Multifactor Explanations of Asset Pricing Anomalies 63 ings on HML).But a hint of the pattern is left in the regression intercepts. Except for the highest sales-rank decile,however,the intercepts are close to 0.0.Moreover,although the intercepts for the sales-rank deciles produce the largest GRS F-statistic(0.87),it is close to the median of its distribution when the true intercepts are all 0.0(its p-value is 0.563).This evidence that the three-factor model describes the returns on the sales-rank deciles is important since sales rank is the only portfolio-formation variable (here and in LSV)that is not a transformed version of stock price.(See also the industry tests in FF (1994).) III.LSV Double-Sort Portfolios LSV argue that sorting stocks on two accounting variables more accurately distinguishes between strong and distressed stocks,and produces larger spreads in average returns.Because accounting ratios with stock price in the denominator tend to be correlated,LSV suggest combining sorts on sales rank with sorts on BE/ME,E/P,or C/P.We follow their procedure and separately sort firms each year into three groups (low 30 percent,medium 40 percent,and high 30 percent)on each variable.We then form sets of nine portfolios as the intersections of the sales-rank sort and the sorts on BE/ME,E/P,or C/P. Confirming their results,Table IV shows that the sales-rank sort increases the spread of average returns provided by the sorts on BE/ME,E/P,or C/P.In fact, the two double-whammy portfolios,combining low BE/ME,E/P,or C/P with high sales growth (portfolio 1-1),and high BE/ME,E/P,or C/P with low sales growth(portfolio 3-3),always have the lowest and highest post-formation average returns. Table V shows that the three-factor model has little trouble describing the returns on the LSV double-sort portfolios.Strong negative loadings on HML (which has a high average premium)bring the low returns on the 1-1 portfolios comfortably within the predictions of the three-factor model;the most extreme intercept for the 1-1 portfolios is-6 basis points (-0.06 percent)per month and less than one standard error from 0.0.Conversely,because the 3-3 port- folios have strong positive loadings on SMB and HML (they behave like smaller distressed stocks),their high average returns are also predicted by the three-factor model.The intercepts for these portfolios are positive,but again quite close to (less than 8 basis points and 0.7 standard errors from)0.0. The GRS tests in Table V support the inference that the intercepts in the three-factor regression(2)are 0.0;the smallest p-value is 0.284.Thus,whether the spreads in average returns on the LSV double-sort portfolios are caused by risk or over-reaction,the three-factor model in equation (1)describes them parsimoniously. IV.Portfolios Formed on Past Returns DeBondt and Thaler (1985)find that when portfolios are formed on long- term (three-to five-year)past returns,losers (low past returns)have high