月收益存储在一个数据框架内
+ self.df_return = pd.DataFrame(index = range(self.numOfPortfolio+1))
+ # 预定事件在SPY的第一个交易日解除
+ self.Schedule.On(self.DateRules.MonthStart("SPY"), self.TimeRules.AfterMarketOpen("SPY"), Action(self.Rebalancing))
+
+
+ 1. 首先,我们按每日美元交易量对股票进行排序,并将美元交易量最高的股票作为候选股票。有一种方便的方法使用我们的集合选择API。在默认情况下,集合每天都会刷新,但也可以根据需要经常刷新。这是由可变UniverseSettings.Resolution控制的。您可以参考documentation了解更多详细信息。在这里,我们使用Scheduled events API来触发在每个月第一个交易日运行的代码,并使用三个标志变量来控制CoarseSelection,FineSelection和Ondata函数的重新平衡。
+
+ 粗略集合选择是由QuantConnect提供的内置集合数据,它允许你对超过16,000个符号的集合进行筛选,在你的算法之前进行粗略的筛选。由于粗选功能考虑了包括基金在内的所有无基础数据股票,所以我们需要属性x.HasFundamentalData将这些股票排除在我们的候选股票池之外。
+
# 按照每日美元交易量对数据进行排序,并取排名最上面的条目 +def CoarseSelectionFunction(self, coarse): + if self.flag1: + CoarseWithFundamental = [x for x in coarse if x.HasFundamentalData] + sortedByVolume = sorted(CoarseWithFundamental, key=lambda x: x.DollarVolume, reverse=True) + top = sortedByVolume[:self.numOfCourseSymbols] + return [i.Symbol for i in top] + else: + return [] ++
+ 2. 我们在每个月初提取候选股票的要素值,并按其要素值的升序对股票进行排序。例如,这里我们使用了12个月的总风险基础资本数据x.FinancialStatements.TotalRiskBasedCapital.TwelveMonths。它是一级资本和二级资本的总和。x.Symbol.Value可以给出所选股票x的串符号,然后将这些排序后的符号保存为self.symbol。
+
def FineSelectionFunction(self, fine): + if self.flag1: + self.flag1 = 0 + self.flag2 = 1 + # 通过删除要素值为零的股票来进行精细筛选 + filtered_fine = [x for x in fine if x.FinancialStatements.TotalRiskBasedCapital.TwelveMonths != 0 ] + # 按照要素值倒序排序 + sorted_fine = sorted(filtered_fine, key=lambda x: x.FinancialStatements.TotalRiskBasedCapital.TwelveMonths, reverse=True) + self.symbol = [str(x.Symbol.Value) for x in sorted_fine] + # 要素值 = [x.ValuationRatios.PERatio for x in sorted_fine] + self.flag3 = self.flag3 + 1 + return [] + else: + return [] ++
+ 1. 在每个月底,我们提取每支股票的一个月历史收盘价,并计算月收益。 +
+ +sorted_symbol = self.symbol
+self.AddEquity("SPY") # 添加基准
+for x in sorted_symbol:
+ self.AddEquity(x)
+history = self.History(20,Resolution.Daily)
+monthly_return =[]
+new_symbol_list =[]
+for j in range(len(sorted_symbol)):
+ try:
+ daily_price = []
+ for slice in history:
+ bar = slice[sorted_symbol[j]]
+ daily_price.append(float(bar.Close))
+ new_symbol_list.append(sorted_symbol[j])
+ monthly_return.append(daily_price[-1] / daily_price[0] - 1)
+ except:
+ self.Log("No history data for " + str(sorted_symbol[j]))
+ del daily_price
+# 月收益列表的长度应能够被投资组合的数量整除
+monthly_return = monthly_return[:int(math.floor(len(monthly_return) / self.numOfPortfolio) * self.numOfPortfolio)]
+
+
+ 2. 我们将股票分为5个投资组合,计算每个投资组合的平均月收益。然后在数据框架df_return的最后一行添加基准“SPY”的月收益。
+
reshape_return = np.reshape(monthly_return, (self.numOfPortfolio, len(monthly_return)/self.numOfPortfolio))
+# 计算不同投资组合的平均收益
+port_avg_return = np.mean(reshape_return,axis=1).tolist()
+# 将"SPY"的收益作为基准添加到收益列表的末尾
+benchmark_syl = self.AddEquity("SPY").Symbol
+history_benchmark = self.History(20,Resolution.Daily)
+benchmark_daily_price = [float(slice[benchmark_syl].Close) for slice in history_benchmark]
+benchmark_monthly_return = (benchmark_daily_price[-1]/benchmark_daily_price[0]) - 1
+port_avg_return.append(benchmark_monthly_return)
+self.df_return[str(self.flag3)] = port_avg_return
+
++ 在得到投资组合的月收益和基准后,我们计算了整个回溯测试期间各投资组合的年平均收益和基准之上的超额收益。然后我们生成三个度量来判断每个因素的重要性。 +
+ +def calculate_criteria(self,df_port_return):
+ total_return = (df_port_return + 1).T.cumprod().iloc[-1,:] - 1
+ annual_return = (total_return+1)**(1./6)-1
+ excess_return = annual_return - np.array(annual_return)[-1]
+ correlation = annual_return[0:5].corr(pd.Series([5,4,3,2,1],index = annual_return[0:5].index))
+ # 高收益的高要素
+ if np.array(total_return)[0] > np.array(total_return)[-2]:
+ loss_excess = df_port_return.iloc[-2,:] - df_port_return.iloc[-1,:]
+ win_excess = df_port_return.iloc[0,:] - df_port_return.iloc[-1,:]
+ loss_prob = loss_excess[loss_excess<0].count()/float(len(loss_excess)) win_prob = win_excess[win_excess>0].count()/float(len(win_excess))
+ win_port_excess_return = np.array(excess_return)[0]
+ loss_port_excess_return = np.array(excess_return)[-2]
+ # 低收益的高要素
+ else:
+ loss_excess = df_port_return.iloc[0,:] - df_port_return.iloc[-1,:]
+ win_excess = df_port_return.iloc[-2,:] - df_port_return.iloc[-1,:]
+ loss_prob = loss_excess[loss_excess<0].count()/float(len(loss_excess)) win_prob = win_excess[win_excess>0].count()/float(len(win_excess))
+ win_port_excess_return = np.array(excess_return)[-2]
+ loss_port_excess_return = np.array(excess_return)[0]
+ test_result = {}
+ test_result["correelation"]=correlation
+ test_result["win probality"]=win_prob
+ test_result["loss probality"]=loss_prob
+ test_result["win portfolio excess return"]=win_port_excess_return
+ test_result["loss portfolio excess return"]=loss_port_excess_return
+
+ return test_result
+| 要素显著性测试结果 | +|||||||
|---|---|---|---|---|---|---|---|
| 要素 | +FCFYield | +BuyBackYield | +PriceChange1M | +TrailingDividendYield | +EVToEBITDA | +RevenueGrowth | +BookValuePerShare | +
| 关联性 | +-0.936 | +-0.987 | +0.918 | +-0.981 | +0.939 | +0.89 | +-0.92 | +
| 盈利概率 | +0.630 | +0.639 | +1 | +0.667 | +0.722 | +0.69 | +0.69 | +
| 亏损概率 | +0.426 | +0.472 | +1 | +0.518 | +0.472 | +0.42 | +0.40 | +
| 超额收益(盈利) | +0.324 | +0.212 | +0.303 | +0.225 | +0.414 | +0.23 | +0.27 | +
| 超额收益(亏损) | +0.060 | +0.037 | +-1.67 | +0.043 | +0.042 | +0.07 | +0.06 | +
+ 我们选择了4个要素:FCFYield、PriceChange1M、BookValuePerShare和RevenueGrowth。 +
diff --git "a/04 Strategy Library/09 Stock Selection Strategy Based on Fundamental Factors/03 \350\202\241\347\245\250\351\200\211\346\213\251.cn.html" "b/04 Strategy Library/09 Stock Selection Strategy Based on Fundamental Factors/03 \350\202\241\347\245\250\351\200\211\346\213\251.cn.html" new file mode 100644 index 0000000..00bbed2 --- /dev/null +++ "b/04 Strategy Library/09 Stock Selection Strategy Based on Fundamental Factors/03 \350\202\241\347\245\250\351\200\211\346\213\251.cn.html" @@ -0,0 +1,17 @@ +接下来我们将选择股票。 ++ 首先,我们删除没有基础数据或要素值为零的股票。对于每种预先选择的因素,我们根据这些因素值对股票进行排序。当要素相关性为负时,顺序递减;要素相关性为正时,顺序递增。 +
+ ++ 第二步是使用不同的选择要素变量来计算每支股票的平均加权综合要素得分。 +
+ +- This strategy is called Short-Term Reversal Strategy which is discussed in detail in the paper written by Wilma de Groot, Joop Huij and Weili Zhou (2011) titled "Another look at trading costs and short-term reversal profits". The standard reversal strategy takes the whole universe of stocks into consideration, while this paper limits the stock universe only to large cap stocks so that trading costs could be significantly reduced. -
-- One simple version of this strategy could be described like this: The investment universe consists of 100 biggest companies by market capitalization. We go long on the 10% stocks which have the?lowest performances in the last month while going short on the 10% stocks with the highest ones. The portfolio is rebalanced weekly. - In the paper, however, strategies with different investment universes and different rebalancing frequencies are all backtested. The results show that, the larger the size of the investment universe, the larger the trading costs caused by extensively trading in small cap stocks which are less liquid; and trading costs become substantially lower when the rebalancing frequency is decreased from daily to weekly, but so do gross returns. - In this tutorial, we only use 100 stocks with weekly rebalancing for illustration. + In this tutorial, we implement a version of the short-term reversal strategy published by De Groot, Huij, & Zhou + (2012). The strategy works by observing the returns of each security in the universe over the previous month. Every + week, the algorithm longs the worst performers and shorts the top performers. The original strategy outlined in the + literature considers the entire universe of stocks when trading. To reduce trading costs, we limit our universe to + the most liquid large cap stocks. Our analysis shows the strategy underperforms the S&P 500 index during all our + backtest periods except the 2020 market crash.
diff --git a/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/02 Method.html b/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/02 Method.html index 63e4b63..8b9f021 100755 --- a/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/02 Method.html +++ b/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/02 Method.html @@ -1,104 +1,141 @@- The strategy code mainly consists of three parts: Initialization, Warm Up, and Weekly Rebalancing. + The strategy code mainly consists of four parts: Initialization, Universe Selection, OnData, and OnSecuritiesChanged.
-- In the Initialize function, we set up look-back period, beginning cash balance, the size of the investment universe, the number of traded stocks, etc. We use self._numOfWeeks to count?the number of weeks that have passed since the start date, and self._LastDay to indicate whether it is a new week. self._ifWarmUp is true when the self._numOfWeeks is 3, which means as long as next week's data come, we can make our investment decisions.??self._stocks is a list containing all the symbols of the 100 stocks that are taken into consideration. self._values is a dictionary with keys the stock symbols and values the lists containing the prices of stock each week since 4 weeks ago. + When initializing the algorithm, we add a coarse universe selection method and specify several parameters to use + when selecting securities.
-def Initialize(self):
- self.SetStartDate(2002, 1, 3)
- self.SetEndDate(2016, 12, 1)
- self.SetCash(1000000)
-
+
+class ShortTimeReversal(QCAlgorithm):
+ def Initialize(self):
+ # ...
+
self.UniverseSettings.Resolution = Resolution.Daily
- self.AddUniverse(self.CoarseSelectionFunction)
- self._numberOfSymbols = 100
- self._numberOfTradings = 0.1 * self._numberOfSymbols
-
- self._numOfWeeks = 0
- self._LastDay = -1
- self._ifWarmUp = False
+ self.AddUniverse(self.SelectCoarse)
+
+ self.dollar_volume_selection_size = 100
+ self.roc_selection_size = int(0.1 * self.dollar_volume_selection_size)
+
+ self.lookback = 22
+ self.roc_by_symbol = {}
+ self.week = 0
- self._stocks = []
- self._values = {}
+
- Also, we need to use?CoarseSelectionFunction to select 100 qualified stocks from the total stock universe. Here, we sort the total stock universe by each stock's DollarVolume in decreasing order. Then, we select the first 100 stocks that have the largest DollarVolume among all the stocks in the universe. -
-def CoarseSelectionFunction(self, coarse): - sortedByDollarVolume = sorted(coarse, key=lambda x: x.DollarVolume, reverse=True) - top100 = sortedByDollarVolume[:self._numberOfSymbols] - list = List[Symbol]() - for x in top100: - list.Add(x.Symbol) - return list --
- Before we are able to make our investment decisions, we must have at least 4 weeks' data to calculate the performance, i.e. the monthly return, of each stock. Hence, we need a warm up period as long as 3 weeks to accumulate price series, so that once the fourth week's data come we can calculate?the return of the whole month. + The coarse universe selection method creates a RateOfChange + indicator for each of the top 100 + most liquid securities in the market. Upon creation, the indicator is manually warmed-up with historical closing + prices. After the indicators are ready, the universe selects the securities with the 10 best and 10 worst + RateOfChange values.
self._stocks = []
-self.uni_symbol = None
-symbols = self.UniverseManager.Keys
-for i in symbols:
- if str(i.Value) == "QC-UNIVERSE-COARSE-USA":
- self.uni_symbol = i
- for i in self.UniverseManager[self.uni_symbol].Members:
- self._stocks.append(i.Value.Symbol)
- self._values[i.Value.Symbol] = [self.Securities[i.Value.Symbol].Price]
-
+
+class ShortTimeReversal(QCAlgorithm):
+ # ...
+
+ def SelectCoarse(self, coarse):
+
+ # We should keep a dictionary for all securities that have been selected
+ for cf in coarse:
+ symbol = cf.Symbol
+ if symbol in self.roc_by_symbol:
+ self.roc_by_symbol[symbol].Update(cf.EndTime, cf.AdjustedPrice)
+
+ # Refresh universe each week
+ week_number = self.Time.date().isocalendar()[1]
+ if week_number == self.week:
+ return Universe.Unchanged
+ self.week = week_number
+
+ # sort and select by dollar volume
+ sortedByDollarVolume = sorted(coarse, key=lambda x: x.DollarVolume, reverse=True)
+ selected = {cf.Symbol: cf for cf in sortedByDollarVolume[:self.dollar_volume_selection_size]}
+
+ # New selections need a history request to warm up the indicator
+ symbols = [k for k in selected.keys()
+ if k not in self.roc_by_symbol or not self.roc_by_symbol[k].IsReady]
+
+ if symbols:
+ history = self.History(symbols, self.lookback, Resolution.Daily)
+ if history.empty:
+ self.Log(f'No history for {", ".join([x.Value for x in symbols])}')
+ history = history.close.unstack(0)
+
+ for symbol in symbols:
+
+ if symbol not in history:
+ continue
+
+ # Create and warm-up the RateOfChange indicator
+ roc = RateOfChange(self.lookback)
+ for time, price in history[symbol].dropna().iteritems():
+ roc.Update(time, price)
+
+ if roc.IsReady:
+ self.roc_by_symbol[symbol] = roc
+
+ # Sort the symbols by their ROC values
+ selectedRateOfChange = {}
+ for symbol in selected.keys():
+ if symbol in self.roc_by_symbol:
+ selectedRateOfChange[symbol] = self.roc_by_symbol[symbol]
+ sortedByRateOfChange = sorted(selectedRateOfChange.items(), key=lambda kv: kv[1], reverse=True)
+
+ # Define the top and the bottom to buy and sell
+ self.rocTop = [x[0] for x in sortedByRateOfChange[:self.roc_selection_size]]
+ self.rocBottom = [x[0] for x in sortedByRateOfChange[-self.roc_selection_size:]]
+
+ return self.rocTop + self.rocBottom
- We get all the symbols of qualified stocks from UniverseManager and keep them in self._stocks which is a list. Then we create for each key in the dictionary self._values a list where its first week's price is stored. And every time new data come, we append the new price to the end of the list of each stock. -
-for stock in self._stocks: - self._values[stock].append(self.Securities[stock].Price)-
- After the warm-up period, we calculate monthly returns every week and based on the returns, we make our investment decisions. + As new data is passed to the OnData method, we issue orders to form a long-short portfolio. We long the securities + with the lowest RateOfChange values and short those with the largest values. After rebalancing, we clear the + `rocTop` and `rocBottom` lists to ensure we don’t trade again until the universe is refreshed.
-returns = {}
-for stock in self._stocks:
- newPrice = self.Securities[stock].Price
- oldPrice = self._values[stock].pop(0)
- self._values[stock].append(newPrice)
- returns[stock] = newPrice/oldPrice
+
+class ShortTimeReversal(QCAlgorithm):
+ # ...
+
+ def OnData(self, data):
+ # Rebalance
+ for symbol in self.rocTop:
+ self.SetHoldings(symbol, -0.5/len(self.rocTop))
+ for symbol in self.rocBottom:
+ self.SetHoldings(symbol, 0.5/len(self.rocBottom))
+
+ # Clear the list of securities we have placed orders for
+ # to avoid new trades before the next universe selection
+ self.rocTop.clear()
+ self.rocBottom.clear()
- Every week when new data come, we use them along with the data four weeks ago to calculate the monthly returns. At the same time, we remove the oldest data from our lists. This step is essential to prevent memory size exceeding the limit. + We are rebalancing the portfolio on a weekly basis, but securities can leave our defined universe between rebalance + days. To accommodate this, we liquidate any securities that are removed from the universe in the + OnSecuritiesChanged method.
-+class ShortTimeReversal(QCAlgorithm): + # ... -newArr = [(v,k) for k,v in returns.items()] -newArr.sort() -for ret, stock in newArr[self._numberOfTradings:-self._numberOfTradings]: - self.SetHoldings(stock, 0) -for ret, stock in newArr[0:self._numberOfTradings]: - self.SetHoldings(stock, 0.5/self._numberOfTradings) -for ret, stock in newArr[-self._numberOfTradings:]: - self.SetHoldings(stock, -0.5/self._numberOfTradings) + def OnSecuritiesChanged(self, changes): + for security in changes.RemovedSecurities: + self.Liquidate(security.Symbol, 'Removed from Universe')-
- Finally, we sort the returns in increasing order. For the stocks whose monthly returns fall into the first 10% (performed badly in last month), we long them; For those fall into the last 10% (performed well in last month), we short them. Others (between 10% and 90%) will be set to 0. -
+- In the paper, the look-back period is from 1990 to 2009. However, we want to test whether the strategy is still profitable in the new time period. Hence we use different look-back periods instead. - If we begin from 2005 and end in 2017, there will be a total return of 131.50%. Although to some extent the performance of this strategy is dependent on different market situations,?nevertheless, in either situation mentioned above, this strategy could significantly beat the S&P 500 benchmark. - Further research and backtesting could be done on different look-back periods, rebalancing frequencies, investment universes, numbers of traded stocks, etc. -
diff --git a/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/04 Algorithm.html b/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/04 Algorithm.html index 058cc18..c2e37d5 100755 --- a/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/04 Algorithm.html +++ b/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/04 Algorithm.html @@ -1,6 +1,6 @@ diff --git a/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/05 References.html b/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/05 References.html deleted file mode 100644 index 6c1e761..0000000 --- a/04 Strategy Library/10 Short-Term Reversal Strategy in Stocks/05 References.html +++ /dev/null @@ -1,5 +0,0 @@ -| Period Name | +Start Date | +End Date | +Strategy | +Sharpe | +Variance | +
|---|---|---|---|---|---|
| 5 Year Backtest | +1/1/2016 | +1/1/2021 | +Strategy | +0.24 | +0.058 | +
| Benchmark | +0.825 | +0.028 | +|||
| 2020 Crash | +2/19/2020 | +3/23/2020 | +Strategy | +-1.025 | +0.917 | +
| Benchmark | +-1.4 | +0.474 | +|||
| 2020 Recovery | +3/23/2020 | +6/8/2020 | +Strategy | +1.688 | +0.16 | +
| Benchmark | +8.765 | +0.103 | +
+ Although this strategy passes several of the + metrics required for Alpha Streams + and the Quant League competition, it requires further work to pass the following requirements: +
+ ++ The short-term reversal strategy implemented in this tutorial produced a lower Sharpe ratio than the S&P + 500 index ETF benchmark over all our testing periods except during the 2020 market crash. To continue the + development of this strategy, future areas of research include: +
+ ++ To continue the development of this strategy, future areas of research include: +
+ ++ The WTI-Brent spread is the difference between the prices of two types of crude oil: West Texas Intermediate (WTI) on the long side and Brent Crude (Brent) on the short side. + For years, the price difference between the two has only been a few dollars on average. As both oils are very similar, their spread shows signs of strong predictability and usually oscillates around some average value. + Therefore, it is possible to use deviations from the fair spread value to bet on convergence back to fair value. Here we present a trading strategy based on the price deviations of the spread. +
diff --git "a/04 Strategy Library/100 Trading with WTI BRENT Spread/01 \347\256\200\344\273\213.cn.html" "b/04 Strategy Library/100 Trading with WTI BRENT Spread/01 \347\256\200\344\273\213.cn.html" new file mode 100644 index 0000000..1645559 --- /dev/null +++ "b/04 Strategy Library/100 Trading with WTI BRENT Spread/01 \347\256\200\344\273\213.cn.html" @@ -0,0 +1,3 @@ ++ WTI-Brent价差指的是两种原油价格之间的差异:即多头的西德克萨斯中质原油(WTI)和空头布伦特原油(Brent)。多年来,两者之间的价格差距平均只有几美元。由于这两种原油非常相似,它们的价差显示出很强的可预测性,通常在某个平均值附近波动。因此,有可能使用偏离公允价差的值来押注回复到公允价值。本文提出了一种基于价差价格差异的交易策略。 +
diff --git a/04 Strategy Library/100 Trading with WTI BRENT Spread/02 Method.html b/04 Strategy Library/100 Trading with WTI BRENT Spread/02 Method.html new file mode 100644 index 0000000..fdcce3d --- /dev/null +++ b/04 Strategy Library/100 Trading with WTI BRENT Spread/02 Method.html @@ -0,0 +1,121 @@ ++ We download the WTI and Brent crude oil price from Macrotrends and import the csv file with the custom data downloader. + The unit is dollars per barrel. +
+
+ class WTI(PythonData):
+ "Class to import WTI Spot Price(Dollars per Barrel) data from Dropbox"
+
+ def GetSource(self, config, date, isLiveMode):
+ return SubscriptionDataSource("https://www.dropbox.com/s/jpie3z6j0stp97d/wti-crude-oil-prices-10-year-daily.csv?dl=1", SubscriptionTransportMedium.RemoteFile)
+
+ def Reader(self, config, line, date, isLiveMode):
+ if not (line.strip() and line[1].isdigit()): return None
+ index = WTI()
+ index.Symbol = config.Symbol
+ try:
+ data = line.split(',')
+ index.Time = datetime.strptime(data[0], "%Y-%m-%d")
+ index.Value = Decimal(data[1])
+ except:
+ return None
+ return index
+
+ class BRENT(PythonData):
+ "Class to import BRENT Spot Price(Dollars per Barrel) data from Dropbox"
+
+ def GetSource(self, config, date, isLiveMode):
+ return SubscriptionDataSource("https://www.dropbox.com/s/w380c4n7xjmdqxl/brent-crude-oil-prices-10-year-daily.csv?dl=1", SubscriptionTransportMedium.RemoteFile)
+
+ def Reader(self, config, line, date, isLiveMode):
+ if not (line.strip() and line[1].isdigit()): return None
+ index = BRENT()
+ index.Symbol = config.Symbol
+ try:
+ data = line.split(',')
+ index.Time = datetime.strptime(data[0], "%Y-%m-%d")
+ index.Value = Decimal(data[1])
+ except:
+ return None
+ return index
+
+
+ The spread is defined as the difference between WTI price and Brent price. Next, we need to calculate the moving average of the spread series.
+ using the the indicator SimpleMovingAverage. As the indicator uses the price difference instead of the price series,
+ we need to manually initialize the indicator with the history request.
+
+self.SpreadSMA = SimpleMovingAverage(20) +hist = self.History(["WTI", "BRENT"], 400, Resolution.Daily)["value"].unstack(level=0).dropna() +hist_20days = hist[-20:] +spread = (hist_20days["WTI"] - hist_20days["BRENT"]).dropna() +for index, value in spread.items(): + self.SpreadSMA.Update(index, value) ++
+ To get the fair value of the spread, we perform the linear regression between WTI and Brent price over the last one year history price. +
+ \[P_{Brent}=\beta \cdot P_{WTI}+\alpha\] ++ Then the fair value of the spread is +
+\[Fair \ Spread =(1-\beta)\cdot CurrentPrice_{WTI}-\alpha\] + ++hist_one_year = hist[-252:] +X = hist_one_year["WTI"][:, np.newaxis] +y = hist_one_year["BRENT"] +self.regr = linear_model.LinearRegression() +self.regr.fit(X, y) ++
+ The fair value is calculated every day. If the current spread value is above SMA 20 then we enter a short position in the spread on close (betting that the spread will decrease to fair value represented by SMA 20). + The trade is closed at the close of the trading day when the spread crosses below fair value. If the current spread value is below SMA 20 then we enter a long position betting that the spread will increase and the trade is closed at the close of the trading day when the spread crosses above fair value. +
+ +
+def OnData(self, data):
+ if not (data.ContainsKey("WTI") and data.ContainsKey("BRENT")): return
+ self.Plot("Spread Plot", "Spread", data["WTI"].Price - data["BRENT"].Price)
+
+ self.SpreadSMA.Update(self.Time, data["WTI"].Price - data["BRENT"].Price)
+ if not self.SpreadSMA.IsReady: return
+ spread = self.Securities["WTI"].Price - self.Securities["BRENT"].Price
+ fair_value =self.Securities["WTI"].Price - Decimal(self.regr.predict([[self.Securities["WTI"].Price]])[0])
+
+ if spread > self.SpreadSMA.Current.Value and not (self.Portfolio["WTI"].IsShort and self.Portfolio["BRENT"].IsLong):
+ self.SetHoldings("WTI", -0.5)
+ self.SetHoldings("BRENT", 0.5)
+ self.Plot("Spread Plot", "Long Spread Trade", data["WTI"].Price - data["BRENT"].Price)
+
+ elif spread < self.SpreadSMA.Current.Value and not (self.Portfolio["WTI"].IsLong and self.Portfolio["BRENT"].IsShort):
+ self.SetHoldings("WTI", 0.5)
+ self.SetHoldings("BRENT", -0.5)
+ self.Plot("Spread Plot", "Short Spread Trade", data["WTI"].Price - data["BRENT"].Price)
+
+ if self.Portfolio["WTI"].IsShort and self.Portfolio["BRENT"].IsLong and spread < fair_value:
+ self.Liquidate()
+
+ if self.Portfolio["WTI"].IsLong and self.Portfolio["BRENT"].IsShort and spread > fair_value:
+ self.Liquidate()
+
++ To demonstrate the trend of the spread series, we add the spread plot and mark the spread long/short point on the spread curve. +
+
+spreadPlot = Chart("Spread Plot")
+spreadPlot.AddSeries(Series("Spread", SeriesType.Line, 0))
+spreadPlot.AddSeries(Series("Long Spread Trade", SeriesType.Scatter, 0))
+spreadPlot.AddSeries(Series("Short Spread Trade", SeriesType.Scatter, 0))
+self.AddChart(spreadPlot)
+
++ 我们从Macrotrends下载WTI和Brent原油价格,并使用自定义数据下载器导入csv文件。单位为美元/桶。 +
+
+ class WTI(PythonData):
+ "Class to import WTI Spot Price(Dollars per Barrel) data from Dropbox"
+
+ def GetSource(self, config, date, isLiveMode):
+ return SubscriptionDataSource("https://www.dropbox.com/s/jpie3z6j0stp97d/wti-crude-oil-prices-10-year-daily.csv?dl=1", SubscriptionTransportMedium.RemoteFile)
+
+ def Reader(self, config, line, date, isLiveMode):
+ if not (line.strip() and line[1].isdigit()): return None
+ index = WTI()
+ index.Symbol = config.Symbol
+ try:
+ data = line.split(',')
+ index.Time = datetime.strptime(data[0], "%Y-%m-%d")
+ index.Value = Decimal(data[1])
+ except:
+ return None
+ return index
+
+ class BRENT(PythonData):
+ "Class to import BRENT Spot Price(Dollars per Barrel) data from Dropbox"
+
+ def GetSource(self, config, date, isLiveMode):
+ return SubscriptionDataSource("https://www.dropbox.com/s/w380c4n7xjmdqxl/brent-crude-oil-prices-10-year-daily.csv?dl=1", SubscriptionTransportMedium.RemoteFile)
+
+ def Reader(self, config, line, date, isLiveMode):
+ if not (line.strip() and line[1].isdigit()): return None
+ index = BRENT()
+ index.Symbol = config.Symbol
+ try:
+ data = line.split(',')
+ index.Time = datetime.strptime(data[0], "%Y-%m-%d")
+ index.Value = Decimal(data[1])
+ except:
+ return None
+ return index
+
+
+ 价差定义为WTI价格与Brent价格之间的差。接下来,我们需要使用指标SimpleMovingAverage来计算价差系列的移动平均值。由于指标使用的是价格差异而不是价格系列,因此需要使用历史请求手动初始化指标。
+
+self.SpreadSMA = SimpleMovingAverage(20) +hist = self.History(["WTI", "BRENT"], 400, Resolution.Daily)["value"].unstack(level=0).dropna() +hist_20days = hist[-20:] +spread = (hist_20days["WTI"] - hist_20days["BRENT"]).dropna() +for index, value in spread.items(): + self.SpreadSMA.Update(index, value) ++
+ 为了得到价差的公允价值,我们对WTI和Brent价格在过去一年的历史价格进行了线性回归。 +
+ \[P_{Brent}=\beta \cdot P_{WTI}+\alpha\] ++ 那么差价的公允价值是 +
+\[Fair \ Spread =(1-\beta)\cdot CurrentPrice_{WTI}-\alpha\] + ++hist_one_year = hist[-252:] +X = hist_one_year["WTI"][:, np.newaxis] +y = hist_one_year["BRENT"] +self.regr = linear_model.LinearRegression() +self.regr.fit(X, y) ++
+ 公允价值每天计算一次。如果当前价差值高于SMA 20,那么我们将在收盘时进入价差空头头寸(押注价差将降至SMA 20所代表的公允价值)。当价差低于公允价值时,交易在交易日收盘时结束。如果当前价差低于SMA 20,那么我们就进入多头头寸,押注价差将会增加,当价差超过公允价值时,交易将在交易日收盘时结束。 +
+ +
+def OnData(self, data):
+ if not (data.ContainsKey("WTI") and data.ContainsKey("BRENT")): return
+ self.Plot("Spread Plot", "Spread", data["WTI"].Price - data["BRENT"].Price)
+
+ self.SpreadSMA.Update(self.Time, data["WTI"].Price - data["BRENT"].Price)
+ if not self.SpreadSMA.IsReady: return
+ spread = self.Securities["WTI"].Price - self.Securities["BRENT"].Price
+ fair_value =self.Securities["WTI"].Price - Decimal(self.regr.predict([[self.Securities["WTI"].Price]])[0])
+
+ if spread > self.SpreadSMA.Current.Value and not (self.Portfolio["WTI"].IsShort and self.Portfolio["BRENT"].IsLong):
+ self.SetHoldings("WTI", -0.5)
+ self.SetHoldings("BRENT", 0.5)
+ self.Plot("Spread Plot", "Long Spread Trade", data["WTI"].Price - data["BRENT"].Price)
+
+ elif spread < self.SpreadSMA.Current.Value and not (self.Portfolio["WTI"].IsLong and self.Portfolio["BRENT"].IsShort):
+ self.SetHoldings("WTI", 0.5)
+ self.SetHoldings("BRENT", -0.5)
+ self.Plot("Spread Plot", "Short Spread Trade", data["WTI"].Price - data["BRENT"].Price)
+
+ if self.Portfolio["WTI"].IsShort and self.Portfolio["BRENT"].IsLong and spread < fair_value:
+ self.Liquidate()
+
+ if self.Portfolio["WTI"].IsLong and self.Portfolio["BRENT"].IsShort and spread > fair_value:
+ self.Liquidate()
+
++ 为了显示价差序列的趋势,我们添加了价差图,并在价差曲线上标记了价差的多头/空头点。 +
+
+spreadPlot = Chart("Spread Plot")
+spreadPlot.AddSeries(Series("Spread", SeriesType.Line, 0))
+spreadPlot.AddSeries(Series("Long Spread Trade", SeriesType.Scatter, 0))
+spreadPlot.AddSeries(Series("Short Spread Trade", SeriesType.Scatter, 0))
+self.AddChart(spreadPlot)
+
++ The expiration date for an options contract is the time when the contract is no longer valid. + The expiration date for listed stock options in the United States is usually the third Friday of the contract month, which is the month when the contract expires. + When that Friday falls on a holiday, the expiration date is on Thursday immediately before the third Friday. + The options expiration week is a week before options expiration. +
++ During option-expiration weeks, a reduction occurs in option open interest as the near-term options approach their expiration and then expire. + According to a research from Chris and Licheng Returns and option activity over the option-expiration week for S&P 100 stocks, + Large-cap stocks with actively traded options tend to have higher average weekly returns during option-expiration weeks. In this algorithm, we'll use the real market data to explore the option expiration week effect. +
diff --git a/04 Strategy Library/102 Option Expiration Week Effect/02 Method.html b/04 Strategy Library/102 Option Expiration Week Effect/02 Method.html new file mode 100644 index 0000000..e89806b --- /dev/null +++ b/04 Strategy Library/102 Option Expiration Week Effect/02 Method.html @@ -0,0 +1,51 @@ ++ S&P 100 index includes 102 leading U.S. stocks with exchange-listed options. The constituents represent almost 51% of the market capitalization of the U.S. equity market. + Here we trade the S&P 100 index ETF as a portfolio of U.S. large-cap stocks. +
++ In the next step, we add the options to get their expiration dates. The range of expiration dates should bigger enough to include the + the contract which expires in this month. +
+
+def Initialize(self):
+ self.SetStartDate(2007, 1, 1)
+ self.SetEndDate(2018, 8, 1)
+ self.SetCash(10000)
+ self.AddEquity("OEF", Resolution.Minute)
+ option = self.AddOption("OEF")
+ option.SetFilter(-3, 3, timedelta(0), timedelta(days = 60))
+ self.SetBenchmark("OEF")
+
+
+ To get a list of expiration dates from the contracts in the current option chain, we can use TradingCalendar object.
+ It allows us to filter the calendar days by the type TradingDayType.OptionExpiration and the start as well as the end date.
+ The expiry at the top of the list is the most recent expiration date.
+
+ The long position is opened at the start of the expiration week. Therefore, we use the scheduled event to fire the rebalance method every Monday. + If the current Monday is in the expiration week, we long the S&P 100 index ETF. +
+
+def Rebalance(self):
+ calendar = self.TradingCalendar.GetDaysByType(TradingDayType.OptionExpiration, self.Time, self.EndDate)
+ expiries = [i.Date for i in calendar]
+ if len(expiries) == 0: return
+ self.lastest_expiry = expiries[0]
+
+ if (self.lastest_expiry - self.Time).days <= 5:
+ self.SetHoldings("OEF", 1)
+
++ The algorithm stays in cash during days out of the options expiration week. +
++def OnData(self, slice): + if self.Time.date() == self.lastest_expiry.date(): + self.Liquidate() ++
+ In this tutorial, we implement an intraday arbitrage strategy that capitalizes on deviations between two closely correlated + index ETFs. Even though at times both ETFs may hold different constituents and different weights of securities while tracking + the index, they are both highly correlated and extremely liquid. Researchers have shown these two properties are essential to + an arbitrage system's success. The algorithm we implement here is inspired by the work of Kakushadze and Serur (2018) and + Marshall, Nguyen, and Visaltanachoti (2010). +
diff --git a/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/02 Background.html b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/02 Background.html new file mode 100644 index 0000000..8c03fe6 --- /dev/null +++ b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/02 Background.html @@ -0,0 +1,9 @@ ++ Marshall et al (2010) define an arbitrage opportunity as when the bid price of ETF A (B) diverts high enough away from the ask + price of ETF B (A) such that their quotient reaches a threshold. In their paper, an arbitrage opportunity is only acted upon + when the threshold is satisfied for 15 seconds. When these criteria are met, the algorithm enters the arbitrage trade by going + long ETF B (A) and short ETF A (B). When the spread reverts back to where the bid of ETF B (A) >= the ask of ETF A (B) for 15 + seconds, the positions are liquidated. An overview of the trade process is illustrated in the image below. +
+ +
\ No newline at end of file
diff --git a/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/03 Method.html b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/03 Method.html
new file mode 100644
index 0000000..ecac338
--- /dev/null
+++ b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/03 Method.html
@@ -0,0 +1,129 @@
++ We implement a manual universe selection model that includes our two ETFs, SPY and IVV. The attached research notebook finds + the correlation of daily returns to be >0.99. +
++tickers = ['IVV', 'SPY'] +symbols = [ Symbol.Create(t, SecurityType.Equity, Market.USA) for t in tickers ] +self.SetUniverseSelection( ManualUniverseSelectionModel(symbols) ) ++
+ Plotting the ratio of the security prices shows its trending behavior. +
+
++ Without adjusting this ratio over time, an arbitrage system would be stuck in a single trade for majority of the backtest. To + resolve this, we subtract a trailing mean from each data point. +
+
++ Both of the above plots can be reproduced in the attached research notebook. During backtesting, this adjustment is done + during trading by setting up a + QuoteBarConsolidator for each security in our + universe. On each new consolidated QuoteBar, we + update the trailing window of L1 data, then calculate the latest spread adjustment values. +
++# In OnSecuritiesChanged +for symbol in self.symbols: + self.consolidators[symbol] = QuoteBarConsolidator(1) + self.consolidators[symbol].DataConsolidated += self.CustomDailyHandler + algorithm.SubscriptionManager.AddConsolidator(symbol, self.consolidators[symbol]) + +def CustomDailyHandler(self, sender, consolidated): + # Add new data point to history while removing expired history + self.history[consolidated.Symbol]['bids'] = np.append(self.history[consolidated.Symbol]['bids'][1:], consolidated.Bid.Close) + self.history[consolidated.Symbol]['asks'] = np.append(self.history[consolidated.Symbol]['asks'][1:], consolidated.Ask.Close) + + self.update_spread_adjusters() + +def update_spread_adjusters(self): + for i in range(2): + numerator_history = self.history[self.symbols[i]]['bids'] + denominator_history = self.history[self.symbols[abs(i-1)]]['asks'] + self.spread_adjusters[i] = (numerator_history / denominator_history).mean() ++
+ The ArbitrageAlphaModel monitors the intraday bid and ask prices of the securities in the universe. In the constructor, we + can specify the model parameters. In this tutorial, we select a shorter window an arbitrage opportunity must be active before + we act on it by setting `order_delay` to 3. +
+
+class ArbitrageAlphaModel(AlphaModel):
+ symbols = [] # IVV, SPY
+ entry_timer = [0, 0]
+ exit_timer = [0, 0]
+ spread_adjusters = [0, 0]
+ long_side = -1
+ consolidators = {}
+ history = {}
+
+ def __init__(self, order_delay = 3, profit_pct_threshold = 0.02, window_size = 400):
+ self.order_delay = order_delay
+ self.pct_threshold = profit_pct_threshold / 100
+ self.window_size = window_size
+
++ To emit insights, we check if either side of the arbitrage strategy warrants an entry. If no new entries are to be made, the + algorithm then looks to exit any current positions. With this design, we can flip our long/short bias without first + flattening our position. We use a practically-infinite insight durations as we do not know how long the algorithm will be in + an arbitrage trade. +
++# Search for entries +for i in range(2): + if quotebars[abs(i-1)].Bid.Close / quotebars[i].Ask.Close - self.spread_adjusters[abs(i-1)] >= self.pct_threshold: + self.entry_timer[i] += 1 + if self.entry_timer[i] == self.order_delay: + self.exit_timer = [0, 0] + if self.long_side == i: + return [] + self.long_side = i + return [Insight.Price(self.symbols[i], timedelta(days=9999), InsightDirection.Up), + Insight.Price(self.symbols[abs(i-1)], timedelta(days=9999), InsightDirection.Down)] + else: + return [] + self.entry_timer[i] = 0 + +# Search for an exit +if self.long_side >= 0: # In a position + if quotebars[self.long_side].Bid.Close / quotebars[abs(self.long_side-1)].Ask.Close - self.spread_adjusters[self.long_side] >= 0: # Exit signal + self.exit_timer[self.long_side] += 1 + if self.exit_timer[self.long_side] == self.order_delay: # Exit signal lasted long enough + self.exit_timer[self.long_side] = 0 + i = self.long_side + self.long_side = -1 + return [Insight.Price(self.symbols[i], timedelta(days=9999), InsightDirection.Flat), + Insight.Price(self.symbols[abs(i-1)], timedelta(days=9999), InsightDirection.Flat)] + else: + return [] +return [] ++
+ Following the guidelines of Alpha Streams + and the Quant League competition, we + utilize the + EqualWeightingPortfolioConstructionModel and the + + ImmediateExecutionModel. +
diff --git a/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/04 Algorithm.html b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/04 Algorithm.html new file mode 100644 index 0000000..c59088b --- /dev/null +++ b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/04 Algorithm.html @@ -0,0 +1,6 @@ + \ No newline at end of file diff --git a/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/05 Relative Performance.html b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/05 Relative Performance.html new file mode 100644 index 0000000..2d3e6c9 --- /dev/null +++ b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/05 Relative Performance.html @@ -0,0 +1,93 @@ ++ We analyze the performance of this strategy by comparing it to the S&P 500 ETF benchmark, SPY. We notice that the + strategy has a lower Sharpe ratio over all of our testing periods than the benchmark, except for the Fall 2015 + crisis where it achieved a 2.8 Sharpe ratio. The strategy also has a lower annual standard deviation of returns + when compared to the SPY, implying more consistent returns over time. A breakdown of the strategy's performance + across all our testing periods is displayed in the table below. +
+ +| Period Name | +Start Date | +End Date | +Strategy | +Sharpe | +ASD | +
|---|---|---|---|---|---|
| Backtest | +8/11/2015 | +8/11/2020 | +Strategy | +-0.447 | +0.053 | +
| Benchmark | +0.732 | +0.192 | +|||
| Fall 2015 | +8/10/2015 | +10/10/2015 | +Strategy | +2.837 | +0.225 | +
| Benchmark | +-0.724 | +0.251 | +|||
| 2020 Crash | +2/19/2020 | +3/23/2020 | +Strategy | +-4.196 | +0.209 | +
| Benchmark | +-1.243 | +0.793 | +|||
| 2020 Recovery | +3/23/2020 | +6/8/2020 | +Strategy | +-3.443 | +0.013 | +
| Benchmark | +13.761 | +0.386 | +
+ The lack of performance for this arbitrage strategy is mostly attributed to the fees it incurs while trading. This + is common for an intraday arbitrage strategy, but we discuss ways to reduces these fees in the conclusion of this + tutorial. After removing the costs of commissions, crossing the spread, and slippage, the strategy outperforms the + SPY over the entire backtesting period. Without these costs, the strategy generates a 1.09 Share ratio while the + SPY generates a 0.732 Sharpe ratio. See the backtest performance without fees below. +
+ + + diff --git a/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/06 Market & Competition Qualification.html b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/06 Market & Competition Qualification.html new file mode 100644 index 0000000..c76ecb6 --- /dev/null +++ b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/06 Market & Competition Qualification.html @@ -0,0 +1,19 @@ ++ Although this strategy passes several of the + metrics required for Alpha Streams + and the Quant League competition, it requires further work to pass the following requirements: +
+ + ++ The algorithm currently places trades during 12 unique months throughout the backtest. Since the backtest spans + across 61 months, it places trades through a minority of the backtest. +
diff --git a/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/07 Conclusion.html b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/07 Conclusion.html new file mode 100644 index 0000000..3df342d --- /dev/null +++ b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/07 Conclusion.html @@ -0,0 +1,10 @@ ++ The intraday arbitrage strategy we built and tested throughout this tutorial underperforms the SPY benchmark in + terms of Sharpe ratio when including trading costs. Without these costs, we found the strategy outperforms the SPY + in terms of Sharpe ratio. In our implementation, we specified the alpha model to initiate trading when atleast a + 0.02% profit threshold is reached for 3 seconds. Both of these parameters are set lower than the strategy examined + in Marshall et al (2010) for demonstration purposes. Increasing the profit threshold will lead to more profitable, + but fewer, trades that may overcome the cost of trading. We leave this area of study for future research. + Additional areas of future research include increasing the resolution of data from second to tick and incorportating + an execution model that utilizes limit orders to reduce fees. +
diff --git a/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/08 References.html b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/08 References.html new file mode 100644 index 0000000..a684227 --- /dev/null +++ b/04 Strategy Library/1023 Intraday Arbitrage Between Index ETFs/08 References.html @@ -0,0 +1,8 @@ ++ In this tutorial, we apply Deep Learning Classification in an attempt to forecast the movement of future stock prices. +
++ Key Concepts: Convolutional Neural Network, Deep Learning, Time-series Forecasting, Classification, Trading +
\ No newline at end of file diff --git a/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/02 Introduction.html b/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/02 Introduction.html new file mode 100644 index 0000000..1fa0f4e --- /dev/null +++ b/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/02 Introduction.html @@ -0,0 +1,8 @@ ++ Various time series forecasting models (SMA, EMA, etc.) have been applied to stocks to forecast price movements. + More recently, with the advent of Neural Networks, which have seen applications in several fields, ranging from + medicine to fraud detection, researchers have tried to apply Neural Networks to the markets in an attempt to forecast price + movements. Convolutional Neural Networks (CNNs) are a class of Neural Networks most widely known for their use in + image classification, and now, researchers are applying CNNs to extract patterns, also known as features, from times-series + data to forecast future stock prices. +
diff --git a/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/03 Method.html b/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/03 Method.html new file mode 100644 index 0000000..e56515f --- /dev/null +++ b/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/03 Method.html @@ -0,0 +1,283 @@ ++ Our strategy is to develop a Temporal Convolutional Neural Network model and train our model on historical OHLCV data + to predict the movement of future prices. Then, when trading, we take the most recent data, feed it into our model, and + bet on the direction of the price movement based on our model prediction. We will walk through the code required + for building the Neural Network Architecture and for preparing the data for our model, as this part is the harder part to understand. +
+ ++ Before we build our Neural Network Architecture, we need to understand the inputs and outputs to our model. + The input to the model will be the OHLC+Volume data for t-14 to t time steps (past 15 time steps). The output is a + direction (Up, Down, Stationary) of the movement of the average close of the t+1 to t+5 time steps (5 future timestamps). + The movement is considered stationary if the abs(% change 5-step average close) < .01%. These three directions will + form the labels for which our model will try to classify, thus we have a classification problem. +
+ + ++ Now, we will need to build our Neural Network Architecture, which we will build using Keras, + a high-level Python Deep Learning API. To begin, we will need a few import statements: +
+ ++ import tensorflow as tf + from tensorflow.keras.layers import Input, Conv1D, Dense, Lambda, Flatten, Concatenate + from tensorflow.keras import Model + from tensorflow.keras import metrics + from tensorflow.keras.losses import CategoricalCrossentropy + from tensorflow.keras import utils + from sklearn.preprocessing import StandardScaler + import numpy as np + import math ++
+ We start with an Input Layer, where training and testing data are initially accepted. With 15 time steps and 5 input + variables (OHLCV), our input shape will be 15 x 5. +
+ ++ inputs = Input(shape=(15, 5)) ++
+ We then feed this Layer into our Convolutional Layer, where we extract features, which will serve as + the Neural Network's method of extracting patterns from the time-series data. +
+ ++ feature_extraction = Conv1D(30, 4, activation='relu')(inputs) ++
+ long_term = Lambda( lambda x: tf.split(x, num_or_size_splits=3, axis=1)[0])(feature_extraction) + mid_term = Lambda( lambda x: tf.split(x, num_or_size_splits=3, axis=1)[1])(feature_extraction) + short_term = Lambda( lambda x: tf.split(x, num_or_size_splits=3, axis=1)[2])(feature_extraction) + + long_term_conv = Conv1D(1, 1, activation='relu')(long_term) + mid_term_conv = Conv1D(1, 1, activation='relu')(mid_term) + short_term_conv = Conv1D(1, 1, activation='relu')(short_term) ++
+ These three layers are then combined, and since we will be working with 2D input matrices, we will then need to flatten + our layer. +
+ ++ combined = Concatenate(axis=1)([long_term_conv, mid_term_conv, short_term_conv]) + flattened = Flatten()(combined) ++
+ Our final layer will be our output layer, and since we have three outputs (Up, Stationary, Down), + this layer will have three nodes. +
+ ++ outputs = Dense(3, activation='softmax')(flattened) ++
+ The resulting Neural Network Architecture is shown in the following: +
+ +
+
+
++ First, we need to define a class and a few variables: +
+ ++ input_vars = ['open', 'high', 'low', 'close', 'volume'] + + class Direction: + UP = 0 + DOWN = 1 + STATIONARY = 2 + + rolling_avg_window_size = 5 + + shift = -(rolling_avg_window_size-1) + + stationary_threshold = .0001 + + scaler = StandardScaler() ++
+ input_vars define the variables we want to use to make our predictions. The class Direction + defines a few integers that we will label our data with (labels are needed for classification problems). The reason + we use integers instead of strings is because Keras, like most ML libraries, only work with numerical data. Moving on, + rolling_avg_window_size is the number of time steps used for the calculate the average of future closing prices, + described earlier in + Inputs/Outputs (t+1 to t+5 is 5 time steps, thus this value accordingly is set to 5). + The constant stationary_threshold defines the threshold for a change in price to be considered + stationary, and this change also described in Inputs/Outputs. The shift is the shift needed to align + the average value (mentioned earlier), in our pandas DataFrame to make it easier for us to slice our DataFrame into pieces + manageable for our Neural Network model. The scaler object will be used later to scale our data. + The purpose of the variables will become clearer in use. +
+ Next, say we are at time t in the pandas DataFrame, to calculate the average closing prices of t+1 to t+5, and calculate + the percent change from the close at t, we use the following lines of code: +
+ ++ df['close_avg'] = df['close'].rolling(window=rolling_avg_window_size).mean().shift(shift) + df['close_avg_change_pct'] = (df['close_avg'] - df['close']) / df['close'] ++
+ The rolling mean should be self explanatory for those familiar with pandas (if not, I hope by now readers realize + this is a more advanced resource). + Here, .shift(shift) aligns the five time step rolling average 'close_avg' column to the end of the last + time step we want to use as an input for prediction, and this action will make slicing up the DataFrame into input + and labeled data for our model much easier. +
+ ++ To label our data, we need to first define a function that we will use with the DataFrame's apply() method. + Usually, lambda functions are used for this purpose, however, our function's logic will not fit inside a lambda. +
+ ++ def label_data(row): + if row['close_avg_change_pct'] > stationary_threshold: + return Direction.UP + elif row['close_avg_change_pct'] < -stationary_threshold: + return Direction.DOWN + else: + return Direction.STATIONARY ++
+ Now, we apply the above function to our DataFrame to get a column of labels: +
+ ++ df['movement_labels'] = df.apply(label_data, axis=1) ++
+ With our labels in place, we can now slice up our DataFrame into pieces manageable for our model and collect them into + lists: +
+ ++ data = [] + labels = [] + + for i in range(len(df)-self.n_tsteps+1+shift): + label = df['movement_labels'].iloc[i+self.n_tsteps-1] + data.append(df[input_vars].iloc[i:i+self.n_tsteps].values) + labels.append(label) + + data = np.array(data) ++
+ Here, we iterate numerically through the DataFrame, with a carefully calculated value in our range() + function to make sure we do access an out-of-bounds index. We cast the list of numpy arrays to a numpy array because + Keras works best with numpy arrays. +
+ ++ Now, we need to scale our data. It is good practice to scale data when using Machine Learning models so that the + range of values is normalized across the features. +
+ ++ dim1, dim2, dim3 = data.shape + data = data.reshape(dim1*dim2, dim3) + data = scaler.fit_transform(data) + data = data.reshape(dim1, dim2, dim3) ++
+ The reason we reshape the data before the scaling is because sklearn is only able to handle 2D data, but right after, + we can return the data to the original shape with another reshaping. +
+ ++ Finally, since Keras requires the labels to be dummified (which essentially turns a list of labels into a matrix of + 1s and 0s, where the index of the 1 is equal to the value of the integer label), we use the following: +
+ ++ labels = utils.to_categorical(labels, num_classes=3) ++
+ Specifying num_classes to 3 ensures our matrix will have three columns, one for each label (Up, Down, Stationary). +
+ ++ We have now finished the walk through of the difficult parts of the code. +
+ +
+ After we feed in the prepared data into the model (the corresponding code, as well as the rest of the code, can be
+ found in Algorithm) we can
+ use our model to make predictions. We take the most recent 15 bars of OHLCV data and apply our model on it to make
+ a prediction. If the model predicts with above 55% confidence that the future direction is up (resp. down), we emit
+ an Price Insight with direction InsightDirection.Up (resp. InsightDirection.Down). Since we are
+ betting on the direction of the average of the future five closing prices, it would be intuitive to emit an Insights
+ in the respective direction for timedeltas of one through five. However, we choose to only emit an Insight
+ with a timedelta with a random integer between one and five to constrain the number of insights we emit.
+
+ As an additional note, we decided to set the trading fees to zero (the default fee
+ is one dollar per trade), or else our algorithm will only lose money due to the frequency at which we trade.
