Fama and French Three Factor Model

Capital Asset Pricing Model (CAPM) is the backbone of modern portfolio theory. According to CAPM, the expected return on stock is a function of its relationship with the market portfolio defined by its beta. However, Eugene Fama and Kenneth French (1992) brought together two more factors and found that stock return is based on a combination of not just market beta but also firm size and value. They came up with a new model known as  Three Factor Model  as an alternative to CAPM.

What is Fama and French Three Factor Model?

Fama and French three factor model expands on the Capital Asset Pricing Model (CAPM) by adding size and value factors in addition to the market risk factor in CAPM. This model considers the fact that value and small cap stocks out-perform markets on a regular basis. Fama and French attempted to approach and measure equity returns in a different manner and found that value stocks outperform growth stocks and also small cap stocks tend to out perform large cap stocks. Thus, the performance of portfolios with a large number of small cap or value stocks is better than one with large cap and growth stocks but lower than the CAPM result. This is because the three factor model adjusts downward for small cap and value out-performance. However, the three factor model is considered to be a better model than its counterparts as by including two additional factors, the model adjusts for the out-performance tendency.

The out-performance tendency of small cap stocks is a debated issue as out-performance may be considered as dependent on market efficiency or market inefficiency and may mean different things under each. In the case of market efficiency, the out-performance is generally explained by the excess risk that value and small cap stocks face as a result of their higher cost of capital and greater business risk. However, in the case of market inefficiency, the out-performance can be explained by market participants arriving at the incorrect value of these companies. This results in excess return in the long run as the value adjusts.

Thus, according to Fama and French three factor model, the expected return on a portfolio in excess of the risk free rate is explained by the sensitivity of its return to three factors. These are:

  1. excess return on a broad market portfolio
  2. Size factor represented as the difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks (SMB) and
  3. Value factor represented as the difference between the return on a portfolio of high-book-to-market stocks and the return on a portfolio of low-book-to- market stocks (HML).

The model can be presented as follows:

(Rpt) = Rf  + ßp[(Rmt) — Rf  ] +  sp(SMB) +  hp(HML) + εpt

where:

  • (Rpt) is the weighted return on portfolio p in period t.
  • Rf  is the risk-free rate;
  • ßp  is the coefficient loading for the excess return of the market portfolio over the risk-free rate
  • sp is the coefficient loading for the excess average return of portfolios with small equity class over portfolios of big equity class.
  • hp is the coefficient loading for the excess average returns of portfolios with high book-to-market equity class over those with low book-to-market equity class.
  • εpt  is the error term for portfolio p at time t.

Fama and French (1995) analysed the characteristics of firms with high book-to-market and those with low book-to-market equity. They found that firms with high book equity to market equity ratio tend to be steadily troubled in comparison to those with low book equity to market equity. In fact firms with low ratio have continued profitability conditions. This led them to conclude that high book equity to market equity stocks are riskier and the returns to holders of such equity is actually a compensation for holding less profitable and riskier stocks. They show that book-to-market equity ratio and slopes on HML in the three factor model is a compensation for relative distress. Weak firms with continuously low earnings tend to have high book equity to market equity ratio and positive slopes on HML. In contrast, strong firms with high earnings have low book equity to market equity and negative slopes on HML.

Fama and French Three Factor Model as a Performance Tool

Fama French Three Factor Model is a highly useful tool for understanding portfolio performance. In recent times, this model has gained more relevance than CAPM. It is now taken as the most widely accepted explanation of stock price movements taken together and investor returns. Unlike CAPM which is a single factor model based on relationship between returns and market factor, the Fama and French three factor model is based on stock return having its basis in not one but three separate risk factors: market, size and value or book to market based factor.

Fama and French reached this conclusion on the basis of two separate studies based on:

  • Returns from a period from 1963 to 1990
  • Returns from a period from 1929 to 1997.

Fama and French discovered that stock returns can best be explained when stocks are separated into portfolios based on size as measured by market capitalization and value-growth as measured by book/market ratios.

Thus, the Fama and French three factor model adopts a different approach to explain market pricing. These three factors, namely market, size and value collectively explain a significant part of the variation in mean returns. In other words, if we assume that stocks are priced rationally then systematic differences in average returns are explained by the market, size and value exposures of the risk factors in returns.

Though on one hand Fama and French three factor model claims that the behavior of stock returns in relation to market, size and value factors is consistent with the behavior of earnings, on the other hand it admits to the weakness of the model especially in relation to the value factor. However, this weakness can be attributed to the measurement error problems in earnings data.

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