Does adding profitability (see “Gross Profitability as a Stock Return Predictor”) to the Fama-French three-factor model of future stock returns result in a better model? In the June 2013 draft of their paper entitled “A Four-Factor Model for the Size, Value, and Profitability Patterns in Stock Returns”, Eugene Fama and Kenneth French examine whether profitability usefully augments their three-factor model. They consider evidence from monthly double sorts into: (1) size and book-to-market capitalization ratio (B/M) quintiles (25 portfolios); and, (2) size and pre-tax profitability (PTP) quintiles (25 portfolios). They also consider monthly triple sorts by size, B/M and PTP. Using price and firm accounting data for a broad sample of U.S. common stocks during July 1963 through December 2012, they find that:
- For 25 size-B/M double-sort portfolios over the entire sample period:
- The size effect (higher gross average returns for small stocks) is generally evident for all B/M quintiles except the lowest (growth stocks), for which is it clearly absent.
- The value premium (higher average gross returns for higher B/M) is evident in all size quintiles, but relatively weak for the largest stocks.
- For 25 Size-PTP double-sort portfolios over the entire sample period:
- The size effect is generally evident in middle PTP quintiles, but absent/weaker for the lowest/highest quintiles.
- The profitability effect is generally evident in all size quintiles, but noticeably unsystematic for the smallest stocks.
- For 32 portfolios formed from triple sorting into two size groups, four B/M quartiles and four PTP quartiles over the entire sample period:
- The value premium is almost uniformly evident in both size groups and all PTP quartiles.
- The profitability effect is almost uniformly evident in both size groups and all B/M quartiles.
- The least profitable, small growth stocks notably generate a lower gross monthly return than U.S. Treasury bills.
- Formal regression tests do not support the belief that the Fama-French three-factor model fully explains the variation in returns of portfolios sorted by size and B/M, but is still arguably useful in explaining the size effect and the value premium.
- Formal regression tests do not support the belief that a four-factor model (market, size, B/M, PTP) fully explains the variation in returns of portfolios sorted by size and B/M, size and PTP and all three of size, B/M and PTP. However, this augmented model is arguably useful in explaining the size effect, the value premium and the profitability effect. It is especially successful in explaining size-PTP portfolio double sorts, but less successful in explaining size- B/M double sorts.
In summary, evidence suggests that investors may find a four-factor (market, size, book-to-market ratio, profitability) model of stock returns useful for exploiting factor premiums and estimating unexplained alpha.
Cautions regarding findings include:
- Return calculations used in factor assessments are gross, not net. Accounting for the trading frictions associated with monthly factor portfolio turnover would reduce reported returns. To the extent that trading frictions vary across factor sorts, findings based on net returns may differ from those based on gross returns.
- The study illustrates the abstractions involved in specifying and testing factor pricing models.
Frequently Asked Questions
What is the Fama-French four-factor model in investing?
The Fama-French four-factor model is a stock return model that adds a profitability factor to the market, size and book-to-market (value) factors of the Fama-French three-factor model. It is used to explain variation in portfolio returns and to estimate unexplained alpha. Fama and French tested it using pre-tax profitability on U.S. stocks from July 1963 through December 2012.
Does adding profitability to the Fama-French three-factor model improve its ability to explain stock returns?
Adding profitability to the Fama-French three-factor model makes it arguably more useful, but it still does not fully explain portfolio returns in formal regression tests. The four-factor model helps explain the size effect, the value premium and the profitability effect over July 1963 through December 2012. It works especially well for size-profitability portfolios and less well for size-book-to-market portfolios.
How do researchers test whether profitability adds to the Fama-French factor model?
Researchers test the Fama-French four-factor model by forming portfolios from monthly double and triple sorts of U.S. common stocks. The double sorts use 25 size-book-to-market portfolios and 25 size-pre-tax profitability portfolios, and the triple sort uses 32 portfolios (two size groups, four book-to-market quartiles, four profitability quartiles). Formal regression tests then check whether the factor models fully explain portfolio return variation over July 1963 through December 2012.
How does the four-factor model compare to the three-factor model for explaining the size and value effects?
The Fama-French four-factor model, which adds profitability, explains portfolio return variation better than the three-factor model, though neither passes formal regression tests as a full explanation. The three-factor model remains arguably useful for the size effect and value premium. The four-factor model additionally captures the profitability effect, which is evident in all size quintiles and almost uniformly in all book-to-market quartiles.
What are the limitations of using the Fama-French four-factor model to forecast stock returns?
The Fama-French four-factor model fails formal regression tests of fully explaining returns for size-book-to-market, size-profitability and triple-sorted portfolios. The study also uses gross rather than net returns, so trading frictions from monthly factor portfolio turnover would reduce the reported returns. If frictions vary across factor sorts, net-return findings may differ from the gross-return findings.