+
+ We have covered the difficult aspects of the code, as well as give an overview of our strategy. The rest of the + necessary code to execute the strategy can be found in Algorithm. +
+ + + + diff --git a/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/04 Algorithm.html b/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/04 Algorithm.html new file mode 100644 index 0000000..0a1b0bd --- /dev/null +++ b/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/04 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/05 Results.html b/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/05 Results.html new file mode 100644 index 0000000..a9d5b42 --- /dev/null +++ b/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/05 Results.html @@ -0,0 +1,6 @@ ++ Since our algorithm is non-deterministic, users should expect to see different results in repeated backtests. From + running our algorithm ten times, we achieved Sharpe Ratios with an average of .211, a maximum of 0.917, and minimum + of -0.312, and a standard deviation of 0.327. As we traded three technology stocks, we compare our results to QQQ. + Comparing our algorithm to QQQ, our average Sharpe of .211 is significantly lower than the 0.967 Sharpe of QQQ. +
\ No newline at end of file diff --git a/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/06 References.html b/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/06 References.html new file mode 100644 index 0000000..dedbeb6 --- /dev/null +++ b/04 Strategy Library/1024 Forecasting Stock Prices using a Temporal CNN Model/06 References.html @@ -0,0 +1,7 @@ ++ In this tutorial, we attempt to beat the returns of the S&P500 Index using leverage and systematic risk management. +
diff --git a/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/02 Introduction.html b/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/02 Introduction.html new file mode 100644 index 0000000..0b1b370 --- /dev/null +++ b/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/02 Introduction.html @@ -0,0 +1,9 @@ ++ When measuring the profitability of a strategy, it is usually not enough to be profitable, as it should also beat + the benchmark, for which the SP500 Index is most commonly used. If not, what would be the reason to not just invest + in a low-cost SP500 index instead (not accounting for risk)? However, what if we could beat the SP500 with the SP500? + This is what Gayed et al. proposed with their strategy of using Leveraged SP500 indices with Systematic Risk Management. + They propose that Moving Averages are a good method to assess volatility in the market, and they use it to manage risk, + which is especially important since the effects of price swings in a leveraged ETF are magnified due to the leverage. + With this method, we hope to outperform the SP500 while at the same time, attempt to reduce drawdown. +
diff --git a/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/03 Method.html b/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/03 Method.html new file mode 100644 index 0000000..a43a70e --- /dev/null +++ b/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/03 Method.html @@ -0,0 +1,12 @@ ++ We develop hold/liquidate positions based on the 200-day Simple Moving Average (SMA) of our ETF, for which we use SSO, + a 2x leveraged SP500 index ETF. With 200 days instead of using fewer days, say 50, we reduce the number of trades per year, + thereby reducing transaction costs and the effects of slippage. Moving on, if the current price of SOO is above the 200-day SMA, + we hold SSO, and if SSO dips below our 200-day SMA, we sell liquidate our position and rotate our position into short-term + treasuries, which is done through SHY, an ETF that tracks 1-3 year U.S. Treasury Bonds. If we are holding SHY, and the + current price of SSO moves above the 200-day SMA, then we rotate back into SSO and liquidate SHY. +
+ + + + diff --git a/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/04 Algorithm.html b/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/04 Algorithm.html new file mode 100644 index 0000000..3b0ead5 --- /dev/null +++ b/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/04 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/05 Results.html b/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/05 Results.html new file mode 100644 index 0000000..ade26d7 --- /dev/null +++ b/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/05 Results.html @@ -0,0 +1,4 @@ ++ We use the S&P 500 as our benchmark, which we track by using the SPY ETF. Our strategy yielded a Sharpe Ratio of .732 + over the past five years, while buying and holding SPY for the same period yielded a Sharpe Ratio of .572. +
\ No newline at end of file diff --git a/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/06 References.html b/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/06 References.html new file mode 100644 index 0000000..c1ce885 --- /dev/null +++ b/04 Strategy Library/1025 Leveraged ETFs with Systematic Risk Management/06 References.html @@ -0,0 +1,7 @@ ++ In this tutorial, we implement an intraday momentum strategy that trades some of the most actively traded ETFs. + Specifically, we observe the return generated from the first half-hour of the trading day to predict the sign of + the trading day's last half-hour return. Researchers have shown that this momentum pattern is statistically and + economically significant, even after accounting for trading fees. The algorithm we design here is a recreation of + the research completed by Gao, Han, Li, and Zhou (2017). +
diff --git a/04 Strategy Library/1026 Intraday ETF Momentum/02 Background.html b/04 Strategy Library/1026 Intraday ETF Momentum/02 Background.html new file mode 100644 index 0000000..c06af0a --- /dev/null +++ b/04 Strategy Library/1026 Intraday ETF Momentum/02 Background.html @@ -0,0 +1,19 @@ ++ News items are usually released before the opening bell. As it takes time for traders to digest and interpret the + news, the first half-hour of trading typically has relatively higher levels of volume and volatility. Additionally, + as traders attempt to mitigate overnight risk by unloading positions near the close, the last half-hour of trading + also sees these higher levels of volume and volatility. These characteristics can be observed from the image below, + which is reproducible in the attached research notebook. +
+ +
+
++ Bogousslavsky (2016) points out that some investors are late-informed or simply prefer to delay their trading until + the market close. As a result, a positive correlation exists between the direction of the opening and closing + periods. Gao et al (2017) find that when trading this momentum strategy, the average annual return over their + sample period was 6.67% for SPY, 11.72% for IWM, and 24.22% for IYR. Equal-weighting these returns leads to a + combined average annual return of 14.2%. +
\ No newline at end of file diff --git a/04 Strategy Library/1026 Intraday ETF Momentum/03 Method.html b/04 Strategy Library/1026 Intraday ETF Momentum/03 Method.html new file mode 100644 index 0000000..29481ab --- /dev/null +++ b/04 Strategy Library/1026 Intraday ETF Momentum/03 Method.html @@ -0,0 +1,143 @@ ++ We implement a manual universe selection model that supplies a subset of the proposed ETFs in the attached research + paper. Gao et al (2017) select the following tickers: DIA, QQQ, IWM, EEM, FXI, EFA, VWO, XLF, IYR, and TLT. In an + effort to increase the backtest performance, we narrow our universe to SPY, IWM, and IYR. +
++tickers = ['SPY', # S&P 500 + 'IWM', # Russell 2000 + 'IYR' # Real Estate ETF +] +symbols = [ Symbol.Create(ticker, SecurityType.Equity, Market.USA) for ticker in tickers ] +self.SetUniverseSelection( ManualUniverseSelectionModel(symbols) ) +self.UniverseSettings.Resolution = Resolution.Minute ++
+ The IntradayMomentumAlphaModel emits insights to take positions for the last `return_bar_count` minutes of the day + in the direction of the return for the first `return_bar_count` minutes of the day. During construction, we create + a dictionary to store IntradayMomentum data for each symbol, define a method to determine the sign of returns, and + specify the value of `return_bar_count`. In this tutorial, we follow Gao et al (2017) in setting `return_bar_count` + to 30 by default. +
+
+class IntradayMomentumAlphaModel(AlphaModel):
+ intraday_momentum_by_symbol = {}
+ sign = lambda _, x: int(x and (1, -1)[x < 0])
+
+ def __init__(self, algorithm, return_bar_count = 30):
+ self.return_bar_count = return_bar_count
+
++ When a new security is added to the universe, we create an IntradayMomentum object for it to store information + needed to calculate morning returns. The management of the IntradayMomentum objects occurs in the alpha model's + OnSecuritiesChanged method. +
++def OnSecuritiesChanged(self, algorithm, changes): + for security in changes.AddedSecurities: + self.intraday_momentum_by_symbol[security.Symbol] = IntradayMomentum(security, algorithm) + + for security in changes.RemovedSecurities: + self.intraday_momentum_by_symbol.pop(security.Symbol, None) ++
+ The definition of the IntradayMomentum class is shown below. We save a reference to the security's exchange so we + can access the market hours of the exchange when generating insights. +
++class IntradayMomentum: + def __init__(self, security, algorithm): + self.symbol = security.Symbol + self.exchange = security.Exchange + + self.bars_seen_today = 0 + self.yesterdays_close = algorithm.History(self.symbol, 1, Resolution.Daily).loc[self.symbol].close[0] + self.morning_return = 0 ++
+ With each call to the alpha model's Update method, we count the number of bars the algorithm has received for each + symbol. If we've reached the end of the morning window, we calculate the morning return. If we are at the + beginning of the close window, we emit an insight in the direction of the morning window's return. If we are at + the end of the day, we save the closing price and reset the counter for the number of bars seen today. +
++def Update(self, algorithm, slice): + insights = [] + + for symbol, intraday_momentum in self.intraday_momentum_by_symbol.items(): + if slice.ContainsKey(symbol) and slice[symbol] is not None: + intraday_momentum.bars_seen_today += 1 + + # End of the morning return + if intraday_momentum.bars_seen_today == self.return_bar_count: + intraday_momentum.morning_return = (slice[symbol].Close - intraday_momentum.yesterdays_close) / intraday_momentum.yesterdays_close + + ## Beginning of the close + next_close_time = intraday_momentum.exchange.Hours.GetNextMarketClose(slice.Time, False) + mins_to_close = int((next_close_time - slice.Time).total_seconds() / 60) + + if mins_to_close == self.return_bar_count + 1: + insight = Insight.Price(intraday_momentum.symbol, + next_close_time, + self.sign(intraday_momentum.morning_return)) + insights.append(insight) + continue + + # End of the day + if not intraday_momentum.exchange.DateTimeIsOpen(slice.Time): + intraday_momentum.yesterdays_close = slice[symbol].Close + intraday_momentum.bars_seen_today = 0 + + return insights ++
+ The attached research paper holds positions for the last 30 minutes of the trading day, exiting at the market close. + In order to accomplish this, we create a custom execution model. The model defined below submits a market order for + the entry while also submitting a market on close order in the same time step. +
++class CloseOnCloseExecutionModel(ExecutionModel): + def __init__(self): + self.targetsCollection = PortfolioTargetCollection() + self.invested_symbols = [] + + def Execute(self, algorithm, targets): + # for performance we check count value, OrderByMarginImpact and ClearFulfilled are expensive to call + self.targetsCollection.AddRange(targets) + if self.targetsCollection.Count > 0: + for target in self.targetsCollection.OrderByMarginImpact(algorithm): + # calculate remaining quantity to be ordered + quantity = OrderSizing.GetUnorderedQuantity(algorithm, target) + if quantity == 0: + continue + + algorithm.MarketOrder(target.Symbol, quantity) + algorithm.MarketOnCloseOrder(target.Symbol, -quantity) + + self.targetsCollection.ClearFulfilled(algorithm) ++
+ We conclude that the momentum pattern documented by Gao et al (2017) produces lower returns over our testing period. + Comparing the strategy to the S&P 500 benchmark, the strategy has a lower Sharpe ratio during the backtesting + period and during the recovery from the 2020 stock market crash. However, the strategy greatly outperforms the + benchmark during the downfall of the 2020 crash, achieving a 4.8 Sharpe ratio. Throughout all of the time periods + we tested, the strategy had a lower annual standard deviation than the benchmark, meaning more consistent returns. + A breakdown of the results from all of the testing periods can be seen in the table below. +
+ +| Period Name | +Start Date | +End Date | +Strategy | +Sharpe | +ASD | +
|---|---|---|---|---|---|
| Backtest | +1/1/2015 | +8/16/2020 | +Strategy | +-0.764 | +0.05 | +
| Benchmark | +0.709 | +0.185 | +|||
| Fall 2015 | +8/10/2015 | +10/10/2015 | +Strategy | +-0.696 | +0.058 | +
| Benchmark | +-1.243 | +0.793 | +|||
| 2020 Crash | +2/19/2020 | +3/23/2020 | +Strategy | +4.818 | +0.266 | +
| Benchmark | +-1.243 | +0.793 | +|||
| 2020 Recovery | +3/23/2020 | +6/8/2020 | +Strategy | +0.602 | +0.103 | +
| Benchmark | +13.761 | +0.386 | +
+ We find the lack of performance for this strategy is not largely attributed to the inclusion of transaction costs + in our analysis while Gao et al (2017) decide to ignore them. Even with ignoring the transaction fees, spread costs, + and slippage, the strategy still has a lower Sharpe ratio than the S&P 500 and doesn't match the results found in the + original research paper. Refer to the backtest results. +
+ ++ Throughout their research paper, Gao et al (2017) provide several suggestions to increase the return generated by + this momentum pattern. These areas of future research include: +
+ ++ Several studies have found that press releases and other media can impact the perspective of investors. In this + tutorial, we implement an intraday strategy to capitalize on the upward drift in the stock prices of drug + manufacturers following positive news releases. Our findings show that when combining the effect with the + day-of-the-week anomaly documented by Berument & Kiymaz (2001), there is enough directional accuracy for the + trading system to remain profitable throughout the 2020 stock market crash. However, the algorithm + underperforms the S&P 500 market index ETF, SPY, over the same time period. The algorithm we design here is + inspired by the work of Isah, Shah, & Zulkernine (2018). +
diff --git a/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/02 Background.html b/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/02 Background.html new file mode 100644 index 0000000..60fe4eb --- /dev/null +++ b/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/02 Background.html @@ -0,0 +1,14 @@ ++ The use of alternative data sets to forecast stock prices has increased in recent years as the fundamental and + technical analysis spaces increase in competition. Utilizing Natural Language Processing (NLP) techniques to + analyze the sentiment of news releases and other text related to publicly traded companies has caught the interest + of many quant researchers. Such online information is frequently released and can be interpreted in a virtually + unlimited number of ways, leading to a novel approach to determining the "societal mood" (Isah et al, 2018, p. 2) + towards a company. +
+ ++ There are several ways to implement a NLP system. In this tutorial, we utilize a dictionary to quantify the + sentiment of news releases. The dictionary provided herein was sourced from Isah et al (2018), where it's use + achieved a 70% accuracy when targeting several hand-picked stocks in India's pharmaceutical industry. +
\ No newline at end of file diff --git a/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/03 Method.html b/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/03 Method.html new file mode 100644 index 0000000..ac080d3 --- /dev/null +++ b/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/03 Method.html @@ -0,0 +1,183 @@ ++ We implement a universe selection model that provides the trading system with companies classified by + MorningStar as being in the drug + manufacturing industry group. We narrow our universe to include only the drug manufacturers with the greatest PE + ratios and dollar volume. +
++def SelectCoarse(self, algorithm, coarse): + has_fundamentals = [c for c in coarse if c.HasFundamentalData] + sorted_by_dollar_volume = sorted(has_fundamentals, key=lambda c: c.DollarVolume, reverse=True) + return [ x.Symbol for x in sorted_by_dollar_volume[:self.coarse_size] ] + +def SelectFine(self, algorithm, fine): + drug_manufacturers = [f for f in fine if f.AssetClassification.MorningstarIndustryGroupCode == MorningstarIndustryGroupCode.DrugManufacturers] + sorted_by_pe = sorted(drug_manufacturers, key=lambda f: f.ValuationRatios.PERatio, reverse=True) + return [ x.Symbol for x in sorted_by_pe[:self.fine_size] ] ++
+ The DrugNewsSentimentAlphaModel emits insights to take long intraday positions for securities that have positive + news sentiment. During construction of the model, we: +
+ ++ The `bars_before_insight` parameter determines how many bars the alpha model should observe after the market opens + before emitting insights. Isah et al (2018) batch the news released by each company into 30-minute intervals + before analyzing the sentiment of the batch. In this tutorial, we follow a similar procedure by setting + `bars_before_insight` to 30. +
+ +
+class DrugNewsSentimentAlphaModel(AlphaModel):
+ symbol_data_by_symbol = {}
+ sentiment_by_phrase = SentimentByPhrase.dictionary
+ max_phrase_words = max([len(phrase.split()) for phrase in sentiment_by_phrase.keys()])
+ sign = lambda _, x: int(x and (1, -1)[x < 0])
+
+ def __init__(self, bars_before_insight=30):
+ self.bars_before_insight = bars_before_insight
+
++ When a new security is added to the universe, we create a SymbolData object for it to store information unique to + each security. The management of the SymbolData objects occurs in the alpha model's OnSecuritiesChanged method. +
+ ++def OnSecuritiesChanged(self, algorithm, changes): + for security in changes.AddedSecurities: + self.symbol_data_by_symbol[security.Symbol] = SymbolData(security, algorithm) + + for security in changes.RemovedSecurities: + symbol_data = self.symbol_data_by_symbol.pop(security.Symbol, None) + if symbol_data: + algorithm.RemoveSecurity(symbol_data.tiingo_symbol) ++
+ The definition of the SymbolData class is shown below. We add properties to it to track the cumulative sentiment + of news releases over time and the number of bars the alpha model has received for each security since the market + open. In the constructor, we save a reference to the security's exchange so we can access the market hours of the + exchange when generating insights. This is also where we initialize the + Tiingo news feed for each security. +
+ ++class SymbolData: + cumulative_sentiment = 0 + bars_seen_today = 0 + + def __init__(self, security, algorithm): + self.exchange = security.Exchange + self.tiingo_symbol = algorithm.AddData(TiingoNews, security.Symbol).Symbol ++
+ As new Tiingo objects are provided to the alpha model's Update method, we update the cumulative sentiment for each + security. The cumulative sentiment counter is reset at each market close. Therefore, when we emit insights + 30-minutes after the open, we are considering the sentiment of the news articles released from the previous close + to the current time. We employ the findings of Berument & Kiymaz (2001), restricting the alpha model's trading to + Wednesday, the most profitable day of the week. Positions are entered 30-minutes after the open and exited at the + close. +
+ ++def Update(self, algorithm, data): + insights = [] + + for symbol, symbol_data in self.symbol_data_by_symbol.items(): + + # If it's after-hours or within 30-minutes of the open, update + # cumulative sentiment for each symbol + if symbol_data.bars_seen_today < self.bars_before_insight: + tiingo_symbol = symbol_data.tiingo_symbol + if data.ContainsKey(tiingo_symbol) and data[tiingo_symbol] is not None: + article = data[tiingo_symbol] + symbol_data.cumulative_sentiment += self.CalculateSentiment(article) + + if data.ContainsKey(symbol) and data[symbol] is not None: + symbol_data.bars_seen_today += 1 + + # 30-mintes after the open, emit insights in the direction of the cumulative sentiment. + # Only emit insights on Wednesdays to capture the analomaly documented by Berument and + # Kiymaz (2001). + if symbol_data.bars_seen_today == self.bars_before_insight and data.Time.weekday() == 2: + next_close_time = symbol_data.exchange.Hours.GetNextMarketClose(data.Time, False) + direction = self.sign(symbol_data.cumulative_sentiment) + if direction == 0: + continue + insight = Insight.Price(symbol, + next_close_time - timedelta(minutes=2), + direction) + insights.append(insight) + + # At the close, reset the cumulative sentiment + if not symbol_data.exchange.DateTimeIsOpen(data.Time): + symbol_data.cumulative_sentiment = 0 + symbol_data.bars_seen_today = 0 + + return insights ++
+ We define the following helper method to return the sentiment of a Tiingo news article by analyzing the article's + title and description. The `sentiment_by_phrase` dictionary was retrieved from queensbamlab's + NewsSentiment GitHub repository. Although we have + adjusted the dictionary to lowercase and removed some redundancies, this is the same dictionary used by Isah et + al (2018). "The dictionary was created by leveraging author's domain expertise and thorough analysis of news + articles over the years" (p. 3). +
+ ++def CalculateSentiment(self, article): + sentiment = 0 + for content in (article.Title, article.Description): + words = content.lower().split() + for num_words in range(1, self.max_phrase_words + 1): + for gram in ngrams(words, num_words): + phrase = ' '.join(gram) + if phrase in self.sentiment_by_phrase.keys(): + sentiment += self.sentiment_by_phrase[phrase] + return sentiment ++
+ Following the guidelines of Alpha Streams and the + Quant League competition, we utilize the + + EqualWeightingPortfolioConstructionModel and the + + ImmediateExecutionModel. +
+ diff --git a/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/04 Algorithm.html b/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/04 Algorithm.html new file mode 100644 index 0000000..43dfb6f --- /dev/null +++ b/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/04 Algorithm.html @@ -0,0 +1,6 @@ + \ No newline at end of file diff --git a/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/05 Conclusion.html b/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/05 Conclusion.html new file mode 100644 index 0000000..8f0a19e --- /dev/null +++ b/04 Strategy Library/1027 Using News Sentiment to Predict Price Direction of Drug Manufacturers/05 Conclusion.html @@ -0,0 +1,27 @@ ++ We conclude that deploying the sentiment analysis strategy on the US drug manufacturing industry does not provide + as accurate of results as found by Isah et al (2018). Only after restricting trading to the most profitable day of + the week (Berument & Kiymaz, 2001) does the strategy achieve profitability over our testing period. Overall, the + strategy produces a Sharpe ratio of 0.116, while the + SPY benchmark + produces a 0.971 Sharpe ratio during the same period. We attribute the decrease in performance to the commissions + and spread costs simulated by LEAN. +
+ ++To continue the development of this strategy, future areas of research include: +
+ ++ Gurrib (2020) is the first published research paper to analyze the predictive power of Ichimoku Clouds for the + largest 10 stocks in the US energy sector. In this tutorial, we implement a similar strategy while reducing the + effect of look-ahead bias integrated into the original study. Our findings show that while the strategy has an + impressive 176 Sharpe ratio during the downfall of the 2020 oil price war, the strategy has worse performance than + found by Gurrib (2020). We discover that throughout a 5 year backtest, the strategy fails to beat the benchmark of + a popular energy sector ETF. +
diff --git a/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/02 Introduction.html b/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/02 Introduction.html new file mode 100644 index 0000000..c5efef1 --- /dev/null +++ b/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/02 Introduction.html @@ -0,0 +1,35 @@ ++ A vast amount of research studies have been published which document mixed results when utilizing technical + analysis to forecast future prices of securities. The Ichimoku Cloud, one of the most widely-used technical + indicators in Japan, was first publicized by Goichi Hosoda. In 1996, Hidenobu Sasaki reworked the framework to + form the current charting analysis tool. This indicator is composed of 5 lines in a time series, each of which + are described mathematically in + online resources. +
+ ++ Gurrib (2020) finds that applying a simple trading strategy using the time series of the Ichimoku Cloud can + increase the mean return of a basket containing the top energy stocks from 21.5% (buy-and-hold) to 194% over a 7 + year period. The components of the Ichimoku Cloud that Gurrib (2020) utilizes in this strategy are the Chikou + Span, Senkou Span A, and Senkou Span B. The Senkou Span lines form the top and bottom of the Ichimoku Cloud. The + strategy that we trade off of these lines is defined as follows: +
+ ++ For better understanding, here is a visualization of the price of XOM, it's Ichimoku Cloud time series, and the + resulting buy/sell signals. +
+ +
+
++ Note: all of the plots throughout this tutorial are reproducible in the attached research notebook, along with + some descriptive statistics for securities in the universe. +
\ No newline at end of file diff --git a/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/03 Method.html b/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/03 Method.html new file mode 100644 index 0000000..8669ce3 --- /dev/null +++ b/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/03 Method.html @@ -0,0 +1,150 @@ ++ Gurrib (2020) selects a universe of the 10 largest-weighed constituents of the S&P Composite 1500 Energy Index + over the testing period. This inherently incorporates lookahead-bias into the study as the security weights are + sourced over the period the trading simulation occurs. Furthermore, since the publication of Gurrib (2020), some + of the securities have even been delisted. Thus, to eliminate lookahead-bias and avoid delistings, we implement a + universe selection model that provides the trading system with the 10 largest companies in the energy sector as of + the current date in the backtest. Since the largest companies change infrequently, we only refresh the universe on + a monthly basis. +
+ ++def SelectCoarse(self, algorithm, coarse): + if algorithm.Time.month == self.month: + return Universe.Unchanged + return [ x.Symbol for x in coarse if x.HasFundamentalData ] + +def SelectFine(self, algorithm, fine): + self.month = algorithm.Time.month + + energy_stocks = [ f for f in fine if f.AssetClassification.MorningstarSectorCode == MorningstarSectorCode.Energy ] + sorted_by_market_cap = sorted(energy_stocks, key=lambda x: x.MarketCap, reverse=True) + return [ x.Symbol for x in sorted_by_market_cap[:self.fine_size] ] ++
+ The IchimokuCloudCrossOverAlphaModel emits insights to hold a long position after the Chikou Span crosses over the + top of the cloud for a given security. Additionally, the strategy is made symmetrical by entering short positions + after the Chikou Span crosses below the bottom of the cloud. During construction of this alpha model, we simply + set up a dictionary to hold a SymbolData object for each symbol in the universe. +
+ +
+class IchimokuCloudCrossOverAlphaModel(AlphaModel):
+ symbol_data_by_symbol = {}
+
++ The SymbolData class constructor is shown below. We first set up two class variables, `previous_location` and + `direction`. The former enables the algorithm to signal when the Chikou Span crosses over the boundaries of the + Ichimoku Cloud. The latter is added to ensure we continue to emit daily insights in the proper direction. Inside + the `__init__` method is where we create the + IchimokuKinkoHyo indicator and warm + it up. +
+ ++class SymbolData: + previous_location = None + direction = None + + def __init__(self, symbol, algorithm): + # Create Ichimoku indicator + self.ichimoku = IchimokuKinkoHyo() + + # Warm up indicator + history = algorithm.History(symbol, self.ichimoku.WarmUpPeriod + 1, Resolution.Daily).loc[symbol] + for idx, row in history.iterrows(): + if self.ichimoku.IsReady: + self.previous_location = self.get_location() + + tradebar = TradeBar(idx, symbol, row.open, row.high, row.low, row.close, row.volume) + self.ichimoku.Update(tradebar) ++
+ We define the following helper method to return the location of the Chikou Span with respect to the cloud. The + alpha model utilizes this helper method to determine when the Chikou Span is exiting the Ichimoku Cloud. +
+ ++def get_location(self): + chikou = self.ichimoku.Chikou.Current.Value + + senkou_span_a = self.ichimoku.SenkouA.Current.Value + senkou_span_b = self.ichimoku.SenkouB.Current.Value + cloud_top = max(senkou_span_a, senkou_span_b) + cloud_bottom = min(senkou_span_a, senkou_span_b) + + if chikou > cloud_top: + return 1 # Above cloud + if chikou < cloud_bottom: + return -1 # Below cloud + + return 0 # Inside cloud ++
+ As new TradeBars are provided to the + alpha model's Update method, we update the Ichimoku indicator of each symbol. We then emit insights for the + symbols that have their Chikou Span breaking out of their respective Ichimoku Cloud in a new direction. To + maintain positions while we wait for another crossover in the Ichimoku Cloud, we emit insights on a daily basis + with 1-day duration. +
+ ++def Update(self, algorithm, data): + insights = [] + + for symbol, symbol_data in self.symbol_data_by_symbol.items(): + if not data.ContainsKey(symbol) or data[symbol] is None: + continue + + # Update indicator with the latest TradeBar + symbol_data.ichimoku.Update(data[symbol]) + + # Determine insight direction + current_location = symbol_data.get_location() + if symbol_data.previous_location is not None: # Indicator is ready + if symbol_data.previous_location != 1 and current_location == 1: + symbol_data.direction = InsightDirection.Up + if symbol_data.previous_location != -1 and current_location == -1: + symbol_data.direction = InsightDirection.Down + + symbol_data.previous_location = current_location + + # Emit insight + if symbol_data.direction: + insight = Insight.Price(symbol, timedelta(days=1), symbol_data.direction) + insights.append(insight) + + return insights ++
+ Following the guidelines of Alpha Streams + and the Quant League competition, we + utilize the + EqualWeightingPortfolioConstructionModel and the + + ImmediateExecutionModel. +
diff --git a/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/04 Algorithm.html b/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/04 Algorithm.html new file mode 100644 index 0000000..56ab2db --- /dev/null +++ b/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/04 Algorithm.html @@ -0,0 +1,6 @@ + \ No newline at end of file diff --git a/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/05 Relative Performance.html b/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/05 Relative Performance.html new file mode 100644 index 0000000..07a20e4 --- /dev/null +++ b/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/05 Relative Performance.html @@ -0,0 +1,94 @@ ++ To analyze the value of this trading strategy, we compare its performance to buying and holding a popular ETF + tracking the energy sector. In this study, we use XLE, the Energy Select Sector SPDR® Fund, as the benchmark. We + can see from the plot below how the portfolio would have performed just had we had just invested in the benchmark. +
+ +
+
++ We now analyze the Sharpe ratio and annual standard deviation of returns for both the strategy and the benchmark. + From the table below, we can see the results of the strategy and the benchmark over the entire backtest period, the + Fall 2015 crisis, and the 2020 oil price war. The strategy has a lower Sharpe ratio than the benchmark across all + of the time periods we tested, except for the crash during the 2020 oil price war, where it generated an impressive + 176 Sharpe ratio. We can also see the strategy has a lower annual standard deviation accross all of the time + frames, implying that the strategy has more consistent returns than the benchmark. +
+ +| Period Name | +Start Date | +End Date | +Strategy | +Sharpe | +ASD | +
|---|---|---|---|---|---|
| Backtest | +1/1/2015 | +8/16/2020 | +Strategy | +-0.31 | +0.223 | +
| Benchmark | +-0.083 | +0.312 | +|||
| Fall 2015 | +8/10/2015 | +10/10/2015 | +Strategy | +-0.31 | +0.294 | +
| Benchmark | +0.242 | +0.351 | +|||
| 2020 Crash | +2/19/2020 | +3/23/2020 | +Strategy | +176.524 | +0.949 | +
| Benchmark | +-0.902 | +1.108 | +|||
| 2020 Recovery | +3/23/2020 | +6/8/2020 | +Strategy | +-1.556 | +0.447 | +
| Benchmark | +46.068 | +0.703 | +
+ We find the lack of performance for this strategy is not largely attributed to the transaction costs. After + ignoring the transaction fees, spread costs, and slippage, the strategy still has a lower Sharpe ratio than the + benchmark and doesn't match the results found in the original research paper. See the backtest results + here. +
\ No newline at end of file diff --git a/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/06 Market & Competition Qualification.html b/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/06 Market & Competition Qualification.html new file mode 100644 index 0000000..e63b0d3 --- /dev/null +++ b/04 Strategy Library/1028 Ichimoku Clouds in the Energy Sector/06 Market & Competition Qualification.html @@ -0,0 +1,13 @@ ++ Although this strategy passes several of the + metrics required for Alpha Streams + and the Quant League competition, it requires further work to pass the following requirements: +
+ ++ While the strategy examined herein produces a 176 Sharpe ratio throughout the downfall of the 2020 oil price war + and stock market crash, we conclude the strategy does not currently provide as profitable of results as documented + by Gurrib (2020). The strategy experiences a -0.234 Sharpe ratio over the entire backtest period. To continue the + development of this strategy, future areas of research include: +
+ ++ In this tutorial, we apply Ornstein-Uhlenbeck model to a Pairs Trading process and derive the Optimal Entry and Liquidation + levels. +
diff --git a/04 Strategy Library/1029 Optimal Pairs Trading/02 Introduction.html b/04 Strategy Library/1029 Optimal Pairs Trading/02 Introduction.html new file mode 100644 index 0000000..d0a7cd5 --- /dev/null +++ b/04 Strategy Library/1029 Optimal Pairs Trading/02 Introduction.html @@ -0,0 +1,9 @@ ++ Pairs trading is holding one stock while simultaneously shorting another stock, typically in an attempt to profit + from the convergence of the spread between these two stocks. One method of execution is to apply a Kalman Filter, + which we have implemented in this post. + However, today, we will model the portfolio values of holding positions in + a pair of stocks as an Ornstein-Uhlenbeck (OU) process in order to derive the optimal values to enter and liquidate + the position in the pair of stocks. Let (number) refer to the corresponding equation in the given paper, which can + be found under the References section. For example, (2.1) refers to equation 2.1 in the paper. +
diff --git a/04 Strategy Library/1029 Optimal Pairs Trading/03 Method.html b/04 Strategy Library/1029 Optimal Pairs Trading/03 Method.html new file mode 100644 index 0000000..83986fa --- /dev/null +++ b/04 Strategy Library/1029 Optimal Pairs Trading/03 Method.html @@ -0,0 +1,50 @@ +Say there are two arbitrary stocks A and B. For each value β in .01, .02, .03, …, 1.00:
+where
+xj is the value at the jth index of the portfolio values
+and
+\[\widetilde{\sigma}^2 = \sigma ^2\frac{1-e^{-2\mu\Delta t}}{2\mu}\] +and n = the number of portfolio values
+and Δt = 1 ÷ (days between the start and end dates of the portfolio values),
+We then select the β, which we differentiate as β*, that maximizes the average log-likelihood defined in the equation in step 2, while keeping the corresponding θ*, µ*, σ* values. The implementation of finding θ*, µ*, and σ* can be found in ou_mle.py in the Algorithm section.
+ + +With the OU coefficients in hand, we can now calculate the optimal entry level, the portfolio value at which we buy, and liquidation level, the portfolio value at which we sell. We don’t buy the portfolio of $1 of A and -$β* of B immediately (note: to scale up a position, for each additional dollar we invest in A, we short an additional -$β* of B). Instead, we wait until our portfolio reaches the computed entry level, before we buy the portfolio of the pair of stocks. Once we bought this portfolio, we wait until the portfolio value reaches the computed liquidation level before we liquidate our portfolio. By waiting for our optimal entry and liquidation values to be reached, we can mathematically maximize our expected gain. To compute the optimal entry and liquidation levels, we first need to define a few equations:
+\[F(x):=\int_{0}^{\infty}u^{\frac{r}{\mu}-1}e^{\sqrt{\frac{2\mu}{\sigma^2}}(x-\theta)u-\frac{u^2}{2}}du\quad(3.3)\] +\[G(x):=\int_{0}^{\infty}u^{\frac{r}{\mu}-1}e^{\sqrt{\frac{2\mu}{\sigma^2}}(\theta-x)u-\frac{u^2}{2}}du\quad(3.4)\] +\[V(x)=(x\in (-\infty, b^*)\ ?\ (b^*-c) \frac{F(x)}{F(b^*)}:x-c)\quad(4.2)\] +Where constants c = the cost of transaction and r = investor’s subject discount rate. We choose to set c = r = .05 as these were the values given in the paper.
+With these equations, we can now solve for the optimal liquidation level, which we denote as b*, as well as the optimal entry level, which we denote at d*. Note: the reason we derive the optimal liquidation level first is because we use b* in the computation of d*.
+As deriving b* and d* require the derivative of the functions given above, given an arbitrary function input x and an arbitrary function f(x), we approximate f’(x) with the following equation equation:
+\[f'(x) = \frac{f(x+h)-f(x)}{h}\] +where h is some arbitrarily small value (we set h = 1 x 10-4 in our implementation).
+To find b*, we solve for b in the following equation:
+\[F(b)=(b-c)F'(b)\quad(4.3)\] +We solve this equation by getting all terms to one side:
+\[F(b)-(b-c)F'(b)=0\] +Finding the root of the above equation results in b*.
+Now to derive d*, we solve for d in the following equation:
+\[G(d)(V'(d)-1)=G'(d)(V(d)-d-c)\] +Again, we will move all terms to one side:
+\[G(d)(V'(d)-1)-G'(d)(V(d)-d-c)=0\] +And finding the root of this equation results in d*.
+
The full method of finding b* and d* can be found in the OptimalStopping.py
+ file in the Algorithm section.
+ Our trading logic is very simple. First, we feed in 252 points of the most recent data for the daily closing prices + for stocks A and B. We then train our model on these data points, and we get the + b*, d*, and β* values. We then keep track of a hypothetical portfolio of holding $1 + of A and -$β* of B. Once the value of our hypothetical portfolio is less than or equal to b*, + we allocate 1.0 of our capital to long of A and short B using (β* x capital used for A) worth of stock. + Once the hypothetical portfolio value we tracking reaches d*, we liquidate our positions. We repeat these + trading rules when possible. On the first day of every quarter, we retrain our model with the most recent 252 points of data to + update our b*, d*, and β* values. +
diff --git a/04 Strategy Library/1029 Optimal Pairs Trading/04 Algorithm.html b/04 Strategy Library/1029 Optimal Pairs Trading/04 Algorithm.html new file mode 100644 index 0000000..04066ff --- /dev/null +++ b/04 Strategy Library/1029 Optimal Pairs Trading/04 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/1029 Optimal Pairs Trading/05 Video Walkthrough.html b/04 Strategy Library/1029 Optimal Pairs Trading/05 Video Walkthrough.html new file mode 100644 index 0000000..1e7e3ae --- /dev/null +++ b/04 Strategy Library/1029 Optimal Pairs Trading/05 Video Walkthrough.html @@ -0,0 +1,5 @@ + \ No newline at end of file diff --git a/04 Strategy Library/1029 Optimal Pairs Trading/06 Results.html b/04 Strategy Library/1029 Optimal Pairs Trading/06 Results.html new file mode 100644 index 0000000..3eb8a0f --- /dev/null +++ b/04 Strategy Library/1029 Optimal Pairs Trading/06 Results.html @@ -0,0 +1,8 @@ ++ Our algorithm yielded a Sharpe ratio of 0.898 over a five year period, while holding SPY over the same period + yielded a Sharpe ratio of 0.667. However it should be noted, due to the fact the algorithm had to wait periods + of time before our optimal entry and liquidation levels were reached, our algorithm only made twelve trades over the + entire backtest duration. To increase the number of trades, we can add additional pairs, such as GLD-GDX. We encourage + our users to clone this algorithm and and to experiment with different ideas for pairs and to play with the parameters + of the algorithm. +
\ No newline at end of file diff --git a/04 Strategy Library/1029 Optimal Pairs Trading/07 References.html b/04 Strategy Library/1029 Optimal Pairs Trading/07 References.html new file mode 100644 index 0000000..10b2dac --- /dev/null +++ b/04 Strategy Library/1029 Optimal Pairs Trading/07 References.html @@ -0,0 +1,7 @@ ++ In this tutorial, we apply G-Score Investing to choose a Universe of stocks to invest in. +
diff --git a/04 Strategy Library/1030 G-Score Investing/02 Introduction.html b/04 Strategy Library/1030 G-Score Investing/02 Introduction.html new file mode 100644 index 0000000..b26b9f7 --- /dev/null +++ b/04 Strategy Library/1030 G-Score Investing/02 Introduction.html @@ -0,0 +1,10 @@ ++ Analyzing a company’s fundamentals is a method of trading that doesn’t + rely purely on price and volume data. We will apply the use of computers to automate + the analysis of this data, and we will do so using a method of + Factor Investing, + the process of using different attributes, in this case, fundamental data, to choose + stocks to purchase. More specifically, we will use G-Score investing, and evaluate companies + on seven factors that we will detail later. We specifically choose companies with Book-to-Market + due to abnormal returns as a result of the Risk Premium Effect. +
diff --git a/04 Strategy Library/1030 G-Score Investing/03 Method.html b/04 Strategy Library/1030 G-Score Investing/03 Method.html new file mode 100644 index 0000000..3a493ab --- /dev/null +++ b/04 Strategy Library/1030 G-Score Investing/03 Method.html @@ -0,0 +1,57 @@ ++ We first sort all companies that have fundamental data by their Book-to-Market ratio, and narrow our universe to the + bottom quartile. We measure the Book-to-Market ratio using + fine.FinancialStatements.BalanceSheet.NetTangibleAssets.TwelveMonths divided by + fine.MarketCap. In this strategy, we will use Technology as the industry of choice, thus, we further + narrow this universe to Technology stocks only. +
+ ++ For each of the conditions that are described below, if met, one point will be added to the G-Score. + Thus, with seven factors, our G-Score can range from 0 to 7. We evaluate a company based on the following: +
+ + ++ The fundamental data used in our algorithms is sourced from MorningStar, and to read more about our fundamental data, + please visit the Fundamentals section of our + documentation. +
+ ++ Once we have computed the G-Scores for each of the securities, we long the securities with G-Scores of 5 or higher. +
+ diff --git a/04 Strategy Library/1030 G-Score Investing/04 Algorithm.html b/04 Strategy Library/1030 G-Score Investing/04 Algorithm.html new file mode 100644 index 0000000..2c62d81 --- /dev/null +++ b/04 Strategy Library/1030 G-Score Investing/04 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/1030 G-Score Investing/05 Results.html b/04 Strategy Library/1030 G-Score Investing/05 Results.html new file mode 100644 index 0000000..5f327af --- /dev/null +++ b/04 Strategy Library/1030 G-Score Investing/05 Results.html @@ -0,0 +1,5 @@ ++ Since we use Technology as the industry, we decided to use Nasdaq-100, or ^NDX, as the benchmark, which we track + using the QQQ ETF. Our algorithm achieves a Sharpe Ratio of 0.778 from April 2016 to September 2020, and so it is + outperformed by simply holding QQQ, which yielded a Sharpe Ratio of 1.22 over the same period. +
\ No newline at end of file diff --git a/04 Strategy Library/1030 G-Score Investing/06 References.html b/04 Strategy Library/1030 G-Score Investing/06 References.html new file mode 100644 index 0000000..f21473a --- /dev/null +++ b/04 Strategy Library/1030 G-Score Investing/06 References.html @@ -0,0 +1,6 @@ ++ In this tutorial, we apply an SVM Wavelet model in an attempt to forecast EURJPY prices. +
diff --git a/04 Strategy Library/1031 SVM Wavelet Forecasting/02 Introduction.html b/04 Strategy Library/1031 SVM Wavelet Forecasting/02 Introduction.html new file mode 100644 index 0000000..6fe7274 --- /dev/null +++ b/04 Strategy Library/1031 SVM Wavelet Forecasting/02 Introduction.html @@ -0,0 +1,10 @@ ++ Several methods have been developed to forecast time-series, from ARIMA to Neural Networks. In this strategy, we + combine a Support Vector Machine (SVM) and Wavelets in an attempt to forecast EURJPY. Although SVMs are generally + used for classification problems, such as classifying proteins, they can also be applied in regression problems, valued + for their ability to handle non-linear data. Furthermore, Wavelets are often applied in Signal Processing applications. Wavelets allow us + to decompose a time-series into multiple components, where each individual component can be denoised using thresholding, and this + leads to a cleaner time-series after the components are recombined. To use these two models in conjunction, we first + decompose the EURJPY data into components using Wavelet decomposition, then we apply the SVM to forecast one time-step + ahead of each of the components. After we recombine the components, we get the aggregate forecast of our SVM-Wavelet model. +
diff --git a/04 Strategy Library/1031 SVM Wavelet Forecasting/03 Method.html b/04 Strategy Library/1031 SVM Wavelet Forecasting/03 Method.html new file mode 100644 index 0000000..5cd8e93 --- /dev/null +++ b/04 Strategy Library/1031 SVM Wavelet Forecasting/03 Method.html @@ -0,0 +1,56 @@ ++ Given EURJPY data, our first step is to decompose our data into multiple resolutions. + We work with wavelets using the pywt package. For denoising, Daubechies and + Symlets are good choices for Wavelets, and we use Symlets 10 in our strategy. We create a Symlets 10 Wavelet + using the following: +
+ +
+w = pywt.Wavelet('sym10')
+
+To determine the length of the data we’d need for a certain number of levels after decomposition, we can solve for:
+\[log_{2}(\frac{len(data)}{wavelength-1})=levels\] ++ Given the length of a Symlet 10 wavelet is 20, if we want three levels, we + solve for len(data) to get len(data) = 152, which means data would need to have at least + 152 values. Since we will denoise our components using thresholding, + we specify threshold = 0.5 to indicate the strength of the thresholding. + This threshold value can be any number between 0 and 1. +
+To decompose our data, we use:
+ ++coeffs = pywt.wavedec(data, w) ++
For each component, we threshold/denoise the component (except for the first component, the approximation coefficients), + roll the values of the component one spot to the left, + and replace the last value of the component with a value forecasted from an SVM. This process looks like the following in code:
+ ++for i in range(len(coeffs)): + if i > 0: + # we don't want to threshold the approximation coefficients + coeffs[i] = pywt.threshold(coeffs[i], threshold*max(coeffs[i])) + forecasted = __svm_forecast(coeffs[i]) + coeffs[i] = np.roll(coeffs[i], -1) + coeffs[i][-1] = forecasted ++
The __svm_forecast method fits partitioned data to an SVM model then predicts one value into the + future, and can be found under SVMWavelet.py file under the Algorithm section
+Once we forecast one value into the future, we can aggregate the forecasts by recombining the components into a simple time-series. We do this with:
++datarec = pywt.waverec(coeffs, w) ++
Since we want the aggregate forecast one time-step into the future, we return the last element of this time-series, or datarec[-1].
+ +Our trading rules are simple: feed in the past 152 points of daily closing prices of EURJPY into our SVM Wavelet forecasting method, and divide that number by the current close of EURJPY to get the forecasted percent change. Then, we emit an Insight based on the direction of the percent change with the weight of the Insight as the absolute value of the percent change. We use the InsightWeightPortfolioConstructionModel so that the weight of the Insight determines the portfolio allocation percentage, which means larger forecasted moves will have a larger allocation.
diff --git a/04 Strategy Library/1031 SVM Wavelet Forecasting/04 Algorithm.html b/04 Strategy Library/1031 SVM Wavelet Forecasting/04 Algorithm.html new file mode 100644 index 0000000..935af6f --- /dev/null +++ b/04 Strategy Library/1031 SVM Wavelet Forecasting/04 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/1031 SVM Wavelet Forecasting/05 Results.html b/04 Strategy Library/1031 SVM Wavelet Forecasting/05 Results.html new file mode 100644 index 0000000..96be5b5 --- /dev/null +++ b/04 Strategy Library/1031 SVM Wavelet Forecasting/05 Results.html @@ -0,0 +1,8 @@ +The performance of the algorithm was decent. Over the past five years, the algorithm achieved a Sharpe Ratio of 0.252, + while buying and holding SPY over the same period would have achieved a Sharpe Ratio of 0.713. Some ideas for improvement include:
+If a user comes across any interesting results with modifications of this algorithm, we’d love to hear about it in the Community Forum.
\ No newline at end of file diff --git a/04 Strategy Library/1031 SVM Wavelet Forecasting/06 References.html b/04 Strategy Library/1031 SVM Wavelet Forecasting/06 References.html new file mode 100644 index 0000000..1cc8866 --- /dev/null +++ b/04 Strategy Library/1031 SVM Wavelet Forecasting/06 References.html @@ -0,0 +1,5 @@ ++ In this tutorial, we train a Gradient Boosting Model (GBM) to forecast the intraday price movements of the SPY ETF using a + collection of technical indicators. The implementation is based on the research produced by Zhou et al (2013), where a GBM + was found to produce an annualized Sharpe ratio greater than 20. Our research shows that throughout a 5 year backtest, the + model underperforms the SPY with its current parameter set. However, we finish the tutorial with highlighting potential + areas of further research to improve the model’s performance. +
diff --git a/04 Strategy Library/1033 Gradient Boosting Model/02 Background.html b/04 Strategy Library/1033 Gradient Boosting Model/02 Background.html new file mode 100644 index 0000000..597b32d --- /dev/null +++ b/04 Strategy Library/1033 Gradient Boosting Model/02 Background.html @@ -0,0 +1,24 @@ ++ A GBM is trained by setting the initial model prediction to the mean target value in the training set. The model then + iteratively builds regression trees to predict the model’s pseudo-residuals on the training set to tighten the fit. The + pseudo-residuals are the differences between the target value and the model’s prediction on the current training iteration + for each sample. The model’s predictions are made by summing the mean target value and the products of the learning rate + and the regression tree outputs. The full algorithm is shown here. +
+ +
++ We provide technical indicator values as inputs to the GBM. The model is trained to predict the security’s return over the + next 10 minutes and the performance of the model’s predictions are assessed using the mean squared error loss function. +
+ +\[ MSE = \frac{\Sigma_{i=1}^n(y_i - \hat{y}_i)^2}{n} \] + ++ Zhou et al (2013) utilize custom loss functions to fit their GBM in a manner that aims to maximize the profit-and-loss or + Sharpe ratio over the training data set. The attached notebook shows training the GBM with these custom loss functions + leads to poor model predictions. +
\ No newline at end of file diff --git a/04 Strategy Library/1033 Gradient Boosting Model/03 Method.html b/04 Strategy Library/1033 Gradient Boosting Model/03 Method.html new file mode 100644 index 0000000..7e88ae2 --- /dev/null +++ b/04 Strategy Library/1033 Gradient Boosting Model/03 Method.html @@ -0,0 +1,163 @@ ++ We use a ManualUniverseSelectionModel to subscribe to the SPY ETF. The algorithm is designed to work with minute and + second data resolutions. In our implementation, we use data on a minute resolution. +
+
+symbols = [ Symbol.Create("SPY", SecurityType.Equity, Market.USA) ]
+self.SetUniverseSelection( ManualUniverseSelectionModel(symbols) )
+self.UniverseSettings.Resolution = Resolution.Minute
+
++ The GradientBoostingAlphaModel predicts the direction of the SPY at each timestep. Each position taken is held for + 10 minutes, although this duration is customizable in the constructor. During construction of this alpha model, we + simply set up a dictionary to hold a SymbolData object for each symbol in the universe. In the case where the + universe consists of multiple securities, the alpha model holds each with equal weighting. +
+
+class GradientBoostingAlphaModel(AlphaModel):
+ symbol_data_by_symbol = {}
+
+ def __init__(self, hold_duration = 10):
+ self.hold_duration = hold_duration
+ self.weight = 1
+
++ When a new security is added to the universe, we create a SymbolData object for it to store information unique to + the security. The management of the SymbolData objects occurs in the alpha model's OnSecuritiesChanged method. +
++def OnSecuritiesChanged(self, algorithm, changes): + for security in changes.AddedSecurities: + symbol = security.Symbol + self.symbol_data_by_symbol[symbol] = SymbolData(symbol, algorithm, self.hold_duration) + + for security in changes.RemovedSecurities: + symbol_data = self.symbol_data_by_symbol.pop(security.Symbol, None) + if symbol_data: + symbol_data.dispose() + + self.weight = 1 / len(self.symbol_data_by_symbol) + ++
+ The SymbolData class is used in this algorithm to manage indicators, train the GBM, and produce trading predictions. + The constructor definition is shown below. The class is designed to train at the end of each month, using the + previous 4 weeks of data to fit the GBM that consists of 20 stumps (regression trees with 2 leaves). To ensure + overnight holds are avoided, the class uses + Scheduled Events to stop trading + near the market close. +
++class SymbolData: + def __init__(self, symbol, algorithm, hold_duration, k_start=0.5, k_end=5, + k_step=0.25, training_weeks=4, max_depth=1, num_leaves=2, num_trees=20, + commission=0.02, spread_cost=0.03): + self.symbol = symbol + self.algorithm = algorithm + self.hold_duration = hold_duration + self.resolution = algorithm.UniverseSettings.Resolution + self.training_length = int(training_weeks * 5 * 6.5 * 60) # training_weeks in minutes + self.max_depth = max_depth + self.num_leaves = num_leaves + self.num_trees = num_trees + self.cost = commission + spread_cost + + self.indicator_consolidators = [] + + # Train a model at the end of each month + self.model = None + algorithm.Train(algorithm.DateRules.MonthEnd(symbol), + algorithm.TimeRules.BeforeMarketClose(symbol), + self.train) + + # Avoid overnight holds + self.allow_predictions = False + self.events = [ + algorithm.Schedule.On(algorithm.DateRules.EveryDay(symbol), + algorithm.TimeRules.AfterMarketOpen(symbol, 0), + self.start_predicting), + algorithm.Schedule.On(algorithm.DateRules.EveryDay(symbol), + algorithm.TimeRules.BeforeMarketClose(symbol, hold_duration + 1), + self.stop_predicting) + ] + + self.setup_indicators(k_start, k_end, k_step) + self.train() ++
+ For brevity, we omit the model training logic. Although, the code can be seen in the attached backtest. To make + predictions, we define the following method inside the SymbolData class. A position is held in the predicted + direction only if the predicted return in that direction exceeds the cost of the trade. +
++def predict_direction(self): + if self.model is None or not self.allow_predictions: + return 0 + + input_data = [[]] + for _, indicators in self.indicators_by_indicator_type.items(): + for indicator in indicators: + input_data[0].append(indicator.Current.Value) + + return_prediction = self.model.predict(input_data) + if return_prediction > self.cost: + return 1 + if return_prediction < -self.cost: + return -1 + return 0 ++
+ As new TradeBars are provided to the alpha model's Update method, each SymbolData object makes a directional + prediction for its security. If the prediction is not flat, the alpha model emits an insight in that direction with + a duration of 10 minutes. +
++def Update(self, algorithm, data): + insights = [] + for symbol, symbol_data in self.symbol_data_by_symbol.items(): + direction = symbol_data.predict_direction() + if direction: + hold_duration = timedelta(minutes=self.hold_duration) # Should match universe resolution + insights.append(Insight.Price(symbol, hold_duration, direction, None, None, None, self.weight)) + + return insights ++
+ Following the guidelines of Alpha Streams + and the Quant League competition, we + utilize the + InsightWeightingPortfolioConstructionModel and the + + ImmediateExecutionModel. +
diff --git a/04 Strategy Library/1033 Gradient Boosting Model/04 Algorithm.html b/04 Strategy Library/1033 Gradient Boosting Model/04 Algorithm.html new file mode 100644 index 0000000..223e7f3 --- /dev/null +++ b/04 Strategy Library/1033 Gradient Boosting Model/04 Algorithm.html @@ -0,0 +1,6 @@ + \ No newline at end of file diff --git a/04 Strategy Library/1033 Gradient Boosting Model/05 Relative Performance.html b/04 Strategy Library/1033 Gradient Boosting Model/05 Relative Performance.html new file mode 100644 index 0000000..415eea9 --- /dev/null +++ b/04 Strategy Library/1033 Gradient Boosting Model/05 Relative Performance.html @@ -0,0 +1,56 @@ +| Period Name | +Start Date | +End Date | +Strategy | +Sharpe | +Variance | +
|---|---|---|---|---|---|
| 5 Year Backtest | +9/1/2015 | +9/17/2020 | +Strategy | +-0.716 | +0.006 | +
| Benchmark | +0.845 | +0.036 | +|||
| 2020 Crash | +2/19/2020 | +3/23/2020 | +Strategy | +-2.879 | +0.101 | +
| Benchmark | +-1.243 | +0.628 | +|||
| 2020 Recovery | +3/23/2020 | +6/8/2020 | +Strategy | +-2.329 | +0.027 | +
| Benchmark | +13.761 | +0.149 | +
+ Although this strategy passes several of the + metrics required for Alpha Streams + and the Quant League competition, it requires further work to pass the following requirements: +
+ + ++ The GBM implemented in this tutorial has a lower Sharpe ratio than the S&P 500 index ETF benchmark over the periods + we tested. However, the strategy generates a lower annual variance over all the testing period, implying more + consistent returns than buy-and-hold. To continue the development of this strategy, future areas of research + include: +
+ ++ Naïve Bayes models have become popular for their success in spam email filtering. In this tutorial, we train + Gaussian Naïve Bayes (GNB) classifiers to forecast the daily returns of stocks in the technology sector given the + historical returns of the sector. Our implementation shows the strategy has a greater Sharpe and lower variance + than the SPY ETF over a 5 year backtest and during the 2020 stock market crash. The algorithm we build here follows + the research done by Lu (2016) and Imandoust & Bolandraftar (2014). +
diff --git a/04 Strategy Library/1036 Gaussian Naive Bayes Model/02 Background.html b/04 Strategy Library/1036 Gaussian Naive Bayes Model/02 Background.html new file mode 100644 index 0000000..f576900 --- /dev/null +++ b/04 Strategy Library/1036 Gaussian Naive Bayes Model/02 Background.html @@ -0,0 +1,47 @@ ++ Naïve Bayes models classify observations into a set of classes by utilizing + Bayes’ Theorem +
+ +\[\text{posterior} = \frac{ \text{prior } * \text{ likelihood} } {\text{evidence}}\] + ++ In symbols, this translates to +
+ +\[P(c_i | x_1, ..., x_n) = \frac{P(c_i)P(x_1, ..., x_n | c_i)}{P(x_1, ..., x_n)}\] + ++ where \(c_i\) represents one of the \(m\) classes and \(x_1, ..., x_n\) are the features. +
+ ++ The Naïve Bayes model assumes the features are independent, so that +
+ +\[P(c_i | x_1, ..., x_n) = \frac{P(c_i)\prod_{j=1}^{n} P(x_j | c_i)}{P(x_1, ..., x_n)} \propto P(c_i)\prod_{j=1}^{n} P(x_j|c_i)\] + ++ The class that is most probable given the observation is then determined by solving +
+ +\[\hat{c} = \arg\max_{i \in \{1, ..., m\}} P(c_i) \prod_{j=1}^{n} P(x_j | c_i)\] + + ++ In our use case, the classes in the model are: positive, negative, or flat future return for a security. The features + are the last 4 daily returns of the universe constituents. Since we are dealing with continuous data, we extend the + model to a GNB model by replacing \(P(x_j|c_i)\) in the equation above. First, we find the mean \(\mu_j\) and standard + deviation \(\sigma_j^2\) of the \(x_j\) feature vector in the training set labeled class \(c_i\). A normal distribution + parameterized by \(\mu_j\) and \(\sigma_j^2\) is then used to determine the likelihood of the observations. If \(o\) is the + observation for the \(j\)th feature. The likelihood of the observation given the class \(c_i\) is +
+ +\[P(x_j = o | c_i) = \frac{1} {\sqrt{2 \pi{} \sigma{}_j^2 }}e^{- \frac{(o - \mu{}_j)^2} {2 \sigma{}_j^2}} \] + ++ The mechanics of the GNB model can be seen visually in + this video. Note that the GNB model has 2 underlying + assumptions: the feature vectors are independent and normally distributed. We do not test for these properties, but + rather leave it as an area of future research. +
\ No newline at end of file diff --git a/04 Strategy Library/1036 Gaussian Naive Bayes Model/03 Video Walkthrough.html b/04 Strategy Library/1036 Gaussian Naive Bayes Model/03 Video Walkthrough.html new file mode 100644 index 0000000..3a3ef40 --- /dev/null +++ b/04 Strategy Library/1036 Gaussian Naive Bayes Model/03 Video Walkthrough.html @@ -0,0 +1,5 @@ + \ No newline at end of file diff --git a/04 Strategy Library/1036 Gaussian Naive Bayes Model/04 Method.html b/04 Strategy Library/1036 Gaussian Naive Bayes Model/04 Method.html new file mode 100644 index 0000000..8ef11c2 --- /dev/null +++ b/04 Strategy Library/1036 Gaussian Naive Bayes Model/04 Method.html @@ -0,0 +1,223 @@ ++ Following Lu (2016), we implement a custom universe selection model to select the largest stocks from the technology + sector. We restrict our universe to have a size of 10, but this can be easily customized via the `fine_size` + parameter in the constructor. +
++class BigTechUniverseSelectionModel(FundamentalUniverseSelectionModel): + def __init__(self, fine_size=10): + self.fine_size = fine_size + self.month = -1 + super().__init__(True) + + def SelectCoarse(self, algorithm, coarse): + if algorithm.Time.month == self.month: + return Universe.Unchanged + return [ x.Symbol for x in coarse if x.HasFundamentalData ] + + def SelectFine(self, algorithm, fine): + self.month = algorithm.Time.month + + tech_stocks = [ f for f in fine if f.AssetClassification.MorningstarSectorCode == MorningstarSectorCode.Technology ] + sorted_by_market_cap = sorted(tech_stocks, key=lambda x: x.MarketCap, reverse=True) + return [ x.Symbol for x in sorted_by_market_cap[:self.fine_size] ] ++
+ The GaussianNaiveBayesAlphaModel predicts the direction each security will move from a given day’s open to the next + day’s open. When constructing this alpha model, we set up a dictionary to hold a SymbolData object for each symbol + in the universe and a flag to show the universe has changed. +
+
+class GaussianNaiveBayesAlphaModel(AlphaModel):
+ symbol_data_by_symbol = {}
+ new_securities = False
+
++ When a new security is added to the universe, we create a SymbolData object for it to store information unique to + the security. The management of the SymbolData objects occurs in the alpha model's OnSecuritiesChanged method. In + this algorithm, since we train the Gaussian Naive Bayes classifier using the historical returns of the securities + in the universe, we flag to train the model every time the universe changes. +
++class GaussianNaiveBayesAlphaModel(AlphaModel): + ... + + def OnSecuritiesChanged(self, algorithm, changes): + for security in changes.AddedSecurities: + self.symbol_data_by_symbol[security.Symbol] = SymbolData(security, algorithm) + + for security in changes.RemovedSecurities: + symbol_data = self.symbol_data_by_symbol.pop(security.Symbol, None) + if symbol_data: + symbol_data.dispose() + + self.new_securities = True ++
+ The SymbolData class is used to store training data for the GaussianNaiveBayesAlphaModel and manage a consolidator + subscription. In the constructor, we specify the training parameters, setup the consolidator, and warm up the + training data. +
+
+class SymbolData:
+ def __init__(self, security, algorithm, num_days_per_sample=4, num_samples=100):
+ self.exchange = security.Exchange
+ self.symbol = security.Symbol
+ self.algorithm = algorithm
+ self.num_days_per_sample = num_days_per_sample
+ self.num_samples = num_samples
+ self.previous_open = 0
+ self.model = None
+
+ # Setup consolidators
+ self.consolidator = TradeBarConsolidator(timedelta(days=1))
+ self.consolidator.DataConsolidated += self.CustomDailyHandler
+ algorithm.SubscriptionManager.AddConsolidator(self.symbol, self.consolidator)
+
+ # Warm up ROC lookback
+ self.roc_window = np.array([])
+ self.labels_by_day = pd.Series()
+
+ data = {f'{self.symbol.ID}_(t-{i})' : [] for i in range(1, num_days_per_sample + 1)}
+ self.features_by_day = pd.DataFrame(data)
+
+ lookback = num_days_per_sample + num_samples + 1
+ history = algorithm.History(self.symbol, lookback, Resolution.Daily)
+ if history.empty or 'close' not in history:
+ algorithm.Log(f"Not enough history for {self.symbol} yet")
+ return
+
+ history = history.loc[self.symbol]
+ history['open_close_return'] = (history.close - history.open) / history.open
+
+ start = history.shift(-1).open
+ end = history.shift(-2).open
+ history['future_return'] = (end - start) / start
+
+ for day, row in history.iterrows():
+ self.previous_open = row.open
+ if self.update_features(day, row.open_close_return) and not pd.isnull(row.future_return):
+ row = pd.Series([np.sign(row.future_return)], index=[day])
+ self.labels_by_day = self.labels_by_day.append(row)[-self.num_samples:]
+
++ The update_features method is called to update our training features with the latest data passed to the algorithm. + It returns True/False, representing if the features are in place to start updating the training labels. +
+ ++class SymbolData: + ... + + def update_features(self, day, open_close_return): + self.roc_window = np.append(open_close_return, self.roc_window)[:self.num_days_per_sample] + + if len(self.roc_window) < self.num_days_per_sample: + return False + + self.features_by_day.loc[day] = self.roc_window + self.features_by_day = self.features_by_day[-(self.num_samples+2):] + return True ++
+ The GNB model is trained each day the universe has changed. By default, it uses 100 samples to train. The features + are the historical open-to-close returns of the universe constituents. The labels are the returns from the open at + T+1 to the open at T+2 at each time step for each security. +
+
+class GaussianNaiveBayesAlphaModel(AlphaModel):
+ ...
+
+ def train(self):
+ features = pd.DataFrame()
+ labels_by_symbol = {}
+
+ # Gather training data
+ for symbol, symbol_data in self.symbol_data_by_symbol.items():
+ if symbol_data.IsReady:
+ features = pd.concat([features, symbol_data.features_by_day], axis=1)
+ labels_by_symbol[symbol] = symbol_data.labels_by_day
+
+ # Train the GNB model
+ for symbol, symbol_data in self.symbol_data_by_symbol.items():
+ if symbol_data.IsReady:
+ symbol_data.model = GaussianNB().fit(features.iloc[:-2], labels_by_symbol[symbol])
+
++ As new TradeBars are provided to the alpha model's Update method, we collect the latest TradeBar’s open-to-close + return for each security in the universe. We then predict the direction of each security using the security’s + corresponding GNB model, and return insights accordingly. +
+
+class GaussianNaiveBayesAlphaModel(AlphaModel):
+ ...
+
+ def Update(self, algorithm, data):
+ if self.new_securities:
+ self.train()
+ self.new_securities = False
+
+ tradable_symbols = {}
+ features = [[]]
+
+ for symbol, symbol_data in self.symbol_data_by_symbol.items():
+ if data.ContainsKey(symbol) and data[symbol] is not None and symbol_data.IsReady:
+ tradable_symbols[symbol] = symbol_data
+ features[0].extend(symbol_data.features_by_day.iloc[-1].values)
+
+ insights = []
+ if len(tradable_symbols) == 0:
+ return []
+ weight = 1 / len(tradable_symbols)
+ for symbol, symbol_data in tradable_symbols.items():
+ direction = symbol_data.model.predict(features)
+ if direction:
+ insights.append(Insight.Price(symbol, data.Time + timedelta(days=1, seconds=-1),
+ direction, None, None, None, weight))
+
+ return insights
+
++ Following the guidelines of Alpha Streams + and the Quant League competition, we + utilize the + InsightWeightingPortfolioConstructionModel and the + + ImmediateExecutionModel. +
diff --git a/04 Strategy Library/1036 Gaussian Naive Bayes Model/05 Algorithm.html b/04 Strategy Library/1036 Gaussian Naive Bayes Model/05 Algorithm.html new file mode 100644 index 0000000..7f48965 --- /dev/null +++ b/04 Strategy Library/1036 Gaussian Naive Bayes Model/05 Algorithm.html @@ -0,0 +1,6 @@ + \ No newline at end of file diff --git a/04 Strategy Library/1036 Gaussian Naive Bayes Model/06 Relative Performance.html b/04 Strategy Library/1036 Gaussian Naive Bayes Model/06 Relative Performance.html new file mode 100644 index 0000000..3ddfffe --- /dev/null +++ b/04 Strategy Library/1036 Gaussian Naive Bayes Model/06 Relative Performance.html @@ -0,0 +1,56 @@ +| Period Name | +Start Date | +End Date | +Strategy | +Sharpe | +Variance | +
|---|---|---|---|---|---|
| 5 Year Backtest | +10/1/2015 | +10/13/2020 | +Strategy | +0.97 | +0.016 | +
| Benchmark | +0.805 | +0.029 | +|||
| 2020 Crash | +2/19/2020 | +3/23/2020 | +Strategy | +-0.981 | +0.353 | +
| Benchmark | +-1.4 | +0.474 | +|||
| 2020 Recovery | +3/23/2020 | +6/8/2020 | +Strategy | +-2.011 | +0.035 | +
| Benchmark | +8.765 | +0.103 | +
+ Although this strategy passes several of the + metrics required for Alpha Streams + and the Quant League competition, it requires further work to pass the following requirements: +
+ ++ The GNB model strategy implemented in this tutorial produced a greater Sharpe ratio and lower annual variance than + buying and holding the S&P 500 index ETF benchmark over the backtesting period. In addition to outperforming during + the entire backtest, the strategy also outperformed during the 2020 stock market crash. +
+ ++ To continue the development of this strategy, future areas of research include: +
+ ++ January barometer is a calendar anomaly saying that the January performance of equity index could foretell February to December returns on equity index - a strong January shows strong rest of the year and otherwise. + This algorithm is going to explore the estimation effect of the January barometer in equity index market. +
diff --git a/04 Strategy Library/113 January Barometer/02 Method.html b/04 Strategy Library/113 January Barometer/02 Method.html new file mode 100644 index 0000000..c8d3623 --- /dev/null +++ b/04 Strategy Library/113 January Barometer/02 Method.html @@ -0,0 +1,20 @@ ++ We use the S&P500 ETF as the underlying. In January, the algorithm buys SPY and hold until the end of January. + At the end of January, we calculate the January return, if the return is greater than zero, the algorithm will continue to hold the SPY. If the January return is negative instead, the algorithm will liquidate the SPY asset and invest in the treasury bill for the rest of the year. The portfolio is rebalanced every year in January. +
+
+def Rebalance(self):
+ if self.Time.month == 1:
+ self.Liquidate("BIL")
+ self.SetHoldings("SPY", 1)
+ self.startPrice = self.Securities["SPY"].Price
+ if self.Time.month == 2 and self.startPrice is not None:
+ returns = (self.Securities["SPY"].Price - self.startPrice)/self.startPrice
+ if returns > 0:
+ self.SetHoldings("SPY", 1)
+ else:
+ self.Liquidate("SPY")
+ self.SetHoldings("BIL", 1)
+
++ The January effect is a calendar anomaly saying that small-cap stocks returns in January are especially strong. + The most common explanation of this phenomenon is that individual investors, who are income tax-sensitive and who disproportionately hold small stocks, sell stocks for tax reasons at year end and reinvest during the first month of the year. + In this algorithm, we will explore the January effect in the stock market. +
diff --git a/04 Strategy Library/114 January Effect in Stocks/02 Method.html b/04 Strategy Library/114 January Effect in Stocks/02 Method.html new file mode 100644 index 0000000..ae1f295 --- /dev/null +++ b/04 Strategy Library/114 January Effect in Stocks/02 Method.html @@ -0,0 +1,69 @@ ++ The investment universe consists of US-listed companies. A minimum stock price filter is used to avoid penny stocks. To avoid stocks that are not liquid enough, we select 1000 stocks with the highest dollar volume. +
++def CoarseSelectionFunction(self, coarse): + if self.monthly_rebalance: + self.coarse = True + coarse = [x for x in coarse if (x.AdjustedPrice > 10)] + topDollarVolume = sorted(coarse, key=lambda x: x.DollarVolume, reverse=True)[:1000] + return [i.Symbol for i in topDollarVolume] + else: + return [] ++
+ In FineSelectionFunction(self, fine), we calculate the market cap value with shares outstanding, earning per shares and the PE ratio.
+ Then stocks are sorted by their market capitalization. The top 10 stocks are selected as the large-cap group and the bottom 10 stocks belong to the small-cap group.
+
+def FineSelectionFunction(self, fine): + if self.monthly_rebalance: + fine =[i for i in fine if i.EarningReports.BasicAverageShares.ThreeMonths>0 + and i.EarningReports.BasicEPS.TwelveMonths>0 + and i.ValuationRatios.PERatio>0] + for i in fine: + i.MarketCap = float(i.EarningReports.BasicAverageShares.ThreeMonths * (i.EarningReports.BasicEPS.TwelveMonths*i.ValuationRatios.PERatio)) + sorted_market_cap = sorted(fine, key = lambda x:x.MarketCap, reverse=True) + symbols = [i.Symbol for i in sorted_market_cap] + self.top_market_cap = symbols[:10] + self.bottom_market_cap = symbols[-10:] + return self.top_market_cap + self.bottom_market_cap + else: + return [] ++
+ The algorithm invests into small-cap stocks at the beginning of each January and stays invested in large-cap stocks for rest of the year. + The portfolio is rebalanced every month. +
++ def OnData(self, data): + if not (self.monthly_rebalance and self.coarse): return + self.coarse = False + self.monthly_rebalance = False + stocks_invested = [x.Key for x in self.Portfolio if x.Value.Invested] + # invest in small cap stocks at the beginning of each January + if self.Time.month == 1: + # liquidate stocks not in the small-cap group + for i in stocks_invested: + if i not in self.bottom_market_cap: + self.Liquidate(i) + weight = 1/len(self.bottom_market_cap) + for i in self.bottom_market_cap: + self.SetHoldings(i, weight) + # invest in large cap stocks for rest of the year + else: + # liquidate stocks not in the large-cap group + for i in stocks_invested: + if i not in self.top_market_cap: + self.Liquidate(i) + + weight = 1/len(self.top_market_cap) + for i in self.top_market_cap: + self.SetHoldings(i, weight) ++
+Time series momentum is related to, but different from the phenomenon known as “momentum” in the finance literature, which is primarily cross-sectional in nature. +The momentum literature focuses on the relative performance of securities in the cross section, finding that securities that recently outperformed their peers over the past 3 to 12 months continue to do so on average over the next month. +Rather than focus on the relative returns of securities in the cross section, this time series momentum strategy focuses purely on the past returns of each individual futures contract. +Every month, the investor considers whether the excess return of each asset over the past 12 months is positive or negative and goes long on the contract if it is positive and short if negative. +The position size is set to be inversely proportional to the volatility of the security's returns. +A univariate GARCH model could be used to estimate volatility. +However, other simple models could probably be easily used with good results (for example, the easiest one would be using historical volatility). For the sake of simplicity, we will use historical volatility. +The portfolio is rebalanced monthly. +
diff --git a/04 Strategy Library/118 Time Series Momentum Effect/02 Method.html b/04 Strategy Library/118 Time Series Momentum Effect/02 Method.html new file mode 100644 index 0000000..3e2ec91 --- /dev/null +++ b/04 Strategy Library/118 Time Series Momentum Effect/02 Method.html @@ -0,0 +1,60 @@ ++ As the strategy needs the continuous futures contract, we import the custom data from Quandl. + We create a universe of highly liquid commodity futures that are traded on CME, ICE and CBOT (more contracts can be added using the Quandl API). + We will use Quandl's daily, non-adjusted price data, which is based on spot-month continuous contract calculations. +
++ The first step is importing the data. +
+from QuantConnect.Python import PythonQuandl +for symbol in self.symbols : + self.AddData(QuandlFutures, symbol, Resolution.Daily) + +class QuandlFutures(PythonQuandl): + def __init__(self): + self.ValueColumnName = "Settle" ++
+ Here we use a 12-month RateOfChange(period) indicator to simulate the momentum returns.
