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<p>
This model was proposed in 1993 by <strong>Eugene Fama</strong> and <strong>Kenneth French</strong> to describe stock returns.[ref] <strong>Fama, E F; French, K R</strong> (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]
</p>
<p>
The 3-factor model is
This model was proposed in 1993 by <strong>Eugene Fama</strong> and <strong>Kenneth French</strong> to describe stock returns. The 3-factor model is
</p>
\[ R = \alpha + \beta_m MKT + \beta_s SMB + \beta_h HML \]

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<ul>
<li>MKT is the excess return of the market. It's the value-weighted return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ minus the 1-month Treasury Bill rate.</li>
<li>SMB (Small Minus Big) measures the excess return of stocks with small market cap over those with larger market cap.</li>
<li>HML (High Minus Low) measures the excess return of value stocks over growth stocks. Value stocks have high book to price ratio (B/P) than growth stocks.</li>
<li>HML (High Minus Low) measures the excess return of value stocks over growth stocks. Value stocks have a higher book to price ratio (B/P) than growth stocks.</li>
</ul>

<p>
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<p>
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.
</p>
<p>
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.
</p>
30 changes: 15 additions & 15 deletions ...nch Multi-Factor Models/07 Algorithm.html → ...nch Multi-Factor Models/06 Algorithm.html
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<p>
Multi-factor strategies are <strong>stock picking</strong> 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.
</P>
<p>
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.
</p>
<div class="qc-embed-frame" style="display: inline-block; position: relative; width: 100%; min-height: 100px; min-width: 300px;">
<div class="qc-embed-dummy" style="padding-top: 56.25%;"></div>
<div class="qc-embed-element" style="position: absolute; top: 0; bottom: 0; left: 0; right: 0;">
<iframe class="qc-embed-backtest" height="100%" width="100%" style="border: 1px solid #ccc; padding: 0; margin: 0;" src="https://www.quantconnect.com/terminal/index.php?key=processCache&request=embedded_backtest_d0f89f7876841581a8eee32cf007cd75.html"></iframe>
</div>
</div>
<p>
Multi-factor strategies are <strong>stock picking</strong> 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.
</P>
<p>
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.
</p>
<div class="qc-embed-frame" style="display: inline-block; position: relative; width: 100%; min-height: 100px; min-width: 300px;">
<div class="qc-embed-dummy" style="padding-top: 56.25%;"></div>
<div class="qc-embed-element" style="position: absolute; top: 0; bottom: 0; left: 0; right: 0;">
<iframe class="qc-embed-backtest" height="100%" width="100%" style="border: 1px solid #ccc; padding: 0; margin: 0;" src="https://www.quantconnect.com/terminal/processCache?request=embedded_backtest_45b5f4ad1eddc1d37543cc4199a34a40.html"></iframe>
</div>
</div>
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<li>
Robert Novy-Marx (2013). The Other Side of Value: The Gross Profitability Premium Journal of Financial Economics 108 (1), 1-28. Retrieved from <a href="http://rnm.simon.rochester.edu/research/OSoV.pdf" target="_blank">rnm.simon.rochester.edu/research/OSoV.pdf</a>
</li>
<li>
Fama, E. F. & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. <i>Journal of Financial Economics</i>, 33, 3-56. doi: 10.1016/0304-405X(93)90023-5. Retrieved from <a href="https://rady.ucsd.edu/faculty/directory/valkanov/pub/classes/mfe/docs/fama_french_jfe_1993.pdf">rady.ucsd.edu</a>.
</li>
</ol>