Contrartan Profits and Stock Market Overreaction in the time t portfolio,and vice versa.Such a strategy is designed to take advantage of stock market overreactions as characterized,for example,by DeBondt and Thaler (1985):"(1)Extreme movements in stock prices will be followed by extreme movements in the oppo- site direction.(2)The more extreme the initial price movement,the greater will be the subsequent adjustment."The profit (k)from such a strategy is simply x,()=∑@()R。 (3) Rearranging Equation (3)and taking expectations yields the follow- ing: 肉1-g-点如)一片这a- (4) where um=E[Rm]=u'/N and tr()denotes the trace operator.8 The first term of Equation (4)is simply the kth-order autocovariance of the equal-weighted market index.The second term is the cross-sec- tional average of the kth-order autocovariances of the individual secu- rities,and the third term is the cross-sectional variance of the mean returns.Since this last term is independent of the autocovariances Ie and does not vary with k,we define the profitability indexL=L(T) and the constant o2(u)as (5) Thus, E[T,()]=L。-σ2(4) (6) For purposes that will become evident below,we rewrite L as Lw=C6十O (7) where G=1 KT4-tr(T] (8) Hence, π(k]=C+O。-σ2(u) (9) The derivation of Equation(4)is included in Appendix 1 for completeness.This is the population counterpart of Lehmann's (1988)sample moment equation (5)divided by N. 183