+ All indicators are saved in the dictionary self.roc.
+
+self.period = 252
+self.roc = {}
+for symbol in self.symbols:
+ self.roc[symbol] = self.ROC(symbol, self.period) #Initialize ROC indicator : ROC is short for RateofChange
+
+
+
+ We use history request to obtain historical prices. Here, history is the daily returns, which will be used to calculate volatilities.
+
+ history = self.History(self.symbols, self.period, Resolution.Daily) + history = history.value.unstack(level=0).pct_change().dropna() ++
Then we calculate the historical volatilities and place orders.
+ Note that the weights are inversely proportional to volatilities and np.sign determines whether to long or short.
+
+ vol_inv = 1 / history.std(ddof=1) + vol_sum = vol_inv.sum() + weights = (vol_inv / vol_sum).fillna(0).to_dict() + self.Liquidate() + for symbol, roc in self.roc.items(): + percentage = np.sign(roc.Current.Value) * weights[symbol] *.5 + self.SetHoldings(symbol, percentage) ++
+ Asset class trend following is a strategy that tries to exploit a momentum anomaly between various assets. It uses various moving averages or momentum filters to gain an exposure to an asset class only at the time when there is a higher probability for outperformance with less risk. + The basic logic behind the trend following is finding a method to detect the trend of price movement and buy an asset when its price trend goes up, and sell when its trend goes down. +
diff --git a/04 Strategy Library/12 Asset Class Trend Following/02 Method.html b/04 Strategy Library/12 Asset Class Trend Following/02 Method.html new file mode 100644 index 0000000..cf3215f --- /dev/null +++ b/04 Strategy Library/12 Asset Class Trend Following/02 Method.html @@ -0,0 +1,5 @@ ++ This algorithm applies to trend following ideas to 5 ETFs in different asset classes like stocks, bonds, and commodities. The simple moving average is used to detect the trend. When the closing price is over its ten-month simple moving average, + we give equal allocation to those ETFs, otherwise stay in cash. + SMA(symbol, period, resolution) is used to generate the moving average value In LEAN implementation. A warm-up period of ten months is set to prime the data and initialize the indicator so the SMA is ready to use when the algorithm starts. +
diff --git a/04 Strategy Library/12 Asset Class Trend Following/03 Algorithm.html b/04 Strategy Library/12 Asset Class Trend Following/03 Algorithm.html new file mode 100644 index 0000000..77b7892 --- /dev/null +++ b/04 Strategy Library/12 Asset Class Trend Following/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/12 Asset Class Trend Following/04 Source.html b/04 Strategy Library/12 Asset Class Trend Following/04 Source.html new file mode 100644 index 0000000..1c941c0 --- /dev/null +++ b/04 Strategy Library/12 Asset Class Trend Following/04 Source.html @@ -0,0 +1,5 @@ + diff --git a/04 Strategy Library/125 12 Month Cycle in Cross-Section of Stocks Returns/01 Introduction.html b/04 Strategy Library/125 12 Month Cycle in Cross-Section of Stocks Returns/01 Introduction.html new file mode 100644 index 0000000..e5ef779 --- /dev/null +++ b/04 Strategy Library/125 12 Month Cycle in Cross-Section of Stocks Returns/01 Introduction.html @@ -0,0 +1,5 @@ ++ January effect in stocks market says that stocks perform especially well in the first month of the year. This seasonal effect might lead us to think + that stocks performed well in the last year's January will perform well in this year's January. In this tutorial, we're going to implement a strategy based + on this yearly seasonal effect. +
diff --git a/04 Strategy Library/125 12 Month Cycle in Cross-Section of Stocks Returns/02 Method.html b/04 Strategy Library/125 12 Month Cycle in Cross-Section of Stocks Returns/02 Method.html new file mode 100644 index 0000000..8663ff7 --- /dev/null +++ b/04 Strategy Library/125 12 Month Cycle in Cross-Section of Stocks Returns/02 Method.html @@ -0,0 +1,74 @@ +
+ The investment universe consists of all stocks from AMEX and NYSE. Firstly, in CoarseSelectionFunction, we remove stocks which do not have fundamental data.
+
+def CoarseSelectionFunction(self, coarse): + if self.monthly_rebalance: + coarse = [x for x in coarse if (x.HasFundamentalData) + and (x.Market == "usa")] + return [i.Symbol for i in coarse] + else: + return [] ++
+ Next, we are going to filter the top 30% of stocks based on their market cap.
+ In implementation, the market cap is calculated with the BasicAverageShares, BasicEPS and PERatio.
+ Then we request the history price 12 months ago and 11 months ago to calculate the January return of the last year.
+
+def FineSelectionFunction(self, fine): + if self.monthly_rebalance: + fine =[i for i in fine if ((i.SecurityReference.ExchangeId == "NYS") or (i.SecurityReference.ExchangeId == "ASE"))] + self.filtered_fine = [] + + for i in fine: + i.MarketCap = float(i.EarningReports.BasicAverageShares.TwelveMonths * (i.EarningReports.BasicEPS.TwelveMonths*i.ValuationRatios.PERatio)) + history_start = self.History([i.Symbol], TimeSpan.FromDays(365)) + history_end = self.History([i.Symbol],TimeSpan.FromDays(335)) + if not history_start.empty and not history_end.empty: + i.Returns = float(history_end.iloc[0]["close"] - history_start.iloc[0]["close"]) + self.filtered_fine.append(i) + + size = int(len(fine)*.3) + self.filtered_fine = sorted(self.filtered_fine, key = lambda x: x.MarketCap, reverse=True) + self.filtered_fine = self.filtered_fine[:size] + self.filtered_fine = sorted(self.filtered_fine, key = lambda x: x.Returns, reverse=True) + symbols = [i.Symbol for i in self.filtered_fine] + self.filtered_fine = symbols + return symbols + else: + return [] ++
+ Every month, stocks are grouped into ten portfolios with the equal number of stocks in each portfolio according to their performance in January one year ago. + Investors go long in stocks from the winner decile and shorts stocks from loser decile. The portfolio is equally weighted and rebalanced every month. +
+ + ++def OnData(self, data): + if not (self.monthly_rebalance): return + if not (self.filtered_fine): return + self.monthly_rebalance = False + + portfolio_size = int(len(self.filtered_fine)/10) + short_stocks = self.filtered_fine[-portfolio_size:] + long_stocks = self.filtered_fine[:portfolio_size] + stocks_invested = [x.Key for x in self.Portfolio] + for i in stocks_invested: + #liquidate the stocks not in the filtered balance sheet accrual list + if i not in self.filtered_fine: + self.Liquidate(i) + #long the stocks in the list + elif i in long_stocks: + self.SetHoldings(i, 1/(portfolio_size*2)) + #short the stocks in the list + elif i in short_stocks: + self.SetHoldings(i,-1/(portfolio_size*2)) ++
+This trend following algorithm finds its entry points using the momentum effect. The momentum anomaly says that what was strongly going up in the past will probably continue to go up in the near future. +The calculation performed uses the rate of change in price movements for a particular asset. +
diff --git a/04 Strategy Library/13 Asset Class Momentum/02 Method.html b/04 Strategy Library/13 Asset Class Momentum/02 Method.html new file mode 100644 index 0000000..0869d5c --- /dev/null +++ b/04 Strategy Library/13 Asset Class Momentum/02 Method.html @@ -0,0 +1,3 @@ ++ The portfolio of this algorithm contains 5 ETFs in different asset classes. LEAN has the momentum indicator MOM(symbol, period). The period is 12 months. After obtaining the most recent momentum value, we pick 3 ETFs with the strongest 12-month momentum into the portfolio and weight them equally. Hold for 1 month and then rebalance the portfolio with new momentum. Unlike asset class trend following strategy which combines asset classes into one portfolio, this rotational momentum system compares the performance of asset classes and picks only the best-performing assets from investment universe into investor's portfolio. The portfolio is rebalanced every month and portfolio's holdings are rotated so that only the best-performing assets are held. +
diff --git a/04 Strategy Library/13 Asset Class Momentum/03 Algorithm.html b/04 Strategy Library/13 Asset Class Momentum/03 Algorithm.html new file mode 100644 index 0000000..d001aad --- /dev/null +++ b/04 Strategy Library/13 Asset Class Momentum/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/13 Asset Class Momentum/04 Source.html b/04 Strategy Library/13 Asset Class Momentum/04 Source.html new file mode 100644 index 0000000..ef94c60 --- /dev/null +++ b/04 Strategy Library/13 Asset Class Momentum/04 Source.html @@ -0,0 +1,5 @@ + diff --git a/04 Strategy Library/136 Residual Momentum/01 Introduction.html b/04 Strategy Library/136 Residual Momentum/01 Introduction.html new file mode 100644 index 0000000..57d67e1 --- /dev/null +++ b/04 Strategy Library/136 Residual Momentum/01 Introduction.html @@ -0,0 +1,6 @@ ++ Residual momentum is the phenomenon that stocks with greater monthly residual returns (normalized by the volatility of the + residual returns) tend to outperform those with less. Research has shown the strategy experiences less exposure to the dynamic + Fama-French factors, produces greater sharpe ratios, and is more robust out-of-sample than a total return momentum strategy. + This strategy is claimed to be more stable throughout the business cycle than a total return momentum strategy. It tends to underperform during trending regimes and outperform during reverting regimes. Additionally, this strategy is less concentrated is small-cap stocks than a total return strategy can sometimes be, leading to less trading costs and reducing the effect of tax-loss selling. +
diff --git a/04 Strategy Library/136 Residual Momentum/02 Method.html b/04 Strategy Library/136 Residual Momentum/02 Method.html new file mode 100644 index 0000000..7ed4ada --- /dev/null +++ b/04 Strategy Library/136 Residual Momentum/02 Method.html @@ -0,0 +1,31 @@ ++ The first step of algorithm is to load 3 years of trailing values of the Fama-French factors. We call the AddData method and provide the Fama-French data source URL from our Tutorials repo. We save the loaded data into a DataFrame in the alpha model. +
+ ++ In coarse universe selection, we return the first 400 symbols that have fundamental data. In fine universe selection, we rank the stocks by market cap and return the symbols that are in the top 10%. We only create ResidualMomentum objects for stocks added to the universe that have atleast 3 years of historical prices. +
+ ++ During construction of ResidualMomentum objects, we manually warmup the trailing 3 years of monthly returns for the security. We also set up a monthly consolidator to update the trailing returns each month and to recalculate the score. The score is calculated by fitting a linear regression model to the trailing 36 months of data, using the Fama-French factors as independent variables and the monthly returns of each stock as the dependent variable. +
+ +\[r_t = \alpha + \beta_1 * Mkt_t + \beta_2 * SMB_t + \beta_3 * HML_t + \epsilon_t \] + ++ Where \(r_t\) is the monthly return of the stock in month \(t\); \(Mkt_t\), \(SMB_t\), and \(HML_t\) are the Fama-French factor values in month \(t\); and \(epsilon_t\) is the residual return in month \(t\). After fitting, we test the model on the trailing 12 months of data (excluding the most recent month) to calculate the score. We simply sum the residuals and divide by the standard deviation of the residuals to get the score. +
+ +\[score = \frac{\sum{} \epsilon}{\sigma_\epsilon} \] + ++ If a stock's price is below $1 when calculating the score, it's score is set to None, excluding it from trading during the rebalance. +
+ ++ We rebalance the portfolio at the beginning of each month. After calculating a score for each security, we long the 10% of stocks with the greatest scores and short the 10% of stocks with the lowest scores, holding until the next rebalance. +
\ No newline at end of file diff --git a/04 Strategy Library/136 Residual Momentum/03 Algorithm.html b/04 Strategy Library/136 Residual Momentum/03 Algorithm.html new file mode 100644 index 0000000..a989254 --- /dev/null +++ b/04 Strategy Library/136 Residual Momentum/03 Algorithm.html @@ -0,0 +1,6 @@ + \ No newline at end of file diff --git a/04 Strategy Library/136 Residual Momentum/04 References.html b/04 Strategy Library/136 Residual Momentum/04 References.html new file mode 100644 index 0000000..bd3b043 --- /dev/null +++ b/04 Strategy Library/136 Residual Momentum/04 References.html @@ -0,0 +1,8 @@ ++Sector rotation is a popular strategy with which capital is actively reallocated from one sector to another based upon changing market conditions. +
diff --git a/04 Strategy Library/14 Sector Momentum/02 Method.html b/04 Strategy Library/14 Sector Momentum/02 Method.html new file mode 100644 index 0000000..74709a4 --- /dev/null +++ b/04 Strategy Library/14 Sector Momentum/02 Method.html @@ -0,0 +1,5 @@ ++This algorithm is an adaptation of asset class momentum. Instead of rotating ETFs in different asset classes, +the sector momentum algorithm picks 10 sector ETFs and pick 3 ETFs with the strongest 12-month momentum into +the portfolio and weight them equally. The portfolio is rebalanced at the start of each month. +
diff --git a/04 Strategy Library/14 Sector Momentum/03 Algorithm.html b/04 Strategy Library/14 Sector Momentum/03 Algorithm.html new file mode 100644 index 0000000..80765bc --- /dev/null +++ b/04 Strategy Library/14 Sector Momentum/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/14 Sector Momentum/04 Source.html b/04 Strategy Library/14 Sector Momentum/04 Source.html new file mode 100644 index 0000000..7023847 --- /dev/null +++ b/04 Strategy Library/14 Sector Momentum/04 Source.html @@ -0,0 +1,5 @@ ++The short-term reversal is the phenomenon that stocks with relatively low returns over the past month or week earn positive abnormal returns in the following month or week, and stocks with high returns earn negative abnormal returns. +
diff --git a/04 Strategy Library/15 Short Term Reversal/02 Method.html b/04 Strategy Library/15 Short Term Reversal/02 Method.html new file mode 100644 index 0000000..2393a78 --- /dev/null +++ b/04 Strategy Library/15 Short Term Reversal/02 Method.html @@ -0,0 +1,6 @@ ++ To apply short-term reversal in stocks market, first, we use the universe selection API to pick the stocks with the price higher than 4 and rank those stocks by dollar volume and + choose the top 100 stocks as our asset pool. In fine universe selection, the prescreened stocks are sorted by market cap we choose the top 20. To detect the reversal effect, + the return is the most straightforward measure of the stock history performance. The RateOfReturn indicator is used to calculate the monthly return. We go long on the 10 stocks + with the lowest performance in the previous month and go short on the 10 stocks with the greatest performance from the previous month. +
diff --git a/04 Strategy Library/15 Short Term Reversal/03 Algorithm.html b/04 Strategy Library/15 Short Term Reversal/03 Algorithm.html new file mode 100644 index 0000000..1970b93 --- /dev/null +++ b/04 Strategy Library/15 Short Term Reversal/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/15 Short Term Reversal/04 Source.html b/04 Strategy Library/15 Short Term Reversal/04 Source.html new file mode 100644 index 0000000..df7d579 --- /dev/null +++ b/04 Strategy Library/15 Short Term Reversal/04 Source.html @@ -0,0 +1,5 @@ + diff --git a/04 Strategy Library/152 Momentum Effect in REITs/01 Introduction.html b/04 Strategy Library/152 Momentum Effect in REITs/01 Introduction.html new file mode 100644 index 0000000..4cf8481 --- /dev/null +++ b/04 Strategy Library/152 Momentum Effect in REITs/01 Introduction.html @@ -0,0 +1,3 @@ ++ The momentum effect is a classic anomaly that says what was strongly going up in the past will probably continue to go up in the near future. The calculation performed uses the rate of change in price movements. We see this effect in REITs through studies where REITs with the highest annual past performance beat lower performing trusts. This strategy will take a long position in companies with the strongest momentum and rebalance quarterly. +
\ No newline at end of file diff --git a/04 Strategy Library/152 Momentum Effect in REITs/02 Method.html b/04 Strategy Library/152 Momentum Effect in REITs/02 Method.html new file mode 100644 index 0000000..4473eb4 --- /dev/null +++ b/04 Strategy Library/152 Momentum Effect in REITs/02 Method.html @@ -0,0 +1,58 @@ +
+ The first step is coarse and fine universe selection. During coarse selection, we create an investment universe of stocks that have prices greater than $1, contain fundamental data and do not have a very low trading volume for liquidity purposes. During the fine selection we take all available REITs by using the Morningstar field IsREIT.
+
+ In the fine selection we also calculate each REIT's past 11-month return one-month lagged and rank them. This is used to determine the top tercile of portfolio. +
++ def CoarseSelectionFunction(self, coarse): + if self.quarterly_rebalance: + self.filtered_coarse = [x.Symbol for x in coarse if (float(x.Price) > 1) + and (x.HasFundamentalData) + and float(x.Volume) > 10000] + return self.filtered_coarse + else: + return [] + +def FineSelectionFunction(self, fine): + if self.quarterly_rebalance: + fine = [x for x in fine if (x.CompanyReference.IsREIT == 1)] + + start = self.Time-timedelta(days = 365) + end = self.Time-timedelta(days = 30) + for x in fine: + hist = self.History([x.Symbol],start,end,Resolution.Daily) + if not hist.empty: + start_price = hist["close"].iloc[0] + end_price = hist["close"].iloc[-1] + x.momentum = (end_price-start_price)/start_price + + fine = [x for x in fine if hasattr(x, 'momentum')] + sorted_filter = sorted(fine, key=lambda x: x.momentum) + self.filtered_fine = [i.Symbol for i in sorted_filter] + return self.filtered_fine + else: + return [] ++
+ In OnData(), we buy the stocks in the best performing tercile for three months and the portfolio is rebalanced every three months.
+
+def OnData(self, data): + if not self.quarterly_rebalance: return + if self.filtered_fine: + portfolio_size = int(len(self.filtered_fine)/3) + long_stocks = self.filtered_fine[-portfolio_size:] + stocks_invested = [x.Key for x in self.Portfolio] + for i in stocks_invested: + if i not in long_stocks: + self.Liquidate(i) + elif i in long_stocks: + self.SetHoldings(i, 1/(portfolio_size)) + self.quarterly_rebalance = False + self.filtered_fine = False ++
+ Momentum is a well-known strategy that buys stocks with the best return over the past three to twelve months and sells stocks with the worst performances over the same time horizon. + The reversal strategy buys the stocks with relatively low returns and sells stocks with high returns. In this algorithm, we will develop a long-short strategy combining the momentum/reversal effect with the realized volatility. +
diff --git a/04 Strategy Library/155 Momentum and Reversal Combined with Volatility Effect in Stocks/02 Method.html b/04 Strategy Library/155 Momentum and Reversal Combined with Volatility Effect in Stocks/02 Method.html new file mode 100644 index 0000000..94a7056 --- /dev/null +++ b/04 Strategy Library/155 Momentum and Reversal Combined with Volatility Effect in Stocks/02 Method.html @@ -0,0 +1,134 @@ +
+ The investment universe consists of NYSE, AMEX and NASDAQ stocks with prices higher than $5 per share.
+ In FineSelectionFunction, we divide the universe into two equal halves by size of the company.
+ Here size is defined as the share price times the number of shares outstanding.
+
+def CoarseSelectionFunction(self, coarse): + # update the price of stocks in universe everyday + for i in coarse: + if i.Symbol not in self.dataDict: + self.dataDict[i.Symbol] = SymbolData(i.Symbol, self.lookback) + self.dataDict[i.Symbol].Update(i.AdjustedPrice) + + if self.monthly_rebalance: + # drop stocks which have no fundamental data or have too low prices + filteredCoarse = [x.Symbol for x in coarse if (x.HasFundamentalData) and (float(x.Price) > 5)] + return filteredCoarse + else: + return [] + +def FineSelectionFunction(self, fine): + + if self.monthly_rebalance: + sortedFine = sorted(fine, key = lambda x: x.EarningReports.BasicAverageShares.Value * self.dataDict[x.Symbol].Price, reverse=True) + # select stocks with large size + topFine = sortedFine[:int(0.5*len(sortedFine))] + self.filteredFine = [x.Symbol for x in topFine] + return self.filteredFine + else: + return [] ++
+ At the beginning of each month, realized returns and realized (annualized) volatilities are calculated for each stock. + The realized volatility refers to the historical volatility. The formula of the realized volatility \(\sigma\) is +
+\[R_{avg}=\frac{\sum_{i=1}^n R_i}{n}\] +\[\sigma=\sqrt{\frac{\sum_{i=1}^n(R_i-R_{avg})^2}{n-1}}\] ++ To annualize the volatility, we multiply the 1-day volatility by the square root of the number of trading days in a year – in our case square root of 252. +
+
+ A 6-month warm-up period is required to initialize the history price for stocks in the universe. We create the class
+ SymbolData to save all required variables associated with a single stock.
+ One week (5 trading days) prior to the beginning of each month is skipped to avoid biases due to microstructures.
+
+ class SymbolData: + '''Contains data specific to a symbol required by this model''' + + def __init__(self, symbol, lookback): + self.symbol = symbol + # self.History = RollingWindow[Decimal](lookback) + self.History = deque(maxlen=lookback) + self.Price = None + + def Update(self, value): + # update yesterday's close price + self.Price = value + # update the history price series + self.History.append(float(value)) + # self.History.Add(value) + + def IsReady(self): + return len(self.History) == self.History.maxlen + + def Volatility(self): + # one week (5 trading days) prior to the beginning of each month is skipped + prices = np.array(self.History)[:-5] + returns = (prices[1:]-prices[:-1])/prices[:-1] + # calculate the annualized realized volatility + return np.std(returns)*np.sqrt(252) + + def Return(self): + # one week (5 trading days) prior to the beginning of each month is skipped + prices = np.array(self.History)[:-5] + # calculate the annualized realized return + return (prices[-1]-prices[0])/prices[0] ++
+ After the warm-up period, the historical price series is ready. Stocks are sorted into quintiles based on their realized volatility. + Stocks in the top 20% highest volatility are further sorted into quintiles by their six-month realized returns. + The algorithm goes long on stocks from the highest performing quintile from the highest volatility group and short on stocks from the lowest performing quintile from the highest volatility group. +
+
+def OnData(self, data):
+ if self.monthly_rebalance and self.filteredFine:
+ filtered_data = {symbol: symbolData for (symbol, symbolData) in self.dataDict.items() if symbol in self.filteredFine and symbolData.IsReady()}
+ self.filteredFine = None
+ self.monthly_rebalance = False
+ if len(filtered_data) < 100: return
+ # sort the universe by volatility and select stocks in the top high volatility quintile
+ sortedByVol = sorted(filtered_data.items(), key=lambda x: x[1].Volatility(), reverse = True)[:int(0.2*len(filtered_data))]
+ sortedByVol = dict(sortedByVol)
+ # sort the stocks in top-quintile by realized return
+ sortedByReturn = sorted(sortedByVol, key = lambda x: sortedByVol[x].Return(), reverse = True)
+ long = sortedByReturn[:int(0.2*len(sortedByReturn))]
+ short = sortedByReturn[-int(0.2*len(sortedByReturn)):]
+
+
+ The methodology of Jegadeesh and Titamn (1993) is used to rebalance the portfolio.
+ Specifically, at the beginning of each month, stocks are sorted into quintiles based on their realized returns and equally weighted portfolios are formed to be held for the next six months.
+ This sorting and portfolio formation procedure is performed each month. In any given month t, the strategy holds 6 portfolios that are selected in the current month as well as the previous 5 months.
+ Therefore 1/6 of the portfolio is rebalanced every month. We save those 6 portfolios in a deque list self.portfolios and the list is updated every month. The portfolio of the current month is added while the portfolio selected from six months ago is removed from the list.
+
+def Initialize(self): + self.portfolios = deque(maxlen=6) +def OnData(self, data): + self.portfolios.append(short+long) + # 1/6 of the portfolio is rebalanced every month + if len(self.portfolios) == self.portfolios.maxlen: + for i in list(self.portfolios)[0]: + self.Liquidate(i) + # stocks are equally weighted and held for 6 months + short_weight = 1/len(short) + for i in short: + self.SetHoldings(i, -1/6*short_weight) + + long_weight = 1/len(long) + for i in long: + self.SetHoldings(i, 1/6*long_weight) ++
+Instead of collecting profit from intraday trading, this algorithm tries to capture the overnight returns of the index. +
diff --git a/04 Strategy Library/16 Overnight Anomaly/02 Method.html b/04 Strategy Library/16 Overnight Anomaly/02 Method.html new file mode 100644 index 0000000..6a5e21a --- /dev/null +++ b/04 Strategy Library/16 Overnight Anomaly/02 Method.html @@ -0,0 +1,7 @@ ++ The strategy buys SPY ETF at its closing price and sells it at the opening each day. + The strategy makes a lot of trades, therefore, the whole strategy is very sensitive + to slippage costs and fees. Those returns are canceled out once transaction costs + are taken into account. With the InteractiveBrokers transaction model, fees for 20 + years backtest is almost 25% of the initial cash. +
diff --git a/04 Strategy Library/16 Overnight Anomaly/03 Algorithm.html b/04 Strategy Library/16 Overnight Anomaly/03 Algorithm.html new file mode 100644 index 0000000..cb7b3a9 --- /dev/null +++ b/04 Strategy Library/16 Overnight Anomaly/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/16 Overnight Anomaly/04 Source.html b/04 Strategy Library/16 Overnight Anomaly/04 Source.html new file mode 100644 index 0000000..d9a91da --- /dev/null +++ b/04 Strategy Library/16 Overnight Anomaly/04 Source.html @@ -0,0 +1,5 @@ ++ The main reason for the momentum anomaly is the behavioral biases of the investor like underreaction and confirmation bias. + Momentum strategy usually uses portfolios filled by thousands of stocks to compute the momentum factor return. + This is not possible for small retail investors with small portfolios. They are constrained compared to big hedge funds and cannot diversify so well. + In this tutorial, we'll construct a small portfolio consisting of up to 50 stocks to check the effect of momentum. +
diff --git "a/04 Strategy Library/162 Momentum Effect in Stocks in Small Portfolios/01 \347\256\200\344\273\213.cn.html" "b/04 Strategy Library/162 Momentum Effect in Stocks in Small Portfolios/01 \347\256\200\344\273\213.cn.html" new file mode 100644 index 0000000..e81a4a4 --- /dev/null +++ "b/04 Strategy Library/162 Momentum Effect in Stocks in Small Portfolios/01 \347\256\200\344\273\213.cn.html" @@ -0,0 +1,3 @@ ++ 动量异常的主要原因是投资者的行为偏差,例如反应不足和确认偏差。动量策略通常会使用由成千上万只股票组成的投资组合来计算动量要素收益。这对于持有小型投资组合的小型散户投资者来说是不可能的。与大型对冲基金相比,它们受到限制,无法进行多样化投资。在本教程中,我们将构建一个由50支股票组成的小型投资组合,以检查动量所产生影响。 +
diff --git a/04 Strategy Library/162 Momentum Effect in Stocks in Small Portfolios/02 Method.html b/04 Strategy Library/162 Momentum Effect in Stocks in Small Portfolios/02 Method.html new file mode 100644 index 0000000..e614895 --- /dev/null +++ b/04 Strategy Library/162 Momentum Effect in Stocks in Small Portfolios/02 Method.html @@ -0,0 +1,66 @@ ++ The investment universe consists of all US listed companies. Stocks which have no fundamental data are ruled out from the universe. +
++def CoarseSelectionFunction(self, coarse): + if self.yearly_rebalance: + # drop stocks which have no fundamental data + self.filtered_coarse = [x.Symbol for x in coarse if (x.HasFundamentalData)] + return self.filtered_coarse + else: + return [] ++
+ In FineSelectionFunction, stocks with the lowest market capitalization (25% of the universe) are excluded due to low liquidity.
+ The momentum is defined as the stock market return over the previous 12 months. Momentum profits are calculated by ranking companies on the basis of yearly return.
+ The ranking period is one year.
+
+ def FineSelectionFunction(self, fine): + if self.yearly_rebalance: + # Calculate the yearly return and market cap + for i in fine: + i.MarketCap = float(i.EarningReports.BasicAverageShares.ThreeMonths * (i.EarningReports.BasicEPS.TwelveMonths*i.ValuationRatios.PERatio)) + top_market_cap = sorted(fine, key = lambda x:x.MarketCap, reverse=True)[:int(len(fine)*0.75)] + has_return = [] + for i in top_market_cap: + history = self.History([i.Symbol], timedelta(days=365), Resolution.Daily) + if not history.empty: + close = history.loc[str(i.Symbol)]['close'] + i.returns = (close[0]-close[-1])/close[-1] + has_return.append(i) + sorted_by_return = sorted(has_return, key = lambda x: x.returns) + self.long = [i.Symbol for i in sorted_by_return[-10:]] + self.short = [i.Symbol for i in sorted_by_return[:10]] + + return self.long+self.short + else: + return [] ++
+ The investor goes long in the ten stocks with the highest performance and goes short in the ten stocks with the lowest performance. + The portfolio is equally weighted and rebalanced yearly. +
++ def OnData(self, data): + if not self.yearly_rebalance: return + if self.long and self.short: + stocks_invested = [x.Key for x in self.Portfolio if x.Value.Invested] + # liquidate stocks not in the trading list + for i in stocks_invested: + if i not in self.long+self.short: + self.Liquidate(i) + for i in self.short: + self.SetHoldings(i, -0.5/len(self.short)) + for i in self.long: + self.SetHoldings(i, 0.5/len(self.long)) + self.long = None + self.short = None + self.yearly_rebalance = False ++
+ 投资集合包括所有美国上市公司。没有基本数据的股票被排除在集合之外。 +
++def CoarseSelectionFunction(self, coarse): + if self.yearly_rebalance: + # 放弃没有基本数据的股票 + self.filtered_coarse = [x.Symbol for x in coarse if (x.HasFundamentalData)] + return self.filtered_coarse + else: + return [] ++
+ 在FineSelectionFunction中,由于流动性较低,市值最低的股票(占集合的25%)被排除在外。动量被定义为过去12个月的股市收益。动量利润是根据排名公司的年度收益进行计算的。排名周期为一年。
+
+ def FineSelectionFunction(self, fine): + if self.yearly_rebalance: + # 计算年收益和市值 + for i in fine: + i.MarketCap = float(i.EarningReports.BasicAverageShares.ThreeMonths * (i.EarningReports.BasicEPS.TwelveMonths*i.ValuationRatios.PERatio)) + top_market_cap = sorted(fine, key = lambda x:x.MarketCap, reverse=True)[:int(len(fine)*0.75)] + has_return = [] + for i in top_market_cap: + history = self.History([i.Symbol], timedelta(days=365), Resolution.Daily) + if not history.empty: + close = history.loc[str(i.Symbol)]['close'] + i.returns = (close[0]-close[-1])/close[-1] + has_return.append(i) + sorted_by_return = sorted(has_return, key = lambda x: x.returns) + self.long = [i.Symbol for i in sorted_by_return[-10:]] + self.short = [i.Symbol for i in sorted_by_return[:10]] + + return self.long+self.short + else: + return [] ++
+ 投资者做多表现最好的10支股票,做空表现最差的10支股票。投资组合每年都进行平均加权和重新平衡。 +
++ def OnData(self, data): + if not self.yearly_rebalance: return + if self.long and self.short: + stocks_invested = [x.Key for x in self.Portfolio if x.Value.Invested] + # 平仓未进入交易清单的股票 + for i in stocks_invested: + if i not in self.long+self.short: + self.Liquidate(i) + for i in self.short: + self.SetHoldings(i, -0.5/len(self.short)) + for i in self.long: + self.SetHoldings(i, 0.5/len(self.long)) + self.long = None + self.short = None + self.yearly_rebalance = False ++
+ Momentum is a trend following strategy, where the strategy buys the assets which have performed well in the past and sells the assets which have performed bad. +
diff --git a/04 Strategy Library/17 Forex Momentum/02 Method.html b/04 Strategy Library/17 Forex Momentum/02 Method.html new file mode 100644 index 0000000..6347296 --- /dev/null +++ b/04 Strategy Library/17 Forex Momentum/02 Method.html @@ -0,0 +1,5 @@ ++ This algorithm applies momentum to the forex market. Our universe consists of 15 forex pairs + and covers period from 2006 to 2018. The algorithm goes long 3 currencies with strongest 12-month + momentum against USD and goes short 3 currencies with lowest 12-month momentum against USD. +
diff --git a/04 Strategy Library/17 Forex Momentum/03 Algorithm.html b/04 Strategy Library/17 Forex Momentum/03 Algorithm.html new file mode 100644 index 0000000..f8b0c4d --- /dev/null +++ b/04 Strategy Library/17 Forex Momentum/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/17 Forex Momentum/04 Source.html b/04 Strategy Library/17 Forex Momentum/04 Source.html new file mode 100644 index 0000000..1b4d99a --- /dev/null +++ b/04 Strategy Library/17 Forex Momentum/04 Source.html @@ -0,0 +1,5 @@ ++ The low volatility effect in equities refers to that stocks which previously + exhibited lower volatility will earn higher risk-adjusted returns than those with higher volatility. + This algorithm extends the study of the low volatility effect to U.S stocks with higher market capital. +
diff --git a/04 Strategy Library/18 Volatility Effect in Stocks/02 Method.html b/04 Strategy Library/18 Volatility Effect in Stocks/02 Method.html new file mode 100644 index 0000000..8f3cdc8 --- /dev/null +++ b/04 Strategy Library/18 Volatility Effect in Stocks/02 Method.html @@ -0,0 +1,17 @@ ++ To construct the investment universe which consists of US large cap stocks, first in coarse universe selection, + we exclude stocks without fundamental data and the price is below 5. A universe of 100 stocks is selected based on the dollar volume. In fine universe selection, we pick 50 stocks from the coarse universe with the highest market cap. +
+
+ We create SymbolData class and use RollingWindow to store the price data for symbols returned by fine universe.
+ The lookback period is 252 trading days. First, we request history data to initialize the RollingWindow for the added symbols and update it's value with the closing price every day in OnData().
+
+ The standard deviation is the typical statistic used to measure volatility. It is defined as the square root of the average variance of the data from its mean. We use the closing price series in RollingWindow to calculate the volatility. +
++ The trading logic is we go long 5 stocks with the lowest volatility and liquidate stocks in the portfolio which does not in the lowest volatility list. The portfolio is rebalanced at the first trading day each month. +
diff --git a/04 Strategy Library/18 Volatility Effect in Stocks/03 Algorithm.html b/04 Strategy Library/18 Volatility Effect in Stocks/03 Algorithm.html new file mode 100644 index 0000000..97890a9 --- /dev/null +++ b/04 Strategy Library/18 Volatility Effect in Stocks/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/18 Volatility Effect in Stocks/04 Source.html b/04 Strategy Library/18 Volatility Effect in Stocks/04 Source.html new file mode 100644 index 0000000..e9be339 --- /dev/null +++ b/04 Strategy Library/18 Volatility Effect in Stocks/04 Source.html @@ -0,0 +1,5 @@ + diff --git a/04 Strategy Library/19 Pairs Trading with Stocks/01 Introduction.html b/04 Strategy Library/19 Pairs Trading with Stocks/01 Introduction.html new file mode 100644 index 0000000..d22f310 --- /dev/null +++ b/04 Strategy Library/19 Pairs Trading with Stocks/01 Introduction.html @@ -0,0 +1,6 @@ ++ The pairs trading algorithm aims to find two stocks which have prices that moved historically together. + If price series diverges, long and short positions are opened in the opposite direction. With the assumption + of mean reversion, the algorithm expects to make profits from the abnormal fluctuation of prices. + The crucial part of pairs trading is determining which stocks are correlated and how to define a price divergence. +
diff --git a/04 Strategy Library/19 Pairs Trading with Stocks/02 Method.html b/04 Strategy Library/19 Pairs Trading with Stocks/02 Method.html new file mode 100644 index 0000000..0a9dd73 --- /dev/null +++ b/04 Strategy Library/19 Pairs Trading with Stocks/02 Method.html @@ -0,0 +1,14 @@ ++ The first step of this algorithm is to select stock pairs from a universe of stocks. We use the history request to get the history closing price for the last one year. This is called the formation period. + The matching partner for each stock is found by looking for the security that minimizes the sum of squared deviations between two normalized price series. Assume there are two stocks A and B with the price series X and Y. For price normalization, the starting price during formation period is set to $1. + The formula of distance measure is + \[\sum_{i=1}^n{(\frac{x_i}{x_1}-\frac{y_i}{y_1}})^2\] + Top 4 pairs with the smallest historical distance measure are then traded. The trading pairs are selected + every half year. We use the schedule event method to fire the rebalance function. +
++ As prices in a pair of stocks were closely cointegrated in past, there is high probability that those two securities share common sources of fundamental return correlations. A temporary shock could move one stock out of the common price band which presents statistical arbitrage opportunity. Given the trading pairs, the trading period is the next six months. We calculate the price spread series of the last one year. When pair prices have diverged by two standard deviations, + which means the spread is 2 times standard deviation away from its long-term mean, the algorithm will go short the stock which price is diverging up and go long the stock which price is diverging down. The position is closed when prices revert back. +
diff --git a/04 Strategy Library/19 Pairs Trading with Stocks/03 Algorithm.html b/04 Strategy Library/19 Pairs Trading with Stocks/03 Algorithm.html new file mode 100644 index 0000000..4b088a3 --- /dev/null +++ b/04 Strategy Library/19 Pairs Trading with Stocks/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/19 Pairs Trading with Stocks/04 Source.html b/04 Strategy Library/19 Pairs Trading with Stocks/04 Source.html new file mode 100644 index 0000000..e8be166 --- /dev/null +++ b/04 Strategy Library/19 Pairs Trading with Stocks/04 Source.html @@ -0,0 +1,5 @@ + diff --git a/04 Strategy Library/198 Exploiting Term Structure of VIX Futures/01 Introduction.html b/04 Strategy Library/198 Exploiting Term Structure of VIX Futures/01 Introduction.html new file mode 100644 index 0000000..f975737 --- /dev/null +++ b/04 Strategy Library/198 Exploiting Term Structure of VIX Futures/01 Introduction.html @@ -0,0 +1,8 @@ ++ The Chicago Board Options Exchange (CBOE) introduced the Volatility Index (VIX) in 1993 to provide a measure of the implied volatility of 30-day, at the money S&P 100 index options. + Volatility has become a widely accepted asset class since the introduction of the VIX futures contracts in 2004. VIX futures are often used for hedging purpose because of its negative correlation with the equity market return. When we talk about the term structure of futures, we often refer to the forward curve. + The VIX forward curve consists of VIX futures prices at various delivery times in the future. + Academic research states that volatility follows a mean reverting process. When the VIX futures curve is upward sloped (in contango), + the VIX is expected to rise because it is low relative to long-term average levels and vice versa for the downward sloped VIX future curve. + In this study, we will create a strategy with the term structure effect of VIX futures and hedge the term structure risk with the S&P500 futures. +
diff --git a/04 Strategy Library/198 Exploiting Term Structure of VIX Futures/02 Method.html b/04 Strategy Library/198 Exploiting Term Structure of VIX Futures/02 Method.html new file mode 100644 index 0000000..3463891 --- /dev/null +++ b/04 Strategy Library/198 Exploiting Term Structure of VIX Futures/02 Method.html @@ -0,0 +1,182 @@ ++ The trading strategy uses VIX futures as a trading vehicle and S&P E-mini for hedging purposes. The spot VIX price data and + the continuous front contract price of VIX and E-mini S&P500 futures in the daily resolution are from Quandl. +
++def Initialize(self): + self.SetStartDate(2011, 1, 1) # Set Start Date + self.SetEndDate(2018, 9, 1) # Set End Date + self.SetCash(10000000) # Set Strategy Cash + self.vix = self.AddData(QuandlVix, "CBOE/VIX", Resolution.Daily).Symbol # Add Quandl VIX price (daily) + self.vx1 = self.AddData(QuandlFutures, "CHRIS/CBOE_VX1", Resolution.Daily).Symbol # Add Quandl VIX front month futures data (daily) + self.es1 = self.AddData(QuandlFutures, "CHRIS/CME_ES1", Resolution.Daily).Symbol # Add Quandl E-mini S&P500 front month futures data (daily) + # Add VIX futures contract data + self.AddFuture(Futures.Indices.VIX).SetFilter(timedelta(0), timedelta(days=180)) + # Add E-mini S&P500 futures contract data + self.AddFuture(Futures.Indices.SP500EMini).SetFilter(timedelta(0), timedelta(days=180)) ++
+ Futures basis is defined as the difference between the underlying product cash price and futures contract price at a given time. +
+\[Basis_t=S_t-F_t\] ++ Where \(S_t\) is the spot VIX price, \(F_t\) is the VIX futures price. The basis is in contango means the futures price is higher than the spot price. + The opposite of Contango is Backwardation. It refers to the market condition in which the futures price is less than the spot price. +
+\[Contango=S_t+ We select the nearest VIX and E-mini futures with at least ten trading days to maturity in the futures chains. +
++def OnData(self, data): + # select the nearest VIX and E-mini S&P500 futures with at least 10 trading days to maturity + # if the front contract expires, roll forward to the next nearest contract + for chain in data.FutureChains: + if chain.Key.Value == Futures.Indices.VIX: + if self.front_VX is None or ((self.front_VX.Expiry-self.Time).days <= 1): + contracts = list(filter(lambda x: x.Expiry >= self.Time + timedelta(days = 10), chain.Value)) + self.front_VX = sorted(contracts, key = lambda x: x.Expiry)[0] + if chain.Key.Value == Futures.Indices.SP500EMini: + if self.front_ES is None or ((self.front_ES.Expiry-self.Time).days <= 1): + contracts = list(filter(lambda x: x.Expiry >= self.Time + timedelta(days = 10), chain.Value)) + self.front_ES = sorted(contracts, key = lambda x: x.Expiry)[0] ++
+ While this trading strategy takes advantage of the roll by selling VIX futures at a premium to the VIX and by buying VIX futures at a discount to the VIX, + it is exposed to the potentially substantial risks associated with adverse moves in the VIX futures curve. However, as the tendency of VIX futures prices to move inversely to equity returns, + much of this risk can be hedged by open the E-mini S&P 500 futures position in the same direction. +
++ The number of mini-S&P futures contracts to buy or sell per VIX futures contract is based on the hedge ratio estimates. + The hedge ratios are constructed from regressions of VIX futures price changes on a constant and + on contemporaneous percentage changes of the front mini-S&P 500 futures contract both alone and + multiplied by the number of business days that the VIX futures contract is from the settlement, as shown below. +
+\[\Delta P^{VX}_t=\beta_0+\beta_1* Return^{ES}_t+\beta_2*(Return^{ES}_t*TimeToSettlement^{VX}_t)+\mu_t\] ++ After we get the parameters \(beta_0\), \(beta_1\) and \(beta_2\), the formula for the hedge ratio is +
+\[HR_t=\frac{\beta_1*1000+\beta_2*TimeToSettlement_{t-1}*1000}{0.01*P^{ES}_{t-1}*50}\] +
+ def CalculateHedgeRatio(self):
+ price_VX = np.array(self.price_VX)
+ price_ES = np.array(self.price_ES)
+ delta_VX = np.diff(price_VX)
+ res_ES = np.diff(price_ES)/price_ES[:-1]*100
+ tts = np.array(self.days_to_maturity)[1:]
+ df = pd.DataFrame({"delta_VX":delta_VX, "SPRET":res_ES, "product":res_ES*tts}).dropna()
+ # remove rows with zero value
+ df = df[(df != 0).all(1)]
+ y = df['delta_VX'].astype(float)
+ X = df[['SPRET', "product"]].astype(float)
+ X = sm.add_constant(X)
+ model = sm.OLS(y, X).fit()
+ beta_1 = model.params[1]
+ beta_2 = model.params[2]
+ hedge_ratio = abs((1000*beta_1 + beta_2*((self.front_VX.Expiry-self.Time).days)*1000)/(0.01*50*float(self.Securities[self.es1].Price)))
+ self.Plot("Trade", "Hedge Ratio", hedge_ratio)
+ return hedge_ratio
+
++ Our daily futures price data is from the continuous front contract. To measure the time to settlement, we import the custom data of the VIX futures expiration dates from 2011 to 2018. + We populate the date index with the backward fill method to make it easy to calculate the time to settlement. +
+
+# import the futures expiry calendar
+url = "https://www.dropbox.com/s/5k4rbuzfsfn3w0h/expiry.csv?dl=1"
+data = self.Download(url).split('\r\n')
+expiry = [x.split(',')[1] for x in data][1:]
+date = [x.split(',')[0] for x in data][1:]
+df_date = pd.DataFrame(expiry, index = date, columns = ['expiry'])
+df_date.index = pd.to_datetime(df_date.index)
+df_date['expiry'] = pd.to_datetime(df_date['expiry'])
+idx = pd.date_range('01-01-2011', '04-19-2019')
+# populate the date index and backward fill the dataframe
+return df_date.reindex(idx, method='bfill')
+
++ To perform the regression, we save the history price in deque list and update the list every day. +
++# the rolling window to save the front month VX future price +self.price_VX = deque(maxlen=252) +# the rolling window to save the front month ES future price +self.price_ES = deque(maxlen=252) +# the rolling window to save the time-to-maturity of the contract +self.days_to_maturity = deque(maxlen=252) +# initialize the deque list +for index, row in df.iterrows(): + self.price_VX.append(row[self.vx1]) + self.price_ES.append(row[self.es1]) + self.days_to_maturity.append((row['expiry']-index).days) ++
+ The daily roll is defined as the difference between the front VIX futures price and the VIX, divided by the number of business days until the VIX futures contract settles. + Short VIX futures positions are entered when the VIX futures basis is in contango and the daily roll exceeds 0.10 and + long VIX futures positions are entered when the VIX futures basis is in backwardation and the daily roll is less than -0.10. +
+
+# calculate the daily roll
+daily_roll = (self.Securities[self.vx1].Price - self.Securities[self.vix].Price)/(self.front_VX.Expiry-self.Time).days
+self.Plot("Trade", "VIX", self.Securities[self.vix].Price)
+self.Plot("Trade", "VIX Futures", self.Securities[self.vx1].Price)
+self.Plot("Trade", "Daily Roll", daily_roll)
+if not self.Portfolio[self.front_VX.Symbol].Invested:
+ # Short if the contract is in contango with adaily roll greater than 0.10
+ if daily_roll > 0.1:
+ hedge_ratio = self.CalculateHedgeRatio()
+ self.Plot("Trade", "Sell", self.Securities[self.vx1].Price)
+ self.SetHoldings(self.front_VX.Symbol, -0.5)
+ self.SetHoldings(self.front_ES.Symbol, -0.5*hedge_ratio)
+ # Long if the contract is in backwardation with adaily roll less than -0.10
+ elif daily_roll < -0.1:
+ hedge_ratio = self.CalculateHedgeRatio()
+ self.Plot("Trade", "Buy", self.Securities[self.vx1].Price)
+ self.SetHoldings(self.front_VX.Symbol, 0.5)
+ self.SetHoldings(self.front_ES.Symbol, 0.5*hedge_ratio)
+
++ Trades are exited when the motivating conditions no longer exist. + The exit condition is defined as the daily roll being less than 0.05 for short trades and higher than -0.05 VIX futures points for long trades. + If these exit conditions are not triggered, trades are exited two days before the contract expires. +
++# exit if the daily roll being less than 0.05 if holding short positions +if self.Portfolio[self.front_VX.Symbol].IsShort and daily_roll < 0.05: + self.Liquidate() + self.front_VX = None + self.front_ES = None + return + +# exit if the daily roll being greater than -0.05 if holding long positions +if self.Portfolio[self.front_VX.Symbol].IsLong and daily_roll > -0.05: + self.Liquidate() + self.front_VX = None + self.front_ES = None + return + +if self.front_VX and self.front_ES: +# if these exit conditions are not triggered, trades are exited two days before it expires +if self.Portfolio[self.front_VX.Symbol].Invested and self.Portfolio[self.front_ES.Symbol].Invested: + if (self.front_VX.Expiry-self.Time).days <=2 or (self.front_ES.Expiry-self.Time).days <=2: + self.Liquidate() + self.front_VX = None + self.front_ES = None + return ++
+ Return on Equity(ROE) is defined as the ratio of net income over shareholders equity, + where shareholders’ equity is the difference between a company's total assets and total liabilities. Shareholders' equity is often referred to as the book value of the company. + ROE is a measure of how efficiently a company uses its assets to produce earnings. It can explain many anomalies related to earnings and profitability. This algorithm will build a long-short portfolio with ROE factor. +
diff --git a/04 Strategy Library/199 ROA Effect within Stocks/02 Method.html b/04 Strategy Library/199 ROA Effect within Stocks/02 Method.html new file mode 100644 index 0000000..774d359 --- /dev/null +++ b/04 Strategy Library/199 ROA Effect within Stocks/02 Method.html @@ -0,0 +1,74 @@ +
+ The investment universe contains all stocks on NYSE and AMEX and Nasdaq.
+ In CoarseSelectionFunction, we eliminated ETFs which does not have fundamental data.
+
+def CoarseSelectionFunction(self, coarse): + if self.monthly_rebalance: + self.coarse = True + filteredCoarse = [x.Symbol for x in coarse if x.HasFundamentalData] + return filteredCoarse + else: + return [] ++
+ In FineSelectionFunction, stocks with sales greater than 10 milion USD are selected.
+ Then we calculate the market cap for those stocks and sort them into two groups: Big size group with the higher market cap and small size group with the lower market cap. Each half is then divided into deciles based on Return on assets (ROA).
+
+def FineSelectionFunction(self, fine): + if self.monthly_rebalance: + fine =[i for i in fine if i.EarningReports.BasicAverageShares.ThreeMonths != 0 + and i.EarningReports.BasicEPS.TwelveMonths != 0 + and i.ValuationRatios.PERatio != 0 + # sales is greater than 10 million + and i.ValuationRatios.SalesPerShare*i.EarningReports.DilutedAverageShares.Value > 10000000 + and i.OperationRatios.ROA.Value != 0] + for i in fine: + i.MarketCap = float(i.EarningReports.BasicAverageShares.ThreeMonths * (i.EarningReports.BasicEPS.TwelveMonths*i.ValuationRatios.PERatio)) + # sort into 2 halfs based on market capitalization + sorted_market_cap = sorted(fine, key = lambda x:x.MarketCap, reverse=True) + top = sorted_market_cap[:int(len(sorted_market_cap)*0.5)] + bottom = sorted_market_cap[-int(len(sorted_market_cap)*0.5):] + # each half is then divided into deciles based on Return on Assets (ROA) + sortedTopByROA = sorted(top, key = lambda x: x.OperationRatios.ROA.Value, reverse = True) + sortedBottomByROA = sorted(bottom, key = lambda x: x.OperationRatios.ROA.Value, reverse = True) + # long top decile from each market capitalization group + long = sortedTopByROA[:int(len(sortedTopByROA)*0.1)] + sortedBottomByROA[:int(len(sortedTopByROA)*0.1)] + self.longStocks = [i.Symbol for i in long] + # short bottom decile from each market capitalization group + short = sortedTopByROA[-int(len(sortedTopByROA)*0.1):] + sortedBottomByROA[-int(len(sortedTopByROA)*0.1):] + self.shortStocks = [i.Symbol for i in short] + + return self.longStocks+self.shortStocks + else: + return [] ++
+ The algorithm goes long the top decile from each market capitalization group and short the bottom decile. + The strategy is rebalanced monthly and stocks are equally weighted. +
++ def OnData(self, data): + if not (self.monthly_rebalance and self.coarse): return + self.coarse = False + self.monthly_rebalance = False + stocks_invested = [x.Key for x in self.Portfolio if x.Value.Invested] + for i in stocks_invested: + if i not in self.longStocks+self.shortStocks: + self.Liquidate(i) + + long_weight = 0.5/len(self.longStocks) + for i in self.longStocks: + self.SetHoldings(i, long_weight) + + short_weight = 0.5/len(self.shortStocks) + for i in self.shortStocks: + self.SetHoldings(i, -short_weight) ++
+ Carry trade is very common in the foreign exchange market. + The strategy systematically sells low-interest rate currencies and buys high-interest rates currencies. The “carry” of an asset is the opportunity cost of holding that asset. Carry trade strategy holds one currency relative to another in order to capture the spread between the rates. We can think of this strategy as borrowing money from one country with a lower interest rate and investing it in another country with a higher interest rate. +
diff --git "a/04 Strategy Library/20 Forex Carry Trade/01 \347\256\200\344\273\213.cn.html" "b/04 Strategy Library/20 Forex Carry Trade/01 \347\256\200\344\273\213.cn.html" new file mode 100644 index 0000000..f770bb0 --- /dev/null +++ "b/04 Strategy Library/20 Forex Carry Trade/01 \347\256\200\344\273\213.cn.html" @@ -0,0 +1,3 @@ ++ 套利交易在外汇市场上很常见。此策略系统性地出售低利率货币,买入高利率货币。资产的“套利”是持有该资产的机会成本。套利交易策略持有相对于其他货币的某一种货币,以获取利率之间的价差。我们可以把这种策略看作是从一个利率较低的国家借钱,然后将钱投资到另一个利率较高的国家。 +
diff --git a/04 Strategy Library/20 Forex Carry Trade/02 Method.html b/04 Strategy Library/20 Forex Carry Trade/02 Method.html new file mode 100644 index 0000000..673aa83 --- /dev/null +++ b/04 Strategy Library/20 Forex Carry Trade/02 Method.html @@ -0,0 +1,22 @@ +
+ The central bank interest rate data is from Quandl. For the trading universe, we choose 9 currencies
+ whose central bank interest rate data is available in Quandl. The method to import the custom data is
+ AddData(type, symbol, resoltuion, timeZone, fillDataForward). As the custom file has it's unique
+ colume name, we need to create a class to specify the colume name of interest rate.
+
+from QuantConnect.Python import PythonQuandl +class QuandlRate(PythonQuandl): + def __init__(self): + self.ValueColumnName = 'Value' ++
+ We save the interest rate symbol and the correspondent forex asset symbol into a dictionary. +
++ Next step we sort the forex symbol by the value of interest rate. The algorithm goes long the currency with the highest interest rates and goes short the currency with the lowest interest rate. The strategy is rebalanced monthly. The schedule event method is used to fire the rebalance event at the first trading day each month. +
diff --git "a/04 Strategy Library/20 Forex Carry Trade/02 \346\226\271\346\263\225.cn.html" "b/04 Strategy Library/20 Forex Carry Trade/02 \346\226\271\346\263\225.cn.html" new file mode 100644 index 0000000..2fc26c1 --- /dev/null +++ "b/04 Strategy Library/20 Forex Carry Trade/02 \346\226\271\346\263\225.cn.html" @@ -0,0 +1,19 @@ +
+ 央行利率数据来自Quandl。对于交易集合来说,我们选择了央行利率数据在Quandl中可用的9种货币。导入自定义数据的方法是AddData(type, symbol, resoltuion, timeZone, fillDataForward)。由于自定义文件具有唯一的colume名称,因此我们需要创建一个类别来指定利率的colume名称。
+
+from QuantConnect.Python import PythonQuandl +class QuandlRate(PythonQuandl): + def __init__(self): + self.ValueColumnName = 'Value' ++
+ 我们将利率符号和对应的外汇资产符号保存到字典中。 +
++ 下一步,我们根据利率的值对外汇符号进行排序。这种算法会做多利率最高的货币,做空利率最低的货币。该战略每月都会重新调整。采用日程事件法在每个月的第一个交易日触发重新调整事件。 +
diff --git a/04 Strategy Library/20 Forex Carry Trade/03 Algorithm.html b/04 Strategy Library/20 Forex Carry Trade/03 Algorithm.html new file mode 100644 index 0000000..d433b13 --- /dev/null +++ b/04 Strategy Library/20 Forex Carry Trade/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git "a/04 Strategy Library/20 Forex Carry Trade/03 \347\256\227\346\263\225.cn.html" "b/04 Strategy Library/20 Forex Carry Trade/03 \347\256\227\346\263\225.cn.html" new file mode 100644 index 0000000..d433b13 --- /dev/null +++ "b/04 Strategy Library/20 Forex Carry Trade/03 \347\256\227\346\263\225.cn.html" @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/20 Forex Carry Trade/04 Source.html b/04 Strategy Library/20 Forex Carry Trade/04 Source.html new file mode 100644 index 0000000..18f54dd --- /dev/null +++ b/04 Strategy Library/20 Forex Carry Trade/04 Source.html @@ -0,0 +1,5 @@ ++ Equity valuation may be a predictive signal for future equity return. There are various methodologies to evaluate whether + the equity is undervalued or overvalued using metrics like price-to-earnings (P/E), return on equity (ROE), dividend yield, book-to-equity and so on. + In this algorithm, we use a ten-year normalized earnings metrics invented by Yale University professor Robert Shiller to find the fair value of the equity market. +
diff --git a/04 Strategy Library/207 Value Effect within Countries/02 Method.html b/04 Strategy Library/207 Value Effect within Countries/02 Method.html new file mode 100644 index 0000000..a6db2f9 --- /dev/null +++ b/04 Strategy Library/207 Value Effect within Countries/02 Method.html @@ -0,0 +1,88 @@ ++ The cyclically adjusted price-to-earnings ratio (CAPE) compares the stock prices with earnings smoothed across multiple years. + It is the price divided by the average of ten years of earnings (moving average), adjusted for inflation. + The backward-looking earnings smooth out the economic cycle as well as the price fluctuations. +
++ The investment universe consists of 22 countries with easily accessible equity markets via ETFs. + We import the custom CAPE ratio(Shiller PE Ratio) data of those 22 countries and create a dictionary to save the corresponding country ETF. + This data from Quandl is in monthly resolution and starts January 2000. +
+
+ class CAPE(PythonData):
+
+ def GetSource(self, config, date, isLiveMode):
+ return SubscriptionDataSource("https://www.dropbox.com/s/fcv8x1xeqamg5lx/CAPERatio.csv?dl=1", SubscriptionTransportMedium.RemoteFile)
+
+ def Reader(self, config, line, date, isLiveMode):
+ if not (line.strip() and line[1].isdigit()): return None
+ index = CAPE()
+ index.Symbol = config.Symbol
+ # data format
+ # Date Canada UK United States France Germany Italy Spain ...
+ # 1/31/00 45.7 25.08 42.18 55.94 51.35 54.34 32.16 ...
+ data = line.split(',')
+ index.Time = datetime.strptime(data[0], "%m/%d/%y")
+ symbols = Symbols().tickers
+ for key, value in symbols.items():
+ index[key] = float(data[value[0]]) if data[value[0]] else None
+ return index
+
+
+ class Symbols:
+ def __init__(self):
+ # the indiex is the country name
+ # the first element of the value is the column number of CAPE ratio value in custom dataset
+ # the second element of the value is the corresponding country ETF
+
+ self.tickers = {"Canada":[1, "XIC"], # S&P/TSX Composite Index: iShares S&P TSX Capped Cmpst Indx Fnd
+ "Uk":[2, "EWU"], # FTSE 100 Index: iShares MSCI United Kingdom ETF
+ "Us":[3, "SPY"], # S&P 500 Index: SPDR S&P 500 ETF
+ "France":[4, "EWQ"], # CAC 40 Index: iShares MSCI France ETF
+ "Germany":[5, "EWG"], # HDAX Index: iShares MSCI Germany ETF
+ "Italy":[6, "EWI"], # FTSE MIB Index: iShares MSCI Italy ETF
+ "Spain":[7, "EWP"], # IBEX 35 Index: iShares MSCI Spain ETF
+ "Russia":[8, "ERUS"], # RTS Index: iShares MSCI Russia ETF
+ "India":[9, "INDY"], # NIFTY 50 Index: iShares India 50 ETF
+ "Japan":[10, "EWJ"], # All Public Companies: iShares MSCI Japan ETF
+ "Singapore":[11, "EWS"], # STI Index: iShares MSCI Singapore ETF
+ "Korea":[12,"EWY"], # KOSPI Index: iShares MSCI South Korea ETF
+ "China":[13, "MCHI"], # SSE Composite: iShares MSCI China Index Fund
+ "Hongkong":[14, "EWH"], # Hang Seng Index: iShares MSCI Hong Kong Index Fund
+ "Brazil":[15, "EWZ"], # Indice Bovespa (Ibovespa): iShares MSCI Brazil ETF
+ "Mexico":[16, "EWW"], # &P/BMV IPC Index: iShares MSCI Mexico ETF
+ "Southafrica":[17, "EZA"], # FTSE/JSE CAP Top 40 Index: iShares MSCI South Africa ETF
+ "Australia":[18, "EWA"], # ASX All Ordinaries Index: iShares MSCI Australia ETF
+ "Turkey":[19, "TUR"], # BIST 100: iShares MSCI Turkey ETF
+ "Poland":[20, "EPOL"], # WIG Index: iShares MSCI Poland ETF
+ "Indonesia":[21, "EIDO"], # IDX Composite: iShares MSCI Indonesia ETF
+ "Philippines":[22, "EPHE"]} # PSE Composite: iShares MSCI Philippines Investable
+
++ According to the academic research of Shiller and Campbell using market data from the S&P index, the lower the CAPE, the higher the investors' likely return from equities. + Therefore, the algorithm then invests in the cheapest 33% of countries from the sample with the lowest CAPE ratio if those countries have a CAPE below 15. + If there are no countries with CAPE lower than 15, the algorithm holds cash instead of country ETFs. + The portfolio is equally weighted and rebalanced monthly. +
+
+ def Rebalance(self):
+ self.cape = {}
+ for key, value in self.symbols.items():
+ cape = getattr(self.slice["CAPE"], key)
+ if cape is not None:
+ self.cape[value[1]] = cape
+ sorted_cape = sorted(self.cape, key = lambda x: self.cape[x])
+ # invests the cheapest 33% of countries if those countries have a CAPE below 15
+ lowest_cape = sorted_cape[:int(1/3*len(sorted_cape))]
+ long_list = [i for i in lowest_cape if self.cape[i]<15]
+ invested = [x.Key for x in self.Portfolio if x.Value.Invested]
+ for i in invested:
+ if i.Value not in long_list:
+ self.Liquidate(i)
+ for i in long_list:
+ self.SetHoldings(i, 1/len(long_list))
+
++The momentum anomaly says that what was strongly going up in the near past will probably continue to go up shortly. Stocks which outperform peers on 3-12 month period tend to perform well also in the future. This algorithm will explore the momentum effect on large-cap stocks. +
diff --git a/04 Strategy Library/21 Momentum Effect in Stocks/02 Method.html b/04 Strategy Library/21 Momentum Effect in Stocks/02 Method.html new file mode 100644 index 0000000..2dc76cf --- /dev/null +++ b/04 Strategy Library/21 Momentum Effect in Stocks/02 Method.html @@ -0,0 +1,20 @@ ++ We use the universe selection API to create a momentum portfolio. Our coarse-universe selection eliminates stocks with a price lower than $5 and ETFs which do not have fundamental data. Fine-universe selection chooses the 50 largest companies ranked by market capitalization. +
++ Momentum is the absolute difference in stocks. + \[Momentum = Close_{today}-Close_{N-days-ago}\] +
+ Dictionary self.mom is used to save the LEAN Momentum class instance Momentum for each symbol.
