432 The Journal of finance We allocate the full-period post ranking B of a size-B portfolio to each stock in the portfolio. These are the Bs that will be used in the Fama-MacBeth cross-sectional regressions for individual stocks. We judge that the precision of the full-period post - ranking portfolio Bs, relative to the imprecise B esti nates that would be obtained for individual stocks, more than makes up for the fact that true As are not the same for all stocks in a portfolio. And note B 2. B Estimates Table I shows that forming portfolios on size and pre-ranking Bs, rather than on size alone, magnifies the range of full-period post-ranking As Sorted on size alone, the post-ranking As range from 1. 44 for the smallest ME portfolio to 0.92 for the largest. This spread of As across the 10 size deciles is smaller than the spread of post -ranking Bs produced by the B sort of any size decile. For example, the post -ranking Bs for the 10 portfolios in the smallest size decile range from 1.05 to 1.79. Across all 100 size-A portfolios, the post-ranking As range from 0.53 to 1.79, a spread 2. 4 times the spread, 0.52 obtained with size portfolios alone T'wo other facts about the Bs are important. First, in each size decile the post-ranking Bs closely reproduce the ordering of the pre-ranking As. We take this to be evidence that the pre-ranking B sort captures the ordering of true post-ranking As. (The appendix gives more evidence on this important issue. )Second, the B sort is not a refined size sort In any size decile, the average values of In(ME)are similar across the B-sorted portfolios. Thus the pre- ranking B sort achieves its goal. It produces strong variation in post- ranking Bs that is unrelated to size. This is important in allowing our tests to distinguish between B and size effects in average returns II. B and Size The Sharpe-Lintner-Black(SLB)model plays an important role in the way academics and practitioners think about risk and the relation between risk and expected return. We show next that when common stock portfolios are formed on size alone there seems to be evidence for the model s central prediction: average return is positively related to B. The Bs of size portfolios are, however, almost perfectly correlated with size, so tests on size portfolios are unable to disentangle B and size effects in average returns. Allowing for variation in B that is unrelated to size breaks the logjam, but at the expen of B. Thus, when we subdivide size portfolios on the basis of pre-ranking Ss ve find a strong relation between average return and size, but no relation between average return and B