The Cross-Section of Expected Stock Returns asset-pricing tests lack power to separate size from A effects in average returns To allow for variation in b that is unrelated to size, we subdivide each size decile into 10 portfolios on the basis of pre-ranking Bs for individual stocks The pre-ranking Bs are estimated on 24 to 60 monthly returns(as available) in the 5 years before July of year t. We set the B breakpoints for each size decile using only NYSE stocks that satisfy our COMPUSTAT-CRSP data requirements for year t-1. Using NYSE stocks ensures that the B break points are not dominated after 1973 by the many small stocks on NASDAQ Setting A breakpoints with stocks that satisfy our COMPUSTAT-CRSP data requirements guarantees that there are firms in each of the 100 size B portfolios After assigning firms to the size B portfolios in June, we calculate the equal-weighted monthly returns on the portfolios for the next 12 months, from July to June. In the end, we have post-ranking monthly returns for July 68 to December 1990 on 100 portfolios formed on size and pre- ranking Bs We then estimate Bs using the full sample (330 months) of post-ranking returns on each of the 100 portfolios, with the CRSP value-weighted portfolio f NYSE, AMEX, and(after 1972) NASDAQ stocks used as the proxy for the market. We have also estimated As using the value-weighted or the equal weighted portfolio of NYSE stocks as the proxy for the market. These as produce inferences on the role of a in average returns like those reported below We estimate 3 as the sum of the slopes in the regression of the return on a portfolio on the current and prior month's market return. (An additional lead and lag of the market have little effect on these sum Bs. )The sum Bs are meant to adjust for nonsynchronous trading (Dimson(1979)). Fowler and Rorke (1983)show that sum As are biased when the market return is autocorrelated. The 1st- and 2nd-order autocorrelations of the monthly mar ket returns for July 1963 to December 1990 are 0.06 and -0.05, both about 1 standard error from 0. If the Fowler- Rorke corrections are used, they lead to trivial changes in the Bs. We stick with the simpler sum As. Appendix Table ai shows that using sum Bs produces large increases in the Bs of the smallest Me portfolios and small declines in the As of the largest me portfolios Chan and Chen how that full-period B estimates for portfolios can work well in tests of the SLB model, even if the true Bs of the portfolios vary through time, if the variation in the Bs is proportional ,=k(8-B) where B, is the true A for portfolio j at time t, B; is the mean of Bi across t, and p is the mean of the a;. The Appendix argues that (1)is a good approximation for the variation through time in the true s of portfolios () ze and B. For diehard B fans, sure to be skeptical of our results on the weak role of p in average stock returns, we can also report that the results stand up to robustness checks that use 5-year pre-ranking Bs,or 5-year post-ranking Bs, instead of the full-period post-ranking Bs