Question

1. Your co-worker and you agree that the Fama-French five-factor model explains stock returns better than the market model. Your co-worker ran two sets of 100 time-series regressions of the excess returns of the stocks in the S&P100 index on: 1) the five factors that make up the Fama-French five-factor model and 2) the market factor only. Your co-worker argues that if the five-factor model is indeed better, she should find a smaller number of statistically significant alphas in set 1) where she used all five factors than in set 2) where she used only the market factor as the regressor. Do you agree or disagree? Briefly explain.

Answer 1

The five factors in the Fama French Model are

· Market return – risk free rate

· SMB shows the small minus large size stock

· HML is the value effect

· RMW is the spread between most profitable and least profitable

· CMA is for firms who invest conservatively vs Aggressively.

When you are using five factor and then calculating the required return based on beta factor for all these then naturally risk can be attributed to many factors rather than just one factor of market risk premium, in these circumstance the required return would increase and the alpha that is the difference between the estimated return minus the required rate will reduce because now the risk premium has been estimated more accurately. If you look at the return of small cap stocks and use one factor to calculate the required rate and then use the size premium in addition to the existing factor then you will notice that the required rate has increased and the alpha will be reduced. We often say that small cap stocks generate excess return but if we look at it on risk adjusted basis for size premium then that excess return would not be very attractive to many investors.