Fama-French Three Factor Model: Definition & Formula
Fama and French hypothesized that the Security Market Line should have three factors. The first is the stock’s CAPM beta and the second is the market value of its equity (size of the company). The third factor is the book value of equity divided by the market value of equity or book- to- market ratio.
We expect small companies to have higher stock returns than large companies. If the market value is larger than the book value, then investors are optimistic about the stock’s future. So, a stock with a high B/M ratio might be risky and investors reqıuire a higher return to induce them.
When Fama and French tested their hypothesis, they found that small companies and firms with high B/M ratio had higher rates of return than average stock. However, they found no relation between beta and return.
In their second study, they developed a three factor model:
- The first factor is the market risk premium (Rm-Rf)
- To form the second factor , they ranked all actively traded stocks by size and divided them into two portfolios, consisting of small and big stocks.They calculated the return on each of these two portfolios and created a third portfolio by subtracting the return from the big portfolio from that of the small one.They called this SMB (small minus big size) portfolio. This portfolio is designed to measure the variation in stock returns that is caused by the size effect.
- To form the third portfolio, they ranked all stocks according to their B/M ratios.They placed the 30% of stocks with highest B/M ratios into a portfolio called , H, portfolio (high B/M). They placed the 30% of stocks with lowest B/M in a portfolio called the L portfolio.They subtract the return of the L portfolio from H portfolio and called the result HML portfolio( High B/M minus low B/M)
( ki – krf) = ai + bi (km- krf) +ci (kSMB) + di (kHML) +ei
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