The Cross-Section of Expected Stock Returns

Fama, Eugene F. and Kenneth R. French, 1992, “The Cross-Section of Expected Stock Returns,” The Journal of Finance 47 (2), 427-465.

Purpose:  This paper evaluates the joint effect of market beta, firm size, E/P ratio, leverage, and book-to-market equity in explaining the cross-section of average stock returns on NYSE, AMEX, and NASDAQ.

Findings:  Beta does not explain the cross-section of average returns.  Size and book-to-market equity each have explanative power both when used alone and in the presence of other variables.

Motivation:  The Sharpe, Lintner, and Black asset pricing model (beta) has been very influential, but there are notable exceptions to its premises.  Banz (1981) finds a significant size effect.  Bhandari (1988) finds a leverage effect.  Others have argued for effects of the book-to-market equity ratio and the earnings-to-price ratio.  Furthermore, Reinganum (1981) and Lakonishok and Shapiro (1986) find that the beta-return relationship disappears after 1963.


  • Data:  Nonfinancial NYSE, AMEX, and NASDAQ firms from 1962-1989
    • Monthly return data from CRSP
    • Annual accounting data from COMPUSTAT
  • Create portfolios based on size and pre-ranked beta (using trailing data)
  • Calculate the beta for each portfolio-year and assign it to each stock in that portfolio-year
  • Fama-MacBeth Regressions
    • Beta-size portfolios
      • For each month, for the entire cross-section, regress average return on beta, ln(ME), ln(BE/ME), ln(A/ME), ln(A/BE), and E/P
      • Sort stocks into 10 size deciles and then into 100 sub-deciles on “pre-ranking” beta
        • pre-ranking beta is each security’s beta for the 60 months prior to portfolio creation (requiring at least 24 months of data for inclusion in any portfolio)
        • Pre-ranking beta cutoffs are established using only NYSE stocks
    • Book-to-market portfolios and E/P portfolios
      • formed in a similar manner, with stocks sorted on either BE/ME or E/P
    • Size & book-to-market portfolios
      • Match accounting data for fiscal year-ends in calendar year t-1 to returns for the period starting in July of year t and ending in June of year t+1.
      • Use market equity in December of year t-1 to calculate leverage, book-to-market, and E/P ratios.
      • Use market equity in June of year t to measure size.
      • sort stocks into 10 market equity deciles, then into 100 book-to-market sub-deciles.


  • Controlling for size, there is no relationship between beta and average return
  • Size is significant in predicting average returns
  • Book-to-market equity is also significant in predicting average returns, and has an even bigger effect than size
  • The effects of leverage and E/P are captured by size and book-to-market equity