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Adding Profitability and Investment to the Three-factor Model

Posted in Equity Premium, Size Effect, Value Premium

Does adding profitability and asset growth (investment) factors improve the performance of the widely used Fama-French three-factor (market, size, book-to-market) model of stock returns? In the September 2014 version of their paper entitled “A Five-Factor Asset Pricing Model” Eugene Fama and Kenneth French assess whether extensions of their three-factor model to include profitability and investment improves model predictive power. They measure profitability as prior-year revenue minus cost of goods sold, interest expense and selling, general and administrative expenses divided by book equity. They define investment as prior-year growth in total assets divided by total assets. Using returns and stock/firm characteristics for a broad sample of U.S. stocks during July 1963 through December 2013 (606 months), they find that:

  • For all sizes of stocks:
    • Very high profitability beats very low profitability, with the effect perhaps a little concentrated among small stocks.
    • Very low investment strongly beats very high investment, with the effect concentrated among small stocks.
  • The five-factor model outperforms the widely used three-factor model:
    • It predicts 71% and 94% of the variance in future returns across different sets of portfolios sorted by size, book-to-market ratio, profitability and investment.
    • Performance is not sensitive to the way the factors are defined.
  • However, the five-factor model fails to predict adequately the low average returns on small stocks with very high investment.
  • After adding profitability and investment factors, the book-to-market factor is redundant. In other words, a four-factor model that excludes the book-to-market factor performs about as well as the five-factor model.

In summary, evidence indicates that models of future stock returns that include market, size, profitability and investment (asset growth) factors are more effective at predicting return differences across stocks than the widely used Fama-French three-factor model.

Investors may want to consider size, profitability and asset growth screens.

Cautions regarding findings include:

  • Analyses use gross, not net, returns. Accounting for portfolio formation/rebalancing frictions and shorting costs would reduce these returns. Shorting of some stocks may not be feasible. Moreover, since these obstacles may vary across factor sorts, net factor predictive power may differ from gross factor predictive power.
  • To the extent that randomness is present in stock returns, examination of many factor models introduces snooping bias, such that the best-performing model incorporates luck. See “Taming the Factor Zoo?” and “Stock Return Model Snooping”.
  • Many investors may not be able to hold enough stocks to ensure statistical reliability of outcomes from factor tilts (or they pay a fee to a fund manager who can hold many stocks).

See “Better Four-factor Model of Stock Returns?” for another recent entry in the stock return modeling competition.

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