Question

According to the Fama and French 3-factor model，do you think that the three factors included make up a logical explanation of how share returns may be explained? What criticisms could be made of the model? (give academic support or example)

Answer 1

A mathematical expression of three factor model of Fama & French is:

Expected return = E(R) = R_f + B₁ x (R_m - R_f) + B₂ x (SMB) + B₃ x (HML) where the symbols have the usual meanings.

The model is an extension of CAPM and improves upon the CAPM by including two more terms: SMB and HML

SMB factor

= small minus big in a way reflects that there is an incremental riskiness associated with stocks with relatively smaller market capitalization, hence the expected return on a portfolio should be impacted by the SMB factor. The argument is rational as a small capitalization stock does have higher riskiness in comparison to a large cap stock. So, SMB factor goes in line with the fact that a portfolio comprising of higher proportion of "Small" cap stocks should outperform the portfolio comprising of higher proportion of large cap stocks. Hence, expected return on such a portfolio should be higher.

HML factor = High minus Low

High refers stock with higher book value to market value ratio; Such stocks are also called value stocks.

Low refers to stock with lower book value to market value ratio; such stocks are called growth stocks.

Empirical studies have shown that values stocks have outperformed the growth stocks in long run.

So, HML factor goes in line with the argument that in the long run a portfolio comprising of higher proportion of value stocks i.e. "High" stocks will perform better in the long return. Hence, expected return on such a portfolio should be higher.

Fama and French rationalise their SMB and HML factors as reflecting the extra riskiness of small stocks and low price-to-book value stocks respectively. And the arguments are in line with the academic point that:

• Risk and reward go hand in hand
• Portfolio with higher risk should have higher expected return and similarly, portfolio offering higher reward (return) should have relatively higher risk profile otherwise there will be risk return arbitrage.

In fact, many of the research papers and empirical studies have built upon this model and included the fourth and even the fifth factor in the model.

Possible Criticism of the model:

1. Based on empirical studies and coefficients are derived based on regression of date over a given span of time. Hence none of the betas used in the model will have a constant value. They will change depending upon the span of time chosen for regression analysis.
2. Incremental effort required to include the additional two factors is high and not commensurate with the kind of improvement it does over the expected return predicted by CAPM. Hence, CAPM continues to remain the most popular model for calculating the expected return from a security and portfolio.