+ In OnSecuritiesChanged event method, we add the newly selected symbol to the dictionary and initialize the momentum indicator with the history request. For symbols removed from the universe, we remove it from the dictionary and liquidate its positions. Each day in OnData, the Momentum indicator for all symbols in the dictionary will be updated with the latest closing price.
+
+ We choose a period of 12 months for the momentum indicator. Stocks with the best 12-month momentum (12-month performance) are then added to our portfolio and are weighted equally. +
+ +
+ The portfolio is rebalanced once a month. The coarse and fine universe selection is set to default to run at midnight once a day. To make the universe selection run at the first trading day each month, we use the int variable self.month that tracks the current month to manage the universe selection. At the start of each month, the universe selection will filter new stocks. On all other days, the universe selection function will return Universe.Unchanged. In contrast to returning an empty list or a list of previously selected symbols, returning Universe.Unchanged is the best way for monthly rebalance universe selection. If there are no open positions for certain symbol, returning an empty list will stop the data subscription of that symbol and halt updates of the indicator.
+
+ In this tutorial we will take a close look at a principal component analysis (PCA)-based statistical arbitrage strategy + derived from the paper + Statistical Arbitrage in the U.S. Equities Market. +
++ Statistical arbitrage strategies uses mean-reversion models to take advantage of pricing inefficiencies between groups of correlated + securities. This class of short-term financial trading strategies produce moves that can contrarian to the broader market movement and are often discussed in conjunction with + Pairs Trading. + In our algorithm, we will be using a PCA-based approach as opposed to an ETF-based approach to limit our universe of stocks. + Backtests from the period 1997-2007 support our strategy by showing that PCA-based strategies have Sharpe ratios that outperform Sharpe ratios + from ETF-based strategies. +
+ diff --git a/04 Strategy Library/211 Mean-Reversion Statistical Arbitrage Strategy in Stocks/02 Method.html b/04 Strategy Library/211 Mean-Reversion Statistical Arbitrage Strategy in Stocks/02 Method.html new file mode 100644 index 0000000..bdbfa32 --- /dev/null +++ b/04 Strategy Library/211 Mean-Reversion Statistical Arbitrage Strategy in Stocks/02 Method.html @@ -0,0 +1,66 @@ ++ We will select our universe of stocks by dropping securities with prices lower than $5 and pick the ones with the highest dollar traded volume. +
+ ++ # Sort the equities in DollarVolume decendingly + selected = sorted([x for x in coarse if x.Price > 5], + key=lambda x: x.DollarVolume, reverse=True) + symbols = [x.Symbol for x in selected[:self.num_equities]] ++
+ We want to minimize our algorithm's exposure to market factors. PCA is a procedure that extracts uncorrelated components of a possibly-correlated set of observations to reveal the factors that contribute most to a the variance of the observations as a whole. Applying PCA to the data above enables us to reduce dimensionality and select the most relevant market factors to shape our asset universe. + Based on the results found in the cited paper, and for the sake of demonstration, we chose 3 components to account for the bulk of the variance. + In our algorithm, the 3 principal components of the feature space are formed by the historical close values. +
+ ++ # Sample data for PCA (smooth it using np.log function) + sample = np.log(history.dropna(axis=1)) + sample -= sample.mean() # Center it column-wise + + # Fit the PCA model for sample data + model = PCA().fit(sample) + + # Get the first n_components factors + factors = np.dot(sample, model.components_.T)[:,:self.num_components] ++
+ We will model the mean-reverting residuals of our assets from a regression line. + We use linear regression to derive the weight of each stock in the portfolio based on its price deviation, which is measured by the residual. + If the absolute value of a stock's residual is large, it means that the level of price deviation is high and we should give it + more weight in the portfolio. Similarly, if the absolute value of the residual is small, + it is reasonable to give the stock less weight in the portfolio. To facilitate this, we can first standardize the residuals to get + their z-scores. Then, based on the z-scores, it is easy to detect the level of price deviation. + Specifically, the level of deviation is higher when the absolute values of the z-scores are large. + From this it is natural to use the inverse of the absolute values of the z-scores as a measurement of the weights of the portfolio. +
+ +
+ # Train Ordinary Least Squares linear model for each stock
+ OLSmodels = {ticker: sm.OLS(sample[ticker], factors).fit() for ticker in sample.columns}
+
+ # Get the residuals from the linear regression after PCA for each stock
+ resids = pd.DataFrame({ticker: model.resid for ticker, model in OLSmodels.items()})
+
+ # Get the Z scores by standarize the given pandas dataframe X
+ zscores = ((resids - resids.mean()) / resids.std()).iloc[-1] # residuals of the most recent day
+
+ # Get the stocks far from mean (for mean reversion)
+ selected = zscores[zscores < -1.5]
+
+ # Return the weights for each selected stock
+ weights = selected * (1 / selected.abs().sum())
+
++ In our alorithm, the portfolio is rebalanced every 30 days and the backtest period runs from Jan 2010 to Aug 2019. + Our result is an annual rate of return over 7% with a max drawdown of around 40% for nearly 10 years. Our performance indicates + using PCA combined with linear regression to measure the deviation level is reasonable. +
++ To tune the model, we could expand our universe of stocks beyond the current 20 equities or incorporate more PCA components. + We could also come up with another way to measure the level of deviation or change the rebalance frequency of the algorithm + (30 days in this example). +
+ diff --git a/04 Strategy Library/211 Mean-Reversion Statistical Arbitrage Strategy in Stocks/04 Algorithm.html b/04 Strategy Library/211 Mean-Reversion Statistical Arbitrage Strategy in Stocks/04 Algorithm.html new file mode 100644 index 0000000..78e62f1 --- /dev/null +++ b/04 Strategy Library/211 Mean-Reversion Statistical Arbitrage Strategy in Stocks/04 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/211 Mean-Reversion Statistical Arbitrage Strategy in Stocks/05 Reference.html b/04 Strategy Library/211 Mean-Reversion Statistical Arbitrage Strategy in Stocks/05 Reference.html new file mode 100644 index 0000000..218aff7 --- /dev/null +++ b/04 Strategy Library/211 Mean-Reversion Statistical Arbitrage Strategy in Stocks/05 Reference.html @@ -0,0 +1,5 @@ + diff --git a/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/01 Introduction.html b/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/01 Introduction.html new file mode 100644 index 0000000..37a614e --- /dev/null +++ b/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/01 Introduction.html @@ -0,0 +1,3 @@ ++ This algorithm examines the momentum effect in country indexes exchange-traded funds. +
diff --git "a/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/01 \347\256\200\344\273\213.cn.html" "b/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/01 \347\256\200\344\273\213.cn.html" new file mode 100644 index 0000000..6b02628 --- /dev/null +++ "b/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/01 \347\256\200\344\273\213.cn.html" @@ -0,0 +1,3 @@ ++ 此算法检验了国家指数交易所交易基金的动量效应。 +
diff --git a/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/02 Method.html b/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/02 Method.html new file mode 100644 index 0000000..6b6f900 --- /dev/null +++ b/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/02 Method.html @@ -0,0 +1,8 @@ +
+The algorithm picks 35 country indexes ETFs as the trading universe. As the symbols in the universe don't change over time, we use the momentum indicator helper method
+ self.MOM(symbol, period, resolution). This helper method creates a new momentum indicator and computes the absolute n-period change in the security. In contrast to the indicator constructor Momentum(period), the helper method indicator will be automatically updated on the given resolution.
+
+ In Initialize(), we set the warm-up period to the momentum period and create the dictionary self.data to save the indicator of
+ each symbol. On each month, the top five indexes ETFs with the best 6-month momentum will be selected to open long position. ETFs which are no longer in this top list will be liquidated. The scheduled event API is used to schedule the portfolio to rebalance at the start of each month.
+
+此算法选取35个国家的指数基金作为交易集合。由于集合中的符号不会随时间发生变化,我们使用动量指示器辅助方法self.MOM(symbol, period, resolution)。这种辅助方法会创建一个新的动量指示器,并计算证券在绝对n周期中的变化。与指示器构造函数Momentum(period)相反,辅助方法指示器将根据给定的分辨率自动更新。
+
+ 在Initialize()中,我们将预热周期设置为动量周期并创建字典self.data,以保存每个符号的指示符。每个月,将选择6个月势头最好的前5支指数基金进行多头仓位。没有列在榜首的基金将被斩仓。采用日程事件API制定投资组合,在每个月月初时重新平衡。
+
+ The algorithm result shows that momentum effects do exist in the country indices. + The strategy of holding for one month, a portfolio of the five best performing country indices ETFs over the previous six months, was found to out-perform the equal-weighted portfolio by around 40% per annum over the 16-year period from 2002 to 2018. +
diff --git "a/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/03 \347\273\223\350\256\272.cn.html" "b/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/03 \347\273\223\350\256\272.cn.html" new file mode 100644 index 0000000..b3aecfd --- /dev/null +++ "b/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/03 \347\273\223\350\256\272.cn.html" @@ -0,0 +1,3 @@ ++ 算法结果表明,国家指数存在动量效应。在2002年至2018年的16年时间里,持有一个月的策略(即在过去6个月中表现最好的5个国家指数基金投资组合)的表现每年要超出平均加权投资组合约40%。 +
diff --git a/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/04 Algorithm.html b/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/04 Algorithm.html new file mode 100644 index 0000000..1f5050c --- /dev/null +++ b/04 Strategy Library/22 Momentum Effect in Country Equity Indexes/04 Algorithm.html @@ -0,0 +1,14 @@ ++ Multiple factors can explain abnormal equity returns which could be used to build profitable equity long-short strategy. + The most common factors are momentum, short-term reversal, market value, size factors and so on. + In this tutorial, we will choose a few factors associated with earnings quality to investigate the return premium on stocks. +
diff --git a/04 Strategy Library/229 Earnings Quality Factor/02 Method.html b/04 Strategy Library/229 Earnings Quality Factor/02 Method.html new file mode 100644 index 0000000..cbce69f --- /dev/null +++ b/04 Strategy Library/229 Earnings Quality Factor/02 Method.html @@ -0,0 +1,157 @@ ++ Earnings quality refers to the ability of reported earnings to predict a company's future earnings. + The earnings should be attributable to higher sales or lower costs, rather than artificial profits created by accounting anomalies or tricks such as inflation of inventories or changing depreciation. + It is one of the most critical measures in financial reporting systems. High earnings quality indicates a healthy development in the firm's business and can improve the market efficiency. +
++ The first metric of earnings quality is accruals. It is defined by cash flow relative to reported earnings. The high-quality earnings firms are characterized by low accruals while the low-quality firms are characterized by high accruals. + The formula is +
+\[Accruals= ( \Delta CA - \Delta Cash) - ( \Delta CL - \Delta STD - \Delta ITP) - Dep\] +Where
++ We use an annual change reported for two consecutive fiscal years. + To calculate the accruals, we save the fine fundamental object in the last year and calculate the difference in the next year. + The algorithm will start to trade after one-year initialization. +
++ def CalculateAccruals(self, current, previous): + accruals = [] + for stock_data in current: + #compares this and last year's fine fundamental objects + try: + prev_data = None + for x in previous: + if x.Symbol == stock_data.Symbol: + prev_data = x + break + + #calculates the balance sheet accruals and adds the property to the fine fundamental object + delta_assets = float(stock_data.FinancialStatements.BalanceSheet.CurrentAssets.Value)-float(prev_data.FinancialStatements.BalanceSheet.CurrentAssets.Value) + delta_cash = float(stock_data.FinancialStatements.BalanceSheet.CashAndCashEquivalents.Value)-float(prev_data.FinancialStatements.BalanceSheet.CashAndCashEquivalents.Value) + delta_liabilities = float(stock_data.FinancialStatements.BalanceSheet.CurrentLiabilities.Value)-float(prev_data.FinancialStatements.BalanceSheet.CurrentLiabilities.Value) + delta_debt = float(stock_data.FinancialStatements.BalanceSheet.CurrentDebt.Value)-float(prev_data.FinancialStatements.BalanceSheet.CurrentDebt.Value) + delta_tax = float(stock_data.FinancialStatements.BalanceSheet.IncomeTaxPayable.Value)-float(prev_data.FinancialStatements.BalanceSheet.IncomeTaxPayable.Value) + dep = float(stock_data.FinancialStatements.IncomeStatement.DepreciationAndAmortization.Value) + avg_total = (float(stock_data.FinancialStatements.BalanceSheet.TotalAssets.Value)+float(prev_data.FinancialStatements.BalanceSheet.TotalAssets.Value))/2 + #accounts for the size difference + stock_data.Accrual = ((delta_assets-delta_cash)-(delta_liabilities-delta_debt-delta_tax)-dep)/avg_total + accruals.append(stock_data) + except: + #value in current universe does not exist in the previous universe + pass + return accruals ++
+ The second metric is cash flow to assets ratio. It is calculated by dividing cash flows from operations by the average total assets. Firms with high cash flow to total assets are of high earnings quality. + The other two metrics are Return on Equity(ROE) and Debt to Assets(DA) which are available properties of fine fundamental objects. The Higher the ROE ratio, the better the earnings quality. + Low debt to assets means low leverage. It leads to more stable earnings and less dependence on the current financing conditions in the economy. Therefore, low debt to assets ratios is a signal of high earnings quality. + Before calculating those variables, we should make sure their values are all positive. +
++def FineSelectionFunction(self, fine): + if self.yearly_rebalance: + #filters out the non-financial companies that don't contain the necessary data + fine = [x for x in fine if (x.CompanyReference.IndustryTemplateCode != "B") + and (x.FinancialStatements.BalanceSheet.CurrentAssets.Value != 0) + and (x.FinancialStatements.BalanceSheet.CashAndCashEquivalents.Value != 0) + and (x.FinancialStatements.BalanceSheet.CurrentLiabilities.Value != 0) + and (x.FinancialStatements.BalanceSheet.CurrentDebt.Value != 0) + and (x.FinancialStatements.BalanceSheet.IncomeTaxPayable.Value != 0) + and (x.FinancialStatements.IncomeStatement.DepreciationAndAmortization.Value != 0)] + + if not self.previous_fine: + # will wait one year in order to have the historical fundamental data + self.previous_fine = fine + self.yearly_rebalance = False + return [] + else: + # calculate the accrual for each stock + fine = self.CalculateAccruals(fine, self.previous_fine) + filtered_fine = [x for x in fine if (x.FinancialStatements.CashFlowStatement.OperatingCashFlow.Value != 0) + and (x.EarningReports.BasicEPS.Value != 0) + and (x.EarningReports.BasicAverageShares.Value != 0) + and (x.OperationRatios.DebttoAssets.Value != 0) + and (x.OperationRatios.ROE.Value != 0)] + for i in filtered_fine: + # cash flow to assets + i.CFA = i.FinancialStatements.CashFlowStatement.OperatingCashFlow.Value/(i.EarningReports.BasicEPS.Value * i.EarningReports.BasicAverageShares.Value) + # debt to assets + i.DA = i.OperationRatios.DebttoAssets.Value + # return on equity + i.ROE = i.OperationRatios.ROE.Value ++
+ The investment universe consists of all non-financial stocks from NYSE, Amex and Nasdaq. Next, we will build a composite scoring system to rank the stocks in the universe. + The first step is sorting stocks by four factors respectively. “good” quality has a high score, so ideally a stock has low accruals, low debt to assets, high ROE, and high cash flow to assets will be allocated high score. + Therefore, we sort the accruals and debt to assets ratio in descending orders and sort the ROE and cash flow to assets ratios in ascending order. + Then the score of each stock is the sum of rank in four factors. +
+
+ # sort stocks by four factors respectively
+ sortedByAccrual = sorted(filtered_fine, key=lambda x: x.Accrual, reverse=True) # high score with low accrual
+ sortedByCFA = sorted(filtered_fine, key=lambda x: x.CFA) # high score with high CFA
+ sortedByDA = sorted(filtered_fine, key=lambda x: x.DA, reverse=True) # high score with low leverage
+ sortedByROE = sorted(filtered_fine, key=lambda x: x.ROE) # high score with high ROE
+ # create dict to save the score for each stock
+ score_dict = {}
+ # assign a score to each stock according to their rank with different factors
+ for i,obj in enumerate(sortedByAccrual):
+ scoreAccrual = i
+ scoreCFA = sortedByCFA.index(obj)
+ scoreDA = sortedByDA.index(obj)
+ scoreROE = sortedByROE.index(obj)
+ score = scoreAccrual + scoreCFA + scoreDA + scoreROE
+ score_dict[obj.Symbol] = score
+
+ sortedByScore = sorted(score_dict, key = lambda x: score_dict[x], reverse = True)
+ # long stocks with the top score (> 30%) and short stocks with the bottom score (< 70%)
+ self.long = sortedByScore[:int(0.3*len(sortedByScore))]
+ self.short = sortedByScore[-int(0.3*len(sortedByScore)):]
+
++ Based on the composite factor score, the algorithm goes long the top 30% of high score stocks and short the bottom 30% of low score stocks. + Final factor portfolio is formed at the end of each June and is rebalanced yearly. +
++def OnData(self, data): + if not self.yearly_rebalance: return + if self.long and self.short: + long_stocks = [x.Key for x in self.Portfolio if x.Value.IsLong] + short_stocks = [x.Key for x in self.Portfolio if x.Value.IsShort] + # liquidate the stocks not in the filtered long/short list + for long in long_stocks: + if long not in self.long: + self.Liquidate(long) + + for short in short_stocks: + if short not in self.short: + self.Liquidate(short) + + long_weight = 0.8/len(self.long) + for i in self.long: + self.SetHoldings(i, long_weight) + short_weight = 0.8/len(self.short) + for i in self.short: + self.SetHoldings(i, -short_weight) ++
+ Mean reversion in stock price is the assumption that the price will tend to move back to the average price over time. + Mean reversion trading often refers to counter-trend or reversal trading. This algorithm will explore the mean reversion effect in country equity indexes. +
diff --git a/04 Strategy Library/23 Mean Reversion Effect in Country Equity Indexes/02 Method.html b/04 Strategy Library/23 Mean Reversion Effect in Country Equity Indexes/02 Method.html new file mode 100644 index 0000000..b5578d7 --- /dev/null +++ b/04 Strategy Library/23 Mean Reversion Effect in Country Equity Indexes/02 Method.html @@ -0,0 +1,8 @@ +
+ The investment universe consists of 19 ETFs which invest in individual country equity indexes.
+ The strategy is going to long on the bottom four countries with the worst 36-month return and short on the top 4 countries with the best 36-month return. The helper indicator method self.ROC(symbol, period, resolution)
+ is used to calculate 36-month return where the resolution is daily and the period is 36*21.
+
+ The portfolio is reweighted every three years. We schedule the event to fire every month. self.months is the variable to save the number of months, and the algorithm jumps the rebalance execution if the amount of passed months does not equate to 36.
+
+ Liquidity has a powerful impact on price and the valuation of equities. Stocks with little liquidity are used to earning higher returns than stocks with high liquidity. In this algorithm, we present the effect of liquidity on returns for the lowest capitalization quartile from the largest 1500 stocks. +
diff --git a/04 Strategy Library/24 Liquidity Effect in Stocks/02 Method.html b/04 Strategy Library/24 Liquidity Effect in Stocks/02 Method.html new file mode 100644 index 0000000..6fd2878 --- /dev/null +++ b/04 Strategy Library/24 Liquidity Effect in Stocks/02 Method.html @@ -0,0 +1,15 @@ +
+ In coarse universe selection, we filter stocks whose price is higher than $5. ADRs, ETFs and closed-end funds are all excluded with the property of coarse fundamental object HasFundamentalData.
+
+ In fine universe selection, in the first step, we exclude stocks with the market cap less than ten million.
+ To evaluate the liquidity of stocks, we choose the annual turnover which is the number of shares traded divided by the stock’s outstanding shares.
+ The main advantage of turnover against volume is its market capitalization-neutrality, as either small-cap or large-cap stocks can have low or high turnover rates.
+ Although turnover is capitalization neutral, the liquidity effect is the strongest among small-cap stocks. Therefore, stocks are then divided into quartiles based on their market capitalization. Stocks from the lowest market-cap quartile are again divided into 5% and 95% quantiles based on their turnover. To calculate the turnover,
+ we request the historical daily volume for the last one year and compute the mean volume. The turnover is the average annual volume divided by BasicAverageShares in EarningReports.
+ Stocks in the 5% quantile and in the top 95% percentile are saved in self.long and self.short lists respectively.
+
+ In OnData(), the algorithm goes long on stocks in the lowest turnover list and short on stocks in the highest turnover list. Stocks not in those two lists are liquidated. + The portfolio is rebalanced once a year and stocks are weighted equally. +
diff --git a/04 Strategy Library/24 Liquidity Effect in Stocks/03 Algorithm.html b/04 Strategy Library/24 Liquidity Effect in Stocks/03 Algorithm.html new file mode 100644 index 0000000..15edb83 --- /dev/null +++ b/04 Strategy Library/24 Liquidity Effect in Stocks/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/24 Liquidity Effect in Stocks/04 Source.html b/04 Strategy Library/24 Liquidity Effect in Stocks/04 Source.html new file mode 100644 index 0000000..e09165f --- /dev/null +++ b/04 Strategy Library/24 Liquidity Effect in Stocks/04 Source.html @@ -0,0 +1,5 @@ + diff --git a/04 Strategy Library/25 Volatility Risk Premium Effect/01 Introduction.html b/04 Strategy Library/25 Volatility Risk Premium Effect/01 Introduction.html new file mode 100644 index 0000000..c517ab8 --- /dev/null +++ b/04 Strategy Library/25 Volatility Risk Premium Effect/01 Introduction.html @@ -0,0 +1,7 @@ ++ Long volatility means that the value of your portfolio increases when the volatility goes up. + Short volatility means that you make money when the volatility goes down. The simplest example of volatility selling involves the sale of put and call contracts. + Traders often long volatility by holding the long position of put or call options for hedging purpose. + In contrast, the short volatility strategy expects to earn the systematic risk premium by selling options. + This algorithm will explore the risk premium effect in volatility selling. +
diff --git a/04 Strategy Library/25 Volatility Risk Premium Effect/02 Method.html b/04 Strategy Library/25 Volatility Risk Premium Effect/02 Method.html new file mode 100644 index 0000000..3bc10d3 --- /dev/null +++ b/04 Strategy Library/25 Volatility Risk Premium Effect/02 Method.html @@ -0,0 +1,48 @@ ++ This short volatility algorithm first prescreens the option contracts by the expiry and the strike. + To include the weekly contract, we use the universe function +
+def Initialize(self): + option.SetFilter(self.UniverseFunc) + def UniverseFunc(self, universe): + return universe.IncludeWeeklys().Strikes(-20, 20).Expiration(timedelta(25), timedelta(35)) ++
+ The algorithm selects contracts with one month until maturity so we choose a small range for expiration. +
+
+ In OnData(), we divide the option chain into put and call options. Then we create two lists
+ expiries and strikes to save all available expiration dates and stike prices to facilitate
+ sorting and filtering.
+
+ The algorithm needs three option contracts with one month to the maturity: one ATM call, one ATM put to contruct the ATM straddle,
+ one 15% OTM put. As it's difficult to find the contract with the specified days to maturity and strikes,
+ we use min() to find the most closest contract.
+
expiries = [i.Expiry for i in puts] +# determine expiration date nearly 30 days +expiry = min(expiries, key=lambda x: abs((x.date()-self.Time.date()).days-30)) +strikes = [i.Strike for i in puts] +# determine at-the-money strike +strike = min(strikes, key=lambda x: abs(x-underlying_price)) +# determine 15% out-of-the-money strike +otm_strike = min(strikes, key = lambda x:abs(x-Decimal(0.85)*underlying_price)) ++
+ From the above expiration date and strike price, we pick three option contracts +
+self.atm_call = [i for i in calls if i.Expiry == expiry and i.Strike == strike] +self.atm_put = [i for i in puts if i.Expiry == expiry and i.Strike == strike] +self.otm_put = [i for i in puts if i.Expiry == expiry and i.Strike == otm_strike] ++
+ In trading, we sell the ATM straddle by selling one ATM call and one ATM put. Then we buy an OTM put option as insurance against a market crash. + Then we wait until the expiration and sell the underlying positions after option exercise and assignment. The portfolio is rebalanced once a month. +
diff --git a/04 Strategy Library/25 Volatility Risk Premium Effect/03 Algorithm.html b/04 Strategy Library/25 Volatility Risk Premium Effect/03 Algorithm.html new file mode 100644 index 0000000..0733d81 --- /dev/null +++ b/04 Strategy Library/25 Volatility Risk Premium Effect/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/25 Volatility Risk Premium Effect/04 Source.html b/04 Strategy Library/25 Volatility Risk Premium Effect/04 Source.html new file mode 100644 index 0000000..887095d --- /dev/null +++ b/04 Strategy Library/25 Volatility Risk Premium Effect/04 Source.html @@ -0,0 +1,5 @@ + diff --git a/04 Strategy Library/26 Quantpedia/02 Quantpedia.php b/04 Strategy Library/26 Quantpedia/02 Quantpedia.php new file mode 100644 index 0000000..32dd198 --- /dev/null +++ b/04 Strategy Library/26 Quantpedia/02 Quantpedia.php @@ -0,0 +1,155 @@ + +
+ | + Strategy Name + | +
|---|
|
+ = $strategy['name'] ?>
+ = $strategy['description'] ?> + = $sources ?> + |
+
+ This tutorial implements a seasonality strategy that trades based on historical same-calendar-month returns. The strategy is + derived from the paper Common Factors in Return Seasonalities. +
++ A great deal of research on seasonality effects in algorithmic trading exists. Seasonality patterns are well documented in stock returns across numerous + countries and in commodity and country portfolios. The phenomenon’s occurrence is not isolated to specific stocks or monthly time intervals, for example, seasonality is observed at the daily frequency as well. Our implementation reflects the existing research. +
++ In our algorithm, we will first use a coarse selection filter function to narrow down our universe to the top 100 liquid securities with a price greater than $5. +
++ Next, for each security in the universe, we will calculate the monthly return for the same-calendar month of the previous year. For example, if we implement this strategy on a backtest for the period of August 2019, we would base our long and short positions on monthly returns from August 2018. We will long the securities with top monthly returns and short those with the bottom monthly returns. +
++ At the end of each month we will rebalance and repeat the strategy. The following section offers further explanation of how to implement each step of the strategy. +
+ + \ No newline at end of file diff --git a/04 Strategy Library/269 Seasonality Effect based on Same-Calendar Month Returns/02 Method.html b/04 Strategy Library/269 Seasonality Effect based on Same-Calendar Month Returns/02 Method.html new file mode 100644 index 0000000..5b5da95 --- /dev/null +++ b/04 Strategy Library/269 Seasonality Effect based on Same-Calendar Month Returns/02 Method.html @@ -0,0 +1,70 @@ ++ We first select the top 100 liquid securities and ETFs with prices greater than $5 based on Dollar Volume for our universe. Research from "Common Factors" suggests that the U.S. equity, commodity, and index markets are all affected by seasonality patterns. Therefore, we can include any assets in our universe. Note that while this strategy does not require fundamental data for implementation, other strategies in the library do. In those cases we would need to remove ETFs from the universe because we don’t have fundamental data for ETFs. +
+ ++ # Sort the securities with prices > 5 in DollarVolume decendingly + selected = sorted([x for x in coarse if x.Price > 5], + key=lambda x: x.DollarVolume, reverse=True) + + # Get securities after coarse selection + symbols = [x.Symbol for x in selected[:self.num_coarse]] ++
+ "Common Factors" indicates that taking long and short positions based on historical same-calendar month returns earns an average monthly return of 1.88%. Our implementation also selects securities to long and short based on their same-calendar month returns. For each security in the universe, we calculate the monthly return for the same-calendar month of the previous year and choose the symbols as follows: +
+ +
+ # Get historical close data for coarse-selected symbols of the same calendar month
+ start = self.Time.replace(day = 1, year = self.Time.year-1)
+ end = Expiry.EndOfMonth(start) - timedelta(1)
+ history = self.History(symbols, start, end, Resolution.Daily).close.unstack(level=0)
+
+ # Get the same calendar month returns for the symbols
+ MonthlyReturn = {ticker: prices.iloc[-1]/prices.iloc[0] for ticker, prices in history.iteritems()}
+
+ # Sorted the values of monthly return
+ sortedReturn = sorted(MonthlyReturn.items(), key=lambda x:x[1], reverse=True)
+
+ # Get the symbols to long / short
+ self.longSymbols = [x[0] for x in sortedReturn[:self.num_long]]
+ self.shortSymbols = [x[0] for x in sortedReturn[-self.num_short:]]
+
+ # Note that self.longSymbols/self.shortSymbols contains strings instead of symbols
+ return [x for x in symbols if str(x) in self.longSymbols + self.shortSymbols]
+
++ At the end of each month, we rebalance our portfolio, liquidate the securities that are not part of the new month’s universe, and repeat step 1 and 2. Keep in mind we use equal weights for the long and short positions of securities in our portfolio. +
+ ++ ''' + Rebalance every month based on same-calendar month returns effect + ''' + # Before next rebalance, do nothing + if self.Time < self.nextRebalance: + return + + count = len(self.longSymbols + self.shortSymbols) + # Open long positions + for symbol in self.longSymbols: + self.SetHoldings(symbol, 1/count) + + # Open short positions + for symbol in self.shortSymbols: + self.SetHoldings(symbol, -1/count) + + # Rebalance at the end of every month + self.nextRebalance = Expiry.EndOfMonth(self.Time) - timedelta(1) ++
+ In backtesting our algorithm achieves a Sharpe ratio of 0.332 relative to S&P 500 (SPY) Sharpe ratio of 0.893 for the past 10 years. + The performance indicates using the idea of same-calendar month returns makes sense. Interested users can build upon this implementation by trying the following extensions: +
++ Commodity futures are excellent portfolio diversifiers and some of them are an effective hedge against inflation. + This algorithm will explore the momentum effect in commodity futures with the momentum return. +
diff --git a/04 Strategy Library/27 Momentum Effect in Commodities Futures/02 Method.html b/04 Strategy Library/27 Momentum Effect in Commodities Futures/02 Method.html new file mode 100644 index 0000000..9870587 --- /dev/null +++ b/04 Strategy Library/27 Momentum Effect in Commodities Futures/02 Method.html @@ -0,0 +1,42 @@ ++ As the strategy needs the continuous futures contract, we import the custom data from Quandl. + We create a universe of tradable commodity futures from all available commodity futures traded on CME and ICE. + They are all liquid and active continuous contracts #1. The data from Quandl are non-adjusted price based on spot-month continuous contract calculations. + The data resolution is daily. +
++ The first step is importing the data. +
+from QuantConnect.Python import PythonQuandl +for symbol in self.symbols: + self.AddData(QuandlFutures, symbol, Resolution.Daily) + +class QuandlFutures(PythonQuandl): + def __init__(self): + self.ValueColumnName = "Settle" ++
+ Here we use the indicator RateOfChange(period) to simulate the momentum return. Here the period is 12 months.
+ As we are using the custom data, the indicator initialization should use the history request to update the value manually.
+ All indicators are saved in the dictionary self.roc.
+
self.roc = {}
+for symbol in self.symbols:
+ self.AddData(QuandlFutures, symbol, Resolution.Daily)
+ self.roc[symbol] = RateOfChange(period)
+ hist = self.History([symbol], 400, Resolution.Daily).loc[symbol]
+ for i in hist.itertuples():
+ self.roc[symbol].Update(i.Index, i.value)
+
+
+ In OnData(self, data), indicators for all futures contracts are updated every day with the settlement price.
+
+ We rank the contracts by the last 12-month return and divide them into quintiles. + In the trading part, the algorithm goes long on the quintile with the highest momentum return and goes short on the quintile with the lowest momentum return. + The portfolio is rebalanced each month. +
diff --git a/04 Strategy Library/27 Momentum Effect in Commodities Futures/03 Algorithm.html b/04 Strategy Library/27 Momentum Effect in Commodities Futures/03 Algorithm.html new file mode 100644 index 0000000..ad5e9f8 --- /dev/null +++ b/04 Strategy Library/27 Momentum Effect in Commodities Futures/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/27 Momentum Effect in Commodities Futures/04 Source.html b/04 Strategy Library/27 Momentum Effect in Commodities Futures/04 Source.html new file mode 100644 index 0000000..7b964a7 --- /dev/null +++ b/04 Strategy Library/27 Momentum Effect in Commodities Futures/04 Source.html @@ -0,0 +1,5 @@ + diff --git a/04 Strategy Library/270 Risk Premia in Forex Markets/01 Introduction.html b/04 Strategy Library/270 Risk Premia in Forex Markets/01 Introduction.html new file mode 100644 index 0000000..2c85d7e --- /dev/null +++ b/04 Strategy Library/270 Risk Premia in Forex Markets/01 Introduction.html @@ -0,0 +1,7 @@ ++ This tutorial implements a risk premia strategy that enters long-short positions in the forex market based on signals from a skewness indicator. The strategy is derived from the paper “Risk Premia: Asymmetric Tail Risks and Excess Returns” by Lemperiere, Deremble, Nguyen, Seager, Potters, and Bouchaud. +
+ ++ One of the pillars in modern finance theory is the concept of risk premium, which states the riskier an investment is today the more profitable it should be in the long run. Risk premia strategies aim to profit from risk premiums. Lemperiere et al. describe a positive linear relationship between the Sharpe ratio of risk premia strategies and their negative skewness. It provides extensive evidence that risk premium is indeed strongly correlated with the skewness of a strategy, not only in the equity world but also in currencies, options, credit, etc. +
diff --git a/04 Strategy Library/270 Risk Premia in Forex Markets/02 Method.html b/04 Strategy Library/270 Risk Premia in Forex Markets/02 Method.html new file mode 100644 index 0000000..fd1d64a --- /dev/null +++ b/04 Strategy Library/270 Risk Premia in Forex Markets/02 Method.html @@ -0,0 +1,73 @@ ++ In this algorithm, we use a fixed forex universe which contains four symbols: "EURUSD", "AUDUSD", "USDCAD" and "USDJPY". By using self.AddForex(), we add the requested forex data into the data feed. +
+ ++ # Add forex data of the following symbols + for pair in ['EURUSD', 'AUDUSD', 'USDCAD', 'USDJPY']: + self.AddForex(pair, Resolution.Hour, Market.FXCM) ++
+ In statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Lemperiere et al. suggest there is a positive relationship between risk premia strategies and their negative skewness. We will use this relationship in our trading logic. Our implementation goes long for a forex pair when the skewness indicator is lower than a minimum threshold (-0.6) and short the pair when the indicator exceeds a maximum threshold (0.6). For each forex pair in the universe, we will calculate the skewness indicator with historical close prices and select the symbols as follows: +
+ ++ ### In OnData() + # Get historical close data for the symbols + history = self.History(self.Securities.Keys, self.lookback, Resolution.Daily) + history = history.drop_duplicates().close.unstack(level=0) + + # Get the skewness of the historical data + skewness = self.GetSkewness(history) + + longSymbols = [k for k,v in skewness.items() if v < self.longSkewLevel] + shortSymbols = [k for k,v in skewness.items() if v > self.shortSkewLevel] + + def GetSkewness(self, values): + ''' + Get the skewness for all forex symbols based on its historical data + Ref: https://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm + ''' + # Get the numerator of the skewness + numer = ((values - values.mean()) ** 3).sum() + + # Get the denominator of the skewness + denom = self.lookback * values.std() ** 3 + + # Return the skewness + return (numer/denom).to_dict() ++
+ We rebalance every week, liquidate the forex pairs not on the trading list, then repeat steps 1-2. We use equal weights for the long and short positions of securities in our portfolio. +
+ ++ # Liquidate the holdings for pairs that will not trade + for holding in self.Portfolio.Values: + symbol = holding.Symbol + if holding.Invested and symbol.Value not in longSymbols + shortSymbols: + self.Liquidate(symbol, 'Not selected pair') + + # Open positions for the symbols with equal weights + count = len(longSymbols) + len(shortSymbols) + + for pair in longSymbols: + self.SetHoldings(pair, 1/count) + + for pair in shortSymbols: + self.SetHoldings(pair, -1/count) + + # Set next rebalance time + self.nextRebalance += timedelta(self.rebalanceDays) ++
+ In this case our backtest results in a low annual return of approximately -0.7% over a decade. The poor performance may be due to several reasons: +
+ In this tutorial, we will develop a strategy based on the price and earnings momentum effect of stocks. This strategy is derived from the paper "Momentum" by N.Jegadeesh and S.Titman. +
+ ++ N.Jegadeesh et al. describe price/return momentum as a tendency for stocks that perform well over a three to twelve month period to continue to perform well over a subsequent three to twelve month period. Similarly, stocks that perform poorly over a three to twelve month period have a tendency to continue to perform poorly. They describe earnings momentum as the tendency for stocks with high earnings per share (EPS) to continue to outperform stocks with low EPS. +
+ ++ Below, we will implement a quarterly-rebalanced stock strategy based on the price and earnings momentum. +
diff --git a/04 Strategy Library/271 Price and Earning Momentum/02 Method.html b/04 Strategy Library/271 Price and Earning Momentum/02 Method.html new file mode 100644 index 0000000..755688e --- /dev/null +++ b/04 Strategy Library/271 Price and Earning Momentum/02 Method.html @@ -0,0 +1,166 @@ ++ We will use both a coarse selection filter and in a later step, a fine universe filter, to narrow down our universe of assets. Our coarse universe filter creates a set of stocks based on volume, price, and whether fundamental data on the stock exists. In this step we filter for the top 100 liquid equities with prices greater than $5. We also exclude the equities missing fundamental data because EPS is needed in the fine selection step. +
+ ++def CoarseSelection(self, coarse): + ''' + Pick the top 100 liquid equities as the coarse-selected universe + ''' + # Before next rebalance time, just remain the current universe + if self.Time < self.nextRebalance: + return Universe.Unchanged + + # Sort the equities (prices > 5) by Dollar Volume descendingly + selectedByDollarVolume = sorted([x for x in coarse if x.Price > 5 and x.HasFundamentalData], + key = lambda x: x.DollarVolume, reverse = True) + + # Pick the top 100 liquid equities as the coarse-selected universe + return [x.Symbol for x in selectedByDollarVolume[:self.numOfCoarse]] ++
+ N.Jegadeesh et al. state price momentum and earnings momentum can be used as two indicators for trading. We will calculate for price momentum with the "GetQuarterlyReturn" method and for earnings momentum with the "GetEarningGrowth" method. +
++ "GetQuarterlyReturn" calculates price momentum for each symbol in our coarse universe and ranks each stock based on its quarterly return. First we request last quarter’s close price for all stocks. Then we calculate quarterly return by taking the delta of the first day’s close price and the last day’s close price. Finally, we store the symbols and their corresponding rankings by quarterly return in a dictionary in preparation for fine selection. +
+ +
+ def GetQuarterlyReturn(self, history):
+ '''
+ Get the rank of securities based on their quarterly return from historical close prices
+ Return: dictionary
+ '''
+ # Get quarterly returns for all symbols
+ # (The first row divided by the last row)
+ returns = history.iloc[0] / history.iloc[-1]
+
+ # Transform them to dictionary structure
+ returns = returns.to_dict()
+
+ # Get the rank of the returns (key: symbol; value: rank)
+ # (The symbol with the 1st quarterly return ranks the 1st, etc.)
+ ranked = sorted(returns, key = returns.get, reverse = True)
+ return {symbol: rank for rank, symbol in enumerate(ranked, 1)}
+
++ "GetEarningGrowth" calculates earnings momentum for each symbol in our coarse universe and ranks each stock based on its earnings growth. First we use a RollingWindow to store and update the BasicEPS to reflect quarterly earnings reports. A RollingWindow holds a set of the most recent entries of data. As we move from time t=0 forward, our rolling window will shuffle data further along to a different index until it leaves the window completely. The object in the window with index[0] refers to the most recent item. The length-1 in the window is the oldest object. +
+ ++ Our rolling window has a length of 2 so index[0] is the current EPS and index[1] is last quarter's EPS. We calculate earnings growth for each stock by taking the delta of this quarter’s EPS and last quarter’s EPS divided by last quarter’s EPS. Finally we rank each asset based on earnings growth. +
+
+ def GetEarningGrowth(self, fine):
+ '''
+ Get the rank of securities based on their EPS growth
+ Return: dictionary
+ '''
+
+ # Earning Growth by symbol
+ egBySymbol = {}
+ for stock in fine:
+
+ # Select the securities with EPS (> 0)
+ if stock.EarningReports.BasicEPS.ThreeMonths == 0:
+ continue
+
+ # Add the symbol in the dict if not exist
+ if not stock.Symbol in self.epsBySymbol:
+ self.epsBySymbol[stock.Symbol] = RollingWindow[float](2)
+
+ # Update the rolling window for each stock
+ self.epsBySymbol[stock.Symbol].Add(stock.EarningReports.BasicEPS.ThreeMonths)
+
+ # If the rolling window is ready
+ if self.epsBySymbol[stock.Symbol].IsReady:
+ rw = self.epsBySymbol[stock.Symbol]
+ # Caculate the Earning Growth
+ egBySymbol[stock.Symbol] = (rw[0] - rw[1]) / rw[1]
+
+ # Get the rank of the Earning Growth
+ ranked = sorted(egBySymbol, key = egBySymbol.get, reverse = True)
+ return {symbol: rank for rank, symbol in enumerate(ranked, 1)}
+
++ We use a fine selection filter in addition to a coarse selection filter to refine our asset selection based on corporate fundamental data. We can use both quarterly return and earnings growth from our two indicators to generate an average rank for each stock. Then we can go long on the top 10 and short the bottom 10. +
+ +
+ def FineSelection(self, fine):
+ '''
+ Select securities based on their quarterly return and their earnings growth
+ '''
+ symbols = [x.Symbol for x in fine]
+
+ # Get the quarterly returns for each symbol
+ history = self.History(symbols, self.rebalanceDays, Resolution.Daily)
+ history = history.drop_duplicates().close.unstack(level = 0)
+ rankByQuarterReturn = self.GetQuarterlyReturn(history)
+
+ # Get the earning growth for each symbol
+ rankByEarningGrowth = self.GetEarningGrowth(fine)
+
+ # Get the sum of rank for each symbol and pick the top ones to long and the bottom ones to short
+ rankSumBySymbol = {key: rankByQuarterReturn.get(key, 0) + rankByEarningGrowth.get(key, 0)
+ for key in set(rankByQuarterReturn) | set(rankByEarningGrowth)}
+
+ # Get 10 symbols to long and short respectively
+ sortedDict = sorted(rankSumBySymbol.items(), key = lambda x: x[1], reverse = True)
+ self.longSymbols = [x[0] for x in sortedDict[:10]]
+ self.shortSymbols = [x[0] for x in sortedDict[-10:]]
+
+ return [x for x in symbols if str(x) in self.longSymbols + self.shortSymbols]
+
++ We choose to rebalance every quarter and use equal weights for the long and short positions of securities in our portfolio. +
+ ++ def OnData(self, data): + ''' + Rebalance quarterly + ''' + # Do nothing until next rebalance + if self.Time < self.nextRebalance: + return + + # Liquidate the holdings if necessary + for holding in self.Portfolio.Values: + symbol = holding.Symbol + if holding.Invested and symbol.Value not in self.longSymbols + self.shortSymbols: + self.Liquidate(symbol, "Not Selected") + + # Open positions for the symbols with equal weights + count = len(self.longSymbols + self.shortSymbols) + if count == 0: + return + + # Enter long positions + for symbol in self.longSymbols: + self.SetHoldings(symbol, 1 / count) + + # Enter short positions + for symbol in self.shortSymbols: + self.SetHoldings(symbol, -1 / count) + + # Set next rebalance time + self.nextRebalance += timedelta(self.rebalanceDays) ++
+ Our backtest results in a Sharpe ratio of 0.59 while the SP500 Sharpe ratio is 0.8 during the same decade. This performance may be due to several factors: +
+ Small caps are typically defined as companies with market caps that are less than $2 billion. + The advantage of investing in small cap companies is that they are young companies with significant growth potential. + However, the risk of failure is greater with small-cap stocks than with large-cap and mid-cap stocks. + In this algorithm, we will explore the performance of the small-capitalization investment. +
diff --git a/04 Strategy Library/28 Small Capitalization Stocks Premium Anomaly/02 Method.html b/04 Strategy Library/28 Small Capitalization Stocks Premium Anomaly/02 Method.html new file mode 100644 index 0000000..98c8577 --- /dev/null +++ b/04 Strategy Library/28 Small Capitalization Stocks Premium Anomaly/02 Method.html @@ -0,0 +1,21 @@ ++ The first step is coarse universe selection. We create an investment universe with stocks that have fundmental data and with a price greater than $5. +
+return [x.Symbol for x in coarse if x.HasFundamentalData and x.Price > 5] ++
In fine universe selection, we sort the stocks in the universe by the market capitalization and choose 10 stocks with the lowest market cap. +
+def FineSelectionFunction(self, fine): + ''' Selects the stocks by lowest market cap ''' + sorted_market_cap = sorted([x for x in fine if x.MarketCap > 0], + key=lambda x: x.MarketCap) + + return [x.Symbol for x in sorted_market_cap[:self.count]] ++
+ In OnData(), we buy 10 stocks in the list of lowest market-cap. The portfolio is rebalanced every year.
+
+ The term structure of commodities usually refers to the difference between futures prices of different maturities at a given time point. The shape of the futures curve is essential to commodity hedgers and speculators as futures price serves as a forecast of future spot price. The futures price curve contains the information about futures supply and demand conditions. This algorithm will examine the role of term structure signals for the design of profitable trading strategies in commodity futures markets. +
diff --git a/04 Strategy Library/29 Term Structure Effect in Commodities/02 Method.html b/04 Strategy Library/29 Term Structure Effect in Commodities/02 Method.html new file mode 100644 index 0000000..616312c --- /dev/null +++ b/04 Strategy Library/29 Term Structure Effect in Commodities/02 Method.html @@ -0,0 +1,61 @@ ++ Before starting the algorithm, we first introduce a few concepts related to commodity futures. Backwardation is defined as conditions when the futures price is below the current spot price and contango as conditions when the futures price is above the current spot price. The futures term structure curve is a representation of the backwardation/contango rate for the different maturities of futures contracts. This price gap between different maturity contracts is quantified as the roll return. + The contango/backwardation rates are calculated by taking the price difference between the spot market price and the futures contract price. This difference can be expressed + as a percentage over the time to expiration and then annualised to calculate an annual roll return. +
+\[R_t = \left[ln(P_{t,n})-ln(P_{t,d})\right]\times\frac{365}{N_{t,d}-N_{t,n}}\] ++ Where \(P_{t,n}\) is the price of the nearest-to-maturity contract at time t. \(P_{t,d}\) is the price of the distant contract at time t. \(N_{t,n}\) is the number of days between time t and the maturity of the nearby contract and \(N_{t,d}\) is the number of days between time t and the maturity of the distant contract. +
++ To calculate the roll return, first we sort the future chain by expiry and select the first two contracts as the nearest-to-maturity contract and the the distant contract. +
+for symbol, chain in self.chains.items():
+ contracts = sorted(chain, key = lambda x: x.Expiry)
+ # R = (log(Pn) - log(Pd)) * 365 / (Td - Tn)
+ # R - Roll returns
+ # Pn - Nearest contract price
+ # Pd - Distant contract price
+ # Tn - Nearest contract expire date
+ # Pd - Distant contract expire date
+ near_contract = contracts[0]
+ distant_contract = contracts[-1]
+ price_near = near_contract.LastPrice if near_contract.LastPrice>0 else 0.5*float(near_contract.AskPrice+near_contract.BidPrice)
+ price_distant = distant_contract.LastPrice if distant_contract.LastPrice>0 else 0.5*float(distant_contract.AskPrice+distant_contract.BidPrice)
+ if distant_contract.Expiry == near_contract.Expiry:
+ self.Debug("ERROR: Near and distant contracts have the same expiry!" + str(near_contract))
+ return
+ expire_range = 365 / (distant_contract.Expiry - near_contract.Expiry).days
+ roll_returns[symbol] = (np.log(float(price_near)) - np.log(float(price_distant)))*expire_range
+
++ In the next step, we will split the futures based on backwardation and contango. If the roll return is greater than 0, the term structure of commodity futures prices + is downward-sloping and so that the market is in backwardation. Conversely, a negative roll return signals an upward-sloping price curve and a contangoed market. +
+positive_roll_returns = { symbol: returns for symbol, returns in roll_returns.items() if returns > 0 }
+negative_roll_returns = { symbol: returns for symbol, returns in roll_returns.items() if returns < 0 }
+backwardation = sorted(positive_roll_returns , key = lambda x: positive_roll_returns[x], reverse = True)[:quintile]
+contango = sorted(negative_roll_returns , key = lambda x: negative_roll_returns[x])[:quintile]
+
++ The algorithm buys 20% of commodities with the highest roll-returns and shorts the 20% of commodities with the lowest roll-returns and holds the long-short positions for one month. +
++for short_symbol in contango: + sort = sorted(self.chains[short_symbol], key = lambda x: x.Expiry) + self.SetHoldings(sort[1].Symbol, -0.5/count) + +for long_symbol in backwardation: + sort = sorted(self.chains[long_symbol], key = lambda x: x.Expiry) + self.SetHoldings(sort[1].Symbol, 0.5/count) ++
Algorithm
+ + + + + + diff --git a/04 Strategy Library/29 Term Structure Effect in Commodities/04 References.html b/04 Strategy Library/29 Term Structure Effect in Commodities/04 References.html new file mode 100644 index 0000000..149276a --- /dev/null +++ b/04 Strategy Library/29 Term Structure Effect in Commodities/04 References.html @@ -0,0 +1,9 @@ + ++ This algorithm will combine the term structure effect and + the momentum effect to exploit the trading signals in commodity futures. + The momentum strategy goes long commodity futures with the highest one-month momentum and shorts on futures with the lowest one-month momentum. Signals are based on the historical return. + While the portfolio in term structure strategy is created with futures contracts in deep contango and backwardation. It goes long commodities with the highest roll-returns and short commodities with the lowest roll-returns and holds the long-short positions for one month. +
diff --git a/04 Strategy Library/30 Momentum Effect Combined with Term Structure in Commodities/02 Method.html b/04 Strategy Library/30 Momentum Effect Combined with Term Structure in Commodities/02 Method.html new file mode 100644 index 0000000..59d56bb --- /dev/null +++ b/04 Strategy Library/30 Momentum Effect Combined with Term Structure in Commodities/02 Method.html @@ -0,0 +1,62 @@ +
+ The universe is created with 22 commodity futures. For multiple commodities, we save the future chain of each commodity in dictionary self.chains.
+ First, we compute the roll-returns at the start of each month and sort the roll-return list. 1/3 breakpoints are used to split the cross-section of futures contracts into 3 portfolios, labeled Low, Med and High. For the formula of the roll-return, please see Term Structure Effect in Commodities.
+ Contracts fall into Med level are eliminated from the universe. Next we'll calculate the mean return of contracts in High and Low.
+
+roll_return = {}
+for symbol, chain in self.chains.items():
+ contracts = sorted(chain, key = lambda x: x.Expiry)
+ expiry_nearest = contracts[0].Expiry
+ price_nearest = float(contracts[0].LastPrice) if contracts[0].LastPrice>0 else 0.5*float(contracts[0].AskPrice+contracts[0].BidPrice)
+ for x in contracts[1:]:
+ roll_return[x] = (price_nearest-float(x.LastPrice))*365 / (x.Expiry-expiry_nearest).days
+sorted_by_roll_return = sorted(roll_return, key = lambda x: roll_return[x], reverse =True)
+tertile = floor(1/3*len(sorted_by_roll_return))
+high = sorted_by_roll_return[:tertile]
+low = sorted_by_roll_return[-tertile:]
+
++ The second filter is the historical mean return. We sort the contracts in the High portfolio into two sub-portfolios (High-Winner and High-Loser) based on the mean return of the commodities over the past one month. +High-Winner is thus made of the commodities that have both the highest roll-returns at the time of portfolio construction and the best past performance. +Similarly, we sort the commodities in the Low portfolio into two sub-portfolios (Low-Winner and Low-Loser) based on their mean return over the past one months. Low-Loser contains, therefore, commodities that have both the lowest roll-returns at the time of portfolio construction and the worst past performance. +
+
+mean_return_high = {}
+for i in high:
+ hist = self.History(i.Symbol, timedelta(days = 21), Resolution.Minute)
+ if hist.empty:
+ continue
+ hist_close = hist['close'][i.Expiry][i.Symbol.Value]
+ mean_return_high[i] = np.mean(hist_close.pct_change())
+high_winners = sorted(mean_return_high, key = lambda x: mean_return_high[x], reverse=True)[:int(len(high)*0.5)]
+
+mean_return_low = {}
+for i in low:
+ hist = self.History(i.Symbol, timedelta(days = 21), Resolution.Minute)
+ if hist.empty:
+ continue
+ hist_close = hist['close'][i.Expiry][i.Symbol.Value]
+ mean_return_low[i] = np.mean(hist_close.pct_change())
+low_losers = sorted(mean_return_low, key = lambda x: mean_return_low[x], reverse=True)[-int(len(low)*0.5):]
+
++The combined strategy buys the High-Winner portfolio, shorts the Low-Loser portfolio and holds this position for one month. At the start of the next month, the strategy liquidates the contracts invested and rebalances the portfolio. +
++short_weight = 0.5/len(low_losers) +for short in low_losers: + self.SetHoldings(short.Symbol, -short_weight) + +long_weight = 0.5/len(high_winners) +for long in high_winners: + self.SetHoldings(long.Symbol, long_weight) ++
+ Book-to-market ratio is used to find the value of a company by comparing the book value of a firm to its market value. The definition of the book-to-market ratio is + \[Book\ to\ Market \ Ratio=\frac{Common\ Shareholders \ Equity}{Market \ Cap}=\frac{book \ value \ per \ share}{Market \ price \ per \ share}\] + Book value represents a company's assets minus its liabilities and sometimes is referred to as shareholders' equity. + Price-to-Book Ratio is defined as + \[Price \ to \ Book\ Ratio=\frac{Market \ price \ per \ share}{book \ value \ per \ share}\] + Therefore, we can see the Book-to-market ratio is the inverse of the P/B ratio. + The book-to-market ratio suggests how much investors are paying against each dollar of book value in the balance sheet. + The bigger the ratio is, the more fundamentally cheap is the investigated company. This algorithm will create the portfolio with this factor. +
diff --git a/04 Strategy Library/31 Book-to-Market Value Anomaly/02 Method.html b/04 Strategy Library/31 Book-to-Market Value Anomaly/02 Method.html new file mode 100644 index 0000000..2af5ef5 --- /dev/null +++ b/04 Strategy Library/31 Book-to-Market Value Anomaly/02 Method.html @@ -0,0 +1,27 @@ +
+ To construct the universe, first we eliminate stocks which don't have fundmental data. In FineSelectionFunction,
+ we calculate the market cap with PE ratio, earning per shares and shares outstanding and assign the property MarketCap
+ to each fine fundamental object. The universe is narrowed to top 20% companies with the highest market cap.
+
+ According to the algorithm, the portfolio is weighted based on market cap. We calculate the weight in FineSelectionFunction and save
+ them in self.weights.
+
+fine = [x for x in fine if (x.ValuationRatios.PBRatio > 0)]
+for i in fine:
+ i.MarketCap = float(i.EarningReports.BasicAverageShares.ThreeMonths * (i.EarningReports.BasicEPS.TwelveMonths*i.ValuationRatios.PERatio))
+top_market_cap = sorted(fine, key = lambda x:x.MarketCap, reverse=True)[:int(len(fine)*0.2)]
+top_bm = sorted(top_market_cap, key = lambda x: 1 / x.ValuationRatios.PBRatio, reverse=True)[:int(len(top_market_cap)*0.2)]
+self.sorted_by_bm = [i.Symbol for i in top_bm]
+total_market_cap = np.sum([i.MarketCap for i in top_bm])
+self.weights = {}
+for i in top_bm:
+ self.weights[str(i.Symbol)] = i.MarketCap/total_market_cap
+return self.sorted_by_bm
+
++In the next step, we sort the stocks with the inverse of P/B ratio by descending order. Quintile portfolios are then formed based on the Book-to-Market ratio and the highest quintile is held for one year. +
diff --git a/04 Strategy Library/31 Book-to-Market Value Anomaly/03 Algorithm.html b/04 Strategy Library/31 Book-to-Market Value Anomaly/03 Algorithm.html new file mode 100644 index 0000000..9029e2c --- /dev/null +++ b/04 Strategy Library/31 Book-to-Market Value Anomaly/03 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/31 Book-to-Market Value Anomaly/04 Summary.html b/04 Strategy Library/31 Book-to-Market Value Anomaly/04 Summary.html new file mode 100644 index 0000000..7d4d947 --- /dev/null +++ b/04 Strategy Library/31 Book-to-Market Value Anomaly/04 Summary.html @@ -0,0 +1,9 @@ ++The portfolio underperforms relatively to the benchmark, S&P 500, during the backtest period. +
++In general, stocks that have a low B/P ratio are considered to be value stocks, and similarly, stocks that have a high B/P ratio are referred to as growth stocks. +
++During a bull market, which is associated with high GDP growth, value stocks tend to underperform growth stocks, as investors are optimistic about future earnings growth. +
diff --git a/04 Strategy Library/31 Book-to-Market Value Anomaly/05 Source.html b/04 Strategy Library/31 Book-to-Market Value Anomaly/05 Source.html new file mode 100644 index 0000000..cd8d0fa --- /dev/null +++ b/04 Strategy Library/31 Book-to-Market Value Anomaly/05 Source.html @@ -0,0 +1,5 @@ + diff --git a/04 Strategy Library/32 Gold Market Timing/01 Introduction.html b/04 Strategy Library/32 Gold Market Timing/01 Introduction.html new file mode 100644 index 0000000..af1149d --- /dev/null +++ b/04 Strategy Library/32 Gold Market Timing/01 Introduction.html @@ -0,0 +1,3 @@ ++Gold plays an essential role as a diversifier due to its low or negative correlation to other asset classes. We explore "The Fed Model," a theory that bonds can be used to judge whether the U.S. stock market is fairly valued and use this to determine entry and exit points for gold. +
diff --git a/04 Strategy Library/32 Gold Market Timing/02 Method.html b/04 Strategy Library/32 Gold Market Timing/02 Method.html new file mode 100644 index 0000000..7aaeaaf --- /dev/null +++ b/04 Strategy Library/32 Gold Market Timing/02 Method.html @@ -0,0 +1,54 @@ ++ Historically, the S&P 500 earning yield has a strong correlation with the 10-year Treasury note. There is the theory that if the forward earnings yield of the S&P 500 is higher than the 10-year government bond yield, stocks are undervalued and vice versa. +
++ We import the custom fundamental data of government 10-year bond yield and S&P 500 earnings yield from Quandl. +
++# United States Government 10-Year Bond Yield +self.bond_yield = "YC/USA10Y" +# S&P 500 Earnings Yield. Earnings Yield = trailing 12 month earnings divided by index price +self.earnings_yield = "MULTPL/SP500_EARNINGS_YIELD_MONTH" +# Gold Prices (Daily) - Currency USD (All values are national currency units per troy ounce) +self.gold = "WGC/GOLD_DAILY_USD" +# Add custom quandl data +self.AddData(QuandlRate, self.bond_yield, Resolution.Daily, DateTimeZone.Utc, True) +self.AddData(QuandlValue, self.earnings_yield, Resolution.Daily, DateTimeZone.Utc, True) +self.AddData(QuandlValue, self.gold, Resolution.Daily, DateTimeZone.Utc, True) ++
+ With gold having a strong negative correlation to equity valuations, then gold prices will rise along with earnings yield, bond yield, and inflation. Taking the above relationship a step further, this algorithm goes long gold when the Fed model shows the market undervalued otherwise liquidate the portfolio. The undervalued market is defined as the earning yield is higher than the bond yield and their ratio is at least 2. Rebalancing is done on a monthly basis. +
++def Rebalance(self): + if self.Securities[self.earnings_yield].Price == 0 or self.Securities[self.bond_yield].Price == 0: return + # Buy gold if E/P is higher than the bond yield and their ratio is at least 2 + if self.Securities[self.earnings_yield].Price > self.Securities[self.bond_yield].Price * Decimal(2): + self.SetHoldings(self.gold, 0.9) + else: + self.Liquidate() ++
+ To demonstrate the relationship between government 10-year bond yield and S&P 500 earnings yield, we plot the two series in equity chart. +
+
+def Initialize(self):
+ yieldPlot = Chart("Yield Plot")
+ yieldPlot.AddSeries(Series("BondYield", SeriesType.Line, 0))
+ yieldPlot.AddSeries(Series("EarningsYield", SeriesType.Line, 0))
+ self.AddChart(yieldPlot)
+def OnData(self, data):
+ if data.ContainsKey(self.bond_yield) and data.ContainsKey(self.earnings_yield):
+ self.Plot("Yield Plot", "BondYield", data[self.bond_yield].Price)
+ self.Plot("Yield Plot", "EarningsYield", data[self.earnings_yield].Price)
+
++ Paired switching is a strategy where in its simplest form, investors pick two assets that are negatively correlated and periodically switch position based on their relative performance. The idea behind this strategy is that if the assets are negatively correlated, then a traditional mixed portfolio might lead to a lower return than the return for the individual assets. If the negative correlation exists, switching positions could improve the performance of a portfolio where two assets are statically weighted. +
\ No newline at end of file diff --git a/04 Strategy Library/33 Paired Switching/02 Method.html b/04 Strategy Library/33 Paired Switching/02 Method.html new file mode 100644 index 0000000..61d91f6 --- /dev/null +++ b/04 Strategy Library/33 Paired Switching/02 Method.html @@ -0,0 +1,26 @@ ++ After two negatively correlated assets are determined, we will analyze them on a quarterly basis. The analysis will consist of retrieving historical prices for the two assets and calculating their performances over the prior quarter. We will buy the asset that yields a higher return during the period. The position is held for one quarter, and then the analysis is repeated. +
++ def Rebalance(self): + self.months +=1 + if(self.months%3==0): + history_call = self.History(self.Securities.Keys,timedelta(days=90)) + if not history_call.empty: + first_bars = history_call.loc[self.first.Symbol.Value] + last_p1 = first_bars["close"].iloc[0] + second_bars = history_call.loc[self.second.Symbol.Value] + last_p2 = second_bars["close"].iloc[0] + first_performance = (float(self.Securities[self.first.Symbol].Price) - float(last_p1))/(float(self.Securities[self.first.Symbol].Price)) + second_performance = (float(self.Securities[self.second.Symbol].Price) - float(last_p2))/(float(self.Securities[self.second.Symbol].Price)) + if(first_performance > second_performance): + if(self.Securities[self.second.Symbol].Invested==True): + self.Liquidate(self.second.Symbol) + self.SetHoldings(self.first.Symbol,1) + else: + if(self.Securities[self.first.Symbol].Invested==True): + self.Liquidate(self.first.Symbol) + self.SetHoldings(self.second.Symbol,1) ++
+ Momentum effect is an anomaly in nearly every market. However, if a stock in the winner group is in the final stages of overreaction, it is not the best long opportunity because of the high probability of its reversal, and therefore profit reduction. Similarly, in the loser group, a stock which is in the final stages of overreaction is also not the best short opportunity because its reversal would lower the profit of short selling within a short time. Based on this logic, + this momentum-reversal strategy seeks to buy winners and sell losers that are less likely to be in the final stages of overreaction. +
diff --git a/04 Strategy Library/34 Momentum-Short Term Reversal Strategy/02 Method.html b/04 Strategy Library/34 Momentum-Short Term Reversal Strategy/02 Method.html new file mode 100644 index 0000000..522b29b --- /dev/null +++ b/04 Strategy Library/34 Momentum-Short Term Reversal Strategy/02 Method.html @@ -0,0 +1,88 @@ ++ All stocks on NYSE and NASDAQ are used as the investment universe. We create a class to save all variables for each symbol. +
++class SymbolData: + def __init__(self, symbol): + self.symbol = symbol + self.window = RollingWindow[float](13) + self.GARR_ratio = None + self.yearly_return = None ++
+ To get the value for the above variables, we save the stock price at the start of each month in the rolling window for the last 12 months and calculate the monthly return and the yearly return. + Then we can compute the last month's geometric average rate of return (GARR) and the previous 12-month GARR. The formulas are as follows +
+\[GARR_{last\ 12\ months}=(1+R_1)^{1/12}\cdot(1+R_2)^{1/12}\cdot\cdot\cdot(1+R_{11})^{1/12}\cdot(1+R_{12})^{1/12}-1\] +\[GARR_{last\ months}=(1+R_{last\ month})^{1/12}-1\] + +
+ We assign the value of two returns to each symbol in SymbolData class. All stocks are sorted based on their past 12-month return.
