Question

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

Alpha is a measure of Excess return i.e. Expected return - Required return.

Under five factor model, the factors considered are

1. Beta

2. Size

3. Value

4. Profitability

5. Investment

The starting point for the five-factor model is the dividend discount model which states that the value of a stock today is dependent upon future dividends.

The purpose of doing regression test is to observe the following:

1. whether the five-factor model captures average returns on the variables

2. to see which variables are positively or negatively correlated to each other

3. identifying the size of the regression slopes

4. how all these factors are related to and affect average returns of stocks values.

A statistically significant alpha is an alpha that's not attributed to chance, which means that if the Null Hypothesis is true (which means there really is no difference), there's a low probability of getting an alpha that large.

Hence, my co-worker's argument is correct, that, if 5 factor model is more efficient, the number of statistically significant alpha should be lower. I agree with my co-worker.