The Cross-Section of Expected Stock Returns

Fama, Eugene F. and Kenneth R. French. “The Cross-Section of Expected Stock Returns” The Journal of Finance Volume 47 No. 2 1992: 427-465.

The authors analyze the shortcomings of β in explaining average returns of U.S. stocks. Using the period of 1963-1990, β is found to be much less related to average monthly returns that either market capitalization, called market equity (ME), or Book-to-Market Equity (BE/ME). This goes against the influential work of Sharpe (1964), Lintner (1965), and Black (1972), but is consistent with and builds upon other empirical research since then. The authors found a negative relationship between size and returns, a positive relationship between book-value to market-value and returns, and no meaningful relationship between β and returns.

In the study, NYSE stocks are sorted into portfolios based on the variables the authors regressed. NYSE stocks were used so the study would not be dominated by smaller stocks such as those on the NASDAQ.

When stocks are sorted into size portfolios in Table 2, Panel A, the smallest stocks, on the left, exhibit higher returns than the increasingly large firms to the right. It also it appears β is positively related to returns. β is estimated using the previous 24 to 60 monthly returns (as available). The value-weighted portfolio of the NYSE, AMEX, and (post 1972) NASDAQ stocks are used as the proxy for the market. Instead of the relationship to returns, this β-return relationship is a result of the relationship between β and size. This is demonstrated in Table 2, Panel B when the stocks are sorted into pre-ranking β and return appears flat across portfolios.

Table 2, Panel A

Table 2, Panel B

When sorting for BE/ME, higher values were shown to correspond to higher returns. This can be seen in Table 4. The authors suggest the BE/ME effect may be even stronger than the size effect.

Table 4

The earnings-price ratio (E/P) was also regressed. The results appeared explanatory on average returns until ME and BE/ME are added to the regression and able to capture the apparent relationship that E/P showed to be having on returns.

The authors ran additional regressions in sub-periods, which were 1963-1976 and 1977-1990. Although some differences are observed between the results of the sub-periods, the results of the full period tests are not weakened. The authors also go into results from 1941-1990, which again demonstrates β to be unrelated to returns despite previous research otherwise. Like the results of 1963-1990, the misleading conclusions of earlier works are due to the size-effect being attributed to β.