+ Stocks are then divided into 3 portfolios (top 30% - winner group, middle 40% and bottom 30% - loser group). In the winner group, stocks are further
+ classified into two categories: the return-increasing winner and return-decreasing winner using the ratio of last month's geometric average rate of return (GARR) over the last 12 month GARR.
+
+def CoarseSelectionFunction(self, coarse): + if self.month_start: + self.coarse = True + coarse = [i for i in coarse if i.AdjustedPrice > 10] + for i in coarse: + if i.Symbol not in self.SymbolPrice: + self.SymbolPrice[i.Symbol] = SymbolData(i.Symbol) + self.SymbolPrice[i.Symbol].window.Add(float(i.AdjustedPrice)) + if self.SymbolPrice[i.Symbol].window.IsReady: + price = np.array([i for i in self.SymbolPrice[i.Symbol].window]) + returns = (price[:-1]-price[1:])/price[1:] + self.SymbolPrice[i.Symbol].yearly_return = (price[0]-price[-1])/price[-1] + GARR_12 = np.prod([(1+i)**(1/12) for i in returns])-1 + GARR_1 = (1+returns[0])**(1/12)-1 + self.SymbolPrice[i.Symbol].GARR_ratio = GARR_1 / GARR_12 ++
+ The decreasing-return winner group contains 13 stocks in winner group with the lowest GARR Ratio and vice-versa for the increasing-return winner group. + The loser group is divided into the increasing-return loser and the decreasing-return loser groups using a similar methodology. The return-increasing loser group + contains 15 stocks in loser group with the highest GARR Ratio. +
+
+ReadySymbolPrice = {symbol: SymbolData for symbol, SymbolData in self.SymbolPrice.items() if SymbolData.window.IsReady}
+if ReadySymbolPrice and len(ReadySymbolPrice)>50:
+ # sort stocks in coarse by last 12-month return
+ sorted_by_return = sorted(ReadySymbolPrice, key = lambda x: ReadySymbolPrice[x].yearly_return)
+ # top 30% with the highest 12-month return goes into winner group
+ winner = sorted_by_return[:int(len(sorted_by_return)*0.3)]
+ # bottom 30% with the lowest 12-month return goes into loser group
+ loser = sorted_by_return[-int(len(sorted_by_return)*0.3):]
+ self.decrease_winner = sorted(winner, key = lambda x: ReadySymbolPrice[x].GARR_ratio)[:15]
+ self.increase_loser = sorted(loser, key = lambda x: ReadySymbolPrice[x].GARR_ratio)[-15:]
+ return self.decrease_winner+self.increase_loser
+
++The algorithm goes long stocks from the decreasing-return winner group and short stocks from the increasing-return loser group. The portfolio is created as equally weighted and rebalanced on a monthly basis. +
++def OnData(self, data): + if self.month_start and self.coarse: + self.month_start = False + self.coarse = False + if all([self.decrease_winner, self.increase_loser]): + stocks_invested = [x.Key for x in self.Portfolio] + for i in stocks_invested: + if i not in self.decrease_winner+self.increase_loser: + self.Liquidate(i) + short_weight = 0.5/len(self.increase_loser) + for j in self.increase_loser: + self.SetHoldings(j, -short_weight) + long_weight = 0.5/len(self.decrease_winner) + for i in self.decrease_winner: + self.SetHoldings(i, long_weight) ++
+ The turn of the month is an effect on stock indices which states that stocks will rise during the last day before the end of the month and the first three days of each month. Researchers believe this significance comes as a result of pension funds receiving cash flows and reinvesting in the market, along with this period being a natural point for portfolio rebalancing between retail and professional investors. This algorithm is an approximation of the following strategy. +
diff --git a/04 Strategy Library/35 Turn of the Month in Equity Indexes/02 Method.html b/04 Strategy Library/35 Turn of the Month in Equity Indexes/02 Method.html new file mode 100644 index 0000000..2f57e97 --- /dev/null +++ b/04 Strategy Library/35 Turn of the Month in Equity Indexes/02 Method.html @@ -0,0 +1,28 @@ +
+ We start by creating a scheduled event, MonthEnd(), that will trigger the algorithm to buy SPY.
+
self.Schedule.On( + self.DateRules.MonthEnd(self.spy), + self.TimeRules.AfterMarketOpen(self.spy, 1), + self.Purchase) ++
+ We will purchase the SPY immediately, and we will wait 3 trading days, as suggested, before liquidating our portfolio. The boolean self.Portfolio.Invested will help us wait 3 days before executing the liquidate order in OnData(). The equity index is bought and sold every month.
+
def Purchase(self): + ''' Immediately purchases the ETF at market opening ''' + self.SetHoldings(self.spy, 1) + self.days = 0 + +def OnData(self, data): + if self.Portfolio.Invested: + self.days += 1 + + # Liquidates after 3 days + if self.days > 3: + self.Liquidate(self.spy, 'Liquidate after 3 days') ++
+ The relationship between return and risk has long been a popular topic for research. Investors have been seeking financial models that quantify risk and use it to estimate the expected return on equity. The Fama French five-factor model, improved from the Fama French three-factor model, is one of the most classic models (Fama and French, 2015). In this post, we will discuss this model and develop a stock-picking strategy based on it. +
\ No newline at end of file diff --git a/04 Strategy Library/353 Fama French Five Factors/02 Method.html b/04 Strategy Library/353 Fama French Five Factors/02 Method.html new file mode 100644 index 0000000..1fd2f52 --- /dev/null +++ b/04 Strategy Library/353 Fama French Five Factors/02 Method.html @@ -0,0 +1,93 @@ ++ The Fama French five-factor model was proposed in 2014 and is adapted from the Fama French three-factor model (Fama and French, 2015). It builds upon the dividend discount model which states that the value of stocks today is dependent upon future dividends. + Fama and French add two factors, investment and profitability, to the dividend discount model to better capture the relationship between risk and return. + The model is as follows +
+\[ R = \alpha + \beta_m MKT + \beta_s SMB + \beta_h HML + \beta_r RMW + \beta_c CMA\] + ++where +
++ Taking inspiration from the Fama French five-factor model, we can develop a multi-factor stock selection strategy that focuses on five factors: size, value, quality, profitability, and investment pattern. +
+ ++ First, we run a Coarse Selection to drop equities which have no fundamental data or have too low prices. Then we select those with the highest dollar volume. + Note that a useful technique is used here: we can use Universe.Unchanged to remain the same universe when there is no necessary change, which greatly speeds up the backtest. +
+ ++def CoarseSelectionFunction(self, coarse): + '''Drop securities which have no fundamental data or have too low prices. + Select those with highest by dollar volume''' + + if self.Time < self.nextLiquidate: + return Universe.Unchanged + + selected = sorted([x for x in coarse if x.HasFundamentalData and x.Price > 5], + key=lambda x: x.DollarVolume, reverse=True) + + return [x.Symbol for x in selected[:self.num_coarse]] ++
+ Secondly, in Fine Selection, we use the terms TotalEquity, BookValuePerShare, OperationProfitMargin, ROE, and TotalAssetsGrowth to account for the five factors, respectively. We then calculate a custom ranking metric for each stock using these five terms. Our algorithm will go long in the five stocks with the highest scores and short the five stocks with the lowest scores. +
+
+def FineSelectionFunction(self, fine):
+ '''Select securities with highest score on Fama French 5 factors'''
+
+ # Select stocks with these 5 factors:
+ # MKT -- Book value per share: Value
+ # SMB -- TotalEquity: Size
+ # HML -- Operation profit margin: Quality
+ # RMW -- ROE: Profitability
+ # CMA -- TotalAssetsGrowth: Investment Pattern
+ filtered = [x for x in fine if x.ValuationRatios.BookValuePerShare
+ and x.FinancialStatements.BalanceSheet.TotalEquity
+ and x.OperationRatios.OperationMargin.Value
+ and x.OperationRatios.ROE
+ and x.OperationRatios.TotalAssetsGrowth]
+
+ # Sort by factors
+ sortedByMkt = sorted(filtered, key=lambda x: x.ValuationRatios.BookValuePerShare, reverse=True)
+ sortedBySmb = sorted(filtered, key=lambda x: x.FinancialStatements.BalanceSheet.TotalEquity.Value, reverse=True)
+ sortedByHml = sorted(filtered, key=lambda x: x.OperationRatios.OperationMargin.Value, reverse=True)
+ sortedByRmw = sorted(filtered, key=lambda x: x.OperationRatios.ROE.Value, reverse=True)
+ sortedByCma = sorted(filtered, key=lambda x: x.OperationRatios.TotalAssetsGrowth.Value, reverse=False)
+
+ stockBySymbol = {}
+
+ # Get the rank based on 5 factors for every stock
+ for index, stock in enumerate(sortedByMkt):
+ mktRank = self.beta_m * index
+ smbRank = self.beta_s * sortedBySmb.index(stock)
+ hmlRank = self.beta_h * sortedByHml.index(stock)
+ rmwRank = self.beta_r * sortedByRmw.index(stock)
+ cmaRank = self.beta_c * sortedByCma.index(stock)
+ avgRank = np.mean([mktRank,smbRank,hmlRank,rmwRank,cmaRank])
+ stockBySymbol[stock.Symbol] = avgRank
+
+ sorted_dict = sorted(stockBySymbol.items(), key = lambda x: x[1], reverse = True)
+ symbols = [x[0] for x in sorted_dict]
+
+ # Pick the stocks with the highest scores to long
+ self.longSymbols= symbols[:self.num_long]
+ # Pick the stocks with the lowest scores to short
+ self.shortSymbols = symbols[-self.num_short:]
+
+ return self.longSymbols + self.shortSymbols
+
++ In this example, the portfolio is rebalanced every 30 days and the backtest period runs from Jan 2010 to Aug 2019. You can improve upon this strategy by changing the fundamental factors, the weight of each factor and the rebalance frequency. +
+ ++ The Fama French five-factor model provides a scientific way to measure asset pricing. For the five aspects that Fama and French mentioned, we used one possible combination in our backtest. We can see from the results that it achieves an annual rate of return around 5% with a max drawdown of 30% over 8 years. + These factors perhaps cannot capture a sufficient amount of information on the assets' pricing, and therefore, there are still many aspects can be improved (e.g. the weights of factors, a different set of factors for different kinds of equities,etc.) We encourage you to explore and create better algorithms upon this tutorial! +
\ No newline at end of file diff --git a/04 Strategy Library/353 Fama French Five Factors/04 Algorithm.html b/04 Strategy Library/353 Fama French Five Factors/04 Algorithm.html new file mode 100644 index 0000000..f3cdbee --- /dev/null +++ b/04 Strategy Library/353 Fama French Five Factors/04 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/353 Fama French Five Factors/05 References.html b/04 Strategy Library/353 Fama French Five Factors/05 References.html new file mode 100644 index 0000000..4a09697 --- /dev/null +++ b/04 Strategy Library/353 Fama French Five Factors/05 References.html @@ -0,0 +1,5 @@ + \ No newline at end of file diff --git a/04 Strategy Library/354 Expected Idiosyncratic Skewness/01 Abstract.html b/04 Strategy Library/354 Expected Idiosyncratic Skewness/01 Abstract.html new file mode 100644 index 0000000..ffa6192 --- /dev/null +++ b/04 Strategy Library/354 Expected Idiosyncratic Skewness/01 Abstract.html @@ -0,0 +1,3 @@ ++ This tutorial implements a strategy that trades stocks with low expected idiosyncratic skewness based on a paper by Boyer, Mitton and Vorkink (2009, hereafter BMV) published in The Review of Financial Studies. Our implementation narrows down our initial universe to liquid assets by selecting 200 stocks based on daily trading volume, price and whether the stock has fundamental data in our data library. We calculate the expected idiosyncratic skewness at the end of each month and sort our universe based on the calculated skewness. This implementation will long the bottom 5%, hold for the next month, and rebalance the portfolio monthly. The Sharpe ratio is 1.03 relative to S&P 500 (SPY) Sharpe ratio of 1.00 during the period of July 1, 2009 to July 30, 2019. +
\ No newline at end of file diff --git a/04 Strategy Library/354 Expected Idiosyncratic Skewness/02 Theory.html b/04 Strategy Library/354 Expected Idiosyncratic Skewness/02 Theory.html new file mode 100644 index 0000000..b49f79e --- /dev/null +++ b/04 Strategy Library/354 Expected Idiosyncratic Skewness/02 Theory.html @@ -0,0 +1,7 @@ ++ BMV tests recent theories that stocks with low idiosyncratic skewness should have high expected returns. For example, Mitton and Vorkink (2007) develop a model that some investors ("lotto investors") have a preference for positive skewness while others ("traditional investors") are mean-variance optimizers seeking to maximize the Sharpe ratio of their portfolios. Lotto investors accept lower average returns on stocks with high idiosyncratic skewness because they have a preference for stocks with lottery-like return properties. In equilibrium, markets clear at prices such that stocks with high idiosyncratic skewness have low expected returns, due to the different portfolio preferences of the two groups of investors. +
+ ++ Despite the theoretical basis for the pricing effects of skewness preference, empirically testing the relation is not straightforward as expected skewness is difficult to measure. BMV accounts for the phenomenon that lagged skewness alone does not adequately forecast skewness by presenting a cross-sectional model of expected skewness using additional predictive variables. Using their model, they reaffirm the existing theory that expected idiosyncratic skewness and returns are negatively correlated. Notably, they find the Fama-French alpha of a low-expected-skewness quintile exceeds the alpha of a high-expected-skewness quintile by 1.00% per month. Furthermore, the Fama-MacBeth cross-sectional regressions have statistically significant, negative coefficients. Besides, BMV finds that the expected skewness helps explain how stocks with low idiosyncratic volatility have high expected returns. +
\ No newline at end of file diff --git a/04 Strategy Library/354 Expected Idiosyncratic Skewness/03 Data Description.html b/04 Strategy Library/354 Expected Idiosyncratic Skewness/03 Data Description.html new file mode 100644 index 0000000..31483b2 --- /dev/null +++ b/04 Strategy Library/354 Expected Idiosyncratic Skewness/03 Data Description.html @@ -0,0 +1,3 @@ ++ To execute our algorithm, we will use daily data from Kenneth French's Data Library that captures the Fama-French three factors for the period July 1, 2009 to June 30, 2019. The raw data is delivered in a zip file which is not directly importable into LEAN. We need to unzip the file and upload the CSV to a Github repository. All other data used for this algorithm, including stock price, volume, and market capitalization, are from QuantConnect's Data Library. In the original paper, BSV also includes firm-specific variables like momentum, turnover, and dummies of properties including Nasdaq-listed stocks, small-size, medium-size, industries. We can refer to this online technical appendix for descriptions of these variables. +
\ No newline at end of file diff --git a/04 Strategy Library/354 Expected Idiosyncratic Skewness/04 Method.html b/04 Strategy Library/354 Expected Idiosyncratic Skewness/04 Method.html new file mode 100644 index 0000000..fa80957 --- /dev/null +++ b/04 Strategy Library/354 Expected Idiosyncratic Skewness/04 Method.html @@ -0,0 +1,50 @@ ++ We can develop a model of estimated expected idiosyncratic skewness using Fama-French three factors. Lower expected idiosyncratic skewness will predict a higher alpha. We will let the investment horizon over which investors are hoping to experience an extreme positive outcome be 1 month. And, let S(t) denote the set of trading days in the current month, and let N(t) denote the number of days in this set. +
+ ++ Let \(\epsilon_{i,d}\) be the regression residual using the Fama and French (1993) three-factor model on day d for firm i, where the regression coefficients that define this residual are estimated using daily data for days in S(t) as the time-series regression below. +
+ +\[R_{i,d} - R_{f,d} = \alpha_i + \beta_i [R_{M,d} - R_{f,d}] + s_i SMB_{d} + h_i HML_{d} + \epsilon_{i,d}\] + ++ for all day \(d \in S(t)\) and each \(i = 1,2,\dots,N\). +
+ ++ Let \(iv_{i,t}\) and \(is_{i,t}\) denote historical estimates of idiosyncratic volatility and skewness (respectively) for firm i using daily data for all days in S(t). We can then define \(iv_{i,t}\) and \(is_{i,t}\) as: +
+ +\[iv_{i,t} = \left( \frac{1}{N(t) - 1} \sum_{d\in S(t)} \epsilon_{i,d}^2 \right)^{1/2}\] + +\[is_{i,t} = \frac{1}{N(t) - 2} \frac{ \sum_{d\in S(t)} \epsilon_{i,d}^3 } { iv_{i,t}^{3/2} }\] + ++ We need measures of expected skewness over a horizon of 1 month for firm i at the end of month t, \(E_t[is_{i,t+1}]\), rather than measures of historical skewness as defined in equation above. To model investor perceptions of expected skewness in a feasible manner, we first estimate cross-sectional regression separately at the end of each month t in our sample, +
+ +\[is_{i,t} = \beta_0^t + \beta_1^t is_{i,t-1} + \beta_2^t iv_{i,t-1} + \varepsilon_{i,t}\] + ++ Superscripts on regression parameters are included to emphasize that we estimate these parameters using information observable at the end of month t. We then use the regression parameters from equation above, along with information observable at the end of each month t, to estimate expected skewness for each firm, +
+ +\[ E_t[is_{i,t+1}] = \beta_0^t + \beta_1^t is_{i,t} + \beta_2^t iv_{i,t} \] + ++ This approach provides feasible estimates of each month's expected skewness and accounts for variation between historical moments and expected skewness across time. +
+ ++ At the end of each month, we use the results of equation above to sort stocks by expected idiosyncratic skewness. We construct our universe using the lowest 5% of expected skewness, and long our assets to construct a value-weighted portfolio. +
+ diff --git a/04 Strategy Library/354 Expected Idiosyncratic Skewness/05 Conclusion and Future Work.html b/04 Strategy Library/354 Expected Idiosyncratic Skewness/05 Conclusion and Future Work.html new file mode 100644 index 0000000..0252ef9 --- /dev/null +++ b/04 Strategy Library/354 Expected Idiosyncratic Skewness/05 Conclusion and Future Work.html @@ -0,0 +1,13 @@ ++ Before the BMV paper was published in 2009, a number of theories on the pricing premium for stocks with idiosyncratic skewness existed, but lacked supporting empirical evidence of the relationship between idiosyncratic skewness and returns. BMV fills this void by estimating a model of predicted skewness and using predicted skewness to explain the cross-section of returns. The paper finds that lagged idiosyncratic volatility is a stronger predictor of skewness than lagged idiosyncratic skewness. +
+ ++ In this implementation, we rely on idiosyncratic volatility and skewness to predict idiosyncratic skewness. Interested users can build from this implementation by trying the following extensions: +
+ ++ This tutorial implements a strategy that standardizes the unexpected earnings of stocks and trades the top 5% of those standardized stocks. It is written based on a paper published in The Accounting Review by Foster, Olsen, and Shevlin (1984). Our implementation narrows down our universe to 1000 liquid assets based on daily trading volume and price, and the availability of fundamental data on the stocks in our data library. We calculate the unexpected earnings at the beginning of each month, standardize the unexpected earnings, go long on the top 5%, and rebalance the portfolio monthly. We observed a Sharpe ratio of 0.83 relative to SPY Sharpe of 0.88 using this implementation during the period of December 1, 2009 to September 1, 2019 in backtesting. +
\ No newline at end of file diff --git a/04 Strategy Library/355 Standardized Unexpected Earnings/02 Theory.html b/04 Strategy Library/355 Standardized Unexpected Earnings/02 Theory.html new file mode 100644 index 0000000..0179e8b --- /dev/null +++ b/04 Strategy Library/355 Standardized Unexpected Earnings/02 Theory.html @@ -0,0 +1,3 @@ ++ In market efficiency literature, one frequently discussed topic is the anomalous behavior of stock returns following earnings announcements. The market does not adjust to news from earning announcements instantaneously. Instead, many studies report evidence that the direction and magnitude of returns in the post-earnings announcement period are positively correlated with the direction and magnitude of the unexpected component in the earnings releases. This observed phenomenon is consistent with suggestions that the capital market is inefficient. +
\ No newline at end of file diff --git a/04 Strategy Library/355 Standardized Unexpected Earnings/03 Method.html b/04 Strategy Library/355 Standardized Unexpected Earnings/03 Method.html new file mode 100644 index 0000000..a1b3ba6 --- /dev/null +++ b/04 Strategy Library/355 Standardized Unexpected Earnings/03 Method.html @@ -0,0 +1,125 @@ ++ Unexpected earnings, or earnings surprise, is the difference between reported earnings and the expected earnings of a firm. Expected earnings is calculated using a combination of analyst forecasts and mathematical models based on earnings of previous periods. In this tutorial, we use standardized unexpected earnings (SUE) to measure earnings surprise. SUE's numerator is the change in quarterly earnings per share (EPS) from EPS four quarters ago. Its denominator is the standard deviation of a series of deltas each calculated by subtracting EPS at quarter q-4 from EPS at quarter q. It can be formulated as +
+ +\[ + SUE_q = \frac{ EPS_q - EPS_{q-4} }{ \sigma( EPS_q - EPS_{q-4} ) } +\] + ++ where \(\sigma(X)\) is the standard deviation of X, EPS a firm's quarterly earnings per share, q the current quarter, and q-4 four quarters ago. Keep in mind that although we use quarterly EPS data, the portfolio rebalances monthly. Additionally, note that SUE's stock ranking changes month to month because each company's earnings announcement release date for the quarter differs (i.e., firm A's Q3 announcement may come out in August while firm B's Q3 announcement comes out in September). +
+ + ++ We use a coarse selection filter to narrow down the universe to 1000 stocks at the beginning of each month according to dollar volume, price and whether the stock has fundamental data in our data library. +
+ +def CoarseSelectionFunction(self, coarse): + '''Get dynamic coarse universe to be further selected in fine selection + ''' + # Before next rebalance time, keep the current universe unchanged + if self.Time < self.next_rebalance: + return Universe.Unchanged + + ### Run the coarse selection to narrow down the universe + # Filter stocks by price and whether they have fundamental data + # Then, sort descendingly by daily dollar volume + sorted_by_volume = sorted([ x for x in coarse if x.HasFundamentalData and x.Price > 5 ], + key = lambda x: x.DollarVolume, reverse = True) + self.new_fine = [ x.Symbol for x in sorted_by_volume[:self.num_coarse] ] + + # Return all symbols that have appeared in Coarse Selection + return list( set(self.new_fine).union( set(self.eps_by_symbol.keys()) ) ) ++
+ Next we use a fine universe selection filter to extract quarterly EPS data and save it in a rolling window for each stock. We don't trade during the first 36-month warm-up period because the window is not ready yet. After the warm-up period, we can calculate quarterly EPS change from four quarters ago and the standard deviation of the change over the prior eight quarters using historical EPS data saved in the rolling windows. Then we sort the universe and assign the top 5% of symbols to self.long. +
+ + +def FineSelectionAndSueSorting(self, fine): + '''Select symbols to trade based on sorting of SUE''' + + sue_by_symbol = dict() + + for stock in fine: + + ### Save (symbol, rolling window of EPS) pair in dictionary + if not stock.Symbol in self.eps_by_symbol: + self.eps_by_symbol[stock.Symbol] = RollingWindow[float](self.months_count) + # update rolling window for each stock + self.eps_by_symbol[stock.Symbol].Add(stock.EarningReports.BasicEPS.ThreeMonths) + + ### Calculate SUE + + if stock.Symbol in self.new_fine and self.eps_by_symbol[stock.Symbol].IsReady: + + # Calculate the EPS change from four quarters ago + rw = self.eps_by_symbol[stock.Symbol] + eps_change = rw[0] - rw[self.months_eps_change] + + # Calculate the st dev of EPS change for the prior eight quarters + new_eps_list = list(rw)[:self.months_count - self.months_eps_change:3] + old_eps_list = list(rw)[self.months_eps_change::3] + eps_std = np.std( [ new_eps - old_eps for new_eps, old_eps in + zip( new_eps_list, old_eps_list ) + ] ) + + # Get Standardized Unexpected Earnings (SUE) + sue_by_symbol[stock.Symbol] = eps_change / eps_std + + # Sort and return the top quantile + sorted_dict = sorted(sue_by_symbol.items(), key = lambda x: x[1], reverse = True) + + self.long = [ x[0] for x in sorted_dict[:math.ceil( self.top_percent * len(sorted_dict) )] ] + # If universe is empty, OnData will not be triggered, then update next rebalance time here + if not self.long: + self.next_rebalance = Expiry.EndOfMonth(self.Time) + + return self.long ++
+ Once the symbols are selected, we form an equal-weighted portfolio and place orders. Finally, we update the next rebalance time to the beginning of the next calendar month. The portfolio will be held until liquidated at next rebalance time. +
+ + +def OnSecuritiesChanged(self, changes): + '''Liquidate symbols that are removed from the dynamic universe + ''' + for security in changes.RemovedSecurities: + if security.Invested: + self.Liquidate(security.Symbol, 'Removed from universe') + + +def OnData(self, data): + '''Monthly rebalance at the beginning of each month. Form portfolio with equal weights. + ''' + # Before next rebalance, do nothing + if self.Time < self.next_rebalance or not self.long: + return + + # Placing orders (with equal weights) + equal_weight = 1 / len(self.long) + for stock in self.long: + self.SetHoldings(stock, equal_weight) + + # Rebalance at the beginning of every month + self.next_rebalance = Expiry.EndOfMonth(self.Time) ++
+ This tutorial shows that SEU is a valid indicator for earnings surprise, which can be used as a trading signal to follow post-earning announcement drifts. Our implementation generates a Sharpe ratio of 0.83 relative to SPY Sharpe ratio of 0.88. Interested users can build from this implementation by trying the following extensions: +
+ ++ In this tutorial we implement a correlation-adjusted time-series momentum strategy (TSMOM-CF) that addresses three weaknesses typically found in traditional time-series momentum strategies (TSMOM). Our implementation is based on the paper "Demystifying Time-Series Momentum Strategies: Volatility Estimators, Trading Rules and Pairwise Correlations" by Nick Baltas and Robert Kosowski. We will also compare TSMOM-CF to the basic momentum strategy implemented in our strategy library - Momentum Effect in Commodities Futures. +
\ No newline at end of file diff --git a/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/02 Introduction.html b/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/02 Introduction.html new file mode 100644 index 0000000..2130e92 --- /dev/null +++ b/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/02 Introduction.html @@ -0,0 +1,16 @@ ++ Baltas and Kosowski modify the basic momentum strategy by incorporating trend strength into the trading signal, using an efficient volatility estimator, and adding a dynamic leverage mechanism. The modifications overcome these three weaknesses: +
+ ++Baltas and Kosowski's modifications to the basic time-series momentum strategy can be summarized in the formula below: +
+ +\[r_{t,t+1}^{TSMOM-CF} = \frac{1}{N_t} \sum_{i=1}^{N_t} X_t^i \frac{\sigma_{P,tgt}}{\sigma_t^i} CF(\bar{\rho}_t)r_{t,t+1}^i\] + ++ where: +
+\[r_{t,t+1}^{TSMOM-CF} = \text{TSMOM-CF portfolio return from time t to time t+1}\] +\[N_t = \text{Number of portfolio constituents at time t}\] +\[X_t^i = \text{Trading signal value of asset i at time t}\] +\[\sigma_{P,tgt} = \text{Target level of volatility for the overall portfolio}\] +\[\sigma_t^i = \text{Estimated volatility of asset i at time t}\] +\[CF(\bar{\rho}_t) = \text{Correlation factor that adjusts the level of leverage applied to each portfolio constituents at time t}\] +\[r_{t,t+1}^i = \text{return of asset i from time t to time t+1}\] + ++ The formula shows that the weights for each portfolio constituent are dependent on three parts: +
+ + ++The TREND trading rule determines the trading signal based on the statistical strength of the realized return: +
+ + +\[ +\text{TREND}_i^{12M} \quad +\begin{cases} +1, \text{ if } t(r_{t-12,t})>+1 \\ +t(r_{t-12,t}), \text{ otherwise} \\ +-1, \text{ if } t(r_{t-12,t})<-1 \\ +\end{cases} +\] + ++where t() is the t-statistic of the daily futures log-returns over the past 12 months to scale the gross exposure to each portfolio constituents. +
+ ++When the absolute value of our t-statistic is greater than 1, the trend is highly statistically significant, so the strategy puts 100% exposure to the asset. When the t-statistic is between -1 and 1, the strength of the trend is not as significant, so the strategy scales its exposure to less than 100%. +
+ + ++ Instead of estimating each asset's volatility as the standard deviation of past close-to-close daily logarithmic returns, Baltas and Kosowski adopt a more efficient volatility estimator proposed by Yang and Zhang (2000). The formula for the Yang and Zhang volatility estimator (\(\sigma_{YZ}\)) is shown below: +
+ +\[\sigma_{YZ}^2(t) = \sigma_{OJ}^2(t) + k \sigma_{SD}^2(t) + (1-k) \sigma_{RS}^2(t)\] + ++ where: +
+ +\[\sigma_{OJ} = \text{Overnight jump estimator (standard deviation of close-to-open daily logarithmic returns)}\] +\[\sigma_{SD} = \text{Standard volatility estimator (standard deviation of close-to-close daily logarithmic returns)}\] +\[\sigma_{RS} = \text{Rogers and Satchell (1991) range estimator}\] +\[k = \text{parameter that minimizes YZ estimator variance, which is a function of the numbers of days in the estimation}\] + ++The formula for parameter k is below: +
+\[k = \frac{0.34}{1.34+\frac{N_D+1}{N_D-1}}\] + ++The Rogers and Satchell range estimator calculation is based on the following formula: +
+ +\[\sigma_{RS}^2(\tau) = h(\tau)[h(\tau)-c(\tau)]+l(\tau)[l(\tau)-c(\tau)]\] + ++ where \(h(\tau)\), \(l(\tau)\) and \(c(\tau)\) denote the logarithmic difference between the high, low and closing prices respectively with the opening price. The RS volatility of an asset at the end of month t, assuming a certain estimation period, is equal to the average daily RS volatility over this period. +
+ ++The estimation period is chosen to be 1 month, or 21 trading days, based on Baltas and Kosowski's suggestions. +
+ + ++ where: +
+ +\[N = \text{number of assets in the portfolio}\] +\[\rho_{i,j} = \text{correlation between asset i, j}\] +\[X_i = \text{trade signal of asset i}\] +\[\bar{\rho} = \text{average pairwise signed correlation for the entire portfolio}\] + diff --git a/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/04 Method.html b/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/04 Method.html new file mode 100644 index 0000000..2014718 --- /dev/null +++ b/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/04 Method.html @@ -0,0 +1,207 @@ ++ The strategy requires the continuous futures contract, so we import the custom data from Quandl. We manually create a universe of tradable commodity futures from all available commodity futures traded on CME and ICE. They are all liquid and active continuous contracts #1. The data from Quandl are non-adjusted price based on spot-month continuous contract calculations. The data resolution is daily. +
+ + ++from QuantConnect.Python import PythonQuandl +class ImprovedCommodityMomentumTrading(QCAlgorithm): + def Initialize(self): + for ticker in tickers: + data = self.AddData(QuandlFutures, ticker, Resolution.Daily) + data.SetLeverage(3) # Leverage was set to 3 for each of the futures contract +class QuandlFutures(PythonQuandl): + def __init__(self): + self.ValueColumnName = "Settle" ++
+def Initialize(self): + # Last trading date tracker to achieve rebalancing the portfolio every month + self.nextRebalance = self.Time + + # Set portfolio target level of volatility, set to 12% + self.portfolio_target_sigma = 0.12 ++
+def GetTradingSignal(self, history): + ''' + TREND Trading Signal + - Uses the t-statistics of historical daily log-returns to reflect the strength of price movement trend + - TREND Signal Conditions: + t-stat > 1 => TREND Signal = 1 + t-stat < 1 => TREND Signal = -1 + -1 < t-stat < 1 => TREND Signal = t-stat + ''' + settle = history.settle.unstack(level = 0) + + # daily futures log-returns based on close-to-close + log_returns = np.log(settle/settle.shift(1)).dropna() + + # Calculate the t-statistics as + # (mean-0)/(stdev/sqrt(n)), where n is sample size + mean = np.mean(log_returns) + std = np.std(log_returns) + n = len(log_returns) + t_stat = mean/(std/np.sqrt(n)) + + # cap holding at 1 and -1 + return np.clip(t_stat, a_max=1, a_min=-1) ++
+def GetYZVolatility(self, history, available_symbols): + ''' + Yang and Zhang 'Drift-Independent Volatility Estimation' + + Formula: sigma_YZ^2 = sigma_OJ^2 + self.k * sigma_SD^2 + (1-self.k)*sigma_RS^2 (Equation 20 in [1]) + where, sigma_OJ - (Overnight Jump Volitility estimator) + sigma_SD - (Standard Volitility estimator) + sigma_RS - (Rogers and Satchell Range Volatility estimator)''' + YZ_volatility = [] + + time_index = history.loc[available_symbols[0]].index + today = time_index[-1] + + #Calculate YZ volatility for each security and append to list + for ticker in available_symbols: + past_month_ohlc = history.loc[ticker].loc[today-timedelta(self.OneMonth):today] + open, high, low, close = past_month_ohlc.open, past_month_ohlc.high, past_month_ohlc.low, past_month_ohlc.settle + estimation_period = past_month_ohlc.shape[0] + + # Calculate constant parameter k for Yang and Zhang volatility estimator + # using the formula found in Yang and Zhang (2000) + k = 0.34 / (1.34 + (estimation_period + 1) / (estimation_period - 1)) + + # sigma_OJ (overnight jump => stdev of close-to-open log returns) + open_to_close_log_returns = np.log(open/close.shift(1)) + open_to_close_log_returns = open_to_close_log_returns[np.isfinite(open_to_close_log_returns)] + sigma_OJ = np.std(open_to_close_log_returns) + + # sigma_SD (standard deviation of close-to-close log returns) + close_to_close_log_returns = np.log(close/close.shift(1)) + close_to_close_log_returns = close_to_close_log_returns[np.isfinite(close_to_close_log_returns)] + sigma_SD = np.std(close_to_close_log_returns) + + # sigma_RS (Rogers and Satchell (1991)) + h = np.log(high/open) + l = np.log(low/open) + c = np.log(close/open) + sigma_RS_daily = (h * (h - c) + l * (l - c))**0.5 + sigma_RS_daily = sigma_RS_daily[np.isfinite(sigma_RS_daily)] + sigma_RS = np.mean(sigma_RS_daily) + + # daily Yang and Zhang volatility + sigma_YZ = np.sqrt(sigma_OJ**2 + k * sigma_SD**2 + (1 - k) * sigma_RS**2) + + # append annualized volatility to the list + YZ_volatility.append(sigma_YZ*np.sqrt(252)) + + return YZ_volatility ++
+def GetCorrelationFactor(self, history, trade_signals, available_symbols): + ''' + Calculate the Correlation Factor, which is a function of the average pairwise correlation of all portfolio contituents + - the calculation is based on past three month pairwise correlation + - Notations: + rho_bar - average pairwise correlation of all portfolio constituents + CF_rho_bar - the correlation factor as a function of rho_bar''' + + # Get the past three month simple daily returns for all securities + settle = history.settle.unstack(level = 0) + past_three_month_returns = settle.pct_change().loc[settle.index[-1]-timedelta(self.ThreeMonths):] + + # Get number of assets + N_assets = len(available_symbols) + + # Get the pairwise signed correlation matrix for all assets + correlation_matrix = past_three_month_returns.corr() + + # Calculate rho_bar + summation = 0 + for i in range(N_assets-1): + for temp in range(N_assets - 1 - i): + j = i + temp + 1 + x_i = trade_signals[i] + x_j = trade_signals[j] + rho_i_j = correlation_matrix.iloc[i,j] + summation += x_i * x_j * rho_i_j + + # Equation 14 in [1] + rho_bar = (2 * summation) / (N_assets * (N_assets - 1)) + + # Calculate the correlation factor (CF_rho_bar) + # Equation 18 in [1] + return np.sqrt(N_assets / (1 + (N_assets - 1) * rho_bar)) ++
+For efficiency purposes, a History() request is called once on each rebalance date to get all the data from the past year for all securities. We retrieve our trade signal, Yang and Zhang volatility, and correlation factor by passing the history data frame to each respective function. +
+ ++def OnData(self, data): + ''' + Monthly rebalance at the beginning of each month. + Portfolio weights for each constituents are calculated based on Baltas and Kosowski weights. + ''' + + # skip if less than 30 days passed since the last trading date + if self.Time < self.nextRebalance: + return + + '''Monthly Rebalance Execution''' + # dataframe that contains the historical data for all securities + history = self.History(self.Securities.Keys, self.OneYear, Resolution.Daily) + history.replace(0, np.nan, inplace = True) + + # Get the security symbols are are in the history dataframe + available_symbols = list(set(history.index.get_level_values(level = 0))) + + # Liquidate symbols that are not in the history dataframe anymore + for security in self.Securities.Keys: + if security.Value not in available_symbols: + self.Liquidate(security, 'Not found in history request') + + # Get the trade signals and YZ volatility for all securities + trade_signals = self.GetTradingSignal(history) + volatility = self.GetYZVolatility(history, available_symbols) + + # Get the correlation factor + CF_rho_bar = self.GetCorrelationFactor(history, trade_signals, available_symbols) + + #Rebalance the portfolio according to Baltas and Kosowski suggested weights + N_assets = len(available_symbols) + for symbol, signal, vol in zip(available_symbols, trade_signals, volatility): + # Baltas and Kosowski weights (Equation 19 in [1]) + weight = (signal*self.portfolio_target_sigma*CF_rho_bar)/(N_assets*vol) + self.SetHoldings(symbol, weight) + + # Set next rebalance time + self.nextRebalance = Expiry.EndOfMonth(self.Time) ++
+The implementation of TSMOM-CF in the post-GFC period, January 2018 to September 2019, shows significant performance improvement over the basic TSMOM. The backtest of TSMOM-CF produces Sharpe ratio of 0.321, compared to TSMOM's Sharpe ratio of -0.746 and SPY Sharpe ratio of 0.46. The exact TSMOM algorithm can be found in the strategy library. +
\ No newline at end of file diff --git a/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/06 Algorithm.html b/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/06 Algorithm.html new file mode 100644 index 0000000..6eebbb0 --- /dev/null +++ b/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/06 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/07 References.html b/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/07 References.html new file mode 100644 index 0000000..5a494dd --- /dev/null +++ b/04 Strategy Library/356 Improved Momentum Strategy on Commodities Futures/07 References.html @@ -0,0 +1,8 @@ ++ In this tutorial we implement a trend following strategy on commodities futures based on a 2014 paper "Two Centuries Of Trend Following" by Y. Lempérière, C. Deremble, P. Seager, M. Potters, and J. P. Bouchaud. +
\ No newline at end of file diff --git a/04 Strategy Library/357 Commodities Futures Trend Following/02 Introduction.html b/04 Strategy Library/357 Commodities Futures Trend Following/02 Introduction.html new file mode 100644 index 0000000..21ba8d1 --- /dev/null +++ b/04 Strategy Library/357 Commodities Futures Trend Following/02 Introduction.html @@ -0,0 +1,21 @@ ++The paper highlights the existence of trends as an anomaly that contradicts the efficient market hypothesis. If financial markets are completely efficient as the hypothesis suggests, then asset price changes should be totally unpredictable. In other words, no systematic excess return based on public information should exist since asset prices ought to reflect all public information available. However observationally, trend existence in the market do exist. They make it possible to use the simple trend following strategy which states, buy when prices goes up and sell when prices goes down. Numerous academic studies have demonstrated that trend following strategies generate persistent returns over long periods of time. +
+ ++The paper extends the backtest period of trend following strategies to two centuries and demonstrates statistically significant systematic excess returns on four asset classes (commodities, currencies, stock indices, and bonds). It implements a risk managed strategy that buys or sells a quantity of \(\sigma_n^{-1}\) of the underlying contract depending on the sign of \(s_n\). +
+ ++The signal \(s_n(t)\) at the beginning of month t is: +
+ +\[s_n(t) = \frac{p(t-1)-\text{<}p\text{>}_{n,t-1}}{\sigma_n(t-1)}\] + ++where \(\text{<}p\text{>}_{n,t-1}\) is last month's exponential moving average of past prices with a decay rate equal to n months,\(p(t-1)\) is the price of last month, and \(\sigma_n(t-1)\) is last month's volatility, estimated as the exponential moving average of the absolute monthly price changes, with a decay rate equal to n months. The decay rate was set to 5 months. +
+ ++Below, we will implement the above monthly-rebalanced trend following strategy on commodities futures. +
\ No newline at end of file diff --git a/04 Strategy Library/357 Commodities Futures Trend Following/03 Method.html b/04 Strategy Library/357 Commodities Futures Trend Following/03 Method.html new file mode 100644 index 0000000..6e8e094 --- /dev/null +++ b/04 Strategy Library/357 Commodities Futures Trend Following/03 Method.html @@ -0,0 +1,123 @@ ++ The strategy requires the continuous futures contract, so we import the custom data from Quandl. We manually create a universe of tradable commodity futures. They are all liquid and active continuous contracts #1. The data from Quandl are non-adjusted price based on spot-month continuous contract calculations. The data resolution is daily. +
+ + ++The paper selected a well-balanced commodities pool to include 7 representative contracts: Crude oil, Henry Hub Natural Gas, Corn, Wheat, Super, Live Cattle and Copper. We will add continuous futures data of these contracts from Quandl. This implementation performs a backtest on 20 years as opposed to 200 years of data for the purpose of comparing to benchmark SPY. +
+ ++from QuantConnect.Python import PythonQuandl +class ImprovedCommodityMomentumTrading(QCAlgorithm): + def Initialize(self): + tickers = ["CHRIS/CME_W1", # Wheat Futures, Continuous Contract #1 + "CHRIS/CME_C1", # Corn Futures, Continuous Contract #1 + "CHRIS/CME_LC1", # Live Cattle Futures, Continuous Contract #1 + "CHRIS/CME_CL1", # Crude Oil Futures, Continuous Contract #1 + "CHRIS/CME_NG1", # Natural Gas (Henry Hub) Physical Futures, Continuous Contract #1 + "CHRIS/LIFFE_W1", # White Sugar Future, Continuous Contract #1 + "CHRIS/CME_HG1"] # Copper Futures, Continuous Contract #1 + for ticker in tickers: + data = self.AddData(QuandlFutures, ticker, Resolution.Daily) + data.SetLeverage(3) +class QuandlFutures(PythonQuandl): + def __init__(self): + self.ValueColumnName = "Settle" ++
+In Initialize(), we create a dictionary to store the SymbolData object for each security. The strategy is designed to trade monthly, so we will create a monthly consolidator for each security as well. When a new monthly data becomes available, the consolidator calls an event handler CalendarHandler. Within this event handler, we will update the SymbolData object with the freshly received monthly data. +
+
+def Initialize(self):
+ # Container to store the SymbolData object for each security
+ self.Data = {}
+
+ for ticker in tickers:
+ # Add Quandl data and set desired leverage
+ data = self.AddData(QuandlFutures, ticker, Resolution.Daily)
+ data.SetLeverage(3)
+
+ # Create a monthly consolidator for each security
+ self.Consolidate(ticker, CalendarType.Monthly, self.CalendarHandler)
+
+ # Create a SymbolData object for each security to store relevant indicators
+ # and calculate quantity of contracts to Buy/Sell
+ self.Data[data.Symbol] = SymbolData()
+def CalendarHandler(self, bar):
+ '''
+ Event Handler that updates the SymbolData object for each security when a new monthly bar becomes available
+ '''
+ self.Data[bar.Symbol].Update(bar)
+
++The SymbolData class is designed to contain everything we need for calculating how many contracts to Buy/Sell at the beginning of each month. LEAN provides helpful indicators to get the exponential moving average and momentum indicators. The Introduction section above detailed the formula for calculating the number of contracts to Buy/Sell. We implement the formula in the Update function. +
+ +
+class SymbolData:
+ '''
+ Contains the relevant indicators used to calculate number of contracts to Buy/Sell
+ '''
+ def __init__(self):
+ self.ema = ExponentialMovingAverage("MonthEMA", 5)
+
+ # Volatility estimation is defined as the EMA of absolute monthly price changes
+ # Use Momentum indicator to get absolute monthly price changes.
+ # Then use the IndicatorExtensions.EMA and pass the momentum indicator values to get the volatility
+ self.mom = Momentum("MonthMOM", 1)
+ # Note: self.vol will automatically be updated with self.mom
+ self.vol = IndicatorExtensions.EMA(self.mom, 5)
+
+ self.Quantity = 0
+
+
+ def Update(self, bar):
+ self.ema.Update(bar.Time, bar.Value)
+ self.mom.Update(bar.Time, bar.Value)
+
+ if self.ema.IsReady and self.vol.IsReady:
+ # Equation 1 in [1]
+ signal = (bar.Value - self.ema.Current.Value) / self.vol.Current.Value
+ # Equation 2 in [1]
+ self.Quantity = np.sign(signal)/abs(self.vol.Current.Value)
+
+ return self.Quantity != 0
+
++Now we’ll place orders based on the quantity of contracts calculated from previous month stored in the SymbolData object. Note that we warm up the algorithm with 150 days of data to allow the algorithm to execute trades on the start date. +
+ ++def OnData(self, data): + ''' + Buy/Sell security every month + ''' + if self.Time < self.nextRebalance or self.IsWarmingUp: + return + + for symbol in data.Keys: + symbolData = self.Data[symbol] + if symbolData.Quantity != 0: + self.MarketOrder(symbol, symbolData.Quantity) + + self.nextRebalance = Expiry.EndOfMonth(self.Time) ++
+For the backtest period (January 1998 to September 2019), the trend following strategy produced a Sharpe ratio of 0.266, compared to SPY’s Sharpe ratio of 0.459. The positive performance of the trend-following strategy over the approximately 20-year time horizon indeed suggests the existence of statistically significant, anomalous, systematic, excess returns from trends. Furthermore, the paper suggests the anomaly is universal across 3 other asset classes (currencies, stock indices and bonds). +
+ ++This tutorial demonstrates trends as one of the most powerful sources of anomalous excess returns in financial markets. We hope to inspire the community to develop more trend-based strategies and encourage you to test out this strategy on other asset classes from the original paper. +
\ No newline at end of file diff --git a/04 Strategy Library/357 Commodities Futures Trend Following/05 Algorithm.html b/04 Strategy Library/357 Commodities Futures Trend Following/05 Algorithm.html new file mode 100644 index 0000000..c56a62c --- /dev/null +++ b/04 Strategy Library/357 Commodities Futures Trend Following/05 Algorithm.html @@ -0,0 +1,6 @@ + diff --git a/04 Strategy Library/357 Commodities Futures Trend Following/06 References.html b/04 Strategy Library/357 Commodities Futures Trend Following/06 References.html new file mode 100644 index 0000000..cb5636b --- /dev/null +++ b/04 Strategy Library/357 Commodities Futures Trend Following/06 References.html @@ -0,0 +1,5 @@ ++ Growth stocks refer to high-quality, successful companies whose earnings are expected to continue growing at an above-average rate relative to the market. + Growth stocks generally have high price-to-earnings (P/E) ratios and high price-to-book(P/B) ratios. At times, growth stocks are considered expensive and overvalued. The value stocks refer to stocks which have high dividend payout ratios or low financial ratios such as P/E ratios and P/B ratios. The value stocks are often considered undervalued by the market. This algorithm will create the long-short positions based on the relation between investor sentiment and the performance of value stocks over growth stocks. +
diff --git "a/04 Strategy Library/36 Sentiment and Style Rotation Effect in Stocks/01 \347\256\200\344\273\213.cn.html" "b/04 Strategy Library/36 Sentiment and Style Rotation Effect in Stocks/01 \347\256\200\344\273\213.cn.html" new file mode 100644 index 0000000..c26b591 --- /dev/null +++ "b/04 Strategy Library/36 Sentiment and Style Rotation Effect in Stocks/01 \347\256\200\344\273\213.cn.html" @@ -0,0 +1,3 @@ ++ 成长型股票指的是高质量、成功的公司,它们的盈利预期将继续以高于市场平均水平的速度增长。成长型股票通常具有高市盈率(P/E)和高市净率(P/B)。有时,成长型股票被认为价格过高。价值型股票是指股息率高或财务比率(如市盈率和市净率)低的股票。价值型股票通常会被市场低估。此算法将基于投资者情绪和价值型股票相对于成长型股票表现之间的关系来建立多空头寸。 +
diff --git a/04 Strategy Library/36 Sentiment and Style Rotation Effect in Stocks/02 Method.html b/04 Strategy Library/36 Sentiment and Style Rotation Effect in Stocks/02 Method.html new file mode 100644 index 0000000..a29b638 --- /dev/null +++ b/04 Strategy Library/36 Sentiment and Style Rotation Effect in Stocks/02 Method.html @@ -0,0 +1,129 @@ ++ To measure investors' sentiment, we use gauges: the CBOE equity put-call ratio and the market volatility (VIX) index. + The VIX index is constructed using the implied volatilities on S&P 500 index options and shows the market's expectation of 30-day volatility. + The CBOE equity put-call ratio is calculated by dividing the trading volume of CBOE equity put options by the trading volume of CBOE equity call options. + A rising put-call ratio means equity traders are buying more puts than calls and indicates a bearish sentiment in the market while a falling put-call ratio + is considered as the bullish market sentiment. +
++ We import the daily VIX data from Quandl. CBOE provides the volume put-call ratio data from 11-01-2006 to present so we import the custom data from CBOE. +
+
+class SentimentAndStyleRotationAlgorithm(QCAlgorithm):
+ def Initialize(self):
+ self.SetStartDate(2010, 1, 1)
+ self.SetEndDate(2018, 7, 1)
+ self.SetCash(100000)
+ self.AddData(QuandlVix, "CBOE/VIX", Resolution.Daily)
+ self.AddData(CBOE, "PutCallRatio", Resolution.Daily)
+
+class QuandlVix(PythonQuandl):
+ '''Quandl VIX data class'''
+ def __init__(self):
+ self.ValueColumnName = "VIX Close"
+
+class CBOE(PythonData):
+ '''Cboe Equity Volume Put/Call Ratios (11-01-2006 to present) Custom Data Class'''
+ def GetSource(self, config, date, isLiveMode):
+ return SubscriptionDataSource("http://www.cboe.com/publish/scheduledtask/mktdata/datahouse/equitypc.csv", SubscriptionTransportMedium.RemoteFile)
+
+ def Reader(self, config, line, date, isLiveMode):
+ if not (line.strip() and line[0].isdigit()): return None
+ index = CBOE()
+ index.Symbol = config.Symbol
+
+ try:
+ # Example File Format:
+ # DATE CALL PUT TOTAL P/C Ratio
+ # 11/1/06 976510 623929 1600439 0.64
+ data = line.split(',')
+ index.Time = datetime.strptime(data[0], "%m/%d/%Y").strftime("%Y-%m-%d")
+ index.Value = Decimal(data[4])
+
+ except ValueError:
+ return None
+
+ return index
+
+
+ All stocks on NYSE and NASDAQ are used as the investment universe. In CoarseSelectionFunction, we eliminate ETFs which don't have fundamental data.
+ In FineSelectionFunction, stocks are sorted into deciles based on a size measure - market capitalization. We use only the first three size deciles
+ for the algorithm to avoid potential problems with small illiquid stocks.
+
+def FineSelectionFunction(self, fine): + if self.month_start: + self.selection = True + + fine = [i for i in fine if i.EarningReports.BasicAverageShares.ThreeMonths>0 + and i.EarningReports.BasicEPS.TwelveMonths>0 + and i.ValuationRatios.PERatio>0 + and i.ValuationRatios.PBRatio>0] + # Calculate the market cap and add the "MakretCap" property to fine universe object + for i in fine: + i.MarketCap = float(i.EarningReports.BasicAverageShares.ThreeMonths * (i.EarningReports.BasicEPS.TwelveMonths*i.ValuationRatios.PERatio)) + # sort fine object by MarketCap + sotrted_market_cap = sorted(fine, key = lambda x:x.MarketCap, reverse=True) + decile_top1 = sotrted_market_cap[:floor(len(sotrted_market_cap)/10)] + decile_top2 = sotrted_market_cap[floor(len(sotrted_market_cap)/10):floor(len(sotrted_market_cap)*2/10)] + decile_top3 = sotrted_market_cap[floor(len(sotrted_market_cap)*2/10):floor(len(sotrted_market_cap)*3/10)] ++
+ In the next step, we subdivide each size decile into five portfolios based on the P/B ratio. For each of the first three size deciles, the value portfolio consists of all firms included in the quintile with the lowest P/B ratio, and the growth portfolio consists stocks with the highest P/B ratio. +
++sorted_PB1 = sorted(decile_top1, key = lambda x: x.ValuationRatios.PBRatio) +sorted_PB2 = sorted(decile_top2, key = lambda x: x.ValuationRatios.PBRatio) +sorted_PB3 = sorted(decile_top3, key = lambda x: x.ValuationRatios.PBRatio) +# The value portfolio consists of all firms included in the quintile with the lowest P/B ratio +PB_bottom1 = sorted_PB1[:floor(len(decile_top1)/5)] +PB_bottom2 = sorted_PB2[:floor(len(decile_top2)/5)] +PB_bottom3 = sorted_PB3[:floor(len(decile_top3)/5)] +self.value_portfolio = [i.Symbol for i in PB_bottom1 + PB_bottom2 + PB_bottom3] +# The growth portfolio consists of all firms included in the quintile with the highest P/B ratio +PB_top1 = sorted_PB1[-floor(len(decile_top1)/5):] +PB_top2 = sorted_PB2[-floor(len(decile_top2)/5):] +PB_top3 = sorted_PB3[-floor(len(decile_top3)/5):] +self.growth_portfolio = [i.Symbol for i in PB_top1 + PB_top2 + PB_top3] ++
+ According to the research paper from Lee and Song, When Do Value Stocks Outperform Growth Stocks?: Investor Sentiment and Equity Style Rotation Strategies, + value stocks tend to outperform growth stocks when the CBOE equity put-call ratio is relatively low, and the VIX is relatively high. The value portfolio significantly underperforms the growth portfolio when the put-call ratio and VIX are both high. + To convert the daily put-call ratio and VIX data into monthly value, we take an average over the recent one month and the previous six months. +
++ If the recent monthly average CBOE put-call ratio is lower than its six-month average and the one-month average of VIX is higher than its six-month average, the algorithm goes long on an equally weighted portfolio consisting of value stocks (the lowest P/B quintile) from the top three size deciles. If recent monthly average CBOE put-call ratio and the VIX index are both higher than their six-month average, the algorithm goes short the value stocks. + Otherwise, the algorithm goes long both value stocks and growth stocks. The position holding period is three months, and the portfolio is rebalanced every three months. +
++stocks_invested = [x.Key for x in self.Portfolio if x.Value.Invested] +for i in stocks_invested: + if i not in self.value_portfolio+self.growth_portfolio: + self.Liquidate(i) + +if self.vix_SMA_1.Current.Value > self.vix_SMA_6.Current.Value: + if self.PCRatio_SMA_1.Current.Value < self.PCRatio_SMA_6.Current.Value: + long_weight = 1/len(self.value_portfolio) + for long in self.value_portfolio: + self.SetHoldings(long, long_weight) + elif self.PCRatio_SMA_1.Current.Value > self.PCRatio_SMA_6.Current.Value: + short_weight = 1/len(self.value_portfolio) + for short in self.value_portfolio: + self.SetHoldings(short, -short_weight) +else: + long_weight = 1/len(self.value_portfolio+self.growth_portfolio) + for long in self.value_portfolio+self.growth_portfolio: + self.SetHoldings(long, long_weight) ++
+ 要衡量投资者的情绪,我们使用的指标是:芝加哥期权交易所(CBOE)的股票看跌/看涨比率和市场波动率(VIX)指数。VIX指数是利用标准普尔500指数期权的隐含波动率构建的,它显示了市场对30天波动率的预期。芝加哥期权交易所(CBOE) 股票看跌/看涨比率的计算方法是将芝加哥期权交易所股票看跌期权的交易量除以芝加哥期权交易所股票看涨期权的交易量。看跌/看涨期权比率上升,意味着股票交易员买入的看跌期权多于看涨期权,表明市场人气看跌,而看跌/看涨比率下降则被视为市场人气上涨。 +
++ 我们从Quandl导入每日波动率数据。CBOE提供了从2006年11月1日到现在的成交量看跌/看涨比率数据,因此我们从CBOE导入自定义数据。 +
+
+class SentimentAndStyleRotationAlgorithm(QCAlgorithm):
+ def Initialize(self):
+ self.SetStartDate(2010, 1, 1)
+ self.SetEndDate(2018, 7, 1)
+ self.SetCash(100000)
+ self.AddData(QuandlVix, "CBOE/VIX", Resolution.Daily)
+ self.AddData(CBOE, "PutCallRatio", Resolution.Daily)
+
+class QuandlVix(PythonQuandl):
+ '''Quandl VIX data class'''
+ def __init__(self):
+ self.ValueColumnName = "VIX Close"
+
+class CBOE(PythonData):
+ '''Cboe Equity Volume Put/Call Ratios (11-01-2006 to present) Custom Data Class'''
+ def GetSource(self, config, date, isLiveMode):
+ return SubscriptionDataSource("http://www.cboe.com/publish/scheduledtask/mktdata/datahouse/equitypc.csv", SubscriptionTransportMedium.RemoteFile)
+
+ def Reader(self, config, line, date, isLiveMode):
+ if not (line.strip() and line[0].isdigit()): return None
+ index = CBOE()
+ index.Symbol = config.Symbol
+
+ try:
+ # 示例文件格式:
+ # 日期 看涨 看跌 合计 看跌/看涨比率
+ # 11/1/06 976510 623929 1600439 0.64
+ data = line.split(',')
+ index.Time = datetime.strptime(data[0], "%m/%d/%Y").strftime("%Y-%m-%d")
+ index.Value = Decimal(data[4])
+
+ except ValueError:
+ return None
+
+ return index
+
+
+ 纽交所和纳斯达克的所有股票都被用作投资集合。在CoarseSelectionFunction中,我们剔除了没有基本数据的基金。在FineSelectionFunction中,股票根据市值大小被分成十等分。我们的算法只使用前百分之三十来避免小型非流动性股票的潜在问题。
+
+def FineSelectionFunction(self, fine): + if self.month_start: + self.selection = True + + fine = [i for i in fine if i.EarningReports.BasicAverageShares.ThreeMonths>0 + and i.EarningReports.BasicEPS.TwelveMonths>0 + and i.ValuationRatios.PERatio>0 + and i.ValuationRatios.PBRatio>0] + # 计算市场价值并将“市值”属性添加到精细集合对象中 + for i in fine: + i.MarketCap = float(i.EarningReports.BasicAverageShares.ThreeMonths * (i.EarningReports.BasicEPS.TwelveMonths*i.ValuationRatios.PERatio)) + # 根据市值对精细对象分类 + sotrted_market_cap = sorted(fine, key = lambda x:x.MarketCap, reverse=True) + decile_top1 = sotrted_market_cap[:floor(len(sotrted_market_cap)/10)] + decile_top2 = sotrted_market_cap[floor(len(sotrted_market_cap)/10):floor(len(sotrted_market_cap)*2/10)] + decile_top3 = sotrted_market_cap[floor(len(sotrted_market_cap)*2/10):floor(len(sotrted_market_cap)*3/10)] ++
+ 在接下来的步骤中,我们根据市净率将十等分中的每一份再细分为五个投资组合。对于前百分之三十的股票,价值型投资组合由市净率最低的五分之一公司组成,而成长型投资组合则由市净率最高的股票组成。 +
++sorted_PB1 = sorted(decile_top1, key = lambda x: x.ValuationRatios.PBRatio) +sorted_PB2 = sorted(decile_top2, key = lambda x: x.ValuationRatios.PBRatio) +sorted_PB3 = sorted(decile_top3, key = lambda x: x.ValuationRatios.PBRatio) +# 价值型投资组合由市净率最低的五分之一公司组成 +PB_bottom1 = sorted_PB1[:floor(len(decile_top1)/5)] +PB_bottom2 = sorted_PB2[:floor(len(decile_top2)/5)] +PB_bottom3 = sorted_PB3[:floor(len(decile_top3)/5)] +self.value_portfolio = [i.Symbol for i in PB_bottom1 + PB_bottom2 + PB_bottom3] +# 成长型投资组合由市净率最高的五分之一公司组成 +PB_top1 = sorted_PB1[-floor(len(decile_top1)/5):] +PB_top2 = sorted_PB2[-floor(len(decile_top2)/5):] +PB_top3 = sorted_PB3[-floor(len(decile_top3)/5):] +self.growth_portfolio = [i.Symbol for i in PB_top1 + PB_top2 + PB_top3] ++
+ 根据Lee和Song的研究论文《When Do Value Stocks Outperform Growth Stocks?: Investor Sentiment and Equity Style Rotation Strategies》,当芝加哥期权交易所股票看跌/看涨比率相对较低,并且波动率指数相对较高时,价值型股票的表现往往优于成长型股票。当看跌/看涨比率和波动率指数均较高时,价值组合的表现明显要逊于成长型投资组合。要将每日看跌/看涨比率和波动率数据转换为月度数值,我们取最近一个月和前六个月的平均值。 +
++ 如果最近芝加哥期权交易所的月平均看跌/看涨比率低于6个月平均水平,而波动率指数(VIX)的一个月平均水平高于6个月平均水平,那么该算法就会做多由排名前百分之三十价值股(市净率最低的五分之一)组成的平均加权投资组合。如果最近芝加哥期权交易所的月平均看跌/看涨比率和VIX指数均高于6个月平均水平,该算法就会做空价值股。否则,该算法既做多价值型股票,也做多成长型股票。持仓期为三个月,投资组合每三个月重新平衡一次。 +
++stocks_invested = [x.Key for x in self.Portfolio if x.Value.Invested] +for i in stocks_invested: + if i not in self.value_portfolio+self.growth_portfolio: + self.Liquidate(i) + +if self.vix_SMA_1.Current.Value > self.vix_SMA_6.Current.Value: + if self.PCRatio_SMA_1.Current.Value < self.PCRatio_SMA_6.Current.Value: + long_weight = 1/len(self.value_portfolio) + for long in self.value_portfolio: + self.SetHoldings(long, long_weight) + elif self.PCRatio_SMA_1.Current.Value > self.PCRatio_SMA_6.Current.Value: + short_weight = 1/len(self.value_portfolio) + for short in self.value_portfolio: + self.SetHoldings(short, -short_weight) +else: + long_weight = 1/len(self.value_portfolio+self.growth_portfolio) + for long in self.value_portfolio+self.growth_portfolio: + self.SetHoldings(long, long_weight) ++
+ The momentum effect states that what was strongly going up in the near past will probably continue to go up shortly. It is one of the most used trading anomalies, but the strategy using only the momentum can suffer significant drawdowns sometimes. + + Some research papers show that the return of momentum strategies depend on the overall market conditions. + This state of the market can be defined in various ways like the investors' sentiment, prior market returns and so on. + Therefore, this algorithm will combine the momentum effect with the market state filter to turn off the momentum trading in down market state times. +
diff --git a/04 Strategy Library/37 Momentum and State of Market Filters/02 Method.html b/04 Strategy Library/37 Momentum and State of Market Filters/02 Method.html new file mode 100644 index 0000000..31414d9 --- /dev/null +++ b/04 Strategy Library/37 Momentum and State of Market Filters/02 Method.html @@ -0,0 +1,114 @@ ++ As we know, a stock market index tracks the price changes of a select group of stocks and compiles those stock price changes into a single value. + For example, S&P500 is composed of only 500 large-cap stocks. A broad market index is characterized by including stocks from companies of all sizes(large, mid and small-cap based on their values). + The most popular U.S. broad market indexes include the Russell 3000, the Wilshire 5000 Total Market Index and the MSCI U.S. Broad Market Index. Those broad-based market indexes attempt to cover the entire market + and their return can be a good benchmark of the current market state. +
+
+class MomentumandStateofMarkeFiltersAlgorithm(QCAlgorithm):
+ def Initialize(self):
+ self.SetStartDate(2011, 1, 1)
+ self.SetEndDate(2018, 1, 1)
+ self.SetCash(100000)
+ # add Wilshire 5000 Total Market Index data from Dropbox
+ self.AddData(Wilshire5000, "W5000", Resolution.Daily)
+ # calculate the index yearly return
+ self.W5000Return = self.ROC("W5000", 252)
+ # initialize the RateOfChange indicator of Wilshire 5000 total market index
+ history = self.History(["W5000"], 500, Resolution.Daily)
+ for tuple in history.loc["W5000"].itertuples():
+ self.W5000Return.Update(tuple.Index, tuple.value)
+
++ In this algorithm, we choose the Wilshire 5000 Total Market Index to be the market state measure. For the period of index return, longer horizons should capture more dramatic changes in the state of the market, but longer horizons also reduce the number of observations of changes in the market's state. Here we choose 12 months return according to the paper Market States and Momentum from Guttierez, Cooper and Hameed. + The daily index price comes from the Yahoo Finance. +
+
+class Wilshire5000(PythonData):
+ "Class to import Wilshire 5000 Total Market Index data from Dropbox"
+
+ def GetSource(self, config, date, isLiveMode):
+ return SubscriptionDataSource("https://www.dropbox.com/s/z9rof4fr9cqzgpt/W5000.csv?dl=1",
+ SubscriptionTransportMedium.RemoteFile)
+ def Reader(self, config, line, date, isLiveMode):
+ if not (line.strip() and line[1].isdigit()): return None
+ index = Wilshire5000()
+ index.Symbol = config.Symbol
+ try:
+ # Example File Format: (Data starts from 01/04/2010)
+ # Date Open High Low Close Adj Close Volume
+ # 1/4/10 11549.13965 11749.37012 11549.13965 11743.54004 11743.54004 0
+ data = line.split(',')
+ index.Time = datetime.strptime(data[0], "%Y-%m-%d")
+ index.Value = Decimal(data[5])
+ except:
+ return None
+ return index
+
+
+ The investment universe contains all stocks on NYSE and NASDAQ with a price higher than $1. We use the momentum indicator to gauge the momentum effect.
