The Review of Financial Studies/v 11 n 3 1998 future (because it is delisted),we use a (k-j)period return in calculating (k),where i is the period of delisting.The estimates in Table I are the time-series averages,for each k,of the profits at each time t,(k). Finally,since the profits of momentum(contrarian)strategies are exactly equal to the losses of contrarian(momentum)strategies [see Equations (1) and (3)],we implement only momentum strategies (i.e.,we use the weights Wit1=+[Ri-1(k)-Rmt-1(k)]k).Consequently,a positive (nega- tive)estimate in Table 1 implies that on average a momentum(contrarian) strategy is profitable. Table 1 also contains the z-statistics in parentheses to test the statistical significance of the average profits (losses);these statistics are asymptoti- cally N(0,1)under the null hypothesis that the "true"profits are zero.We use a generalized method of moments [see Hansen (1982)]procedure to calculate standard errors.This procedure takes into account cross-sectional correlations(within a particular time period)in the realized profits of multi- ple strategies within the medium-and long-term classes,as well providing standard errors that are robust to heteroscedasticity and autocorrelation. Several interesting features of the profitability of trading strategies emerge from an inspection of Table 1.First,the number of positive and negative estimates of average profits are exactly the same;18 versus 18.Therefore, unconditionally,momentum and contrarian strategies are equally likely to be successful (at least based on the 36 strategies evaluated in Table 1).This finding is noteworthy given that momentum and contrarian strategies are (as noted in the introduction)diametrically opposed in philosophy. Second,21 of the 36 trading strategies are statistically significantly prof- itable;again the number of statistically significant contrarian versus mo- mentum strategies is approximately the same,II versus 10,respectively. Third,once we condition on the return horizon and/or the time period,how- ever,the similarities between contrarian and momentum trading strategies disappear.Specifically,there is a systematic relation between the horizon of the strategy and the trading philosophy that appears to"work."A momen- tum strategy is usually profitable at the medium(3-to 12-month)horizons: of the 20 medium-term strategies reported in Table 1,a momentum strategy is profitable in 15 of the cases.More importantly,all 11 of the momen- tum strategies that yield statistically significant profits are medium-horizon strategies.To gauge the success of the momentum strategy at the medium horizon,we test for the joint significance of the 3-to 12-month strategies within each time period.Not surprisingly,there is strong evidence that the medium-horizon momentum strategy is profitable in all time periods ex- cept the 1926-1947 subperiod:the chi-square statistics for each of the other four time periods have p-values of zero.During the 1926-1947 subperiod, however,a contrarian strategy is successful at the medium horizon;the chi- square statistic for the joint significance of the 3-to 12-month strategies has a p-value of 0.016. 496