The Cross-Section of Expected Stock Returns 433 A. Informal Tests Table Ii shows post-ranking average returns for July 1963 to December 1990 for portfolios formed from one-dimensional sorts of stocks on size or The portfolios are formed at the end of June each year and their equal weighted returns are calculated for the next 12 months. We use returns for July to June to match the returns in later tests that use the accounting dat When we sort on just size or 5-year pre- ranking Bs, we form 12 portfolios The middle 8 cover deciles of size or B. The 4 extreme portfolios(1A, 1B, 10A and 10B)split the bottom and top deciles in half. Table II shows that when portfolios are formed on size alone, we observe the familiar strong negative relation between size and average return(banz ( 1981)), and a strong positive relation between average return and B. Aver- age returns fall from 1. 64% per month for the smallest me portfolio to 0.90% for the largest. Post-ranking Bs also decline across the 12 size portfolios, from 1.44 for portfolio 1A to 0.90 for portfolio 10B. Thus, a simple size sort seems to support the slB prediction of a positive relation between B and average return. But the evidence is muddied by the tight relation between size and the Bs of size portfolios 2 The portfolios formed on the basis of the ranked market Bs of stocks in able II produce a wider range of Bs(from 0.81 for portfolio 1A to 1. 73 for 10B)than the portfolios formed on size. Unlike the size portfolios, the B-sorted portfolios do not support the SLB model. There is little spread in erage returns across the B portfolios, and there is no obvious relation between B and average returns. For example, although the two extreme portfolios, 1A and 10B, have much different As, they have nearly identical average returns(1.20% and 1. 18% per month). These results for 1968-1990 confirm Reinganum's(1981)evidence that for B-sorted portfolios, there is no relation between average return and b during the 1964-1979 period The 100 portfolios formed on size and then pre-ranking B in Table i clarify the contradictory evidence on the relation between B and average return produced by portfolios formed on size or B alone. Specifically, the two-pass sort gives a clearer picture of the separate roles of size and B in average returns. Contrary to the central prediction of the SlB model, the second-pass B sort produces little variation in average returns. Although the post ranking Bs in Table I increase strongly in each size decile, average returns are flat or show a slight tendency to decline. In contrast within the columns of th average return and A matrices of Table I, average returns and Bs decrease ith increasing size The two- pass sort on size and A in table i says that variation in B that is tied to size is positively related to average return, but variation in B unrelated to size is not compensated in the average returns of 1968-1990 The proper inference seems to be that there is a relation between size and average return, but controlling for size, there is no relation between B and average return. The regressions that follow confirm this conclusion, and they produce another that is stronger. The regressions show that when one allows