+ In CoarseSelectionFunction, the MOM indicator value for each symbol in coarse is updated with the adjusted price and saved in the dictionary self.mom.
+
+def CoarseSelectionFunction(self, coarse): + coarse = [x for x in coarse if (x.HasFundamentalData and x.AdjustedPrice > 1)] + for i in coarse: + if i.Symbol not in self.mom: + self.mom[i.Symbol] = SymbolData(i.Symbol, self.lookback) + self.mom[i.Symbol].MOM.Update(self.Time, i.AdjustedPrice) ++
+ When the indicator is ready, stocks are then sorted based on the previous six months momentum value. + Top 20 Stocks with the highest MOM are in the long stock list, 20 Stocks with the lowest MOM are in the short stock list. +
+
+self.MOMReady = {symbol: SymbolData for symbol, SymbolData in self.mom.items() if SymbolData.MOM.IsReady}
+if self.MOMReady:
+ # sort stocks by 6 months' momentum
+ sortByMOM = sorted(self.MOMReady, key = lambda x: self.MOMReady[x].MOM.Current.Value, reverse = True)
+ self.long = sortByMOM[:20]
+ self.short = sortByMOM[-20:]
+ return self.long+self.short
+
++ The strategy is rebalanced monthly. At the beginning of each month, we identify the state of the market. + If the market’s one-year return is positive, we define the state of the market as "UP" otherwise the state is "DOWN". + When the market is in "UP" state, we go long on the previous six-month winners (highest Momentum) and goes short on the last six-month losers (lowest Momentum). + Stocks are equally weighted. If the market is in "DOWN" state, we liquidate all asset holdings and invest in the long-term Treasury bond ETF to control the downside risk. +
++def OnData(self, data): + if self.month_start and self.selection: + self.month_start = False + self.selection = False + if self.long is None or self.short is None: return + # if the previous 12 months return on the broad equity market was positive + if self.W5000Return.Current.Value > 0: + stocks_invested = [x.Key for x in self.Portfolio if x.Value.Invested] + for i in stocks_invested: + if i not in self.long+self.short: + self.Liquidate(i) + short_weight = 0.5/len(self.short) + # goes short on the prior six-month losers (lowest decile) + for short_symbol in self.short: + self.SetHoldings(short_symbol, -short_weight) + # goes long on the prior six-month winners (highest decile) + long_weight = 0.5/len(self.long) + for long_symbol in self.long: + self.SetHoldings(long_symbol, long_weight) + else: + self.Liquidate() + self.SetHoldings(self.tlt, 1) ++
+ Accrual anomaly is based upon the reasoning that it is important to measure if a company's earnings are based on real cash inflow or on revenue recognition from questionable accounting practices. Since companies with lower levels of accruals have more certain real earnings, they should earn higher market returns. This strategy will take a long position in low accrual companies and a short position in high accrual accompanies. It is important to note that this strategy requires fundamental data from the current and past year in order to perform its analysis. As a result, it won't be implementable in live trading at this time. +
\ No newline at end of file diff --git a/04 Strategy Library/38 Accrual Anomaly/02 Method.html b/04 Strategy Library/38 Accrual Anomaly/02 Method.html new file mode 100644 index 0000000..e800787 --- /dev/null +++ b/04 Strategy Library/38 Accrual Anomaly/02 Method.html @@ -0,0 +1,69 @@ ++ The first step is coarse and fine universe selection. Using coarse selection, we create an investment universe with stocks that have fundamental data. The universes will be saved so that we can perform analysis on the annual changes of specific balance sheet data in the following year. +
++ def CoarseSelectionFunction(self, coarse): + if self.yearly_rebalance: + self.filtered_coarse = [x.Symbol for x in coarse if (x.HasFundamentalData) + and (x.Market == "usa")] + return self.filtered_coarse + else: + return [] + +def FineSelectionFunction(self, fine): + if self.yearly_rebalance: + fine = [x for x in fine if (float(x.FinancialStatements.BalanceSheet.CurrentAssets.Value) > 0) + and (float(x.FinancialStatements.BalanceSheet.CashAndCashEquivalents.Value) > 0) + and (float(x.FinancialStatements.BalanceSheet.CurrentLiabilities.Value) > 0) + and (float(x.FinancialStatements.BalanceSheet.CurrentDebt.Value) > 0) + and (float(x.FinancialStatements.BalanceSheet.IncomeTaxPayable.Value) > 0) + and (float(x.FinancialStatements.IncomeStatement.DepreciationAndAmortization.Value) > 0)] + + if not self.previous_fine: + self.previous_fine = fine + self.yearly_rebalance = False + return [] + else: + self.filtered_fine = self.CalculateAccruals(fine,self.previous_fine) + sorted_filter = sorted(self.filtered_fine, key=lambda x: x.bs_acc) + self.filtered_fine = [i.Symbol for i in sorted_filter] + self.previous_fine = fine + return self.filtered_fine + else: + return [] ++
+ During fine universe selection we take the stocks from the previous and current year and calculate their balance sheet based accrual values. The stocks are then sorted in ascending order based upon the implemented formula. Note that we account for size difference across the sample firms by scaling the accruals by the average of the beginning and end-of-year book value of total assets. +
++ def CalculateAccruals(self, current, previous): + accruals = [] + for stock_data in current: + try: + prev_data = None + for x in previous: + if x.Symbol == stock_data.Symbol: + prev_data = x + break + + delta_assets = float(stock_data.FinancialStatements.BalanceSheet.CurrentAssets.Value)-float(prev_data.FinancialStatements.BalanceSheet.CurrentAssets.Value) + delta_cash = float(stock_data.FinancialStatements.BalanceSheet.CashAndCashEquivalents.Value)-float(prev_data.FinancialStatements.BalanceSheet.CashAndCashEquivalents.Value) + delta_liabilities = float(stock_data.FinancialStatements.BalanceSheet.CurrentLiabilities.Value)-float(prev_data.FinancialStatements.BalanceSheet.CurrentLiabilities.Value) + delta_debt = float(stock_data.FinancialStatements.BalanceSheet.CurrentDebt.Value)-float(prev_data.FinancialStatements.BalanceSheet.CurrentDebt.Value) + delta_tax = float(stock_data.FinancialStatements.BalanceSheet.IncomeTaxPayable.Value)-float(prev_data.FinancialStatements.BalanceSheet.IncomeTaxPayable.Value) + dep = float(stock_data.FinancialStatements.IncomeStatement.DepreciationAndAmortization.Value) + avg_total = (float(stock_data.FinancialStatements.BalanceSheet.TotalAssets.Value)+float(prev_data.FinancialStatements.BalanceSheet.TotalAssets.Value))/2 + + stock_data.bs_acc = ((delta_assets-delta_cash)-(delta_liabilities-delta_debt-delta_tax)-dep)/avg_total + accruals.append(stock_data) + except: + pass + return accruals ++
+ In OnData(), we short top decile of the stocks in the sorted list and long the bottom decile of stocks. The portfolio is rebalanced every year at the start of June.
+
+ The asset growth effect is based upon the reasoning that high asset growth stocks underperform stocks with low asset growth. Some papers suggest that the return premium achieved by low asset growth stocks is consistent with the compensation for risk. There are two popular arguments to suggest this return premium. One arguments is that as firms grow, the asset mix of the firm becomes less risky as assets-in-place displace the value of assets the firm's expected to invest in the future. The second argument is that there is a systematic market mispricing of growing businesses due to the extrapolation of past gains to growth for high asset growth companies. +
++ This strategy will take a long position in low asset growth companies, and a short position in high asset growth accompanies. It is important to note that this strategy requires fundamental data from the current and past year to perform its analysis. As a result, this strategy would need a year in live trading to determine signals. +
\ No newline at end of file diff --git "a/04 Strategy Library/39 Asset Growth Effect/01 \347\256\200\344\273\213.cn.html" "b/04 Strategy Library/39 Asset Growth Effect/01 \347\256\200\344\273\213.cn.html" new file mode 100644 index 0000000..69d32c7 --- /dev/null +++ "b/04 Strategy Library/39 Asset Growth Effect/01 \347\256\200\344\273\213.cn.html" @@ -0,0 +1,6 @@ ++ 资产增长效基于高资产增长股票的表现弱于低资产增长股票。一些研究认为,低资产成长型股票的收益溢价与风险补偿是一致的。有两种流行的观点支持这种回报溢价。一种观点是,随着公司的成长,公司的资产组合风险会降低,因为现有资产取代了公司未来预期投资的资产价值。第二种观点是,由于将过去的收益推断为高资产成长型企业的增长,导致了对成长型企业的系统性市场定价错误。 +
++ 这一策略将在低资产增长型公司做多,同时在高资产增长的公司做空。值得注意的是,这一策略需要根据当前和过去一年的基本数据来进行分析。因此,这种策略需要一年的实时交易时间来确定信号。 +
\ No newline at end of file diff --git a/04 Strategy Library/39 Asset Growth Effect/02 Method.html b/04 Strategy Library/39 Asset Growth Effect/02 Method.html new file mode 100644 index 0000000..0335c63 --- /dev/null +++ b/04 Strategy Library/39 Asset Growth Effect/02 Method.html @@ -0,0 +1,57 @@ ++ The first step is coarse and fine universe selection. Using coarse selection, we create an investment universe with all non-financial U.S. stocks listed on NYSE, AMEX, and NASDAQ that contain fundamental data. The universes will be saved so that we can perform analysis on the annual changes of the total assets in the following year. +
++def CoarseSelectionFunction(self, coarse): + if self.yearly_rebalance: + filtered_coarse = [x.Symbol for x in coarse if (x.HasFundamentalData) + and (x.Market == "usa")] + return filtered_coarse + else: + return [] + +def FineSelectionFunction(self, fine): + if self.yearly_rebalance: + fine = [x for x in fine if x.FinancialStatements.BalanceSheet.TotalAssets.Value > 0 + and ((x.SecurityReference.ExchangeId == "NYS") or (x.SecurityReference.ExchangeId == "NAS") or (x.SecurityReference.ExchangeId == "ASE")) + and (x.CompanyReference.IndustryTemplateCode!="B") + and (x.CompanyReference.IndustryTemplateCode!="I")] + if not self.previous_fine: + self.previous_fine = fine + self.yearly_rebalance = False + return [] + else: + self.filtered_fine = self.Calculate(fine,self.previous_fine) + sorted_filter = sorted(self.filtered_fine, key=lambda x: x.delta_assets) + self.filtered_fine = [i.Symbol for i in sorted_filter] + self.previous_fine = fine + return self.filtered_fine + else: + return [] ++
+ During fine universe selection we take the stocks from the previous and current year and calculate their total asset growth. The stocks are then sorted in ascending order based upon the implemented calculation. Note that we account for size difference across the sample firms by scaling the growth by last year's total assets. +
++def Calculate(self, current, previous): + growth = [] + for stock_data in current: + try: + prev_data = None + for x in previous: + if x.Symbol == stock_data.Symbol: + prev_data = x + break + stock_data.delta_assets = (float(stock_data.FinancialStatements.BalanceSheet.TotalAssets.Value)-float(prev_data.FinancialStatements.BalanceSheet.TotalAssets.Value))/float(prev_data.FinancialStatements.BalanceSheet.TotalAssets.Value) + growth.append(stock_data) + except: + pass + return growth ++
+ In OnData(), we short top decile of the stocks in the sorted list and long the bottom decile of stocks. The portfolio is rebalanced every year at the end of June.
+
+ 第一步是粗略和精细集合选择。通过粗选,我们创建了一个包含所有在纽交所、美国证券交易所和纳斯达克上市的非金融类美国股票的投资领域,这些股票都包含基本数据。这一集合将被保存下来,这样我们就可以对下一年中总资产的年度变化进行分析。 +
++def CoarseSelectionFunction(self, coarse): + if self.yearly_rebalance: + filtered_coarse = [x.Symbol for x in coarse if (x.HasFundamentalData) + and (x.Market == "usa")] + return filtered_coarse + else: + return [] + +def FineSelectionFunction(self, fine): + if self.yearly_rebalance: + fine = [x for x in fine if x.FinancialStatements.BalanceSheet.TotalAssets.Value > 0 + and ((x.SecurityReference.ExchangeId == "NYS") or (x.SecurityReference.ExchangeId == "NAS") or (x.SecurityReference.ExchangeId == "ASE")) + and (x.CompanyReference.IndustryTemplateCode!="B") + and (x.CompanyReference.IndustryTemplateCode!="I")] + if not self.previous_fine: + self.previous_fine = fine + self.yearly_rebalance = False + return [] + else: + self.filtered_fine = self.Calculate(fine,self.previous_fine) + sorted_filter = sorted(self.filtered_fine, key=lambda x: x.delta_assets) + self.filtered_fine = [i.Symbol for i in sorted_filter] + self.previous_fine = fine + return self.filtered_fine + else: + return [] ++
+ 在精细集合选择中,我们从上一年和当年的股票中计算出它们的总资产增长。然后根据采用的计算按照升序对股票进行排序。要注意的是,我们通过去年总资产的增长比例来计算样本公司之间的规模差异。 +
++def Calculate(self, current, previous): + growth = [] + for stock_data in current: + try: + prev_data = None + for x in previous: + if x.Symbol == stock_data.Symbol: + prev_data = x + break + stock_data.delta_assets = (float(stock_data.FinancialStatements.BalanceSheet.TotalAssets.Value)-float(prev_data.FinancialStatements.BalanceSheet.TotalAssets.Value))/float(prev_data.FinancialStatements.BalanceSheet.TotalAssets.Value) + growth.append(stock_data) + except: + pass + return growth ++
+ 在OnData()中,我们做空排序列表中前百分之十的股票,做多后百分之十的股票。投资组合每年会在6月底重新调整。
+
+ Pairs trading is a non-directional, market-neutral trading strategy which seeks to identify the price divergence from two highly correlated assets. + Pairs trading assumes the co-movement and the mean reversion of two asset prices. It indicates that the price of selected assets + tend to move together, and when they diverge, we can exploit the investment opportunity by taking a market neutral position as we assume their price will tend to move back to the average price over time. + In this algorithm, we use a large family of international exchange-traded funds(ETFs) to examine the performance of the pairs trading strategy. +
diff --git a/04 Strategy Library/40 Pairs Trading with Country ETFs/02 Method.html b/04 Strategy Library/40 Pairs Trading with Country ETFs/02 Method.html new file mode 100644 index 0000000..8a84d14 --- /dev/null +++ b/04 Strategy Library/40 Pairs Trading with Country ETFs/02 Method.html @@ -0,0 +1,69 @@ +
+ The investment universe consists of 25 international ETFs. The pair selection is based on a rolling time period called the formation period.
+ During each formation period, we save the history closing price of each ETF. Here we use a Python list-like container calleddeque to keep a fixed-length price series. From these prices, we compute normalized cumulative price indices which are comparable across the ETFs in the group.
+ According to the paper Pairs Trading on International ETFs from Panagiotis, Dimitrios and Tao,
+ here the formation period is 120 days.
+
+ Where \(r_t^n\) is the simple return of the n-th ETF. \(R_t^n\) is the index value. +
++ For each formation period, we compute the average absolute distance among all pairs in the group and + then rank the distances from the smallest to largest to identify the trading opportunities. + The top 5 pairs with the smallest distance are used in the subsequent 20 day trading period. + The definition of distance is +
+\[D_t^{a,b}=\frac{1}{120}\sum_{t+1}^{t+120}\mid P_t^a-P_t^b\mid \ for \ all\ pairs \ a,b \] ++ class Pair: + def __init__(self, symbol_a, symbol_b, price_a, price_b): + self.symbol_a = symbol_a + self.symbol_b = symbol_b + self.price_a = np.array(price_a) + self.price_b = np.array(price_b) + # compute normalized cumulative price indices + self.index_a = np.cumprod(self.price_a[1:]/self.price_a[:-1]) + self.index_b = np.cumprod(self.price_b[1:]/self.price_b[:-1]) + + def distance(self): + return 1/120*sum(abs(self.index_a -self.index_b)) ++
+ Now we consider the top 5 pairs. For each of the one month trading period, we compute the 120-day normalized cumulative price indices and compare them to a fraction of the distance value \(D_t^{a,b}\) for each pair (a,b). Assume the threshold is 0.5, if the index value of asset A is greater than asset B by 0.5 times the current distance \(D_t^{a,b}\), + then we sell asset A and buy asset B. The quantity of A and B is based on the dollar neutral. We invest the same amount of money in the long leg and the short leg, vice versa if the index value of asset B is greater than asset A by 0.5 times the distance. When the difference between index A and index B falls into the range \(\left(-0.5D_t^{a,b},0.5D_t^{a,b}\right)\), + we liquidate the pair. The above procedure is repeated for all top 5 pairs. At the start of next month, the new pairs are selected and trade for next month. +
++for i in self.sorted_pairs: + pair = Pair(i[0], i[1], self.history_price[i[0].Value], self.history_price[i[1].Value]) + index_a = pair.index_a[-1] + index_b = pair.index_b[-1] + delta = pair.distance() + if index_a - index_b > self.threshold*delta: + if not self.Portfolio[pair.symbol_a].Invested and not self.Portfolio[pair.symbol_b].Invested: + ratio = self.Portfolio[pair.symbol_a].Price / self.Portfolio[pair.symbol_b].Price + quantity = int(self.CalculateOrderQuantity(pair.symbol_a, 0.2)) + self.Sell(pair.symbol_a, quantity) + self.Buy(pair.symbol_b, floor(ratio*quantity)) + + elif index_a - index_b < -self.threshold*delta: + if not self.Portfolio[pair.symbol_a].Invested and not self.Portfolio[pair.symbol_b].Invested: + ratio = self.Portfolio[pair.symbol_b].Price / self.Portfolio[pair.symbol_a].Price + quantity = int(self.CalculateOrderQuantity(pair.symbol_b, 0.2)) + self.Sell(pair.symbol_b, quantity) + self.Buy(pair.symbol_a, floor(ratio*quantity)) + + # the position is closed when prices revert back + elif self.Portfolio[i[0]].Invested and self.Portfolio[i[1]].Invested: + self.Liquidate(pair.symbol_a) + self.Liquidate(pair.symbol_b) ++
+ VIX index is the weighted average of the implied volatilities computed from a total of eight near-the-money, nearby and second nearby American option contracts on the underlying S&P100 index. The index is calculated on an intraday basis by the CBOE. + The extreme levels of the VIX index are a strong indicator of equity index returns. + One could anticipate that the higher the fear in the markets, indicated by the VIX index, the higher the subsequent returns on the broad equity index. + In this algorithm, we will explore if VIX index is the forward-looking indicator of future stock index returns. +
diff --git a/04 Strategy Library/58 VIX Predicts Stock Index Returns/02 Method.html b/04 Strategy Library/58 VIX Predicts Stock Index Returns/02 Method.html new file mode 100644 index 0000000..3564d32 --- /dev/null +++ b/04 Strategy Library/58 VIX Predicts Stock Index Returns/02 Method.html @@ -0,0 +1,49 @@ ++ To assess if the implied volatility turns out to be relevant trading signals for + long and short positions, we must first define what we mean by large or small implied volatility levels. + At any given time, we create 20 equally spaced percentiles for the history close price of VIX in the last two years. + By 20 equally spaced percentiles, it means the 5%, 10%, . . . , 95% percentiles. Then the current VIX index price is compared to these percentiles and ranked accordingly. +
+
+ We import the daily VIX data from Quandl. The correspondent stock index is S&P100 index. We use the iShares S&P 100 ETF OEF
+ In the first step, we create a rolling window to save the history VIX price. The history request is used to initialize the rolling window.
+
+def Initialize(self):
+ self.SetStartDate(2006, 1, 1)
+ self.SetEndDate(2018, 8, 1)
+ self.SetCash(100000)
+ self.AddEquity("OEF", Resolution.Daily)
+ self.vix = 'CBOE/VIX'
+ self.AddData(QuandlVix, self.vix, Resolution.Daily)
+ self.window = RollingWindow[float](252*2)
+ hist = self.History([self.vix], 1000, Resolution.Daily)
+ for close in hist.loc[self.vix]['vix close']:
+ self.window.Add(close)
+
+class QuandlVix(PythonQuandl):
+ def __init__(self):
+ self.ValueColumnName = "VIX Close"
+
++ The rolling past 2-year history of the VIX index is then split to create 20 equally spaced percentiles. + The algorithm goes long on the equity index if the VIX index on the current day is higher than on any other day during the rolling 2-year window or if the VIX index value is in the highest 2 percentile boxes. + If the VIX index on the current day is lower than on any other day during the rolling 2-year window or if the VIX index value is in the lowest two percentile boxes. The algorithm goes short on the equity index. +
+
+def OnData(self, data):
+ if not data.ContainsKey(self.vix): return
+ self.window.Add(self.Securities[self.vix].Price)
+ if not self.window.IsReady: return
+ history_close = [i for i in self.window]
+
+ if self.Securities[self.vix].Price > np.percentile(history_close, 90):
+ self.SetHoldings("OEF", 1)
+ elif self.Securities[self.vix].Price < np.percentile(history_close, 10):
+ self.SetHoldings("OEF", -1)
+
++ The lunar phase is the shape of the direct sunlight portion of the Moon as viewed from Earth. + The lunar phases gradually and cyclically change over the period of a month. + Lunar phases have proven effects on human biology and psychology. + Investors are subject to various psychological and behavioral biases and mood fluctuations. + Therefore if lunar phases affect mood, by extension, these phases may affect investor behavior and thus asset prices. + This tutorial we will build an algorithm based upon the Moon phase. +
diff --git a/04 Strategy Library/61 Lunar Cycle in Equity Market/02 Method.html b/04 Strategy Library/61 Lunar Cycle in Equity Market/02 Method.html new file mode 100644 index 0000000..450d0cf --- /dev/null +++ b/04 Strategy Library/61 Lunar Cycle in Equity Market/02 Method.html @@ -0,0 +1,65 @@ ++ The lunar calendar data is obtained from the United States Naval Observatory (USNO) website. We import the custom data as a CSV file. + The four phases of the lunar cycle are New Moon, First Quarter, Full Moon and Last Quarter. They are in string format in the data file so + we convert the string names to numbers as New Moon(0), First Quarter(1), Full Moon(2) and Last Quarter(3). +
+
+class MoonPhase(PythonData):
+ "Class to import Phases of the Moon data from Dropbox"
+
+ def GetSource(self, config, date, isLiveMode):
+ return SubscriptionDataSource("https://www.dropbox.com/s/q9rt06tpfjlvymt/MoonPhase.csv?dl=1", SubscriptionTransportMedium.RemoteFile)
+
+ def Reader(self, config, line, date, isLiveMode):
+ index = MoonPhase()
+ index.Symbol = config.Symbol
+ try:
+ # Example File Format: (Data starts from 01/07/2004)
+ # date phase
+ # 2004 Jan 07 15:40 Full Moon
+ data = line.split(',')
+ if data[0] == "date": return None
+ index.Time = datetime.strptime(data[0], "%Y %b %d %H:%M").replace(hour=0, minute=0)
+ if data[1] == "New Moon":
+ index.Value = 0
+ elif data[1] == "First Quarter":
+ index.Value = 1
+ elif data[1] == "Full Moon":
+ index.Value = 2
+ elif data[1] == "Last Quarter":
+ index.Value = 3
+ except:
+ return None
+
+ return index
+
+
+ Research shows that the effect is strongest in emerging markets.
+ Here we choose the iShares MSCI Emerging Markets Index ETF EEM.
+ The algorithm therefore goes long in emerging market index ETF 7 days before the new moon and switch to a short position on ETF 7 days before the full moon.
+ The benchmark is set to EEM.
+
+def Initialize(self):
+ self.SetStartDate(2004, 1, 1)
+ self.SetEndDate(2018, 8, 1)
+ self.SetCash(100000)
+ # import the custom data
+ self.AddData(MoonPhase, "phase", Resolution.Daily)
+ self.AddEquity("EEM", Resolution.Daily)
+ self.SetBenchmark("EEM")
+
+def OnData(self, data):
+ # long in emerging market index ETF 7 days before the new moon (It's the Last Quarter)
+ if self.Securities["phase"].Price == 3 and not self.Portfolio["EEM"].IsLong:
+ self.SetHoldings("EEM", 1)
+ # short on emerging market index ETF 7 days before the full moon (It's the First Quarter)
+ elif self.Securities["phase"].Price == 1 and not self.Portfolio["EEM"].IsShort:
+ self.SetHoldings("EEM", -1)
+
++ The Momentum traders take on a long or short position in the stock, in the hopes that the momentum will continue in the same direction. + The momentum strategy has a higher degree of volatility than most other strategies. + In the tutorial, we'll introduce the trading volume factor to enhance the portfolio return and control the risk of momentum strategy. +
diff --git a/04 Strategy Library/66 Combining Momentum Effect with Volume/02 Method.html b/04 Strategy Library/66 Combining Momentum Effect with Volume/02 Method.html new file mode 100644 index 0000000..a2593a9 --- /dev/null +++ b/04 Strategy Library/66 Combining Momentum Effect with Volume/02 Method.html @@ -0,0 +1,108 @@ +
+ The investment universe consists of all stocks on NYSE and NASDAQ. The momentum is usually defined by the stock return in the last N months.
+ The indicator RateOfChange is constructed to represent the return. The lookback period is one year.
+
+ class SymbolData: + def __init__(self, symbol, lookback): + self.Symbol = symbol + self.ROC = RateOfChange(lookback) + self.Volume = None ++
+ The ROC indicator and volume are updated everyday in CoarseSelectionFunction. Securities which do not have fundamental data are eliminated.
+
+ def CoarseSelectionFunction(self, coarse): + for i in coarse: + if i.Symbol not in self.dataDict: + self.dataDict[i.Symbol] = SymbolData(i.Symbol, self.lookback) + self.dataDict[i.Symbol].ROC.Update(i.EndTime, i.AdjustedPrice) + self.dataDict[i.Symbol].Volume = i.Volume + + if self.monthly_rebalance: + # drop stocks which have no fundamental data + filteredCoarse = [x for x in coarse if (x.HasFundamentalData)] + return [i.Symbol for i in filteredCoarse] + else: + return [] ++
+ Trading volume (turnover) serves as a useful indicator of the level of investor interest in stocks. + The number of sellers tends to exceed the number of buyers when the stock falls into disfavor, which will lead to a falling share price. + When a stock is popular, the number of buyers exceeds the number of sellers, the price tends to rise. + As a result, a firm’s turnover may be a measure of investors' interest in the firm's stock so it could help to identify the future trend of stocks. + Here the turnover is calculated as the ratio of the number of shares traded each day to the number of shares outstanding. +
+
+ In FineSelectionFunction, after the indicator is ready for all symbols in dictionary self.dataDict, turnover is calculated
+ with the Volume and EarningReports.BasicAverageShares.
+
+def FineSelectionFunction(self, fine):
+ if self.monthly_rebalance:
+ dataReady = {symbol: symbolData for (symbol, symbolData) in self.dataDict.items() if symbolData.ROC.IsReady}
+ if len(dataReady) < 100:
+ self.filteredFine = []
+ else:
+ sortedFine = [i for i in fine if i.EarningReports.BasicAverageShares.ThreeMonths != 0 and i.Symbol in dataReady]
+ sortedFineSymbols = [i.Symbol for i in sortedFine]
+ filteredData = {symbol: symbolData for (symbol, symbolData) in dataReady.items() if symbol in sortedFineSymbols}
+ for i in sortedFine:
+ if i.Symbol in filteredData and filteredData[i.Symbol].Volume != 0:
+ filteredData[i.Symbol].Turnover = i.EarningReports.BasicAverageShares.ThreeMonths / filteredData[i.Symbol].Volume
+
++ Stocks are sorted into deciles every month based on previous 12-month returns. + Each momentum decile is then divided into terciles based on turnover. The long and short portfolios are constructed with the highest turnover from the top momentum decile and the highest volume from the bottom momentum decile respectively. +
++for i in sortedFine: + if i.Symbol in filteredData and filteredData[i.Symbol].Volume != 0: + filteredData[i.Symbol].Turnover = i.EarningReports.BasicAverageShares.ThreeMonths / filteredData[i.Symbol].Volume +sortedByROC = sorted(filteredData.values(), key = lambda x: x.ROC.Current.Value, reverse = True) +topROC = sortedByROC[:int(len(sortedByROC)*0.2)] +bottomROC = sortedByROC[-int(len(sortedByROC)*0.2):] +HighTurnoverTopROC = sorted(topROC, key = lambda x: x.Turnover, reverse = True) +HighTurnoverBottomROC = sorted(bottomROC, key = lambda x: x.Turnover, reverse = True) +self.long = [i.Symbol for i in HighTurnoverTopROC[:int(len(HighTurnoverTopROC)*0.01)]] +self.short = [i.Symbol for i in HighTurnoverBottomROC[:int(len(HighTurnoverBottomROC)*0.01)]] +self.filteredFine = self.long + self.short +self.portfolios.append(self.filteredFine) ++
+ A long-short portfolio is held for three months, and then it is rebalanced.
+ Therefore, the investor buys 1/3 of its portfolio for three consecutive months and rebalances 1/3 of its portfolio each month.
+ We save each portfolio in deque list self.portfolios and liquidate the portfolio three-months ago when rebalancing.
+
+def OnData(self, data): + if self.monthly_rebalance and self.filteredFine: + self.filteredFine = None + self.monthly_rebalance = False + + # 1/3 of the portfolio is rebalanced every month + if len(self.portfolios) == self.portfolios.maxlen: + for i in list(self.portfolios)[0]: + self.Liquidate(i) + + # stocks are equally weighted and held for 3 months + short_weight = 1/len(self.short) + for i in self.short: + self.SetHoldings(i, -1/3*short_weight) + + long_weight = 1/len(self.long) + for i in self.long: + self.SetHoldings(i, 1/3*long_weight) ++
+ The short-term reversal strategy buys stocks which are past losers and sells stocks which are past winners. + It is commonly used in the equity market. This algorithm will explore the reversal effect in the futures market. + Research also suggests that trading volume contains information about future market movements. The algorithm will + be constructed with both the volume and return reversal effect. +
diff --git a/04 Strategy Library/71 Short Term Reversal with Futures/02 Method.html b/04 Strategy Library/71 Short Term Reversal with Futures/02 Method.html new file mode 100644 index 0000000..6b0c293 --- /dev/null +++ b/04 Strategy Library/71 Short Term Reversal with Futures/02 Method.html @@ -0,0 +1,108 @@ ++ The daily continuous futures data with the adjusted price is from Quandl. + The investment universe consists of 24 types of US futures contracts: 4 currencies, five financial indices, eight agricultural products, and seven commodities. + The contracts are all front month contracts. +
+
+class Futures(PythonData):
+ # import the futures custom data from dropbox
+ def GetSource(self, config, date, isLiveMode):
+ source = "your_custom_source_url"
+ return SubscriptionDataSource(source, SubscriptionTransportMedium.RemoteFile)
+
+ def Reader(self, config, line, date, isLiveMode):
+ futures = Futures()
+ futures.Symbol = config.Symbol
+ data = line.split(',')
+ if data[0] == "date": return None
+ futures.Time = datetime.strptime(data[0], "%m/%d/%y")
+ futures.Value = float(data[4])
+ futures["settle"] = float(data[4]) # add the settle price
+ futures["volume"] = float(data[5]) # add the volume
+ futures["open_interest"] = float(data[6]) # add the open interest
+ return futures
+
+
+ The algorithm uses a weekly time frame(Wednesday-Wednesday interval). Therefore the self.Schedule.On() will fire the trading every Wednesday.
+ To compare the weekly change of volume and open interest, we create the deque list with the length to be two to save the history data frame of
+ the most recent week and the week before.
+
+ def Initialize(self): + self.SetStartDate(2017, 7, 10) + self.SetEndDate(2018, 8, 1) + self.SetCash(10000000) + + self.tickers = ["CME_SF1_EF", "CME_MP1_FF", "CME_CD1_EF", "CME_ED8_FF", # Currencies + "CME_NQ1_EF", "CME_MD1_EF", "CME_ES1_EF", "CME_YM1_EF", "CME_NK1_EF", # Financial indices + "CME_C1_EF", "CME_SM1_EF", "ICE_CC1_EF", "CME_LC1_EF", # Agricultural product + "CME_KW1_EF", "CME_S1_EF", "ICE_KC1_EF", "CME_LC1_EF", + "CME_HG1_FF", "CME_GC1_EF", "SHFE_AL1_EF", "SHFE_CU1_EF", # Commodities + "CME_CL1_EF", "ICE_T1_FR", "CME_HO1_EF"] + self.length = len(self.tickers) + for ticker in self.tickers: + self.AddData(Futures, ticker) + # create the deque list to save the weekly history dataframe + self.window = deque(maxlen=2) + # rebalance the portfolio every week on Wednesday + self.Schedule.On(self.DateRules.Every(DayOfWeek.Wednesday, DayOfWeek.Wednesday), self.TimeRules.At(0, 0), self.WeeklyTrade) ++
+ In the weekly rebalance function, weekly history data frame is saved. The contract is defined as the high(low) volume contract if the contract's volume changes between the period from t-1 to t and period from t-2 to t-1 is above(below) the median volume change of all contracts,
+ In addition, all contracts are also assigned to either high-open interest (top 50% of changes in open interest) or low-open interest groups (bottom 50% of changes in open interest) based on lagged changes in open interest between the period from t-1 to t and period from t-2 to t-1.
+ We created the method CalculateChange to calculate the increment value and rank the contracts based on the weekly history data frame.
+
+ def WeeklyTrade(self):
+ hist = self.History(self.tickers, self.Time-timedelta(days=7), self.Time,Resolution.Daily)
+ self.window.append(hist)
+ if len(self.window) == self.window.maxlen:
+ hist_t2 = self.window[0] # the weekly history dataframe two week ago
+ hist_t1 = self.window[1] # the weekly history dataframe a week ago
+ top_vol, bottom_vol = self.CalculateChange("volume", hist_t2, hist_t1)
+ top_OI, bottom_OI = self.CalculateChange("open_interest", hist_t2, hist_t1)
+
++ def CalculateChange(self, column_name, hist_t2, hist_t1): + # calculate the weekly change and sort by the colume value + value_t2 = hist_t2[column_name].unstack(level=0).sum(axis=0) + value_t1 = hist_t1[column_name].unstack(level=0).sum(axis=0) + delta = (value_t1 - value_t2).sort_values(ascending=True) + top = list(delta[:int(self.length*0.5)].index) + bottom = list(delta[-int(self.length*0.5):].index) + return top, bottom ++
+ We take the intersection of the top volume group and bottom open interest group. The trading candidates are selected from this group. + Next futures in the intersection are sorted based on the return in the previous week. + The algorithm goes long on futures from the high-volume, low-open interest group with the lowest return and shorts the contract with the highest return. +
+
+# the intersection of top volume group and bottom open interest group
+trade_group = list(set(top_vol) & set(bottom_OI))
+returns = {}
+for ticker in trade_group:
+ res = (hist_t1.loc[ticker]["settle"][-1] - hist_t2.loc[ticker]["settle"][-1]) / hist_t2.loc[ticker]["settle"][-1]
+ returns[ticker] = res
+
+sortedByReturn = sorted(returns, key = lambda x: returns[x])
+
+if len(sortedByReturn) >= 2:
+ if self.Portfolio.Invested:
+ self.Liquidate()
+ self.SetHoldings(sortedByReturn[-1], -0.3)
+ self.SetHoldings(sortedByReturn[0], 0.3)
+
++ Beta is a statistical measure of a stock's volatility in relation to the market. Stock analysts use this measure to get a sense of stocks' risk profiles. + It is also a key component of the capital asset pricing model (CAPM), A stock's price variability is essential to consider when assessing risk. It represents the co-movement instead of the volatility. Therefore, it is possible for a stock to have zero beta and higher volatility than the market. +
++ In the real world, some investors are prohibited from using leverage and other investors’ leverage is limited by margin requirements. + Therefore, their only way to achieve higher returns is to buy more risky stocks, which would cause the overvaluation of higher-beta stocks. + This behavior suggests that high-beta (risky) stocks should deliver lower risk-adjusted returns than low-beta stocks. + In this algorithm, we'll use the leverage to explore the inefficiency of the beta factor. +
diff --git a/04 Strategy Library/77 Beta Factors in Stocks/02 Method.html b/04 Strategy Library/77 Beta Factors in Stocks/02 Method.html new file mode 100644 index 0000000..e043cf6 --- /dev/null +++ b/04 Strategy Library/77 Beta Factors in Stocks/02 Method.html @@ -0,0 +1,125 @@ ++ The investment universe consists of all stocks in Nasdaq and NYSE. + We use the Wilshire 5000 Total Market Index which covers all stocks actively traded in the United States. +
+
+def Initialize(self):
+ self.SetStartDate(2011, 1, 1)
+ self.SetEndDate(2018, 9, 1)
+ self.SetCash(1000000)
+ self.UniverseSettings.Resolution = Resolution.Daily
+ self.AddUniverse(self.CoarseSelectionFunction)
+ self.AddEquity("SPY", Resolution.Daily)
+ # add Wilshire 5000 Total Market Index data from Dropbox
+ self.AddData(Wilshire5000, "W5000", Resolution.Daily)
+ self.Schedule.On(self.DateRules.MonthStart("SPY"), self.TimeRules.AfterMarketOpen("SPY"), self.rebalance)
+ self.data = {}
+ self.monthly_rebalance = False
+ self.long = None
+ self.short = None
+ self.market_price = deque(maxlen=253)
+ hist = self.History(["W5000"], 400, Resolution.Daily)
+ for i in hist.loc["W5000"].itertuples():
+ self.market_price.append(i.value)
+
++ The formula for calculating beta is the covariance of the return of an asset with the return of the market divided by the variance of the return of the market over a certain period. +
+\[\beta_i=\frac{cov(R_i,R_{m})}{Var(R_m)}\] +
+ We choose the 1-year rolling window as the period in the beta calculation. We created the SymbolData class to update the rolling window of return
+ and the calculation of beta.
+
+ class SymbolData: + def __init__(self, symbol): + self.Symbol = symbol + self.window = RollingWindow[Decimal](2) + self.returns = deque(maxlen=252) + + def Update(self, price): + if price != 0: + self.window.Add(price) + if self.window.IsReady: + self.returns.append((self.window[0]-self.window[1])/self.window[1]) + + def IsReady(self): + return len(self.returns) == self.returns.maxlen + + def beta(self, market_ret): + asset_return = np.array(self.returns, dtype=np.float32) + market_return = np.array(market_ret, dtype=np.float32) + return np.cov(asset_return, market_return)[0][1]/np.var(market_return) ++
+ In CoarseSelectionFunction, we filter the stocks which price is lower than five as they are not active in the market.
+ When the return rolling window is ready, Stocks are then ranked in ascending order on the basis of their estimated beta.
+ The algorithm goes long on five stocks at the bottom beta list and short on five stocks at the top beta list.
+
+ def CoarseSelectionFunction(self, coarse):
+
+ if self.Securities["W5000"].Price is not None:
+ self.market_price.append(self.Securities["W5000"].Price)
+ for i in coarse:
+ if i.Symbol not in self.data:
+ self.data[i.Symbol] = SymbolData(i.Symbol)
+ self.data[i.Symbol].Update(i.AdjustedPrice)
+
+ if self.monthly_rebalance:
+ sortedByPrice = [i.Symbol for i in coarse if i.AdjustedPrice>5]
+ ready_data = {symbol: data for symbol, data in self.data.items() if symbol in sortedByPrice and data.IsReady()}
+ if len(ready_data) > 20:
+ self.market_return = np.diff(np.array(self.market_price))/np.array(self.market_price)[:-1]
+ # sort the dictionary in ascending order by beta value
+ sorted_beta = sorted(ready_data, key = lambda x: ready_data[x].beta(self.market_return))
+ self.long = sorted_beta[:5]
+ self.short = sorted_beta[-5:]
+ return self.long+self.short
+ else:
+ self.monthly_rebalance = False
+ return []
+ else:
+ return []
+
++ In each portfolio, securities are weighted by the ranked betas. Lower-beta stocks have larger weights in the low-beta portfolio and higher-beta + stocks have larger weights in the high-beta portfolio. The portfolios are rebalanced every calendar month. +
++def OnData(self, data): + if not self.monthly_rebalance: return + if self.long is None or self.short is None: return + + long_invested = [x.Key for x in self.Portfolio if x.Value.IsLong] + short_invested = [x.Key for x in self.Portfolio if x.Value.IsShort] + + for i in long_invested: + if i not in self.long: + self.Liquidate(i) + + for i in short_invested: + if i not in self.short: + self.Liquidate(i) + + long_scale_factor = 0.5/sum(range(1,len(self.long)+1)) + for rank, symbol in enumerate(self.long): + self.SetHoldings(symbol, (len(self.long)-rank+1)*long_scale_factor) + + short_scale_factor = 0.5/sum(range(1,len(self.long)+1)) + for rank, symbol in enumerate(self.short): + self.SetHoldings(symbol, -(rank+1)*short_scale_factor) + + + self.monthly_rebalance = False + self.long = None + self.short = None ++
+ Some investors are prohibited from using leverage and other investors’ leverage is limited by margin requirements. + Their only way to achieve higher returns is to buy more risky stocks which makes these assets more expensive. + High-beta and risky assets should therefore deliver lower risk-adjusted returns than low-beta assets. + Investors could exploit this inefficiency by using ETFs. This algorithm is going to explore this phenomenon. +
diff --git a/04 Strategy Library/78 Beta Factor in Country Equity Indexes/02 Method.html b/04 Strategy Library/78 Beta Factor in Country Equity Indexes/02 Method.html new file mode 100644 index 0000000..d2c9c93 --- /dev/null +++ b/04 Strategy Library/78 Beta Factor in Country Equity Indexes/02 Method.html @@ -0,0 +1,113 @@ +
+ The implementation of this algorithm uses the alpha framework.
+ The algorithm picks 35 country indexes ETFs as the trading universe. As the symbols in the universe don't change over time,
+ we use the ManualUniverseSelectionModel to subscribe the daily data for those symbols.
+
+ Beta is a statistical measure of a stock's volatility in relation to the market. + Stock analysts use this measure to get a sense of stocks' risk profiles. + The formula for calculating beta is the covariance of the return of an asset with the return of the market divided by the variance of the return of the market over a certain period. +
+\[\beta_i=\frac{cov(R_i,R_{m})}{Var(R_m)}\] ++def beta(self, asset_return, market_return): + asset_return = np.array(asset_return, dtype=np.float32) + market_return = np.array(market_return, dtype=np.float32) + return np.cov(asset_return, market_return)[0][1]/np.var(market_return) ++
+ We use S&P500 ETF as the market measure. The beta for each country is calculated with respect to the SPY using a 1-year rolling window.
+ SymbolData class save the one-year rolling window price data.
+
+class SymbolData: + def __init__(self, symbol): + self.Symbol = symbol + self.Price = deque(maxlen=253) ++
+ self.assets is a dictionary to save the price series for each country ETF. The key is the ETF symbol.
+ For new symbols added to the algorithm, we request the one-year history data to initialize the price series.
+
+def OnSecuritiesChanged(self, algorithm, changes): + for added in changes.AddedSecurities: + if added.Symbol.Value == "SPY": + self.market_price = deque(maxlen=253) + hist_SPY = algorithm.History(["SPY"], 500, Resolution.Daily) + for i in hist_SPY.loc["SPY"].itertuples(): + self.market_price.append(i.close) + + if added not in self.assets and added.Symbol.Value != "SPY": + hist = algorithm.History([added.Symbol.Value], 500, Resolution.Daily) + if not hist.empty: + self.assets[added.Symbol] = SymbolData(added) + for i in hist.loc[added.Symbol.Value].itertuples(): + self.assets[added.Symbol].Price.append(i.close) + + for removed in changes.RemovedSecurities: + self.assets.pop(removed.Symbol) ++
+ In the Alpha model, Update(self, algorithm, data) method updates this model with the latest data from the algorithm.
+ This method is called each time the algorithm receives data for subscribed securities. In this method, we update the price series with new trade bars.
+ The price series is converted to return series. We plug the market return and the country ETF return into the beta formula.
+ ETFs are then ranked in ascending order by their estimated beta. The ranked ETFs are assigned to one of two portfolios: low beta and high beta.
+ Each portfolio contains a quarter of the total assets.
+
+def Update(self, algorithm, data):
+ if data.ContainsKey("SPY"):
+ self.market_price.append(float(algorithm.Securities["SPY"].Price))
+ for key, value in self.assets.items():
+ if data.ContainsKey(key):
+ value.Price.append(float(algorithm.Securities[key].Price))
+ insights = []
+ if self.month != algorithm.Time.month:
+ self.month = algorithm.Time.month
+ beta_values = {}
+ market_return = np.diff(np.array(self.market_price))/np.array(self.market_price)[:-1]
+ long = None
+ for key, value in self.assets.items():
+ if key != "SPY" and len(value.Price) == value.Price.maxlen:
+ asset_return = np.diff(np.array(value.Price))/np.array(value.Price)[:-1]
+ beta_values[key] = self.beta(asset_return, market_return)
+ sorted_by_beta = sorted(beta_values, key = lambda x: beta_values[x])
+
+
+ The algorithm shorts the high-beta portfolio and longs the low-beta portfolio. Securities are rebalanced every calendar month.
+ PortfolioConstructionModel is set to emit the target weight monthly.
+ The time period of insight is from the current day to the end of the calendar month.
+ In Python calendar library, calendar.monthrange(year, month) returns the number of days in a month for the specified year and month.
+ The insight direction is set to be flat for symbols removed from the long/short list at the end of the month.
+
+long = sorted_by_beta[:int(0.25*len(sorted_by_beta))] +short = sorted_by_beta[-int(0.25*len(sorted_by_beta)):] +# day: the weekday of first day of the month +# num_days: number of days in month +day, num_days = calendar.monthrange(algorithm.Time.year, algorithm.Time.month) +insight_period = num_days - algorithm.Time.day - 1 +if long and short: + invested = [x.Key for x in algorithm.Portfolio if x.Value.Invested] + for i in invested: + if algorithm.Portfolio[i].IsLong and i not in long: + insights.append(Insight.Price(i, timedelta(days=1), InsightDirection.Flat)) + if algorithm.Portfolio[i].IsShort and i not in short: + insights.append(Insight.Price(i, timedelta(days=1), InsightDirection.Flat)) + for i in long: + insights.append(Insight.Price(i, timedelta(days=insight_period), InsightDirection.Up)) + for i in short: + insights.append(Insight.Price(i, timedelta(days=insight_period), InsightDirection.Down)) ++
+ Pre-holiday days on the market are often characterized with lower liquidity as a lot of market participants are not involved in the market or they lower their exposure. + Historical research shows that stock prices often behave in a specific manner in each of the two trading days preceding these holidays. + This anomaly in equities is often called the pre-holiday effect. It is the market in-efficiency for short-term traders to gain on the final trading day before a holiday. + In this algorithm, we'll construct a simple strategy to exploit this pre-holiday effect in the equity market. +
diff --git a/04 Strategy Library/83 Pre-Holiday Effect/02 Method.html b/04 Strategy Library/83 Pre-Holiday Effect/02 Method.html new file mode 100644 index 0000000..d1c4444 --- /dev/null +++ b/04 Strategy Library/83 Pre-Holiday Effect/02 Method.html @@ -0,0 +1,27 @@ +
+ TradingCalendar class can help us find all the available holidays during a period of time.
+ GetDaysByType returns trading days of the specified TradingDayType that contains trading events associated with the range of dates.
+ Here we choose the type to be TradingDayType.PublicHoliday and list all holidays from today to the next two days. As PublicHoliday includes weekends,
+ we use the type TradingDayType.Weekend to subtract weekend holidays.
+
+ def OnData(self, data): + calendar1 = self.TradingCalendar.GetDaysByType(TradingDayType.PublicHoliday, self.Time, self.Time+timedelta(days=2)) + calendar2 = self.TradingCalendar.GetDaysByType(TradingDayType.Weekend, self.Time, self.Time+timedelta(days=2)) + holidays = [i.Date for i in calendar1] + weekends = [i.Date for i in calendar2] + public_holidays = list(set(holidays) - set(weekends)) ++
+ The investment vehicle is SPDR S&P500 ETF. The algorithm will trade the ETF if there are holidays within the next two days and stays in cash during other trading days. +
+
+if not self.Portfolio.Invested and len(holidays)>0:
+ self.SetHoldings("SPY", 1)
+elif self.Portfolio.Invested and len(holidays)==0:
+ self.Liquidate()
+
++ Researchers have shown that the historical returns of a mutual fund and the nearness of its net asset value (NAV) to + a previous high can provide significant predictive power about the fund's future returns. In respect to the + historical returns, some have attributed the persistence to investor herding and macroeconomic variables. When it + comes to the NAV, some suggest the outperformance of funds with a NAV near its trailing high is a result of + anchoring bias in investors' psychology. As we do not have access to invest in individual mutual funds on the QC + platform or access to NAV metrics, in this tutorial, we trade asset management firms and use their respective share + price as a proxy for fund performance and NAV. +
diff --git a/04 Strategy Library/85 Momentum in Mutual Fund Returns/02 Method.html b/04 Strategy Library/85 Momentum in Mutual Fund Returns/02 Method.html new file mode 100644 index 0000000..a43b163 --- /dev/null +++ b/04 Strategy Library/85 Momentum in Mutual Fund Returns/02 Method.html @@ -0,0 +1,186 @@ ++ In coarse universe selection, we return symbols that have fundamental data. +
++def SelectCoarse(self, algorithm, coarse): + if self.month == algorithm.Time.month: + return Universe.Unchanged + + return [x.Symbol for x in coarse if x.HasFundamentalData] ++
+ In fine universe selection, we return symbols that Morningstar has classified as being in the asset management industry. +
++def SelectFine(self, algorithm, fine): + self.month = algorithm.Time.month + + return [f.Symbol for f in fine if f.AssetClassification.MorningstarIndustryCode == MorningstarIndustryCode.AssetManagement] ++
+ When constructing the alpha model, we can provide parameters for the lookback windows and the percentage of the universe to + long/short. Both of these arguments are validated in the constructor. By default, this alpha model uses the trailing 6 months to + calculate the rate of change factor and the trailing 12 months to calculate the nearness to historical highs. +
++def __init__(self, roc_lookback_months=6, nearness_lookback_months=12, holding_months=6, pct_long_short=10): + if roc_lookback_months <= 0 or nearness_lookback_months <= 0 or holding_months <= 0: + algorithm.Quit(f"Requirement violated: roc_lookback_months > 0 and nearness_lookback_months > 0 and holding_months > 0") + + if pct_long_short <= 0 or pct_long_short > 50: + algorithm.Quit(f"Requirement violated: 0 < pct_long_short <= 50") + + self.roc_lookback_months = roc_lookback_months + self.nearness_lookback_months = nearness_lookback_months + self.holding_months = holding_months + self.pct_long_short = pct_long_short ++
+ For each security added to the universe, we construct a ROCAndNearness indicator which warm up the lookback windows and registers + a data consolidator. When a security is removed from the universe, we unsubscribe the associated consolidator. +
++def OnSecuritiesChanged(self, algorithm, changes): + for added in changes.AddedSecurities: + roc_and_nearness = ROCAndNearness(added.Symbol, algorithm, self.roc_lookback_months, self.nearness_lookback_months) + self.symbol_data_by_symbol[added.Symbol] = roc_and_nearness + + for removed in changes.RemovedSecurities: + symbol_data = self.symbol_data_by_symbol.pop(removed.Symbol, None) + if symbol_data: + symbol_data.dispose() ++
+ On the first trading day of each month, we rank the symbols in the universe and emit insights for the portfolio construction + model. We instruct the alpha model to emit insights on a monthly basis by adding the following guard to the Update method. +
++def Update(self, algorithm, data): + # Emit insights on a monthly basis + time = algorithm.Time + if self.month == time.month: + return [] + self.month = time.month + + ... ++
+ We only rank symbols that have enough history to fill the rate of change lookback window. Therefore, we define the + IsReady method of the ROCAndNearness as +
++@property +def IsReady(self): + return self.get_lookback(self.roc_lookback_months).shape[0] > 1 ++
+ To rank the symbols, we start by filling a DataFrame with the rate of change and nearness to trailing high values for each + symbol. When the DataFrame is full, we rank the symbols by both metrics and sum the ranks. The symbols with a larger final + sum have a greater index in the `ranked_symbols` list. +
+
+def Update(self, algorithm, data):
+ ...
+ ranking_df = pd.DataFrame()
+ for symbol, symbol_data in self.symbol_data_by_symbol.items():
+ if data.ContainsKey(symbol) and symbol_data.IsReady:
+ row = pd.DataFrame({'ROC': symbol_data.roc, 'Nearness': symbol_data.nearness}, index=[symbol])
+ ranking_df = ranking_df.append(row)
+ ranked_symbols = ranking_df.rank().sum(axis=1).sort_values().index
+ ...
+
++ Calculating the rate of change and nearness factors is done by slicing the historical data into the approriate lookback window + size, and then computing the respective values. +
++@property +def roc(self): + lookback = self.get_lookback(self.roc_lookback_months) + start_price = lookback.iloc[0].open + end_price = lookback.iloc[-1].close + return (end_price - start_price) / start_price + +@property +def nearness(self): + lookback = self.get_lookback(self.nearness_lookback_months) + return lookback.iloc[-1].close / lookback.high.max() ++
+ We return insights that instruct the portfolio construction model to form a balance long-short portfolio. The percentage of the + universe we long and short is customizable in the alpha model constructor. Here, we long the 25% of symbols with the highest + rank, short the 25% of symbols with the lowest ranks, and instruct the portfolio construction model to hold positions for 6 months. +
++def Update(self, algorithm, data): + ... + insights = [] + num_long_short = int(len(ranked_symbols) * (self.pct_long_short / 100)) + if num_long_short > 0: + hold_duration = Expiry.EndOfMonth(time) + relativedelta(months=self.holding_months-1, seconds=-1) + for symbol in ranked_symbols[-num_long_short:]: + insights.append(Insight.Price(symbol, hold_duration, InsightDirection.Up)) + for symbol in ranked_symbols[:num_long_short]: + insights.append(Insight.Price(symbol, hold_duration, InsightDirection.Down)) + return insights ++
+ We utilize a custom portfolio construction model that rebalances monthly and performs allocations based on the net direction of + insights for each symbol. A symbol that has two active insights with an up direction will have twice the allocation than a symbol + with only one. Furthermore, a symbol that has an up active insight and a down active insight will have no position. We calculate + the net direction of the symbols with the following helper method. +
+
+def get_net_direction(self, insights):
+ net_direction_by_symbol = {}
+ num_directional_insights = 0
+
+ for insight in insights:
+ symbol = insight.Symbol
+ direction = insight.Direction
+ if symbol in net_direction_by_symbol:
+ net_direction_by_symbol[symbol] += direction
+ else:
+ net_direction_by_symbol[symbol] = direction
+
+ num_directional_insights += abs(direction)
+
+ return net_direction_by_symbol, num_directional_insights
+
++ To analyze the value of this trading strategy, we compare its performance to buying-and-holding the S&P 500 index + ETF, SPY. We can see the results from the table below. The strategy has a lower Sharpe ratio than the SPY for all of + the time frames we tested, except for the downfall of the 2020 stock market crash. During this time it greatly + outperformed the SPY, achieving a 10.4 Sharpe ratio. We also notice that the strategy generates more consistent + returns than the benchmark, documented by the lower annual standard deviation of returns throughout all the testing + periods. +
+ +| Period Name | +Start Date | +End Date | +Strategy | +Sharpe | +ASD | +
|---|---|---|---|---|---|
| Backtest | +1/1/2015 | +8/16/2020 | +Strategy | +0.192 | +0.046 | +
| Benchmark | +0.709 | +0.186 | +|||
| Fall 2015 | +8/10/2015 | +10/10/2015 | +Strategy | +-1.448 | +0.052 | +
| Benchmark | +-0.724 | +0.251 | +|||
| 2020 Crash | +2/19/2020 | +3/23/2020 | +Strategy | +10.386 | +0.104 | +
| Benchmark | +-1.243 | +0.793 | +|||
| 2020 Recovery | +3/23/2020 | +6/8/2020 | +Strategy | +-2.942 | +0.177 | +
| Benchmark | +13.761 | +0.386 | +
+ We find the lack of performance for this strategy is not largely attributed to the trading fees. After ignoring the + transaction fees, spread costs, and slippage, the strategy still has a lower Sharpe ratio than the benchmark. See + the backtest results here. +
diff --git a/04 Strategy Library/85 Momentum in Mutual Fund Returns/05 Market & Competition Qualification.html b/04 Strategy Library/85 Momentum in Mutual Fund Returns/05 Market & Competition Qualification.html new file mode 100644 index 0000000..fbc487d --- /dev/null +++ b/04 Strategy Library/85 Momentum in Mutual Fund Returns/05 Market & Competition Qualification.html @@ -0,0 +1,15 @@ ++ Although this strategy passes several of the + metrics required for Alpha Streams and + the Quant League competition, it requires further work to meet the following requirements: +
+ + ++ The momentum pattern examined throughout this tutorial has a greater Sharpe ratio than the SPY during the downfall + of the 2020 stock market crash and has more a lower annual standard deviation of returns than the SPY over all the + periods we tested. However, we conclude the strategy, which is loosely based on the research of Sapp (2010), does + not consistently outperform our benchmark. To continue the development of this strategy, future areas of research + include: +
+ + ++ Based on the market cap, we can divide the stocks into large-cap, mid-cap and small-cap stocks. In each of those categories, we can subdivide them into value stocks and growth stocks. The growth stocks typically grow revenues faster than the market average and have relatively high P/E ratios and P/B ratios. The value stocks have relatively low P/E ratios and P/B ratios. There are six styles in total. + We've demonstrated various momentum strategies to generate excess returns at the firm, industry, and country level. + In this algorithm, we'll explore the momentum effect at the style index ETF level. +
diff --git a/04 Strategy Library/91 Momentum and Style Rotation Effect/02 Method.html b/04 Strategy Library/91 Momentum and Style Rotation Effect/02 Method.html new file mode 100644 index 0000000..2efbe7b --- /dev/null +++ b/04 Strategy Library/91 Momentum and Style Rotation Effect/02 Method.html @@ -0,0 +1,49 @@ +
+ We choose six index ETFs to represent different equity styles(small-cap value, mid-cap value, large-cap value,
+ small-cap growth, mid-cap growth, large-cap growth). After adding the assets, we save the momentum indicator in
+ the dictionary self.mom for each style. The formation period of 12-month is used to gauge the value of momentum.
