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/Methods:**

- 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.

- Beta-size portfolios

**Conclusions:**

- 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