Risk and Return 77The Fama–French Three Factor Model is estimated by running a time series multiple regression for each
company. The dependent variable is the company’s monthly excess stock returns over Treasury bill returns.
The independent variables are as follows:
- The monthly excess return on the market over Treasury bills.
- SMB (‘small minus big’)—the difference between the monthly return on small-cap stocks and large-cap
stocks. - HML (‘high minus low’)—the difference between monthly returns on high book-to-market stocks and
low book-to-market stocks.
In the Fama–French (FF) model, beta measures the sensitivity of a stock to movements in the market.
The SMB premium represents the return premium that companies with small market capitalization usually
experience relative to companies with large capitalization. It is computed by multiplying the coefficient for
the SMB factor in the multiple regression by the difference between the historical average annual returns on
the small-cap and large-cap portfolios.
The HML premium represents the return that investors expect from companies that have a high book
equity to market equity ratio. The Fama–French model predicts that a company with a high book equity-to-
market equity ratio has an excess return that is not captured in the market return. The number presented is the
coefficient for the HML factor multiplied by the difference between the historical average annual returns on
the high market-to-book and low market-to-book portfolios.
The beta provided by the Fama–French model is similar to the beta provided by the capital asset pricing
model; it is a measure of the risk of a stock relative to the market. By multiplying the Fama–French beta by
the equity risk premium, and adding the HML and SMB premiums and the risk-free rate, the expected re-
turn for a company is obtained.
For the HML and SMB factors, the regression coefficients have been multiplied by the premium for each
of the factors. The data presented is the percent premium over the market return which each stock receives
because of the small company premium and the value premium. An example is in order.
FF beta = 0.70, SMB premium = 2.53 percent, HML premium = 4.17 percent
Expected return = Risk-free rate + (Equity risk premium × FF beta) + SMB premium + HML premium
The expected return for the company assuming a risk-free rate of 5.9 percent and a risk premium of
7.8 percent is:
5.9 percent + (7.8 × 0.70) percent + 2.53 percent + 4.17 percent = 18.06 percentThe Case of Emerging Markets
The risk-return analysis presented so far is appropriate if the portfolio returns can be completely characterized
by the mean and standard deviation. A large number of studies have shown that emerging market returns
are non-normal and hence cannot be described by mean and variance.^6 Exhibit 3.16 presents an example
of Mexico. There are many small returns and a large number of negative returns in the case of Mexico. If the
Mexican returns were generated from a normal distribution, we would not expect so many negative returns
of the magnitude shown in the graph. Thailand is similar to Mexico with some extreme negative observations.
(^6) Erb, Claude B, Campbell Harvey, and Tadas Viskanta (1996). ‘Expected Returns and Volatility in 135 Countries’,
The Journal of Portfolio Management, Vol. 21, No. 2.