+
+def Initialize(self): + + self.SetStartDate(2001, 1, 1) + self.SetEndDate(2018, 8, 1) + self.SetCash(100000) + + tickers = ["IJJ", # iShares S&P Mid-Cap 400 Value Index ETF + "IJK", # iShares S&P Mid-Cap 400 Growth ETF + "IJS", # iShares S&P Small-Cap 600 Value ETF + "IJT", # iShares S&P Small-Cap 600 Growth ETF + "IVE", # iShares S&P 500 Value Index ETF + "IVW"] # iShares S&P 500 Growth ETF + + lookback = 12*20 + + # Save all momentum indicator into the dictionary + self.mom = dict() + for ticker in tickers: + symbol = self.AddEquity(ticker, Resolution.Daily).Symbol + self.mom[symbol] = self.MOM(symbol, lookback) ++
+ Six ETFs are ranked based on their prior 12-month performance in the formation period. The algorithm + goes long the top performing ETF and short the ETF at the bottom and holds the position for one month. + The portfolio is rebalanced at the start of next month. +
++def Rebalance(self): + # Order the MOM dictionary by value + sorted_mom = sorted(self.mom, key = lambda x: self.mom[x].Current.Value) + + # Liquidate the ETFs that are no longer selected + for symbol in sorted_mom[1:-1]: + if self.Portfolio[symbol].Invested: + self.Liquidate(symbol, 'No longer selected') + + self.SetHoldings(sorted_mom[-1], -0.5) # Short the ETF with lowest MOM + self.SetHoldings(sorted_mom[0], 0.5) # Long the ETF with highest MOM ++
+The Price to Earnings ratio, also known as the P/E ratio, is the ratio of a company's +market price per share to the company's earnings per share. +
++ \[Price \ to \ Earnings\ Ratio=\frac{Market \ price \ per \ share}{Earnings \ per \ share \ from \ the \ most \ recent \ financial \ year}\] +
++The P/E ratio is often used by investors to determine the valuation of a company's stock. Research suggests that a portfolio that consists of stocks with relatively low P/E +ratio outperforms a portfolio that consists of stocks with relatively high P/E ratio. +
diff --git a/04 Strategy Library/92 Price Earnings Anomaly/02 Method.html b/04 Strategy Library/92 Price Earnings Anomaly/02 Method.html new file mode 100644 index 0000000..def8def --- /dev/null +++ b/04 Strategy Library/92 Price Earnings Anomaly/02 Method.html @@ -0,0 +1,51 @@ ++We pick the 10 stocks that have the lowest P/E ratio in our universe, at the beginning of each year, +and we invest an equal amount of capital in each stock. +
+ +
+To construct the universe, first, we eliminate stocks which don't have fundamental data and
+stocks that have a lower price than $5 per share, using the CoarseSelectionFunction.
+
+ def CoarseSelectionFunction(self, coarse): + + if self.Time.year == self.year: + return self.symbols + + # drop stocks which have no fundamental data or have low price + CoarseWithFundamental = [x for x in coarse if x.HasFundamentalData and x.Price > 5] + sortedByDollarVolume = sorted(CoarseWithFundamental, key=lambda x: x.DollarVolume, reverse=False) + + return [i.Symbol for i in sortedByDollarVolume[:self._NumCoarseStocks]] ++
+Then, in the FineSelectionFunction, we retrieve the list of 10 stocks, that have the lowest P/E ratio.
+
+ + def FineSelectionFunction(self, fine): + + if self.Time.year == self.year: + return self.symbols + + self.year = self.Time.year + + fine = [x for x in fine if x.ValuationRatios.PERatio > 0] + sortedPERatio = sorted(fine, key=lambda x: x.ValuationRatios.PERatio) + + self.symbols = [i.Symbol for i in sortedPERatio[:self._NumStocksInPortfolio]] + + return self.symbols ++
+In OnData(), we buy the 10 stocks that have the lowest P/E ratio in our universe. We rebalance the portfolio at the beginning of each year.
+
+The portfolio significantly outperforms the benchmark, S&P 500, during the three and half years backtest period, from the beginning of the year 2016 to July of the year 2019. +
++The universe of stocks is filtered using dollar volume and price criteria. Most of the stocks chosen by the algorithm during the backtest period are small market capitalization stocks. +
++In theory, there is an additional factor, to the small P/E ratio factor, contributing to the excess returns of the portfolio, relative to the benchmark. This additional factor is known as the size factor, where size in this respect, is the market capitalization of a stock. +
++Ranking portfolios on market capitalization and subsequently tracking their performance has demonstrated that portfolio of stocks with a small market capitalization outperforms a portfolio of stocks with large market capitalization. Another investment strategy in the strategy library, Small Market Capitalization Stock Premium, demonstrates how to form a portfolio that only consists of stocks with relatively low market capitalization. +
diff --git a/04 Strategy Library/92 Price Earnings Anomaly/05 References.html b/04 Strategy Library/92 Price Earnings Anomaly/05 References.html new file mode 100644 index 0000000..b9f2706 --- /dev/null +++ b/04 Strategy Library/92 Price Earnings Anomaly/05 References.html @@ -0,0 +1,9 @@ +- Here we use data from the yahoo_finance API. -
-import quandl -quandl.ApiConfig.api_key = 'dRQxJ15_2nrLznxr1Nn4' --
- We will create a Series named "aapl" whose values are Apple's daily closing prices, which are of course indexed by dates: -
-aapl_table = quandl.get('WIKI/AAPL')
-aapl = aapl_table['Adj. Close']['2017']
-print aapl
-
-- Recall that we can fetch a specific data point using series['yyyy-mm-dd']. We can also fetch the data in a specific month using series['yyyy-mm']. -
-print aapl['2017-3'] -Date -2017-03-01 138.657681 -2017-03-02 137.834404 -2017-03-03 138.647762 -2017-03-06 138.211326 -2017-03-07 138.389868 -2017-03-08 137.874080 -2017-03-09 137.556672 -2017-03-10 138.012946 -2017-03-13 138.072460 -2017-03-14 137.864161 -2017-03-15 139.322254 -2017-03-16 139.550391 -2017-03-17 138.856061 -2017-03-20 140.314154 -2017-03-21 138.707276 -2017-03-22 140.274478 -2017-03-23 139.778528 -2017-03-24 139.500796 -2017-03-27 139.738852 -2017-03-28 142.635200 -2017-03-29 142.952608 -2017-03-30 142.764147 -2017-03-31 142.496334 --
- Or in several consecutive months: -
-aapl['2017-2':'2017-4'] --
- .head(N) and .tail(N) are methods for quickly accessing the first or last N elements. -
-print aapl.head() -print aapl.tail(10) --
- The output: -
--Date -2017-01-03 114.715378 -2017-01-04 114.586983 -2017-01-05 115.169696 -2017-01-06 116.453639 -2017-01-09 117.520300 -Name: Adj. Close, dtype: float64 -Date -2017-08-08 159.433108 -2017-08-09 160.409148 -2017-08-10 155.270000 -2017-08-11 157.480000 -2017-08-14 159.850000 -2017-08-15 161.600000 -2017-08-16 160.950000 -2017-08-17 157.870000 -2017-08-18 157.500000 -2017-08-21 157.210000 -Name: Adj. Close, dtype: float64 --
+ Here we use the Quandl API to retrieve data... +
+import quandl +quandl.ApiConfig.api_key = 'dRQxJ15_2nrLznxr1Nn4' ++
+ We will create a Series named "aapl" whose values are Apple's daily closing prices, which are of course indexed by dates: +
+aapl_table = quandl.get('WIKI/AAPL')
+aapl = aapl_table['Adj. Close']['2017']
+print aapl
+
++ Recall that we can fetch a specific data point using series['yyyy-mm-dd']. We can also fetch the data in a specific month using series['yyyy-mm']. +
+print aapl['2017-3'] +Date +2017-03-01 138.657681 +2017-03-02 137.834404 +2017-03-03 138.647762 +2017-03-06 138.211326 +2017-03-07 138.389868 +2017-03-08 137.874080 +2017-03-09 137.556672 +2017-03-10 138.012946 +2017-03-13 138.072460 +2017-03-14 137.864161 +2017-03-15 139.322254 +2017-03-16 139.550391 +2017-03-17 138.856061 +2017-03-20 140.314154 +2017-03-21 138.707276 +2017-03-22 140.274478 +2017-03-23 139.778528 +2017-03-24 139.500796 +2017-03-27 139.738852 +2017-03-28 142.635200 +2017-03-29 142.952608 +2017-03-30 142.764147 +2017-03-31 142.496334 ++
+ Or in several consecutive months: +
+aapl['2017-2':'2017-4'] ++
+ .head(N) and .tail(N) are methods for quickly accessing the first or last N elements. +
+print aapl.head() +print aapl.tail(10) ++
+ The output: +
++Date +2017-01-03 114.715378 +2017-01-04 114.586983 +2017-01-05 115.169696 +2017-01-06 116.453639 +2017-01-09 117.520300 +Name: Adj. Close, dtype: float64 +Date +2017-08-08 159.433108 +2017-08-09 160.409148 +2017-08-10 155.270000 +2017-08-11 157.480000 +2017-08-14 159.850000 +2017-08-15 161.600000 +2017-08-16 160.950000 +2017-08-17 157.870000 +2017-08-18 157.500000 +2017-08-21 157.210000 +Name: Adj. Close, dtype: float64 ++
- In the last chapter we had a glimpse of Pandas. In this chapter we will learn about resampling methods and the DataFrame object, which is a powerful tool for financial data analysis. -
-- Here we use data from the yahoo_finance API. -
-import quandl -quandl.ApiConfig.api_key = 'dRQxJ15_2nrLznxr1Nn4' --
- We will create a Series named "aapl" whose values are Apple's daily closing prices, which are of course indexed by dates: -
-aapl_table = quandl.get('WIKI/AAPL')
-aapl = aapl_table['Adj. Close']['2017']
-print aapl
-
-- Recall that we can fetch a specific data point using series['yyyy-mm-dd']. We can also fetch the data in a specific month using series['yyyy-mm']. -
-print aapl['2017-3'] -Date -2017-03-01 138.657681 -2017-03-02 137.834404 -2017-03-03 138.647762 -2017-03-06 138.211326 -2017-03-07 138.389868 -2017-03-08 137.874080 -2017-03-09 137.556672 -2017-03-10 138.012946 -2017-03-13 138.072460 -2017-03-14 137.864161 -2017-03-15 139.322254 -2017-03-16 139.550391 -2017-03-17 138.856061 -2017-03-20 140.314154 -2017-03-21 138.707276 -2017-03-22 140.274478 -2017-03-23 139.778528 -2017-03-24 139.500796 -2017-03-27 139.738852 -2017-03-28 142.635200 -2017-03-29 142.952608 -2017-03-30 142.764147 -2017-03-31 142.496334 --
- Or in several consecutive months: -
-aapl['2017-2':'2017-4'] --
- .head(N) and .tail(N) are methods for quickly accessing the first or last N elements. -
-print aapl.head() -print aapl.tail(10) --
- The output: -
--Date -2017-01-03 114.715378 -2017-01-04 114.586983 -2017-01-05 115.169696 -2017-01-06 116.453639 -2017-01-09 117.520300 -Name: Adj. Close, dtype: float64 -Date -2017-08-08 159.433108 -2017-08-09 160.409148 -2017-08-10 155.270000 -2017-08-11 157.480000 -2017-08-14 159.850000 -2017-08-15 161.600000 -2017-08-16 160.950000 -2017-08-17 157.870000 -2017-08-18 157.500000 -2017-08-21 157.210000 -Name: Adj. Close, dtype: float64 --
- series.resample(freq) is a class called "DatetimeIndexResampler" which groups data in a Series object into regular time intervals. The argument "freq" determines the length of each interval.
-
- series.resample.mean() is a complete statement that groups data into intervals, and then compute the mean of each interval. For example, if we want to aggregate the daily data into monthly data by mean:
-
by_month = aapl.resample('M').mean()
-print by_month
-Date
-2017-01-31 118.093136
-2017-02-28 132.456268
-2017-03-31 139.478802
-2017-04-30 141.728436
-2017-05-31 151.386305
-2017-06-30 147.233064
-2017-07-31 147.706190
-2017-08-31 157.444303
-
-- We can also aggregate the data by week: -
- -by_week = aapl.resample('W').mean()
-print by_week.head()
-
-Date
-2017-01-31 120.932434
-2017-02-28 136.551200
-2017-03-31 143.532630
-2017-04-30 144.179981
-2017-05-31 156.100000
-2017-06-30 155.450000
-2017-07-31 153.460000
-
-- We can choose almost any frequency by using the format 'nf', where 'n' is an integer and 'f' is M for month, W for week and D for day. -
-three_day = aapl.resample('3D').mean()
-two_week = aapl.resample('2W').mean()
-two_month = aapl.resample('2M').mean()
-
-- Besides the mean() method, other methods can also be used with the resampler: -
- -std = aapl.resample('W').std() # standard deviation
-max = aapl.resample('W').max() # maximum value
-min = aapl.resample('W').min() # minimum value
-
-- Often we want to calculate monthly returns of a stock, based on prices on the last day of each month. To fetch those prices, we use the series.resample.agg() method: -
- -last_day = aapl.resample('M').agg(lambda x: x[-1])
-print last_day
-Date
-2017-01-31 119.851150
-2017-02-28 135.880362
-2017-03-31 142.496334
-2017-04-30 142.486415
-2017-05-31 152.142689
-2017-06-30 143.438008
-2017-07-31 148.248489
-2017-08-31 157.210000
-
-- Or directly calculate the monthly rates of return using the data for the first day and the last day: -
- -monthly_return = aapl.resample('M').agg(lambda x: x[-1]/x[1] - 1)
-print monthly_return
-
-Date
-2017-01-31 0.045940
-2017-02-28 0.070409
-2017-03-31 0.033823
-2017-04-30 -0.007736
-2017-05-31 0.039829
-2017-06-30 -0.073528
-2017-07-31 0.033035
-2017-08-31 0.004505
-
-- Series object also provides us some convenient methods to do some quick calculation. -
- -print monthly_return.mean() -print monthly_return.std() -print monthly_return.max() -[out]: 0.0208974076157 - 0.0476398315185 - 0.0704090212384 --
- Another two methods frequently used on Series are .diff() and .pct_change(). The former calculates the difference between consecutive elements, and the latter calculates the percentage change. -
-print last_day.diff() -print last_day.pct_change() - -Date -2017-01-31 NaN -2017-02-28 16.029211 -2017-03-31 6.615972 -2017-04-30 -0.009919 -2017-05-31 9.656274 -2017-06-30 -8.704681 -2017-07-31 4.810482 -2017-08-31 8.961511 -Freq: M, Name: Adj. Close, dtype: float64 -Date -2017-01-31 NaN -2017-02-28 0.133743 -2017-03-31 0.048690 -2017-04-30 -0.000070 -2017-05-31 0.067770 -2017-06-30 -0.057214 -2017-07-31 0.033537 -2017-08-31 0.060449 --
- Notice that we induced a NaN value while calculating percentage changes i.e. returns. -
- -- When dealing with NaN values, we usually either removing the data point or fill it with a specific value. Here we fill it with 0: -
- -daily_return = last_day.pct_change() -print daily_return.fillna(0) - -Date -2017-01-31 0.000000 -2017-02-28 0.133743 -2017-03-31 0.048690 -2017-04-30 -0.000070 -2017-05-31 0.067770 -2017-06-30 -0.057214 -2017-07-31 0.033537 -2017-08-31 0.060449 --
- Alternatively, we can fill a NaN with the next fitted value. This is called 'backward fill', or 'bfill' in short: -
-daily_return = last_day.pct_change() -print daily_return.fillna(method = 'bfill') - -Date -2017-01-31 0.133743 -2017-02-28 0.133743 -2017-03-31 0.048690 -2017-04-30 -0.000070 -2017-05-31 0.067770 -2017-06-30 -0.057214 -2017-07-31 0.033537 -2017-08-31 0.060449 --
- As expected, since there is a 'backward fill' method, there must be a 'forward fill' method, or 'ffill' in short. However we can't use it here because the NaN is the first value. -
- -- We can also simply remove NaN values by .dropna() -
- -daily_return = last_day.pct_change().dropna() -print daily_return - -Date -2017-02-28 0.133743 -2017-03-31 0.048690 -2017-04-30 -0.000070 -2017-05-31 0.067770 -2017-06-30 -0.057214 -2017-07-31 0.038050 --
- The DataFrame is the most commonly used data structure in Pandas. It is essentially a table, just like an Excel spreadsheet. -
-- More precisely, a DataFrame is a collection of Series objects, each of which may contain different data types. A DataFrame can be created from various data types: dictionary, 2-D numpy.ndarray, a Series or another DataFrame. -
-- The most common method of creating a DataFrame is passing a dictionary: -
-dict = {'AAPL': [143.5, 144.09, 142.73, 144.18, 143.77],
- 'GOOG': [898.7, 911.71, 906.69, 918.59, 926.99],
- 'IBM': [155.58, 153.67, 152.36, 152.94, 153.49]}
-dates = pd.date_range('2017-07-03', periods = 5, freq = 'D')
-df = pd.DataFrame(dict, index = dates)
-print df
- AAPL GOOG IBM
-2017-07-03 143.50 898.70 155.58
-2017-07-04 144.09 911.71 153.67
-2017-07-05 142.73 906.69 152.36
-2017-07-06 144.18 918.59 152.94
-2017-07-07 143.77 926.99 153.49
-
-- We can fetch values in a DataFrame by columns and index. Each column in a DataFrame is essentially a Pandas Series. We can fetch a column by square brackets: df['column_name'] -
-- If a column name contains no spaces, then we can also use df.column_name to fetch a column: -
- -df = aapl_table -print df.Close.tail(5) -print df['Adj. Volume'].tail(5) -Date -2017-07-24 152.09 -2017-07-25 152.74 -2017-07-26 153.46 -2017-07-27 150.56 -2017-07-28 149.50 -Name: Close, dtype: float64 -Date -2017-07-24 21122730.0 -2017-07-25 18612649.0 -2017-07-26 15172136.0 -2017-07-27 32175875.0 -2017-07-28 16832947.0 -Name: Adj. Volume, dtype: float64 --
- All the methods we applied to a Series index such as iloc[], loc[] and resampling methods, can also be applied to a DataFrame: -
- -aapl_2016 = df['2016']
-aapl_month = aapl_2016.resample('M').agg(lambda x: x[-1])
-print aapl_month
-
-- Open High Low Close Volume Ex-Dividend \ -Date -2016-01-31 94.79 97.3400 94.35 97.34 64416504.0 0.0 -2016-02-29 96.86 98.2300 96.65 96.69 35216277.0 0.0 -2016-03-31 109.72 109.9000 108.88 108.99 25888449.0 0.0 -2016-04-30 93.99 94.7200 92.51 93.74 68531478.0 0.0 -2016-05-31 99.60 100.4000 98.82 99.86 42307212.0 0.0 -2016-06-30 94.44 95.7700 94.30 95.60 35836356.0 0.0 -2016-07-31 104.19 104.5500 103.68 104.21 27733688.0 0.0 -2016-08-31 105.66 106.5699 105.64 106.10 29662406.0 0.0 -2016-09-30 112.46 113.3700 111.80 113.05 36379106.0 0.0 -2016-10-31 113.65 114.2300 113.20 113.54 26419398.0 0.0 -2016-11-30 111.56 112.2000 110.27 110.52 36162258.0 0.0 -2016-12-31 116.65 117.2000 115.43 115.82 30586265.0 0.0 - - Split Ratio Adj. Open Adj. High Adj. Low Adj. Close \ -Date -2016-01-31 1.0 91.952819 94.426495 91.525989 94.426495 -2016-02-29 1.0 94.466655 95.802804 94.261844 94.300856 -2016-03-31 1.0 107.008893 107.184446 106.189649 106.296931 -2016-04-30 1.0 91.667571 92.379533 90.224141 91.423748 -2016-05-31 1.0 97.732787 98.517789 96.967410 97.987913 -2016-06-30 1.0 92.669522 93.974588 92.532147 93.807775 -2016-07-31 1.0 102.236738 102.589989 101.736299 102.256363 -2016-08-31 1.0 104.237384 105.135033 104.217653 104.671460 -2016-09-30 1.0 110.945828 111.843576 110.294715 111.527885 -2016-10-31 1.0 112.119806 112.691997 111.675865 112.011287 -2016-11-30 1.0 110.629129 111.263789 109.349893 109.597807 -2016-12-31 1.0 115.676657 116.222068 114.466837 114.853583 - - Adj. Volume -Date -2016-01-31 64416504.0 -2016-02-29 35216277.0 -2016-03-31 25888449.0 -2016-04-30 68531478.0 -2016-05-31 42307212.0 -2016-06-30 35836356.0 -2016-07-31 27733688.0 -2016-08-31 29662406.0 -2016-09-30 36379106.0 -2016-10-31 26419398.0 -2016-11-30 36162258.0 -2016-12-31 30586265.0 --
- We may select certain columns of a DataFrame using their names: -
- -aapl_bar = aapl_month[['Open', 'High', 'Low', Close']] -print aapl_bar - - Open High Low Close -Date -2016-01-31 94.79 97.3400 94.35 97.34 -2016-02-29 96.86 98.2300 96.65 96.69 -2016-03-31 109.72 109.9000 108.88 108.99 -2016-04-30 93.99 94.7200 92.51 93.74 -2016-05-31 99.60 100.4000 98.82 99.86 -2016-06-30 94.44 95.7700 94.30 95.60 -2016-07-31 104.19 104.5500 103.68 104.21 -2016-08-31 105.66 106.5699 105.64 106.10 -2016-09-30 112.46 113.3700 111.80 113.05 -2016-10-31 113.65 114.2300 113.20 113.54 -2016-11-30 111.56 112.2000 110.27 110.52 -2016-12-31 116.65 117.2000 115.43 115.82 --
- We can even specify both rows and columns using loc[]. The row indices and column names are separated by a comma: -
- -print aapl_month.loc['2016-03':'2016-06', ['Open', 'High', 'Low', 'Close']] - - Open High Low Close -Date -2016-03-31 109.72 109.90 108.88 108.99 -2016-04-30 93.99 94.72 92.51 93.74 -2016-05-31 99.60 100.40 98.82 99.86 -2016-06-30 94.44 95.77 94.30 95.60 --
- The subset methods in DataFrame is quite useful. By writing logical statements in square brackets, we can make customized subsets: -
- -above = aapl_bar[aapl_bar.Close > np.mean(aapl_bar.Close)] -print above - - Open High Low Close -Date -2016-03-31 109.72 109.9000 108.88 108.99 -2016-08-31 105.66 106.5699 105.64 106.10 -2016-09-30 112.46 113.3700 111.80 113.05 -2016-10-31 113.65 114.2300 113.20 113.54 -2016-11-30 111.56 112.2000 110.27 110.52 -2016-12-31 116.65 117.2000 115.43 115.82 --
- As mentioned, all methods that apply to a Series can also be applied to a DataFrame. Here we add a new column to an existing DataFrame: -
-aapl_bar['rate_return'] = aapl_bar.Close.pct_change() -print aapl_bar - - Open High Low Close rate_return -Date -2016-01-31 94.79 97.3400 94.35 97.34 NaN -2016-02-29 96.86 98.2300 96.65 96.69 -0.006678 -2016-03-31 109.72 109.9000 108.88 108.99 0.127211 -2016-04-30 93.99 94.7200 92.51 93.74 -0.139921 -2016-05-31 99.60 100.4000 98.82 99.86 0.065287 -2016-06-30 94.44 95.7700 94.30 95.60 -0.042660 -2016-07-31 104.19 104.5500 103.68 104.21 0.090063 -2016-08-31 105.66 106.5699 105.64 106.10 0.018136 -2016-09-30 112.46 113.3700 111.80 113.05 0.065504 -2016-10-31 113.65 114.2300 113.20 113.54 0.004334 -2016-11-30 111.56 112.2000 110.27 110.52 -0.026599 -2016-12-31 116.65 117.2000 115.43 115.82 0.047955 --
- Here the calculation introduced a NaN value. If the DataFrame is large, we would not be able to observe it. isnull() provides a convenient way to check abnormal values. -
- -missing = aapl_bar.isnull() -print missing -print '---------------------------------------------' -print missing.describe() - - Open High Low Close rate_return -Date -2016-01-31 False False False False True -2016-02-29 False False False False False -2016-03-31 False False False False False -2016-04-30 False False False False False -2016-05-31 False False False False False -2016-06-30 False False False False False -2016-07-31 False False False False False -2016-08-31 False False False False False -2016-09-30 False False False False False -2016-10-31 False False False False False -2016-11-30 False False False False False -2016-12-31 False False False False False - ---------------------------------------------- - - Open High Low Close rate_return -count 12 12 12 12 12 -unique 1 1 1 1 2 -top False False False False False -freq 12 12 12 12 11 --
- The row labelled "unique" indicates the number of unique values in each column. Since the "rate_return" column has 2 unique values, it has at least one missing value. -
-- We can deduce the number of missing values by comparing "count" with "freq". There are 12 counts and 11 False values, so there is one True value which corresponds to the missing value. -
-- We can also find the rows with missing values easily: -
- -print missing[missing.rate_return == True] - - Open High Low Close rate_return -Date -2016-01-31 False False False False True --
- Usually when dealing with missing data, we either delete the whole row or fill it with some value. As we introduced in the Series chapter, the same method dropna() and fillna() can be applied to a DataFrame. -
- -drop = aapl_bar.dropna() -print drop -print '\n--------------------------------------------------\n' -fill = aapl_bar.fillna(0) -print fill - - Open High Low Close rate_return -Date -2016-02-29 96.86 98.2300 96.65 96.69 -0.006678 -2016-03-31 109.72 109.9000 108.88 108.99 0.127211 -2016-04-30 93.99 94.7200 92.51 93.74 -0.139921 -2016-05-31 99.60 100.4000 98.82 99.86 0.065287 -2016-06-30 94.44 95.7700 94.30 95.60 -0.042660 -2016-07-31 104.19 104.5500 103.68 104.21 0.090063 -2016-08-31 105.66 106.5699 105.64 106.10 0.018136 -2016-09-30 112.46 113.3700 111.80 113.05 0.065504 -2016-10-31 113.65 114.2300 113.20 113.54 0.004334 -2016-11-30 111.56 112.2000 110.27 110.52 -0.026599 -2016-12-31 116.65 117.2000 115.43 115.82 0.047955 - --------------------------------------------------- - - Open High Low Close rate_return -Date -2016-01-31 94.79 97.3400 94.35 97.34 0.000000 -2016-02-29 96.86 98.2300 96.65 96.69 -0.006678 -2016-03-31 109.72 109.9000 108.88 108.99 0.127211 -2016-04-30 93.99 94.7200 92.51 93.74 -0.139921 -2016-05-31 99.60 100.4000 98.82 99.86 0.065287 -2016-06-30 94.44 95.7700 94.30 95.60 -0.042660 -2016-07-31 104.19 104.5500 103.68 104.21 0.090063 -2016-08-31 105.66 106.5699 105.64 106.10 0.018136 -2016-09-30 112.46 113.3700 111.80 113.05 0.065504 -2016-10-31 113.65 114.2300 113.20 113.54 0.004334 -2016-11-30 111.56 112.2000 110.27 110.52 -0.026599 -2016-12-31 116.65 117.2000 115.43 115.82 0.047955 --
- We have seen how to extract a Series from a dataFrame. Now we need to consider how to merge a Series or a DataFrame into another one. -
-- In Pandas, the function concat() allows us to merge multiple Series into a DataFrame: -
- -s1 = pd.Series([143.5, 144.09, 142.73, 144.18, 143.77], name = 'AAPL') -s2 = pd.Series([898.7, 911.71, 906.69, 918.59, 926.99], name = 'GOOG') -data_frame = pd.concat([s1, s2], axis = 1) -print data_frame - - AAPL GOOG -0 143.50 898.70 -1 144.09 911.71 -2 142.73 906.69 -3 144.18 918.59 -4 143.77 926.99 --
- The "axis = 1" parameter will join two DataFrames by columns: -
- -log_price = np.log(aapl_bar.Close) -log_price.name = 'log_price' -print log_price -print '\n--------------------------------------------\n' -concat = pd.concat([aapl_bar, log_price], axis = 1) -print concat - -Date -2016-01-31 4.578210 -2016-02-29 4.571510 -2016-03-31 4.691256 -2016-04-30 4.540525 -2016-05-31 4.603769 -2016-06-30 4.560173 -2016-07-31 4.646408 -2016-08-31 4.664382 -2016-09-30 4.727830 -2016-10-31 4.732155 -2016-11-30 4.705197 -2016-12-31 4.752037 -Freq: M, Name: log_price, dtype: float64 - --------------------------------------------- - - Open High Low Close rate_return log_price -Date -2016-01-31 94.79 97.3400 94.35 97.34 NaN 4.578210 -2016-02-29 96.86 98.2300 96.65 96.69 -0.006678 4.571510 -2016-03-31 109.72 109.9000 108.88 108.99 0.127211 4.691256 -2016-04-30 93.99 94.7200 92.51 93.74 -0.139921 4.540525 -2016-05-31 99.60 100.4000 98.82 99.86 0.065287 4.603769 -2016-06-30 94.44 95.7700 94.30 95.60 -0.042660 4.560173 -2016-07-31 104.19 104.5500 103.68 104.21 0.090063 4.646408 -2016-08-31 105.66 106.5699 105.64 106.10 0.018136 4.664382 -2016-09-30 112.46 113.3700 111.80 113.05 0.065504 4.727830 -2016-10-31 113.65 114.2300 113.20 113.54 0.004334 4.732155 -2016-11-30 111.56 112.2000 110.27 110.52 -0.026599 4.705197 -2016-12-31 116.65 117.2000 115.43 115.82 0.047955 4.752037 --
- We can also join two DataFrames by rows. Consider these two DataFrames: -
- -df_volume = aapl_table.loc['2016-10':'2017-04', ['Volume', 'Split Ratio']].resample('M').agg(lambda x: x[-1])
-print df_volume
-print '\n-------------------------------------------\n'
-df_2017 = aapl_table.loc['2016-10':'2017-04', ['Open', 'High', 'Low', 'Close']].resample('M').agg(lambda x: x[-1])
-print df_2017
-
- Volume Split Ratio
-Date
-2016-10-31 26419398.0 1.0
-2016-11-30 36162258.0 1.0
-2016-12-31 30586265.0 1.0
-2017-01-31 49200993.0 1.0
-2017-02-28 23482860.0 1.0
-2017-03-31 19661651.0 1.0
-2017-04-30 20247187.0 1.0
-
--------------------------------------------
-
- Open High Low Close
-Date
-2016-10-31 113.65 114.230 113.20 113.54
-2016-11-30 111.56 112.200 110.27 110.52
-2016-12-31 116.65 117.200 115.43 115.82
-2017-01-31 121.15 121.390 120.62 121.35
-2017-02-28 137.08 137.435 136.70 136.99
-2017-03-31 143.72 144.270 143.01 143.66
-2017-04-30 144.09 144.300 143.27 143.65
-
-- Now we merge the DataFrames with our DataFrame 'aapl_bar' -
- -concat = pd.concat([aapl_bar, df_volume], axis = 1) -print concat - - Open High Low Close rate_return Volume \ -Date -2016-01-31 94.79 97.3400 94.35 97.34 NaN NaN -2016-02-29 96.86 98.2300 96.65 96.69 -0.006678 NaN -2016-03-31 109.72 109.9000 108.88 108.99 0.127211 NaN -2016-04-30 93.99 94.7200 92.51 93.74 -0.139921 NaN -2016-05-31 99.60 100.4000 98.82 99.86 0.065287 NaN -2016-06-30 94.44 95.7700 94.30 95.60 -0.042660 NaN -2016-07-31 104.19 104.5500 103.68 104.21 0.090063 NaN -2016-08-31 105.66 106.5699 105.64 106.10 0.018136 NaN -2016-09-30 112.46 113.3700 111.80 113.05 0.065504 NaN -2016-10-31 113.65 114.2300 113.20 113.54 0.004334 26419398.0 -2016-11-30 111.56 112.2000 110.27 110.52 -0.026599 36162258.0 -2016-12-31 116.65 117.2000 115.43 115.82 0.047955 30586265.0 -2017-01-31 NaN NaN NaN NaN NaN 49200993.0 -2017-02-28 NaN NaN NaN NaN NaN 23482860.0 -2017-03-31 NaN NaN NaN NaN NaN 19661651.0 -2017-04-30 NaN NaN NaN NaN NaN 20247187.0 - - Split Ratio -Date -2016-01-31 NaN -2016-02-29 NaN -2016-03-31 NaN -2016-04-30 NaN -2016-05-31 NaN -2016-06-30 NaN -2016-07-31 NaN -2016-08-31 NaN -2016-09-30 NaN -2016-10-31 1.0 -2016-11-30 1.0 -2016-12-31 1.0 -2017-01-31 1.0 -2017-02-28 1.0 -2017-03-31 1.0 -2017-04-30 1.0 --
- By default the DataFrame are joined with all of the data. This default options results in zero information loss. We can also merge them by intersection, this is called 'inner join': -
- -concat = pd.concat([aapl_bar, df_volume], axis = 1, join = 'inner') -print concat - - Open High Low Close rate_return Volume \ -Date -2016-10-31 113.65 114.23 113.20 113.54 0.004334 26419398.0 -2016-11-30 111.56 112.20 110.27 110.52 -0.026599 36162258.0 -2016-12-31 116.65 117.20 115.43 115.82 0.047955 30586265.0 - - Split Ratio -Date -2016-10-31 1.0 -2016-11-30 1.0 -2016-12-31 1.0 - --
- Only the intersection part was left if use 'inner join' method. Now let's try to append a DataFrame to another one: -
- -append = aapl_bar.append(df_2017) -print append - Close High Low Open rate_return -Date -2016-01-31 97.34 97.3400 94.35 94.79 NaN -2016-02-29 96.69 98.2300 96.65 96.86 -0.006678 -2016-03-31 108.99 109.9000 108.88 109.72 0.127211 -2016-04-30 93.74 94.7200 92.51 93.99 -0.139921 -2016-05-31 99.86 100.4000 98.82 99.60 0.065287 -2016-06-30 95.60 95.7700 94.30 94.44 -0.042660 -2016-07-31 104.21 104.5500 103.68 104.19 0.090063 -2016-08-31 106.10 106.5699 105.64 105.66 0.018136 -2016-09-30 113.05 113.3700 111.80 112.46 0.065504 -2016-10-31 113.54 114.2300 113.20 113.65 0.004334 -2016-11-30 110.52 112.2000 110.27 111.56 -0.026599 -2016-12-31 115.82 117.2000 115.43 116.65 0.047955 -2016-10-31 113.54 114.2300 113.20 113.65 NaN -2016-11-30 110.52 112.2000 110.27 111.56 NaN -2016-12-31 115.82 117.2000 115.43 116.65 NaN -2017-01-31 121.35 121.3900 120.62 121.15 NaN -2017-02-28 136.99 137.4350 136.70 137.08 NaN -2017-03-31 143.66 144.2700 143.01 143.72 NaN -2017-04-30 143.65 144.3000 143.27 144.09 NaN - --
- 'Append' is essentially to concat two DataFrames by axis = 0, thus here is an alternative way to append: -
- -concat = pd.concat([aapl_bar, df_2017], axis = 0) -print concat - Close High Low Open rate_return -Date -2016-01-31 97.34 97.3400 94.35 94.79 NaN -2016-02-29 96.69 98.2300 96.65 96.86 -0.006678 -2016-03-31 108.99 109.9000 108.88 109.72 0.127211 -2016-04-30 93.74 94.7200 92.51 93.99 -0.139921 -2016-05-31 99.86 100.4000 98.82 99.60 0.065287 -2016-06-30 95.60 95.7700 94.30 94.44 -0.042660 -2016-07-31 104.21 104.5500 103.68 104.19 0.090063 -2016-08-31 106.10 106.5699 105.64 105.66 0.018136 -2016-09-30 113.05 113.3700 111.80 112.46 0.065504 -2016-10-31 113.54 114.2300 113.20 113.65 0.004334 -2016-11-30 110.52 112.2000 110.27 111.56 -0.026599 -2016-12-31 115.82 117.2000 115.43 116.65 0.047955 -2016-10-31 113.54 114.2300 113.20 113.65 NaN -2016-11-30 110.52 112.2000 110.27 111.56 NaN -2016-12-31 115.82 117.2000 115.43 116.65 NaN -2017-01-31 121.35 121.3900 120.62 121.15 NaN -2017-02-28 136.99 137.4350 136.70 137.08 NaN -2017-03-31 143.66 144.2700 143.01 143.72 NaN -2017-04-30 143.65 144.3000 143.27 144.09 NaN --
- Please note that if the two DataFrame have some columns with the same column names, these columns are considered to be the same and will be merged. It's very important to have the right column names. If we change a column names here: -
-df_2017.columns = ['Change', 'High', 'Low', 'Close'] -concat = pd.concat([aapl_bar, df_2017], axis = 0) -print concat - - Change Close High Low Open rate_return -Date -2016-01-31 NaN 97.34 97.3400 94.35 94.79 NaN -2016-02-29 NaN 96.69 98.2300 96.65 96.86 -0.006678 -2016-03-31 NaN 108.99 109.9000 108.88 109.72 0.127211 -2016-04-30 NaN 93.74 94.7200 92.51 93.99 -0.139921 -2016-05-31 NaN 99.86 100.4000 98.82 99.60 0.065287 -2016-06-30 NaN 95.60 95.7700 94.30 94.44 -0.042660 -2016-07-31 NaN 104.21 104.5500 103.68 104.19 0.090063 -2016-08-31 NaN 106.10 106.5699 105.64 105.66 0.018136 -2016-09-30 NaN 113.05 113.3700 111.80 112.46 0.065504 -2016-10-31 NaN 113.54 114.2300 113.20 113.65 0.004334 -2016-11-30 NaN 110.52 112.2000 110.27 111.56 -0.026599 -2016-12-31 NaN 115.82 117.2000 115.43 116.65 0.047955 -2016-10-31 113.65 113.54 114.2300 113.20 NaN NaN -2016-11-30 111.56 110.52 112.2000 110.27 NaN NaN -2016-12-31 116.65 115.82 117.2000 115.43 NaN NaN -2017-01-31 121.15 121.35 121.3900 120.62 NaN NaN -2017-02-28 137.08 136.99 137.4350 136.70 NaN NaN -2017-03-31 143.72 143.66 144.2700 143.01 NaN NaN -2017-04-30 144.09 143.65 144.3000 143.27 NaN NaN --
- Since the column name of 'Open' has been changed, the new DataFrame has an new column named 'Change'. -
-Hereby we introduced the most import part of python: resampling and DataFrame manipulation. We only introduced the most commonly used method in Financial data analysis. There are also many methods used in data mining, which are also beneficial. You can always check the Pandas official documentations for help.
diff --git a/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/02 Rate of Return.html b/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/02 Rate of Return.html index c9641b3..aab985e 100755 --- a/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/02 Rate of Return.html +++ b/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/02 Rate of Return.html @@ -32,36 +32,41 @@- Now consider the following situation: we have two strategies: strategy A and strategy B. We backtested strategy A for 1 years and the cumulative return is 20%, while we backtested strategy B and the cumulative return is 65%. Which strategy has a high rate of return? Our commonly used method is to convert all the returns into compounding annual return, regardless of the investing horizon of each strategy. We can compare the returns of strategies with different time horizon now! + Now consider the following situation: we have two strategies: strategy A and strategy B. We backtested strategy A for 1 years and the cumulative return is 20%, while we backtested strategy B for 3 months(one quarter) and the cumulative return is 6%. Which strategy has a high rate of return? Our commonly used method is to convert all the returns into compounding annual return, regardless of the investing horizon of each strategy. We can compare the returns of strategies with different time horizon now. Since there are four quarters in a year,the annual return of strategy B is
-\[(1+r)^3 = 1+0.65\] -\[ r = \sqrt[3]{1.65} - 1\ = 0.18167\] +\[(1+0.06)^4 = 1+r\] +\[ r = 0.262\]- Strategy A has an higher compounding annual return! + Strategy B has an higher compounding annual return when we compare 26% with 20%.
- We introduced compounding annual return above, which is a kind of effective rate of return. You can regard it as a 'hypothetical return'. Strategy B might never have a 18.167% rate of rate annually during the 3-year backtesting period. However, if we assume that the strategy has a 18.167% rate of return every year, it has the same cumulative return over the 3 years. As we mentioned previously, if we assume a strategy is quarterly compounding, the relation between quarterly effective rate of return and annual return is: + In the above example, strategy A has 6% return over three months. Nominally, the annual return would be 4*6% = 24%. + This nominal annual interest rate is called the stated annual interest rate. + It is calculated as the periodic interest rate times the number of periods per year. It works according to the simple interest and does not take into account the compounding periods, while the effective annual interest rate is 26% as we calculated above and it does account for intra-year compounding. + The effective annual interest rate is an essential tool that allows the evaluation of the real return on investment. + If we assume the number of compounding periods in one year is n, the formula to convert the stated annual interest rate to the effective annual interest rate is
-\[(1+\frac{r}{4})^4 = 1+r\] +\[r_{effective}=(1+\frac{r_{nominal}}{n})^n-1\]- More generally, if the times of compounding in one year is \(n\) and the annual rate of return is \(r\), the relation is given by: -
-\[(1+\frac{r}{n})^n = 1+r\] -- Now imagine the stock markets. The prices of your assets is changing every second, or even every millisecond. If the times of compounding, or n, approach to infinite, this is called continuous compounding. The calculation formula is given below: + Now imagine the price of asset is changing every second or even every millisecond, the period of compounding n approaches infinite. This is called continuous compounding. The calculation formula is given below:
\[\lim_{n \to \infty }(1+\frac{r}{n})^n = e^r\]From the above limitation equation, we know that if we assume continuous compounding:
-\[e^r = 1 + r = \frac{p_t}{p_0}\] +\[e^{r_{nominal}} = 1 + r_{effective} = \frac{p_t}{p_0}\]Then we take \(ln\) on both side of the equation:
-\[r = ln\frac{p_t}{p_0} = lnp_t - lnp_0\] +\[r_{nominal} = ln\frac{p_t}{p_0} = lnp_t - lnp_0\]- Here we got the logarithmic return, or continuously compounded return. This is frequently used when calculating returns, because once we take logarithm of asset prices, we can calculate the logarithm return by simply doing a subtraction. Here we use Apple stock prices as a example: + Here we got the logarithmic return, or continuously compounded return. This return is the nominal return with the interest compounding every millisecond. To see how it is close to effective interest rate, recall the equation above: +
+\[e^{r_{nominal}} = 1 + r_{effective}\] +then we have
+\[r_{effective} = e^{r_{nominal}} - 1 \approx r_{nominal}\] +where the second equality holds due to Taylor Expansion and the interest rate being small. This is frequently used when calculating returns, because once we take the logarithm of asset prices, we can calculate the logarithm return by simply doing a subtraction. Here we use Apple stock prices as an example:
It may sounds incorrect to sum up the daily returns, but we can prove that it's mathematically correct. Let's assume the stock prices in a period of time are represented by \([p_0, p_1, p_2, p_3.....p_n]\). Then the cumulative rate of return is given by:
-\[1+r = ln\frac{p_t}{p_0} = ln\frac{p_t}{p_{t-1}} + ln\frac{p_{t-1}}{p_{t-2}}+......+ln\frac{p_1}{p_0}\] +\[1 + r_{effective} \approx 1+r_{nominal} = ln\frac{p_t}{p_0} = ln\frac{p_t}{p_{t-1}} + ln\frac{p_{t-1}}{p_{t-2}}+......+ln\frac{p_1}{p_0}\]According to the equation above, we can simple sum up each logarithmic return in a period to get the cumulative return. The convenience of this method is also one of the reasons why we use logarithmic return in quantitative finance.
diff --git a/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/03 Mean.html b/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/03 Mean.html index 9d51b9c..72b9534 100755 --- a/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/03 Mean.html +++ b/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/03 Mean.html @@ -24,12 +24,12 @@Let's calculate the geometric mean of a series of single-period return:
-\[1+\bar{r} = \sqrt[n]{\frac{p_t}{p_{t-1}}*\frac{p_{t-1}}{p_{t-2}}*...*\frac{p_2}{p_1}}\] -\[(1+\bar{r}) = \sqrt[n]{\frac{p_t}{p_0}}\] +\[1+\bar{r} = \sqrt[t]{\frac{p_t}{p_{t-1}}*\frac{p_{t-1}}{p_{t-2}}*...*\frac{p_2}{p_1}*\frac{p_1}{p_0}}\] +\[(1+\bar{r}) = \sqrt[t]{\frac{p_t}{p_0}}\]Now the equation becomes the form which we are familiar with:
-\[(1+\bar{r})^n = \frac{p_t}{p_0}\] +\[(1+\bar{r})^t = \frac{p_t}{p_0}\]This is why we said it make sense when applied to growth rates.
diff --git a/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/04 Variance and Standard Deviation.html b/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/04 Variance and Standard Deviation.html index 5161451..f11f818 100755 --- a/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/04 Variance and Standard Deviation.html +++ b/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/04 Variance and Standard Deviation.html @@ -1,6 +1,6 @@- Variance is a measure of dispersion. In finance, most of the time variance is a synonym for risk. The higher the variance of an asset price is, the higher risk the asset bears. Variance is usually represented by \(\sigma\), and it's calculated by + Variance is a measure of dispersion. In finance, most of the time variance is a synonym for risk. The higher the variance of an asset price is, the higher risk the asset bears. Variance is usually represented by \(\sigma^2\), and it's calculated by
\[\sigma^2 = \frac{\sum_{i = 1}^{n}(x_i- \mu)^2}{n}\]diff --git a/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/05 Summary.html b/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/05 Summary.html index 6c1a074..1cc6f60 100755 --- a/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/05 Summary.html +++ b/05 Introduction to Financial Python[]/06 Rate of Return, Mean and Variance/05 Summary.html @@ -1,3 +1,3 @@
- We introduced different types of rate of return in this chapter, which could be a little bit tricky when we calculate them. Mean and standard deviation are also very important concepts when we conduct hypothesis test or measure the risk associated with a asset. We will use those comcepts intensively in our later chapter. + We introduced different types of rate of return in this chapter, which could be a little bit tricky when we calculate them. Mean and standard deviation are also very important concepts when we conduct hypothesis test or measure the risk associated with a asset. We will use those concepts intensively in our later chapter.
diff --git a/05 Introduction to Financial Python[]/07 Random Variables and Distributions/02 Random Variables.html b/05 Introduction to Financial Python[]/07 Random Variables and Distributions/02 Random Variables.html index 30c1882..82718e8 100755 --- a/05 Introduction to Financial Python[]/07 Random Variables and Distributions/02 Random Variables.html +++ b/05 Introduction to Financial Python[]/07 Random Variables and Distributions/02 Random Variables.html @@ -1,3 +1,3 @@- First let's start with the concept of random variable. A random variable can be thought of as a drawing from a distribution whose outcome prior to the draw is uncertain. Imaging rolling a dice, you know that your chance of getting each is 1/6, but you don't know what's the number of your next roll is. If we roll the dice N times and record the number of each roll, a collection of those numbers is called discrete random variable. A discrete variable can take on a finite number of values. For our example, we can only take numbers from{1,2,3,4,5,6}. The other kind of variable is continuous random variable. A continuous variable can take on any value in a given range. You can think the rate of return as a continuous variable, it theoretically can take any value from \((-\infty, +\infty)\). + First let's start with the concept of random variable. A random variable can be thought of as a drawing from a distribution whose outcome prior to the draw is uncertain. Imagine rolling a dice, you know that your chance of getting each is 1/6, but you don't know what's the number of your next roll is. If we roll the dice N times and record the number of each roll, a collection of those numbers is called discrete random variable. A discrete variable can take on a finite number of values. For our example, we can only take numbers from {1,2,3,4,5,6}. The other kind of variable is continuous random variable. A continuous variable can take on any value in a given range. You can think the rate of return as a continuous variable, it theoretically can take any value from \((-\infty, +\infty)\).
diff --git a/05 Introduction to Financial Python[]/07 Random Variables and Distributions/03 Distributions.html b/05 Introduction to Financial Python[]/07 Random Variables and Distributions/03 Distributions.html index d80c6dc..933b38c 100755 --- a/05 Introduction to Financial Python[]/07 Random Variables and Distributions/03 Distributions.html +++ b/05 Introduction to Financial Python[]/07 Random Variables and Distributions/03 Distributions.html @@ -1,10 +1,10 @@- Each random variable follows a probability distribution, which is a function that can be thought of as providing the probabilities of occurrence of different possible outcomes in an experiment. In our dice example, the probability distribution of each number is 1/6. We usually use \(P(X)\) to represents probability distribution function, where X is the outcome value. In our example, \(P(1) = P(2) = p(3) = 1/6\). However, we can't use this for a continuous distribution, because the the probability that draw a specific number from a continuous variable is 0, due to the infinity possible outcomes we have. Instead, we use probability density function(PDF) function to describe the probability that a value is in a specific range. We we cover this later. For each probability distribution function, we have a cumulative distribution function(CDF). It defines as \(P(X<x)\), which models the probability that the random variable X will take a value less than or equal to x. For discrete random variables, we just sum up the values less than or equal to x and then divide it with number of observations. + Each random variable follows a probability distribution, which is a function that can be thought of as providing the probabilities of occurrence of different possible outcomes in an experiment. In our dice example, the probability distribution of each number is 1/6. We usually use \(P(X)\) to represent a probability distribution function, where X is the outcome value. In our example, \(P(1) = P(2) = p(3) = 1/6\). However, we can't use this for a continuous distribution, because the probability of drawing a specific number from a continuous variable is 0, due to the infinite possible outcomes we have. Instead, we use probability density function(PDF) function to describe the probability that a value is in a specific range. We cover this later. For each probability distribution function, we have a cumulative distribution function(CDF). It is defined as \(P(X\leq x)\), which models the probability that the random variable X will take a value less than or equal to x. For discrete random variables, we just sum up the values less than or equal to x and then divide it with number of observations.
- Uniform distribution is the simplest type of probability distribution. A discrete uniform distribution has equal weight assigned to all outcomes. Both rolling a dice and toss a fare coin are classical uniform distributions. Here we use python to simulate rolling a dice 10000 times. + Uniform distribution is the simplest type of probability distribution. A discrete uniform distribution has equal weight assigned to all outcomes. Both rolling a dice and tossing a fare coin are classical uniform distributions. Here we use python to simulate rolling a dice 10000 times.
- We create a series of random variable here. We can plot the values on the x-axis and put their number of occurrences on the y-axis to have a direct view of the distribution: + We create a series of random variables here. We can plot the values on the x-axis and put their numbers of occurrences on the y-axis to have a direct view of the distribution:
- Let's say we want to know the frequency that the observations are less than or equal to 3. In other words we want to seek the value of \(P(X<3)\). + Let's say we want to know the frequency that the observations are less than or equal to 3. In other words we want to seek the value of \(P(X\leq 3)\).
- \(P(X<3)\) is very close to 0.5. This is not surprising because we rolled the dice 1000 times, and the frequency that the observations less than or equal to 3 should be close to the real probability, which is 0.5. For a given uniform distribution, it's straightforward to calculate it's mean: it's the center of the distribution because everyone outcome is equal weight. For our dice example, we can think it as + \(P(X\leq 3)\) is very close to 0.5. This is not surprising because we rolled the dice 1000 times, and the frequency that the observations are less than or equal to 3 should be close to the real probability, which is 0.5. For a given uniform distribution, it's straightforward to calculate its mean: it's the center of the distribution because every outcome is of equal weight. For our dice example, we can think of it as
\[\mu = (1+2+3+4+5+6)/6 = 3.5\]diff --git a/05 Introduction to Financial Python[]/08 Confidence Interval and Hypothesis Testing/02 Confidence Interval.html b/05 Introduction to Financial Python[]/08 Confidence Interval and Hypothesis Testing/02 Confidence Interval.html index 82a7170..2d4404b 100755 --- a/05 Introduction to Financial Python[]/08 Confidence Interval and Hypothesis Testing/02 Confidence Interval.html +++ b/05 Introduction to Financial Python[]/08 Confidence Interval and Hypothesis Testing/02 Confidence Interval.html @@ -8,16 +8,21 @@
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
-import quandl
-quandl.ApiConfig.api_key = 'tAyfv1zpWnyhmDsp91yv'
-#get data from quandl
-spy_table = quandl.get('BCIW/_SPXT')
-spy_total = spy_table[['Open','Close']]
+
+qb = QuantBook()
+spy = qb.AddEquity("SPY").Symbol
+
+#get SPY data from August 2010 to the present
+start_date = datetime(2010, 8, 1, 0, 0, 0)
+end_date = qb.Time
+spy_table = qb.History(spy, start_date, end_date, Resolution.Daily)
+
+spy_total = spy_table[['open','close']]
#calculate log returns
-spy_log_return = np.log(spy_total.Close).diff().dropna()
-print 'Population mean:', np.mean(spy_log_return)
+spy_log_return = np.log(spy_total.close).diff().dropna()
+print('Population mean:', np.mean(spy_log_return))
[out]: Population mean: 0.000443353825615
-print 'Population standard deviation:',np.std(spy_log_return)
+print('Population standard deviation:',np.std(spy_log_return))
[out]: Population standard deviation: 0.00784267293815
@@ -29,13 +34,13 @@
-print '10 days sample returns:', np.mean(spy_log_return.tail(10))
+print('10 days sample returns:', np.mean(spy_log_return.tail(10)))
[out]: 10 days sample returns: 0.000845189915474
-print '10 days sample standard deviation:', np.std(spy_log_return.tail(10))
+print('10 days sample standard deviation:', np.std(spy_log_return.tail(10)))
[out]: 10 days sample standard deviation: 0.00313558001122
-print '1000 days sample returns:', np.mean(spy_log_return.tail(1000))
+print('1000 days sample returns:', np.mean(spy_log_return.tail(1000)))
[out]: 1000 days sample returns: 0.000462827047221
-print '1000 days sample standard deviation:', np.std(spy_log_return.tail(1000))
+print('1000 days sample standard deviation:', np.std(spy_log_return.tail(1000)))
[out]: 1000 days sample standard deviation: 0.00766589174299
bottom = 0 - 1.64*std_1000/np.sqrt(1000) upper = 0 + 1.64*std_1000/np.sqrt(1000) -print (bottom, upper) +print((bottom, upper)) [out]: (-0.00039756352254768874, 0.00039756352254768874)@@ -37,7 +37,7 @@
bottom = 0 - 1.96*std_1000/np.sqrt(1000) upper = 0 + 1.96*std_1000/np.sqrt(1000) -print (bottom, upper) +print((bottom, upper)) [out]: (-0.00047513689280089639, 0.00047513689280089639)@@ -55,7 +55,7 @@
print np.sqrt(1000)*(mean_1000 - 0)/std_1000 +print(np.sqrt(1000)*(mean_1000 - 0)/std_1000) [out]: 1.90922032428
import scipy.stats as st -print (1 - st.norm.cdf(1.9488)) +print((1 - st.norm.cdf(1.9488))) [out]: 0.025659656888
mean_1200 = np.mean(spy_log_return.tail(1200))
std_1200 = np.std(spy_log_return.tail(1200))
z_score = np.sqrt(1200)*(mean_1200 - 0)/std_1200
-print 'z-score = ',z_score
+print('z-score = ',z_score)
[out]: z-score = 2.19793023185
p_value = (1 - st.norm.cdf(z_score))
-print 'p_value = ',p_value
+print('p_value = ',p_value)
[out]: p_value = 0.0139770390655
diff --git a/05 Introduction to Financial Python[]/08 Confidence Interval and Hypothesis Testing/04 Summary.html b/05 Introduction to Financial Python[]/08 Confidence Interval and Hypothesis Testing/04 Summary.html
index 3cc20c3..724eb85 100755
--- a/05 Introduction to Financial Python[]/08 Confidence Interval and Hypothesis Testing/04 Summary.html
+++ b/05 Introduction to Financial Python[]/08 Confidence Interval and Hypothesis Testing/04 Summary.html
@@ -1,216 +1,3 @@
-- In the last chapter we discussed random variables and random distributions. Now we are going to use the distributions we learned to test our hypothesis and also to model the financial data. When building a trading strategy, it's essential to do some research. However, you won't be able to test your idea using all the data, because it's infinity. You can only use a sample to do your experiment. That's why we need to understand the difference between population and sample, and then use confidence interval to test our hypothesis. -
-- As we mentioned before, both mean and standard deviation are point estimation, and they can be deceiving because sample means are different from population means. Financial data is generated every day now and in the future, thus even though we can use all the data available, it's still just a sample. This is why we need to use confidence interval to attempt to determine how accurate our sample mean estimation is. -
- -- Let's use the daily return on S&P 500 index from Aug 2010 to present is our population. If we take the recent 10 daily returns to calculate the mean, will it be the same as the population mean? How about increasing the sample size to 1000? -
- -import matplotlib.pyplot as plt
-import numpy as np
-import pandas as pd
-import quandl
-quandl.ApiConfig.api_key = 'tAyfv1zpWnyhmDsp91yv'
-#get data from quandl
-spy_table = quandl.get('BCIW/_SPXT')
-spy_total = spy_table[['Open','Close']]
-#calculate log returns
-spy_log_return = np.log(spy_total.Close).diff().dropna()
-print 'Population mean:', np.mean(spy_log_return)
-[out]: Population mean: 0.000443353825615
-print 'Population standard deviation:',np.std(spy_log_return)
-[out]: Population standard deviation: 0.00784267293815
-
-- Now let's check the recent 10 days sample and recent 1000 days sample: -
- --print '10 days sample returns:', np.mean(spy_log_return.tail(10)) -[out]: 10 days sample returns: 0.000845189915474 -print '10 days sample standard deviation:', np.std(spy_log_return.tail(10)) -[out]: 10 days sample standard deviation: 0.00313558001122 -print '1000 days sample returns:', np.mean(spy_log_return.tail(1000)) -[out]: 1000 days sample returns: 0.000462827047221 -print '1000 days sample standard deviation:', np.std(spy_log_return.tail(1000)) -[out]: 1000 days sample standard deviation: 0.00766589174299 --
- As we expected, the two samples has different means and variances. -
- -- In order to estimate the range of population mean, we define standard error of the mean as follows: -
-\[SE = \frac{\sigma}{\sqrt{n}}\] -- Where \(\sigma \) is the sample standard deviation and \(n\) is the sample size. -
-- Generally, if we want to estimate an interval of the population so that 95% of the time the interval will contain the population mean, the interval is calculated as: -
-\[(\mu - 1.96*SE, \mu + 1.96*SE)\] -- Where \(\mu\) is the sample mean and SE is the standard error. -
-- This interval is called confidence interval. We usually use 1.96 to calculate a 95% confidence interval because we assume that the sample mean follows normal distribution. We will cover this in detail later. Let's try to calculate the confidence interval using the samples above: -
--#apply the formula above to calculate confidence interval -bottom_1 = np.mean(spy_log_return.tail(10))-1.96*np.std(spy_log_return.tail(10))/(np.sqrt(len((spy_log_return.tail(10))))) -upper_1 = np.mean(spy_log_return.tail(10))+1.96*np.std(spy_log_return.tail(10))/(np.sqrt(len((spy_log_return.tail(10))))) -bottom_2 = np.mean(spy_log_return.tail(1000))-1.96*np.std(spy_log_return.tail(1000))/(np.sqrt(len((spy_log_return.tail(1000))))) -upper_2 = np.mean(spy_log_return.tail(1000))+1.96*np.std(spy_log_return.tail(1000))/(np.sqrt(len((spy_log_return.tail(1000))))) -#print the outcomes -print '10 days 95% confidence inverval:', (bottom_1,upper_1) -[out]: 10 days 95% confidence inverval: (-0.0010982627102681939, 0.002788642541217079) -print '1000 days 95% confidence inverval:', (bottom_2,upper_2) -[out]: 1000 days 95% confidence inverval: (-1.230984558013321e-05, 0.00093796394002165957) --
- As we can see, the 95% confidence interval became much narrower if we increase the sample size from 10 to 1000. Imagine that if N goes positive infinite, then we have \(\lim_{n\rightarrow \infty}\frac{\sigma}{\sqrt{n}} = 0\). The confidence interval would become a certain value, which is the sample mean! -
- -- Normal Distribution is so commonly used that we should be able to remember some critical values of it. Specifically, we usually use 90%, 95% and 99% as the confidence level of a confidence interval. The critical values for these three confidence levels are 1.64, 1.96, and 2.32 respectively. in other words: -
-\[\%90 upperabnd = \mu + 1.64*SE\] -\[\%90 lowerband = \mu + 1.64*SE\] -- The same for other confidence intervals. It's also important to remember the famous 'Three sigma rule' or '68-95-99.7' rule associated with normal distribution. This is used to remember the confidence level of the intervals with a width of two, four and six standard deviation. Mathematically: -
-\[P(\mu - \sigma \leq X \leq \mu+\sigma)\approx 0.6827\] -\[P(\mu - 2\sigma \leq X \leq \mu+2\sigma)\approx 0.9545\] -\[P(\mu - 3\sigma \leq X \leq \mu+3\sigma)\approx 0.9973\] -- This can also be remembered by using the chart: -
-
-- As we mentioned, if we use the sample to estimate the confidence interval of the population, the 95% confidence interval is: -
-\[(\mu - 1.96*SE, \mu + 1.96*SE)\] -- Now you may have some sense to the number 1.96. It's the 95% critical value of a normal distribution. Does this means we assume the mean of sample follows a normal distribution? The answer is yes. This assumption is supported by central limit theorem. This theorem tells us that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population, and the means of the samples will be approximately normal distributed. This is the foundation of population mean confidence interval estimation. -
- -- Now we can talk about hypothesis testing. Hypothesis test is essentially test your inference based on a sample. Let's use our dataset, the daily return of S&P 500 us our population. Assume that we don't know the mean of this population. I guess that the mean of this population is 0. Is my guess correct? I need to test this hypothesis with my sample. Let's start from observing our sample: -
- -mean_1000 = np.mean(spy_log_return.tail(1000)) -std_1000 = np.std(spy_log_return.tail(1000)) -mean_10 = np.mean(spy_log_return.tail(10)) -std_10 = np.std(spy_log_return.tail(10)) -s = pd.Series([mean_10,std_10,mean_1000,std_1000],index = ['mean_10', 'std_10','mean_1000','std_1000']) -print s - -[out]: mean_10 0.000845 - std_10 0.003136 - mean_1000 0.000463 - std_1000 0.007666 --
- We know how to calculate the confidence interval now. If I were right, i.e. the population mean is 0, then the 90% confidence interval of the sample with 1000 observations should be: -
- -bottom = 0 - 1.64*std_1000/np.sqrt(1000) -upper = 0 + 1.64*std_1000/np.sqrt(1000) -print (bottom, upper) -[out]: (-0.00039756352254768874, 0.00039756352254768874) --
- Our mean of the sample is out of the 90% confidence interval. This means on a 90% confidence level, we can claim that the mean of our population is not 0. In other word, we rejected the hypothesis that the daily return on S&P500 from aug 2010 is zero. Can we claim that with 95% confidence level? -
- -bottom = 0 - 1.96*std_1000/np.sqrt(1000) -upper = 0 + 1.96*std_1000/np.sqrt(1000) -print (bottom, upper) -[out]: (-0.00047513689280089639, 0.00047513689280089639) --
- This time the sample mean is within the confidence interval. Thus we can't reject my hypothesis. In other words, we can't claim with 95% confidence level that the mean return is positive. Even though we can claim it with 90% confidence level. We have actually already finished a hypothesis testing above! In general, we have null hypothesis \(H_0\) and alternative hypothesis. They are usually in the following forms: -
-\[H_0:\bar{\mu} = 0\] -\[H_0:\bar{\mu} \neq 0\] -- If the tested value is outside the confidence interval, we reject the null hypothesis, or accept the alternative hypothesis; If the tested value is within the confidence interval, we can't reject the null hypothesis. Although the hypothesis testing method we used above is straightforward, it's not so convenient to implement. Instead, we reverse the process to calculate the critical value, or Z-score. Z-score is defined as: -
-\[Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\] -- Let's calculate the Z score from our sample: -
-print np.sqrt(1000)*(mean_1000 - 0)/std_1000 -[out]: 1.90922032428 --
- We know that the critical value for the 90% confidence level is 1.64 and that for the 95% confidence level is 95%. The higher the Z score is, the further the tested value is from the hypothesized value(which is 0 in this example). Thus with 90% confidence level, we are far away enough from zero and we reject the null hypothesis. However with 95% confidence level, we are not far away enough from zero, so we can't reject the null hypothesis. One reason of doing in this way is that we can know how wide our confidence interval is. In our example, the z-score is 1.8488. We can know the width is the confidence interval referring to a normal distribution table. Of course we can do this in Python: -
- -import scipy.stats as st -print (1 - st.norm.cdf(1.9488)) -[out]: 0.025659656888 --
- It's worth noting that st.norm.cdf will return the probability that a value take from the distribution is less than our tested value. In other words, 1 - st.norm.cdf(1.9488) will return the probability that the value is greater than our tested value, which is 0.025659 in this example. This calculated number is called p-value. If our confidence level our confidence interval is 95%, then we have 2.5% on the left side and 2.5% on the right side. This is called two-tail test. If our null hypothesis is \(\mu = 0\), we are conducting two-tail test because the tested sample mean can be either positive enough or negative enough to reject the null hypothesis. We can see it from the chart: -
-
-- If we use 95% confidence interval, we need a p-value less than 0.025 to reject the null hypothesis. However, now our p-value is 0.025659, which is greater than 0.025, thus we can't reject the null hypothesis. It's obviously less than 0.05, so we can still reject the null hypothesis with 90% confidence level. Now let's test the hypothesis that population mean = 0 again with a large sample, which has 1200 observations: -
-mean_1200 = np.mean(spy_log_return.tail(1200)) -std_1200 = np.std(spy_log_return.tail(1200)) -z_score = np.sqrt(1200)*(mean_1200 - 0)/std_1200 -print 'z-score = ',z_score -[out]: z-score = 2.19793023185 -p_value = (1 - st.norm.cdf(z_score)) -print 'p_value = ',p_value -[out]: p_value = 0.0139770390655 --
- Using the a larger sample, now we can reject the null hypothesis with a higher confidence interval! our p-value is 0.0105, and it's a two-tail test, so our confidence level of the interval is 1-(0.0105*2) = 0.979. We can say at most with 97.9% confidence interval, we can claim that the population mean is not zero. We already know that the population mean is not 0. As our sample size increasing, the accurate rate of our hypothesis goes up. -
-In this chapter we introduced confidence interval, especially that for the normal distribution, and hypothesis test. Now we know how to test our idea rigorously. Normal distribution and it's confidence interval can be applied to many quantitative finance theories, we will see it frequently in our following tutorials.
