- While a five-factor model (beta, size, value, profitability and investment) doesn’t fully explain the cross section of returns (there are still anomalies) it does provide a good description of average returns.
- The model’s main problem is its failure to explain the low average returns on small stocks of companies that invest a lot despite low profitability. It’s interesting to note here that the Fama-French three-factor model has a problem explaining the poor performance of small growth stocks.
- The performance of the model isn’t sensitive to the specifics of the way its factors are defined.
- A four-factor model that excludes the value factor (HML) captures average returns as well as any other four-factor model they considered. A five-factor model (including HML) doesn’t improve the description of average returns over the four-factor model. The reason is that average HML returns are captured by the exposures to HML of other factors. Thus, in the five-factor model, HML is redundant for explaining average returns.

**Finer Observations**

Fama and French did observe that “while the five-factor model doesn’t improve the description of average returns of the four-factor model that drops HML, the five-factor model may be a better choice in applications. For example, though captured by exposures to other factors, there is a large-value premium in average returns that is often targeted by money managers.”

Thus, “in evaluating how investment performance relates to known premiums, we probably want to know the tilts of the portfolios toward each of the factors.”

They added that “for explaining average returns, nothing is lost in using a redundant factor.” Importantly, they also found that the five-factor model performs well. They write: “Unexplained average returns for individual portfolios are almost all close to zero.”