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The ournal of finance for variation in b that is unrelated to size, the relation between B and average return is flat, even when B is the only explanatory variable B. Fama-MacBeth Regressions Table III shows time-series averages of the slopes from the month-by -month Fama-MacBeth(FM)regressions of the cross-section of stock returns on size 6, and the other variables (leverage, E/P, and book-to-market equity) used to plain average returns. The average slopes provide standard FM tests for premiums during the July 1963 to December 1990 periad e non-zero expected Like the average returns in Tables I and Il, the regressions in Table li say that size, In(mE), helps explain the cross-section of average stock returns The average slope from the monthly regressions of returns on size alone is 0.15%, with a t-statistic of-2.58. This reliable negative relation persists no matter which other explanatory variables are in the regressions; the average slopes on In(ME)are always close to or more than 2 standard errors from 0. The size effect (smaller stocks have higher average returns) is th robust in the 1968-1990 returns on NYSE, AMEX, and NASDAQ stocks contrast to the consistent explanatory power of size, the FM regressions that market B does not help explain average stock returns for 1990. In a shot straight at the heart of the SLB model, the average slope from the regressions of returns on 3 alone in Table Ill is 0. 15% per month and only 0.46 standard errors from 0. In the regressions of returns on size and B, size has explanatory power (an average slope -3.41 standard errors from 0), but the average slope for B is negative and only 1. 21 standard errors from 0. Lakonishok and Shapiro(1986)get similar results for NYSE stocks for 1962-1981. We can also report that B shows no power to explain average returns(the average slopes are typically less than 1 standard error from O)in FM regressions that use various combinations of p with size, book-to-market equity, leverage, and E/p C. Can b Be saved? What explains the poor results for p? One possibility is that other explana ory variables are correlated with true As, and this obscures the relation between average returns and measured Bs. but this line of attack cannot explain why B has no power when used alone to explain average returns Moreover, leverage, book-to-market equity, and E/p do not seem to be good proxies for B. The averages of the monthly cross-sectional correlations be tween B and the values of these variables for individual stocks are all within 0.15o0 Another hypothesis is that, as predicted by the SLB model, there is a positive relation between B and average return, but the relation is obscured by noise in the B estimates. However, our full- period post ranking &s do not seem to be imprecise. Most of the standard errors of the Bs(not shown) are
The Cross-Section of Expected Stock Returns 439 Table ill Average Slopes(t-Statistics)from Month-by-Month Regr of Stock Returns on B, Size, Book-to-Market Equity, Leverage, and E/P: July 1963 to December 1990 Stocks are assigned the post-ranking a of the sizeB portfolio they are in at the end of June of year t(Table I) BE is the book value of common equity plus balance-sheet deferred taxes, a is total book assets, and E is earnings(income before extraordinary items, plus income-statement deferred taxes, minus preferred dividends). BE, A, and E are for each firm's latest fiscal year ending in calendar year t-1. The accounting ratios are measured using market equity ME in December of year t-1. Firm size In(ME)is measured in June of year t In the regressions, these values of the explanatory variables for individual stocks are matched with CRSP returns for the months from July of year t to June of year t+ 1. The gap between the accounting data and the eturns ensures that the accounting data are available prior to the returns. If earnings are positive, E(+)/P is the ratio of total earnings to market equity and E/P dummy is 0. If earnings are negative, E(+)/P is 0 and e/p dummy is I The average slope is the time- series average of the monthly regression slopes for July 1963 to December 1990, and the t-statistic is the average slope divided by its time- series standard error On average, there are 2267 stocks in the monthly regressions. To avoid giving extreme observations heavy weight in the regressions, the smallest and largest 0.5% of the observations ratios (the 0.005 and 0.995 fractiles). This has no effect on inferences B In(ME) In(BE/ME) In(A/ME) In(A/BE) Dummy E( 0.15 (046) 0.17 (-121)(-341) 0.50 0.57 (4.57) ( (1.23) 0.13 (-247) (-056(1.57)