diff --git a/05 Introduction to Financial Python[]/12 Modern Portfolio Theory/04 Mean-Variance Analysis.html b/05 Introduction to Financial Python[]/12 Modern Portfolio Theory/04 Mean-Variance Analysis.html index 51a1bf9..e60dcab 100755 --- a/05 Introduction to Financial Python[]/12 Modern Portfolio Theory/04 Mean-Variance Analysis.html +++ b/05 Introduction to Financial Python[]/12 Modern Portfolio Theory/04 Mean-Variance Analysis.html @@ -26,7 +26,7 @@Taking square roots, we deduce that a CML portfolio's risk is proportional to the market portfolio's weight: diff --git a/05 Introduction to Financial Python[]/12 Modern Portfolio Theory/06 Algorithm.html b/05 Introduction to Financial Python[]/12 Modern Portfolio Theory/06 Algorithm.html index 2fc9305..309e3c2 100755 --- a/05 Introduction to Financial Python[]/12 Modern Portfolio Theory/06 Algorithm.html +++ b/05 Introduction to Financial Python[]/12 Modern Portfolio Theory/06 Algorithm.html @@ -1,9 +1,9 @@ -
- Mean-variance analysis is used to optimize portfolios with several strategies. Here we treat Dow 30 stocks as strategy and designed an algorithm to test mean-variance analysis: -
- ++ Mean-variance analysis is used to optimize portfolios with several strategies. Here we treat Dow 30 stocks as strategy and designed an algorithm to test mean-variance analysis: +
+ diff --git a/05 Introduction to Financial Python[]/13 Market Risk/06 Algorithm.html b/05 Introduction to Financial Python[]/13 Market Risk/06 Algorithm.html index 5b8cd66..64474c1 100755 --- a/05 Introduction to Financial Python[]/13 Market Risk/06 Algorithm.html +++ b/05 Introduction to Financial Python[]/13 Market Risk/06 Algorithm.html @@ -1,13 +1,13 @@ - - - + + + diff --git a/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/02 Fama-French Three-Factor Model.html b/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/02 Fama-French Three-Factor Model.html index 21d0568..1f83f6d 100755 --- a/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/02 Fama-French Three-Factor Model.html +++ b/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/02 Fama-French Three-Factor Model.html @@ -1,8 +1,5 @@ - This model was proposed in 1993 by Eugene Fama and Kenneth French to describe stock returns.[ref] Fama, E F; French, K R (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics. 33: 3. CiteSeerX 10.1.1.139.5892 Freely accessible. doi:10.1016/0304-405X(93)90023-5[/ref] -
-- The 3-factor model is + This model was proposed in 1993 by Eugene Fama and Kenneth French to describe stock returns. The 3-factor model is
\[ R = \alpha + \beta_m MKT + \beta_s SMB + \beta_h HML \] @@ -12,7 +9,7 @@diff --git a/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/05 Other Factors.html b/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/05 Other Factors.html deleted file mode 100755 index 510c436..0000000 --- a/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/05 Other Factors.html +++ /dev/null @@ -1,12 +0,0 @@ -
- The Fama-French 5-Factor model comprises two more factors: -
-- RMW was proposed by Novy-Marx (2013) who wrote that: - "Controlling for gross profitability explains most earnings related anomalies, and a wide range of seemingly unrelated profitable trading strategies." CMA was proposed by Fama and French (2014) who pointed out that: A five-factor model directed at capturing the size, value, profitability, and investment patterns in average stock returns is rejected on the GRS test, but for applied purposes it provides an acceptable description of average returns. Finally, momentum is another commonly used factor. It captures excess returns of stocks with highest returns over those with lowest returns -
diff --git a/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/06 Summary.html b/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/05 Summary.html old mode 100755 new mode 100644 similarity index 98% rename from 05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/06 Summary.html rename to 05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/05 Summary.html index 549200f..d2b7e7a --- a/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/06 Summary.html +++ b/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/05 Summary.html @@ -1,3 +1,3 @@ -- In this chapter we expand Capital Asset Pricing Model (CAPM) into multi-factor models: the Fama-French factor models in particular. They are the most empirically successful multi-factor models by far, and are commonly used in practice. -
++ In this chapter we expand Capital Asset Pricing Model (CAPM) into multi-factor models: the Fama-French factor models in particular. They are the most empirically successful multi-factor models by far, and are commonly used in practice. +
diff --git a/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/07 Algorithm.html b/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/06 Algorithm.html old mode 100755 new mode 100644 similarity index 74% rename from 05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/07 Algorithm.html rename to 05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/06 Algorithm.html index 5db089b..3eb4334 --- a/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/07 Algorithm.html +++ b/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/06 Algorithm.html @@ -1,15 +1,15 @@ -- Multi-factor strategies are stock picking strategies. Here we try to implement a 2013 paper published by AQR Capital Management. - The paper recommends picking stocks by their value, quality (profitability) and momentum. - The empirically successful measure of value is book-to-price ratio (B/P), but other measures can be used simultaneously to form a more robust and reliable view of a stock's value. The paper uses 5 measures: book-to-price, earnings-to-price ratio (EPS), forecasted EPS, cash flow-to-enterprise value and sales-to-enterprise value. - The paper suggested a few quality measures: total profit over assets, gross margin and free cash flow over assets. There are also various measures of momentum. 1-year momentum, fundamental momentum and returns around earnings announcement are good choices. -
-- In our backtested strategy, we used operating profit margin to measure quality, P/B value to measure value, and 1-month momentum. The portfolio was rebalanced every 2 months and our backtest period runs from Jan 2012 to Jan 2015. You can build your own version by changing the factor, the weight of each factor, and the rebalance period based on the backtested strategy. -
- ++ Multi-factor strategies are stock picking strategies. Here we try to implement a 2013 paper published by AQR Capital Management. + The paper recommends picking stocks by their value, quality (profitability) and momentum. + The empirically successful measure of value is book-to-price ratio (B/P), but other measures can be used simultaneously to form a more robust and reliable view of a stock's value. The paper uses 5 measures: book-to-price, earnings-to-price ratio (EPS), forecasted EPS, cash flow-to-enterprise value and sales-to-enterprise value. + The paper suggested a few quality measures: total profit over assets, gross margin and free cash flow over assets. There are also various measures of momentum. 1-year momentum, fundamental momentum and returns around earnings announcement are good choices. +
++ In our backtested strategy, we used operating profit margin to measure quality, book value per share to measure value, and 1-month momentum. The portfolio was rebalanced every month. You can build your own version by changing the factor, the weight of each factor, and the rebalance period based on the backtested strategy. +
+ diff --git a/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/08 References.html b/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/07 References.html similarity index 81% rename from 05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/08 References.html rename to 05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/07 References.html index 79b3bcb..eb7216e 100644 --- a/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/08 References.html +++ b/05 Introduction to Financial Python[]/14 Fama-French Multi-Factor Models/07 References.html @@ -14,4 +14,7 @@-For example, an AAPL call option contract which expires after 10 days has strike $143 and premium $10. now the market price of GOOG is $160. The intrinsic value of this contract is 160-143=$17, the time value is 17-10=$7. Although the intrinsic value of OTM and ATM options is zero, they have time values if they still have a certain amount of time until the option expires so for OTM and ATM options, their premiums equal their time values. +For example, an AAPL call option contract which expires after 10 days has strike $143 and premium $10. now the market price of AAPL is $150. The intrinsic value of this contract is 150-143=$7, the time value is 10-7=$3. Although the intrinsic value of OTM and ATM options is zero, they have time values if they still have a certain amount of time until the option expires so for OTM and ATM options, their premiums equal their time values.
diff --git a/06 Introduction to Options[]/01 General Features of Options/05 Options Moneyness.html b/06 Introduction to Options[]/01 General Features of Options/05 Options Moneyness.html index 5f7a43a..a089ece 100755 --- a/06 Introduction to Options[]/01 General Features of Options/05 Options Moneyness.html +++ b/06 Introduction to Options[]/01 General Features of Options/05 Options Moneyness.html @@ -26,5 +26,5 @@ But why are they in the money or out of the money? For a call option as an example, it is ITM because it already has an intrinsic value. If you buy the call option and own the right to buy AAPL at strike price $143 and the current market price is $150, then this call option is in the money 150-143=$7. If you need to exercise it, you can buy shares of AAPL at $143 and sell them immediately for $150 and secure $7 profit.- Likewise, for a call option, it is OTM because it doesn't have any intrinsic value. If you buy the call option and own the right to buy AAPL at strike price $143 and the current market price is $130, then this call option is out of the money 130-143=$13. If you need to exercise it, you can buy shares of AAPL at $143 and sell them immediately for $130 and then you will lose $13. In this case, you would not do that. But why this kind of OTM options still traded in the market and you need to pay for them? That because they still have time values and have time to expiration. There is probability or there is the expectation from the OTM option holders that the apple price will go up and above the strike price before the expiration. + Likewise, for a call option, it is OTM because it doesn't have any intrinsic value. If you buy the call option and own the right to buy AAPL at strike price $143 and the current market price is $130, then this call option is out of the money 130-143=-$13. If you need to exercise it, you can buy shares of AAPL at $143 and sell them immediately for $130 and then you will lose $13. In this case, you would not do that. But why this kind of OTM options still traded in the market and you need to pay for them? That because they still have time values and have time to expiration. There is probability or there is the expectation from the OTM option holders that the apple price will go up and above the strike price before the expiration.
diff --git a/06 Introduction to Options[]/02 QuantConnect Options API/02 Add Options.html b/06 Introduction to Options[]/02 QuantConnect Options API/02 Add Options.html index 0ab569f..44c5959 100755 --- a/06 Introduction to Options[]/02 QuantConnect Options API/02 Add Options.html +++ b/06 Introduction to Options[]/02 QuantConnect Options API/02 Add Options.html @@ -10,7 +10,7 @@def Initialize(self):
- self.SetStartDate(2017, 01, 01) #Set Start Date
- self.SetEndDate(2017, 06, 30) #Set End Date
+ self.SetStartDate(2017, 1, 1) #Set Start Date
+ self.SetEndDate(2017, 6, 30) #Set End Date
self.SetCash(50000) #Set Strategy Cash
- equity = self.AddEquity("GOOG", Resolution.Daily) # Add the underlying stock: Google
- option = self.AddOption("GOOG", Resolution.Daily) # Add the option corresponding to underlying stock
+ equity = self.AddEquity("GOOG", Resolution.Minute) # Add the underlying stock: Google
+ option = self.AddOption("GOOG", Resolution.Minute) # Add the option corresponding to underlying stock
self.symbol = option.Symbol
- The return value of AddOption method is an option security object , please refer to the link for detailed properties and methods of option class. + The return value of AddOption method is an option security object , please refer to the link for detailed properties and methods of option class.
diff --git a/06 Introduction to Options[]/02 QuantConnect Options API/03 Filter Contracts.html b/06 Introduction to Options[]/02 QuantConnect Options API/03 Filter Contracts.html index 02b6927..be1a2be 100755 --- a/06 Introduction to Options[]/02 QuantConnect Options API/03 Filter Contracts.html +++ b/06 Introduction to Options[]/02 QuantConnect Options API/03 Filter Contracts.html @@ -1,5 +1,5 @@- After adding the options for specific underlying stock, you can set the filter criteria with SetFilter method to pull contracts using the specified min and max strike and expiration range values you need for a given symbol. + After adding the options for specific underlying stock, you can set the filter criteria with SetFilter method to pull contracts using the specified min and max strike and expiration range values you need for a given symbol.
- Here parameters min Strike and max Strike are the relative values with respect to the market price. We use Google(NASDAQ: GOOG) as an example to describe the filter criteria. If today is 01/03/2017, the market price of underlying stock is $776, the strike prices of GOOG options are spaced $2.5. Then SetFilter(-1, +2, timedelta(0), timedelta(90)) will fist look up at the money contracts with strike being K=$777.5 (Here K might not being $100 since rarely will option be ATM exactly). Then filter will looks for options with strikes between and including (777.5 + 2.5*2, 777.5 - 2.5*1). The time to expiration of these options are restricted within 90 days from now on.
+ Here parameters min Strike and max Strike are the relative multipliers with respect to the market price. We use Google(NASDAQ: GOOG) as an example to describe the filter criteria. If today is 01/03/2017, the market price of underlying stock is $776, the strike prices of GOOG options are spaced $2.5. Then SetFilter(-1, +2, timedelta(0), timedelta(90)) will fist look up at the money contracts with strike being K=$777.5 (Here K is 777.5 the next closest multiple to the underlying price of 775 since rarely will an option be ATM exactly). Then SetFilter will look for options with strikes between and including ( 777.5 - 2.5*1, 777.5 + 2.5*2). The time to expiration of these options are restricted within 90 days from now on.
- For the strike, the exchange normally chooses the strike prices at which options can be written so that they are spaced $2.50, $5, or $10 apart. Typically the spacing is $2.50 when the stock price is between $5 and $25, $5 when the stock price is between $25 and $200, and $10 for stock prices above $200. So you should carefully choose the parameters of min strike and max Strike in case there is no contracts satisfy the filter criteria if the range is too small, less than the minimum units of strike prices change. + For the strike, the exchange normally chooses the strike prices at which options can be written so that they are spaced $2.50, $5, or $10 apart. Typically the spacing is $2.50 when the stock price is between $5 and $25, $5 when the stock price is between $25 and $200, and $10 for stock prices above $200. So you should carefully choose the parameters of min strike and max Strike in case there are no contracts that satisfy the filter criteria if the range is too small, less than the minimum units of strike prices change.
For the expiry, there are many expiration dates that apply to the different series of options. An option cycle is the pattern of months in which options contracts expire. There are three kinds of common option cycles. The options on the January cycle have contracts available in the first month of each quarter (January, April, July and October). Options assigned to the February cycle use the middle month of each quarter (February, May, August and November). And options in the March cycle have options available during the last month of each quarter (March, June, September and December). In addition, individual stock options typically expire in the current month and the subsequent month. diff --git a/06 Introduction to Options[]/02 QuantConnect Options API/04 Select Contracts.html b/06 Introduction to Options[]/02 QuantConnect Options API/04 Select Contracts.html index 9b62ccc..07ea589 100755 --- a/06 Introduction to Options[]/02 QuantConnect Options API/04 Select Contracts.html +++ b/06 Introduction to Options[]/02 QuantConnect Options API/04 Select Contracts.html @@ -1,11 +1,11 @@
- For QuantConnect API, Slice class provides a data structure for all of an algorithm's data at a single time step. So you need use property Slice.OptionChains to request options data for this slice.
+ For QuantConnect API, Slice class provides a data structure for all of an algorithm's data at a single time step. So you need use property Slice.OptionChains to request options data for this slice.
-OptionChains is a collection of OptionChain keyed by the option's underlying symbol. The elements in Slice.OptionChains have properties Key(the underlying symbol object) Value(the option chain).
+OptionChains is a collection of OptionChain keyed by the option's underlying symbol. The elements in Slice.OptionChains have properties Key(the underlying symbol object) Value(the option chain).
-OptionChain represents an entire chain of option contracts for a single underlying security. In other words, It is a list of option contracts.
+OptionChain represents an entire chain of option contracts for a single underlying security. In other words, It is a list of option contracts.
-OptionContract defines a single option contract at a specific expiration and strike price. For any contract x in option chain, you can use the following statements to check different options properties.
+OptionContract defines a single option contract at a specific expiration and strike price. For any contract x in option chain, you can use the following statements to check different options properties.
x.Right |
Get the right being purchased -x.Right = 1 call option[right to buy] -x.Right = 0 put option[right to sell] | +x.Right = 0 call option[right to buy] +x.Right = 1 put option[right to sell]|||||||||||||||||||||||||||||||||||||||||||||||||||||||
x.UnderlyingLastPrice |
@@ -65,11 +65,11 @@
- Butterfly Spread strategy consists of three legs with a total of four options. In this tutorial, we take Long Butterfly Spread as an example: long one ITM call, short two ATM calls and long one OTM call. All the calls have the same expiration. On the other hand, the middle strike is halfway between the lower and the higher strikes. + A Butterfly Spread consists of three legs with a total of four options. In this tutorial, we use the Long Butterfly Spread as an example: long one ITM call, short two ATM calls and long one OTM call. All the calls have the same expiration. On the other hand, the middle strike is halfway between the lower and the higher strikes.
- The aim of Butterfly Spread strategy is to gain profits when traders think that the underlying stock will not rise or fall much by expiration. + The aim of a Butterfly Spread strategy is for a trader to profit from marginal price changes in the underlying stock in either direction.
- Step 1: Initialize your algorithm including setting the start date and the end date, setting the cash and implement a coarse selection of option contract. SetFilter(-9, 9, timedelta(30), timedelta(60)) helps us choose the contracts which expire in 30 to 60 days from now on. Since ITM call strike and OTM call strike are symmetrical with ATM call strike. For the strike parameter, the first parameter is the minimum strike rank relative to market price, the second parameter is the maximum strike rank relative to market price. The rank of ATM contract is 0. Here we need to choose 2 numbers which are symmetrical with 0.
+ Step 1: Initialize your algorithm including setting the start date and the end date, setting the cash and implement a coarse selection of option contract. SetFilter(-9, 9, timedelta(30), timedelta(60)) helps us choose the contracts which expire in 30 to 60 days. For the strike parameter, the first parameter is the minimum strike rank relative to market price, the second parameter is the maximum strike rank relative to market price. The rank of ATM contract is 0. Here we need to choose 2 numbers which are symmetrical with 0 to get strike prices for both ITM and OTM contracts.
- Step 2: Second we need to choose an expiration date for all the contracts in Butterfly Spread strategy. Then filter out all the call options expire on that date. + Step 2: Second we need to choose an expiration date for all the contracts, then filter out all the call options that expire on that date.
- Step 3: Sort the call options by their strike price in ascending order. Then the ATM option is the one which has the smallest absolute value of the difference between the strike price and the underlying asset price. The OTM option is the last one in this call options list which has the highest strike price. The corresponding ITM option is the first one in the list which has the lowest strike price. + Step 3: Sort the call options by their strike price in ascending order. Then choose the ATM option to be the one with the smallest absolute difference between the strike price and the underlying asset price. The OTM option is the last one in the call options list with the highest strike price. The corresponding ITM option is the first one in the list with the lowest strike price.
- From the following algorithm, at time 0, the GOOG share price is $832.8. We purchase 1 OTM call option strike at $855, 1 ITM call option strike at $810 and sell 2 ATM options strike at 835. At the expiry 05/19/2017, the share price is $930, then the long positions of the ITM option and the OTM option are all exercised, we buy 100 GOOG shares at $810 and buy another 100 shares at $855. At the same time, the 2 short positions of the ATM option are also exercised. We have to sell 200 GOOG shares to option holder at $835. Then we no longer hold positions after the expiration of this Long Call Butterfly Spread. Since the stock price had a sharp increase during the life of options, we make no profits from this strategy. + From the following algorithm, at time 0, the GOOG share price is $832.8. We purchase 1 OTM call option with strike price $855, 1 ITM call option with strike price $810 and sell 2 ATM options with strike prices at 835. At the expiry 05/19/2017, the share price is $930 and so the long positions of the ITM option and the OTM option are exercised: we buy 100 GOOG shares at $810 and buy another 100 shares at $855. At the same time, the 2 short positions of the ATM option are also exercised: we sell 200 GOOG shares to the option holder at $835. After the expiration date, we don't hold any shares of the underlying. Since the stock price had a sharp increase during the life of options, we fail to profit from a Long Call Butterfly Spread.
diff --git a/07 Applied Options[]/05 Butterfly Spread/04 Algorithm.html b/07 Applied Options[]/05 Butterfly Spread/04 Algorithm.html index 2c2b9e4..beb7ac0 100755 --- a/07 Applied Options[]/05 Butterfly Spread/04 Algorithm.html +++ b/07 Applied Options[]/05 Butterfly Spread/04 Algorithm.html @@ -4,7 +4,7 @@ @@ -14,6 +14,6 @@ diff --git a/07 Applied Options[]/06 Iron Condor/01 Definition.html b/07 Applied Options[]/06 Iron Condor/01 Definition.html index 0722b91..5301009 100755 --- a/07 Applied Options[]/06 Iron Condor/01 Definition.html +++ b/07 Applied Options[]/06 Iron Condor/01 Definition.html @@ -1,5 +1,5 @@- Iron Condor is an option strategy which involves four option contracts.All options have the same expiration date. The order of strike for four contracts is A > B > C > D. + An Iron Condor is an option strategy which involves four option contracts. All options have the same expiration date but different strike prices, where generally the spread in the put strike prices is the same as the spread in the calls. The order of strike for four contracts is A > B > C > D.
- Similar to the Iron Condor, Iron Butterfly is a limited risk, limited profit trading strategy. It profits from lower volatility meaning that traders gain profits from this strategy if the stock price changes within a small range. Iron Butterfly has a more narrow range for the price to move up or down compared with Iron Condor. + Similar to the Iron Condor, the Iron Butterfly is a limited risk, limited profit trading strategy. It profits from lower volatility, meaning that traders profit if the stock price has marginal movement within a small range. The Iron Butterfly has a more narrow range for the price to move up or down compared with the Iron Condor.
- From the payoff plot, the maximum gain is simply the net credit you received when you buy and sell 4 options. This occurs if the stock price is exactly the same as the strike price of ATM options. In this condition, all options expire worthless and you keep all premiums received. We can see the Iron Butterfly has more narrow structures than the Iron Condor. However, the profit can be higher than with the Iron Condor as you receive more premium by selling ATM options than OTM options. + From the payoff plot, the maximum gain is simply the net credit you received when you buy and sell 4 options. This occurs if the stock price is exactly the same as the strike price of the ATM options. In this situation, all options expire worthless and you keep all premiums received. Although the Iron Butterfly has a narrower structure than the Iron Condor, the profit can be higher than with the Iron Condor as you receive a higher premium by selling ATM options than OTM options.
- The maximum loss occurs if the underlying price is either below the OTM put strike or above the OTM call strike. In these two conditions, two puts or two calls are exercised and the other two options expire worthless. + The maximum loss occurs if the underlying price is either below the OTM put strike or above the OTM call strike. In these two situations, two puts or two calls are exercised and the other two options expire worthless.
diff --git a/07 Applied Options[]/07 Iron Butterfly/02 Implementation.html b/07 Applied Options[]/07 Iron Butterfly/02 Implementation.html index 3631f5f..c0092a5 100755 --- a/07 Applied Options[]/07 Iron Butterfly/02 Implementation.html +++ b/07 Applied Options[]/07 Iron Butterfly/02 Implementation.html @@ -1,5 +1,5 @@- Step 1: Initialize your algorithm which includes setting the start date and end date, setting the cash and implement the coarse selection of option contracts. + Step 1: Initialize your algorithm by setting the start date, end date and the cash. Then, implement the coarse selection of the options contracts.
- Step 3: Sort the call and put options according to their strike price respectively. option.SetFilter(-10, 10, timedelta(0), timedelta(30)) helps us choose 21 call options and 21 put options which expire within 30 days from now on.Then for call option, the first 10 contracts are in the money, the last 10 contracts are out of the money. The middle one is at the money option. For put options, the first 10 contracts are out of the money, the last 10 contracts are in the money.
+ Step 3: Sort the call and put options according to their strike prices. option.SetFilter(-10, 10, timedelta(0), timedelta(30)) helps us choose 21 call options and 21 put options which expire within 30 days from now. Then for the call options, the first 10 contracts are in the money and the last 10 contracts are out of the money. The middle one is an at the money option. For the put options, the first 10 contracts are out of the money and the last 10 contracts are in the money.
- Step 4: Find the specific contracts to trade. At the money options have the minimum absolute value of the difference between the underlying price and the strike price. + Step 4: Find the specific contracts to trade. At the money options have the minimum absolute difference between the underlying price and the strike price.
- In this algorithm, on 04/03/2017, the share price of Google is $832.8. We buy OTM put(strike = $805) at $2, OTM call(strike = $860) and sell an ATM call and an ATM put. At the expiry 04/21/2017, the share price is $841.53. The ATM call is exercised and the other 3 options expire worthless. As we hold the short position of ATM call, after expiration we hold 100 short positions of GOOG stock. + In this algorithm, on 04/03/2017, the share price of Google is $832.8. We buy OTM put(strike = $805) at $2, OTM call(strike = $860) and sell an ATM call and an ATM put. At the expiry 04/21/2017, the share price is $841.53. The ATM call is exercised and the other 3 options expire worthless. As we hold the short position of the ATM call, after expiration we will be short 100 shares of GOOG.
diff --git a/07 Applied Options[]/07 Iron Butterfly/04 Algorithm.html b/07 Applied Options[]/07 Iron Butterfly/04 Algorithm.html index 968a1fb..05d0e03 100755 --- a/07 Applied Options[]/07 Iron Butterfly/04 Algorithm.html +++ b/07 Applied Options[]/07 Iron Butterfly/04 Algorithm.html @@ -4,7 +4,7 @@ @@ -14,6 +14,6 @@ diff --git a/07 Applied Options[]/08 Protective Collar/01 Definition.html b/07 Applied Options[]/08 Protective Collar/01 Definition.html index 68eb983..3d98e6e 100755 --- a/07 Applied Options[]/08 Protective Collar/01 Definition.html +++ b/07 Applied Options[]/08 Protective Collar/01 Definition.html @@ -1,5 +1,5 @@- Protective Collar is an option strategy that involves both the underlying stock and two option contracts. The trader buys (or already owns) a stock, then buys an out-the-money put option and sells an out-the-money call option. It is similar to the covered call strategy with the purchase of an additional put option. It is being used if the trader is writing covered calls but wish to protect himself from an unexpected downside sharp move in the price of the underlying security. As a tradeoff, the profit will become limited compared with the covered call strategy. + A Protective Collar is an option strategy that involves both the underlying stock and two option contracts. The trader buys (or already owns) a stock, then buys an out-the-money put option and sells an out-the-money call option. It is similar to the covered call strategy but with the purchase of an additional put option. This strategy is employed if the trader is writing covered calls but wishes to protect himself from an unexpected drop in the price of the underlying security. As a tradeoff for loss-protection, the profit is limited compared with the Covered Call strategy.
- According to the payoff plot, the maximum profit is the strike price of short call minus the purchase price of the underlying asset add the net credit from the premium. It occurs when the stock price is beyond the strike price of the short call option. The maximum loss is the purchase price of the underlying asset minus the strike price of the long put minus the net credit from the premium. It occurs when the stock price is below the strike price of the long put. It is a strategy with limit risk and limit profit. + According to the payoff plot, the maximum profit is the strike price of short call minus the purchase price of the underlying asset plus the net credit from the premium. It occurs when the underlying price is beyond the strike price of the short call option. The maximum loss is the purchase price of the underlying asset minus the strike price of the long put minus the net credit from the premium. It occurs when the stock price is below the strike price of the long put. It is a strategy with both limited risk and limited profit.
diff --git a/07 Applied Options[]/08 Protective Collar/02 Implementation.html b/07 Applied Options[]/08 Protective Collar/02 Implementation.html index 57e2c1a..0e3c4c7 100755 --- a/07 Applied Options[]/08 Protective Collar/02 Implementation.html +++ b/07 Applied Options[]/08 Protective Collar/02 Implementation.html @@ -1,5 +1,5 @@- Step 1: Initialize your algorithm that involves setting the start date and the end date, setting the cash and implement the coarse selection of option contracts. + Step 1: Initialize your algorithm by setting the start date, end date and cash. Then implement the coarse selection of options contracts.
- Step 4: In Ondata, if there is no assets in portfolio, we buy the undelying stocks. After that, we trade the options which equivalent to the amount of your stocks holding. (one option contracts equals 100 undelying shares). + Step 4: In OnData, if there are no assets in our portfolio, we buy the undelying stock. After that, we trade the options written on the same number of shares of underlying asset (one option contracts equals 100 undelying shares).
+
+
++BootCamp is an interactive, education system for teaching the community the QuantConnect API, and the structure for building an algorithm. In January 2019, QuantConnect opened up the BootCamp technology to allow contributions of tutorials from the community! This guide seeks to show you how to create a BootCamp tutorial. +
+ ++Education and access to the information required to compete is a the cornerstone of QuantConnect's mission for radical openness, and the democratization of finance. With your help we can train the community on how to make the best algorithms possible. +
diff --git a/08 Meta/01 Creating BootCamp Tutorials/02 Requirements.html b/08 Meta/01 Creating BootCamp Tutorials/02 Requirements.html new file mode 100644 index 0000000..f7f62c6 --- /dev/null +++ b/08 Meta/01 Creating BootCamp Tutorials/02 Requirements.html @@ -0,0 +1,11 @@ ++Ensuring high-quality writing in BootCamp lessons is important to maintain the interest and motivation of the community. The skills required to build a BootCamp lesson cover several areas of expertise: +
++The combination of all these talents is fairly rare so we're reaching out to the community to help us create this content. If you can cover all three of these categories let us know and we'll enable BootCamp editing permissions on your account. In exchange for a completed BootCamp lesson we're offering compensation which we'll cover in the section below. +
diff --git a/08 Meta/01 Creating BootCamp Tutorials/03 Compensation.html b/08 Meta/01 Creating BootCamp Tutorials/03 Compensation.html new file mode 100644 index 0000000..4835b4c --- /dev/null +++ b/08 Meta/01 Creating BootCamp Tutorials/03 Compensation.html @@ -0,0 +1,39 @@ ++QuantConnect is offering contributing authors compensation for their BootCamp Lesson submissions. Depending on the complexity and topics covered a lesson ranges from $2,000 to $4,000USD. +
+ +| + Difficulty + | ++ Compensation + | ++ Estimated Effort + | +
|---|---|---|
Beginner |
+ $2,000USD |
+ 3-5 days fulltime work |
+
Intermediate |
+ $3,000USD |
+ 4-6 days fulltime work |
+
Advanced |
+ $4,000USD |
+ 5-8 days fulltime work |
+
+Before starting a lesson reach out to the QuantConnect team for approval on the lesson concept. We are seeking to provide diverse and complementing content for the community. If you're interested in creating BootCamp lessons but don't have a topic in mind get in touch with us! +
\ No newline at end of file diff --git a/08 Meta/01 Creating BootCamp Tutorials/04 Content Structure.html b/08 Meta/01 Creating BootCamp Tutorials/04 Content Structure.html new file mode 100644 index 0000000..dc4c918 --- /dev/null +++ b/08 Meta/01 Creating BootCamp Tutorials/04 Content Structure.html @@ -0,0 +1,31 @@ ++BootCamp is divided into Lessons, and Tasks. A Lesson focuses on the implementation of a single algorithm. A Task breaks up the algorithm implementation into tiny steps which can each be easily coded, with the aim of guiding the user through each layer of the algorithm design. +
+ + +The central guiding principle of BootCamp lessons is they are focused on the implementation of a single algorithmic trading strategy. At each level of the system, the titles should be directly related to the implementation of the strategy, not the concepts it is covering. This is actually quite difficult, but one way to help to get into this mindset is to focus on teaching how to implement the strategy.
+ + ++A Lesson is a collection of tasks aiming to implement a single algorithmic strategy step by step. A lesson should be comprised of about 6-12 tasks, where each task builds upon the lessons learned from the previous task. We have built a system for the community to design and submit Boot Camp lessons and tasks. +
+ ++A Task is the atomic unit of the Boot Camp system. It is a single step required to be completed in the pathway to an algorithm. Tasks are grouped with a subheading according to algorithm implementation concept. A task should aim to implement just few lines of code so that each task can be easily achieved. +
\ No newline at end of file diff --git a/08 Meta/01 Creating BootCamp Tutorials/05 Planning Your Lesson.html b/08 Meta/01 Creating BootCamp Tutorials/05 Planning Your Lesson.html new file mode 100644 index 0000000..67986a8 --- /dev/null +++ b/08 Meta/01 Creating BootCamp Tutorials/05 Planning Your Lesson.html @@ -0,0 +1,193 @@ ++Carefully planning and structuring your lesson is critical to ensuring its success. In the next section, we'll create this plan step by step. Boot Camp lessons typically fall into one of the following algorithm types: Macro Economics, Technical Indicators, Scaling, Market Making, Market Microstructure, Sentimental, or Value-Fundamental Investing. +
+ ++Every BootCamp lesson is focused on an algorithmic strategy's implementation. The first step to planning a lesson is choosing a strategy which does not overlap with any of the existing BootCamp topics. This can be incrementally more difficult but should introduce new concepts. +
+ ++After selecting your strategy you need to fully implement the algorithm, writing the code in C# and Python as simply as possible. Users new to coding have a hard time deciphering large blocks of code so strategies should be kept very simple. +
+ +In writing the strategy remain aware of the conceptual layers you put into the algorithm's codebase. These layers of concepts are where you can separate out the lesson tasks. For example: in writing a lesson "Buy and Hold, with Trailing Stop" you might start by coding up the buy and hold logic, followed by placing a "trailing stop" (Stop Market Order), then finally you can make the stop move by updating its trigger price. These conceptual layers form the basis for how tasks are grouped together.
+ ++QuantConnect has worked with the community to create a list of lessons to be created which would be eligible for compensation. The table below describes these strategies and their associated difficulty level. +
+ + + +| Beginner BootCamp Lessons | +Status | +
|---|---|
Buy and Hold (Equities/Forex) |
+Completed |
+
Buy and Hold with Trailing Stop |
+Completed |
+
Momentum-Based Tactical Allocation |
+Completed |
+
Open Range Breakout |
+Completed |
+
Liquid Universe Selection |
+Completed |
+
200-50 EMA Momentum Universe |
+Completed |
+
Fading The Gap |
+Completed + |
+
| Intermediate BootCamp Lessons | +Status | +
|---|---|
The Algorithm Framework |
+Assigned |
+
Pairs Trading with SMA |
+Assigned |
+
Pairs Trading with Cointegration Test |
+Assigned |
+
Liquid Value Stocks |
+Assigned |
+
Sector Balanced Universe Selection |
+Assigned |
+
Hedging FX Books with Interest Rate |
++ |
Sentiment Analysis on Stocks |
++ |
| Advanced BootCamp Lessons | +Status | +
|---|---|
Coming Soon |
++ |
+Writing a BootCamp lesson starts by carefully writing out the complete code for the strategy, breaking it into tasks, and write small text summaries for each task with the documentation required to teach the reader how to complete the task. Finally, JavaScript is used to read the exhaust output of the algorithm to validate it achieved the required objective. +
+ + ++Writing a BootCamp lesson starts by carefully writing out the complete code for the strategy. This should be drafted as simply as possible to ensure each task the student needs to complete will only be 2-5 lines of code. +
+Readability is critical and the code should be well commented with descriptive variable names. Depending on the complexity of the algorithm sometimes its more readable to use string tickers instead of class variables. +
++Carefully write code in a way which neatly separates the algorithm concepts as much as possible. Keep in mind the algorithm will be implemented in separate tasks by the student. +
+Write highly readable, concise C# and Python versions of the algorithm and request review by QuantConnect Education team. Plan ahead for divisions of the code into tasks.
++Each task has a short write-up to explain the features needed to complete the next task of BootCamp. This write-up should assume the student has no prior knowledge and include representative code snippets demonstrating the key API code needed. +
+| Style | Example Code Tag |
|---|---|
Headings |
+<h4>Initializaing Algorithms</h4> |
+
Paragraphs |
+<p>Setting cash is done with <span class="python">self.SetCash().</span></p> |
+
Code Snippets |
+<pre class="prettyprint python">self.SetCash()</pre> |
+
+For a fluent experience between lessons, all content should follow the same structure as the sections laid out below. +
+
+
+
+Tasks start their contents divided by subtitle using the h4 tag. Use a short title about the specific API or content you're trying to summarize.
+
+After each heading, write a short paragraph concisely summarizing the content in as few words as possible. Use inline <code> blocks to highlight API syntax, and links to new tabs referencing any documentation required.
+
+Any content which is specific to one programming language should be wrapped in a span tag with the language set in the class, for example: <span class="python">.
+
+Each section should include a code snippet of documentation using a <pre class="prettyprint"> code block.
+
+Finally, each task should define 2-4 objectives to achieve in the task. These tasks should guide the user on the required steps to implement the strategy step. At the end of the task, there should be a measurable output that the system can use to judge if the task is a success. This can be a state change of the algorithm, a debug/log statement, or a trade. This will be covered in the next section, Code Validators.
+
+Validators + Partial Class + Validating algorithm output + + Examples of validation +
diff --git a/08 Meta/01 Creating BootCamp Tutorials/08 Style Guide.html b/08 Meta/01 Creating BootCamp Tutorials/08 Style Guide.html new file mode 100644 index 0000000..5fc6ae1 --- /dev/null +++ b/08 Meta/01 Creating BootCamp Tutorials/08 Style Guide.html @@ -0,0 +1,7 @@ ++H4 titles, verbs describing strategy step +Brief Short sentences, +Aim for no more than 3 todo's per task +Hint should give enough information to complete the task. +technical grammar, present tense. +
diff --git a/08 Meta/01 Creating BootCamp Tutorials/09 Submitting Lesson for Review.html b/08 Meta/01 Creating BootCamp Tutorials/09 Submitting Lesson for Review.html new file mode 100644 index 0000000..b514e77 --- /dev/null +++ b/08 Meta/01 Creating BootCamp Tutorials/09 Submitting Lesson for Review.html @@ -0,0 +1,3 @@ ++Lesson submission +
diff --git a/08 Meta/01 Creating BootCamp Tutorials/10 Summary.html b/08 Meta/01 Creating BootCamp Tutorials/10 Summary.html new file mode 100644 index 0000000..517c4ef --- /dev/null +++ b/08 Meta/01 Creating BootCamp Tutorials/10 Summary.html @@ -0,0 +1,3 @@ ++ +
diff --git a/Data/F-F_Research_Data_5_Factors_2x3.CSV b/Data/F-F_Research_Data_5_Factors_2x3.CSV new file mode 100644 index 0000000..8adb14e --- /dev/null +++ b/Data/F-F_Research_Data_5_Factors_2x3.CSV @@ -0,0 +1,748 @@ +This file was created by CMPT_ME_BEME_OP_INV_RETS using the 202007 CRSP database. +The 1-month TBill return is from Ibbotson and Associates Inc. + +,Mkt-RF,SMB,HML,RMW,CMA,RF +196307, -0.39, -0.47, -0.83, 0.66, -1.15, 0.27 +196308, 5.07, -0.79, 1.67, 0.40, -0.40, 0.25 +196309, -1.57, -0.48, 0.18, -0.76, 0.24, 0.27 +196310, 2.53, -1.29, -0.10, 2.75, -2.24, 0.29 +196311, -0.85, -0.84, 1.71, -0.45, 2.22, 0.27 +196312, 1.83, -1.89, -0.12, 0.07, -0.30, 0.29 +196401, 2.24, 0.08, 1.59, 0.22, 1.50, 0.30 +196402, 1.54, 0.32, 2.83, 0.06, 0.85, 0.26 +196403, 1.41, 1.41, 3.32, -2.01, 2.93, 0.31 +196404, 0.10, -1.52, -0.55, -1.35, -1.08, 0.29 +196405, 1.42, -0.68, 1.98, -0.26, 0.24, 0.26 +196406, 1.27, 0.09, 0.68, -0.42, 0.14, 0.30 +196407, 1.74, 0.53, 0.68, 0.14, 1.84, 0.30 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13.65, 2.81, -1.18, 2.65, -1.03, 0.00 +202005, 5.58, 1.92, -4.92, 0.66, -3.28, 0.01 +202006, 2.45, 1.93, -2.19, -0.02, 0.34, 0.01 +202007, 5.77, -3.11, -1.27, 0.61, 1.07, 0.01 + + Annual Factors: January-December +,Mkt-RF,SMB,HML,RMW,CMA,RF + 1964, 12.54, 0.33, 9.86, -2.99, 6.80, 3.54 + 1965, 10.52, 24.41, 7.36, -0.79, -3.17, 3.93 + 1966, -13.51, 2.15, -0.68, -0.12, -0.34, 4.76 + 1967, 24.49, 50.40, -8.58, 7.53, -15.04, 4.21 + 1968, 8.79, 26.32, 18.49, -12.84, 16.25, 5.21 + 1969, -17.54, -14.06, -9.81, 11.77, -4.14, 6.58 + 1970, -6.49, -12.36, 22.34, -2.65, 24.45, 6.52 + 1971, 11.78, 5.58, -11.29, 10.16, -5.86, 4.39 + 1972, 13.05, -11.43, 1.75, 7.99, -3.05, 3.84 + 1973, -26.19, -20.00, 18.08, -9.03, 6.66, 6.93 + 1974, -35.75, 0.67, 9.67, -4.04, 22.88, 8.00 + 1975, 32.44, 19.05, 9.49, 0.53, 0.48, 5.80 + 1976, 21.91, 19.90, 24.50, -6.67, 7.47, 5.08 + 1977, -8.26, 24.64, 7.51, 2.16, -0.39, 5.12 + 1978, 1.03, 13.68, 0.37, 5.07, 4.15, 7.18 + 1979, 13.09, 21.05, -2.12, -2.80, -0.99, 10.38 + 1980, 22.13, 4.91, -25.06, 14.08, -11.32, 11.24 + 1981, -18.13, 7.48, 25.01, -1.60, 10.36, 14.71 + 1982, 10.66, 7.42, 13.59, -4.46, 18.01, 10.54 + 1983, 13.74, 11.84, 20.85, 0.67, 16.43, 8.80 + 1984, -6.05, -8.45, 19.63, 14.88, 3.84, 9.85 + 1985, 24.91, -0.62, 1.35, 11.89, -2.49, 7.72 + 1986, 10.12, -10.37, 9.58, 7.13, 9.84, 6.16 + 1987, -3.87, -11.28, -1.64, 6.20, 6.90, 5.47 + 1988, 11.55, 6.46, 14.77, 3.08, 9.74, 6.35 + 1989, 20.49, -13.02, -4.29, 2.74, 8.21, 8.37 + 1990, -13.95, -14.30, -9.72, 7.44, 0.60, 7.81 + 1991, 29.18, 15.77, -14.41, 12.06, -14.91, 5.60 + 1992, 6.23, 9.07, 24.28, 7.54, 6.96, 3.51 + 1993, 8.21, 6.01, 18.91, -8.55, 11.99, 2.90 + 1994, -4.10, -2.51, -0.69, 6.35, 3.90, 3.90 + 1995, 31.22, -8.17, 5.30, 1.97, 2.81, 5.60 + 1996, 15.96, -2.80, 6.16, 15.53, 0.52, 5.21 + 1997, 25.96, -6.17, 17.46, 10.51, 5.19, 5.26 + 1998, 19.46, -28.67, -8.89, 0.63, -4.60, 4.86 + 1999, 20.57, 8.56, -31.77, -27.89, -8.44, 4.68 + 2000, -17.60, 4.21, 39.69, 26.67, 32.74, 5.89 + 2001, -15.20, 23.68, 19.52, 19.84, 11.79, 3.83 + 2002, -22.76, 5.82, 7.47, 20.39, 14.47, 1.65 + 2003, 30.75, 24.49, 5.40, -20.46, 17.26, 1.02 + 2004, 10.72, 7.34, 8.08, 8.34, -7.86, 1.20 + 2005, 3.09, -0.75, 8.33, 1.71, -5.03, 2.98 + 2006, 10.60, 1.53, 14.11, 2.08, 8.19, 4.80 + 2007, 1.04, -7.94, -14.65, 4.37, -7.80, 4.66 + 2008, -38.34, 3.34, 0.82, 15.06, 4.16, 1.60 + 2009, 28.26, 7.99, -9.17, 2.78, -2.67, 0.10 + 2010, 17.37, 13.28, -5.31, -1.48, 9.93, 0.12 + 2011, 0.44, -5.78, -8.35, 12.60, -0.88, 0.04 + 2012, 16.28, -0.08, 9.68, -4.71, 9.41, 0.06 + 2013, 35.20, 7.68, 1.33, -4.44, 1.31, 0.02 + 2014, 11.70, -8.10, -1.74, 1.04, -1.70, 0.02 + 2015, 0.07, -5.85, -9.65, 0.89, -8.49, 0.02 + 2016, 13.30, 9.20, 23.02, 4.82, 9.77, 0.20 + 2017, 21.50, -5.84, -13.98, 6.81, -11.80, 0.80 + 2018, -6.93, -5.35, -9.16, -1.37, 0.21, 1.81 + 2019, 28.28, -6.22, -11.67, 4.99, -2.81, 2.14 diff --git a/Data/F-F_Research_Data_5_Factors_2x3_daily.CSV b/Data/F-F_Research_Data_5_Factors_2x3_daily.CSV new file mode 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-14.32, 1.07 + 1932, -9.39, 4.91, 10.49, 0.96 + 1933, 57.05, 48.86, 28.15, 0.30 + 1934, 3.02, 25.43, -27.38, 0.16 + 1935, 44.96, 9.99, 9.78, 0.17 + 1936, 32.07, 17.89, 35.86, 0.18 + 1937, -34.96, -14.00, -3.97, 0.31 + 1938, 28.48, 9.35, -12.18, -0.02 + 1939, 2.70, 5.85, -19.17, 0.02 + 1940, -7.14, 0.79, -0.82, 0.00 + 1941, -10.53, -4.04, 11.13, 0.06 + 1942, 16.20, 5.05, 19.87, 0.27 + 1943, 27.96, 33.35, 38.97, 0.35 + 1944, 20.97, 17.98, 15.61, 0.33 + 1945, 38.38, 25.56, 11.40, 0.33 + 1946, -6.73, -3.79, 2.98, 0.35 + 1947, 2.95, -7.08, 9.76, 0.50 + 1948, 1.07, -9.14, 3.52, 0.81 + 1949, 19.12, 3.93, -4.55, 1.10 + 1950, 28.82, 0.93, 27.01, 1.20 + 1951, 19.22, -4.93, -5.93, 1.49 + 1952, 11.80, -6.66, 3.34, 1.66 + 1953, -1.05, -1.16, -7.71, 1.82 + 1954, 49.35, -2.18, 26.21, 0.86 + 1955, 23.75, -6.71, 5.77, 1.57 + 1956, 5.90, -1.17, -1.60, 2.46 + 1957, -13.16, -2.72, -6.39, 3.14 + 1958, 43.45, 14.81, 13.16, 1.54 + 1959, 9.76, 5.43, 1.86, 2.95 + 1960, -1.46, -2.76, -4.87, 2.66 + 1961, 24.81, 1.49, 5.19, 2.13 + 1962, -12.90, -8.25, 8.80, 2.73 + 1963, 17.84, -5.88, 15.66, 3.12 + 1964, 12.54, -0.99, 9.86, 3.54 + 1965, 10.52, 21.80, 7.36, 3.93 + 1966, -13.51, 2.59, -0.68, 4.76 + 1967, 24.49, 50.69, -8.58, 4.21 + 1968, 8.79, 24.50, 18.49, 5.21 + 1969, -17.54, -13.98, -9.81, 6.58 + 1970, -6.49, -11.79, 22.34, 6.52 + 1971, 11.78, 5.62, -11.29, 4.39 + 1972, 13.05, -11.95, 1.75, 3.84 + 1973, -26.19, -23.44, 18.08, 6.93 + 1974, -35.75, -0.60, 9.67, 8.00 + 1975, 32.44, 15.28, 9.49, 5.80 + 1976, 21.91, 14.69, 24.50, 5.08 + 1977, -8.26, 22.95, 7.51, 5.12 + 1978, 1.03, 14.38, 0.37, 7.18 + 1979, 13.09, 21.12, -2.12, 10.38 + 1980, 22.13, 5.57, -25.06, 11.24 + 1981, -18.13, 7.23, 25.01, 14.71 + 1982, 10.66, 8.89, 13.59, 10.54 + 1983, 13.74, 13.67, 20.85, 8.80 + 1984, -6.05, -8.31, 19.63, 9.85 + 1985, 24.91, 0.12, 1.35, 7.72 + 1986, 10.12, -9.60, 9.58, 6.16 + 1987, -3.87, -11.00, -1.64, 5.47 + 1988, 11.55, 5.90, 14.77, 6.35 + 1989, 20.49, -12.72, -4.29, 8.37 + 1990, -13.95, -14.18, -9.72, 7.81 + 1991, 29.18, 16.13, -14.41, 5.60 + 1992, 6.23, 7.58, 24.28, 3.51 + 1993, 8.21, 5.80, 18.91, 2.90 + 1994, -4.10, -1.06, -0.69, 3.90 + 1995, 31.22, -9.09, 5.30, 5.60 + 1996, 15.96, -3.71, 6.16, 5.21 + 1997, 25.96, -6.76, 17.46, 5.26 + 1998, 19.46, -26.02, -8.89, 4.86 + 1999, 20.57, 14.85, -31.77, 4.68 + 2000, -17.60, -1.51, 39.69, 5.89 + 2001, -15.20, 18.09, 19.52, 3.83 + 2002, -22.76, 4.72, 7.47, 1.65 + 2003, 30.75, 26.18, 5.40, 1.02 + 2004, 10.72, 4.85, 8.08, 1.20 + 2005, 3.09, -1.93, 8.33, 2.98 + 2006, 10.60, 0.24, 14.11, 4.80 + 2007, 1.04, -7.14, -14.65, 4.66 + 2008, -38.34, 3.18, 0.82, 1.60 + 2009, 28.26, 9.39, -9.17, 0.10 + 2010, 17.37, 13.77, -5.31, 0.12 + 2011, 0.44, -6.04, -8.35, 0.04 + 2012, 16.28, -1.28, 9.68, 0.06 + 2013, 35.20, 7.18, 1.33, 0.02 + 2014, 11.70, -8.11, -1.74, 0.02 + 2015, 0.07, -4.03, -9.65, 0.02 + 2016, 13.30, 6.65, 23.02, 0.20 + 2017, 21.50, -4.68, -13.98, 0.80 + 2018, -6.93, -3.40, -9.16, 1.81 + 2019, 28.28, -6.09, -11.67, 2.14 + +Copyright 2020 Kenneth R. French diff --git a/Data/F-F_Research_Data_Factors_daily.CSV b/Data/F-F_Research_Data_Factors_daily.CSV new file mode 100644 index 0000000..f502001 --- /dev/null +++ b/Data/F-F_Research_Data_Factors_daily.CSV @@ -0,0 +1,24797 @@ +This file was created by CMPT_ME_BEME_RETS_DAILY using the 202007 CRSP database. +The Tbill return is the simple daily rate that, over the number of trading days +in the month, compounds to 1-month TBill rate from Ibbotson and Associates Inc. + +,Mkt-RF,SMB,HML,RF +19260701, 0.10, -0.24, -0.28, 0.009 +19260702, 0.45, -0.32, -0.08, 0.009 +19260706, 0.17, 0.27, -0.35, 0.009 +19260707, 0.09, -0.59, 0.03, 0.009 +19260708, 0.21, -0.36, 0.15, 0.009 +19260709, -0.71, 0.44, 0.56, 0.009 +19260710, 0.62, -0.50, -0.15, 0.009 +19260712, 0.04, 0.03, 0.54, 0.009 +19260713, 0.48, -0.26, -0.23, 0.009 +19260714, 0.04, 0.09, -0.48, 0.009 +19260715, -0.43, 0.54, -0.30, 0.009 +19260716, 0.53, 0.01, -0.57, 0.009 +19260717, 0.34, 0.43, -0.63, 0.009 +19260719, -0.01, 0.01, -0.49, 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French diff --git a/Data/F-F_Research_Data_Factors_weekly.CSV b/Data/F-F_Research_Data_Factors_weekly.CSV new file mode 100644 index 0000000..a6741c9 --- /dev/null +++ b/Data/F-F_Research_Data_Factors_weekly.CSV @@ -0,0 +1,4916 @@ +This file was created by CMPT_ME_BEME_RETS_WEEKLY using the 202007 CRSP database. +The Tbill return is the weekly rate that, over four weeks, +compounds to 1-month TBill rate from Ibbotson and Associates Inc. + +,Mkt-RF,SMB,HML,RF +19260702, 1.60, -0.57, -0.90, 0.056 +19260710, 0.36, -0.86, 0.27, 0.056 +19260717, 1.01, 0.83, -1.84, 0.056 +19260724, -2.05, 0.15, -0.25, 0.056 +19260731, 3.04, -1.86, -0.85, 0.056 +19260807, 2.01, 0.08, 0.53, 0.063 +19260814, 0.33, -0.66, 0.76, 0.063 +19260821, -1.11, 0.26, 1.95, 0.063 +19260828, 0.53, 0.07, 0.84, 0.063 +19260903, 1.87, -0.41, 0.55, 0.057 +19260911, -1.27, 0.16, -0.01, 0.057 +19260918, 0.16, -1.10, 0.32, 0.057 +19260925, 0.62, -0.80, -0.39, 0.057 +19261002, 0.48, -0.08, -0.48, 0.080 +19261009, -4.14, -0.31, 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French diff --git a/README.md b/README.md index f49f107..c9846d7 100644 --- a/README.md +++ b/README.md @@ -6,28 +6,24 @@ This repository is a collection of WordPress and Jupyter notebook tutorials for LEAN demonstrating financial concepts and LEAN. Tutorials are categorized into folders with each Category and Tutorial Series. The Jupyter notebook and the associated HTML webpage must use matching file names. The HTML is generated and displayed with wordpress. -Lean Engine is an open-source fully managed C# algorithmic trading engine built for desktop and cloud usage. It was designed in Mono and operates in Windows, Linux and Mac platforms. For more information about the LEAN Algorithmic Trading engine see the [Lean Engine Repository][4]. +Lean Engine is an open-source fully managed C# algorithmic trading engine built for desktop and cloud usage. It was designed in Mono and operates in Windows, Linux and Mac platforms. For more information about the LEAN Algorithmic Trading engine see the [Lean][4] Engine repository. +## Contributors and Pull Requests ## -## New Tutorial Requests and Edits ## - -Please submit new tutorial requests as an issue to the [Tutorial Repository][5]. Before submitting an issue please read others to ensure it is not a duplicate. Edits and fixes for clarity are warmly welcomed! - -We've made a simple editor to help with drafting HTML tutorials: https://www.quantconnect.com/tutorials/editor. Once you've drafted the content there copy the code into a pull-request for the tutorials website. +Contributions are warmly very welcomed but we ask you read the existing code to see how it is formatted, commented and ensure contributions match the existing style. All code submissions must include accompanying tests. Please see the [contributor guide lines][7]. -## Mailing List ## +## Strategy Library Development Workflow ## -The mailing list for the project can be found on [Google Groups][6] +To publish a strategy to our [Strategy Library](https://www.quantconnect.com/tutorials/strategy-library/strategy-library), follow the steps on the [documentation page](https://www.quantconnect.com/docs/v2/writing-algorithms/strategy-library#03-Contribute-Tutorials) -## Contributors and Pull Requests ## +## New Tutorial Requests and Edits ## -Contributions are warmly very welcomed but we ask you read the existing code to see how it is formatted, commented and ensure contributions match the existing style. All code submissions must include accompanying tests. Please see the [contributor guide lines][7]. +Please submit new tutorial requests as an issue to the [Tutorials][5] repository. Before submitting an issue please read others to ensure it is not a duplicate. Edits and fixes for clarity are warmly welcomed! [1]: https://www.quantconnect.com/tutorials "Tutorials Viewer" [2]: https://www.quantconnect.com/lean/docs "Lean Documentation" [3]: https://github.com/QuantConnect/Lean/archive/master.zip -[4]: https://github.com/QuantConnect/Lean/archive/master.zip +[4]: https://github.com/QuantConnect/Lean [5]: https://github.com/QuantConnect/Tutorials/issues -[6]: https://groups.google.com/forum/#!forum/lean-engine [7]: https://github.com/QuantConnect/Lean/blob/master/CONTRIBUTING.md [8]: https://www.quantconnect.com/slack diff --git a/quantpedia.json b/quantpedia.json new file mode 100644 index 0000000..22f8d06 --- /dev/null +++ b/quantpedia.json @@ -0,0 +1,52 @@ +{ + 1 : "6caef9a7716468be0d790b63b7f463f6", + 2 : "1cb38e96cec6120fc85152da661605c1", + 3 : "4191ffdf07f9d7dec396f148a20b3eef", + 4 : "d31f2d20f4a060418985dd8c0c606c13", + 5 : "798687a2edab75475f0c9095ecd71c1f", + 7 : "34e8ae2763e7e2122634d4091120d320", + 8 : "336bbb8e9e4a55a6adfa00c0d9f904bb", + 12: "72532ccafeaa844c81aa75c5696b4b24", + 13: "05d0edd633b1438852d1d641af0224ae", + 14: "e7b55d46fa8677ed8ec91dd1a0159a6e", + 15: "bd83aa417032f8407382a1c065aa7511", + 16: "afd2c9d67fd51d602bf8eac2ef28d712", + 18: "ba1bb35b26896e2e710a510f62230a24", + 20: "f0fca76a72227c5bee77d59bdbf5a53d", + 21: "203a6729604c80a71b5c3b2baa2b3f69", + 22: "d7285b5353d51cd5bd033f205e5faf44", + 23: "12a417567b5706fdff6cf6265506b98c", + 25: "ae6b2ce97f01f10af90c8823828ae5c9", + 26: "d8cd05d85b47eea4381d2ca20abf2f74", + 38: "55081a6fa81c88fd75579c2f838a1180", + 41: "d91ba9f0676ddc619a573b4d9135d988", + 43: "707c5bb33fede32269a986370bf8a0a9", + 44: "6fe04ea9049f2cf36d3c64ee672254ea", + 51: "b6d06b2074e4efe807c29135507fa2ab", + 52: "813285e2c02ffca1afa114e668301ea8", + 55: "2d6bcad96d965a04cd7eac846d54f129", + 53: "e8a75429c6a43e969e4a9243290e05f4", + 54: "12769f4ad4513269d8f771c99046deb2", + 58: "6f1f8cae87849a2aa65aa318f6554dfc", + 61: "17611f8cf05678b9bd09d98ba3581854", + 66: "ace0e17cc133feceaf4aa83035309116", + 71: "124aa2fdf4ae34bc022a00b54c26b10d", + 77: "0483e5a7094604254ab37eda8b5141b8", + 78: "27fb5f05b0e48f488f0994d8d83ddc77", + 83: "fdfcddd132eaf55039d867c03efe3012", + 85: "a86b19f12b40d8a676bf7f885742631d", + 91: "95cffbeec0d003da873b791d3a10f60f", + 100: "5ee5507fef6bf190ae533ce05ccaa785", + 102: "cd2d187e44a00c7b19f64aee8b0895d9", + 113: "9b1291a5f08dcc07df86363e46144084", + 114: "7a404f43e9191ac5bce9a9446572cb98", + 125: "1f9f254c932d8e7ae85e803affd52a7b", + 136: "d8932a9697f7e98e9a00761d37e627dd", + 152: "b35034509d95c173fed1c0adcecc5be0", + 155: "886a9f73bc29142f14fcb2c2d01404a9", + 162: "5761c1817a9dcb805be487f9e32adfa1", + 198: "59a110653538ebcbfccacbe237c33091", + 199: "2deff750ba4eff5bf2f2138ecffb4a7c", + 207: "9bcf7ac117397af393ca59f795c4abdd", + 229: "5544552803512ca667342d5011dedd1d", +}