110 Journal of Financial and Quantitative Analysis TABLE Estimates of Slope Coefficients for Up Markets and Down Markets ( CRSP Equally-Weighted Inde n=0+个1*6*月+2*(1 Panel A Up Markets Pane/ B Down Markets d f1 TStatistic P-Value12 P-Value Total Sample 1936-1990)0.0336 1261 00001 13820.0001 (1936-1950)0.0482 (1951-1970)0.0185674000010029686700001 1971-1990)0.0392 00001-00309 600001 Up markets(down markets)are periods of positive(negative)market excess returns positive. In these periods, the high beta portfolios should outperform the low beta ortfolios. This expectation is confirmed by the mean value of 0.0336 for 11 hich is significantly different from zero at the 0.01 level(t= 12. 61). This result shows that high beta portfolios receive a positive risk premium during up markets 2 is estimated for the 280 months in which market excess return is negative The expected negative relationship between realized returns and portfolio beta should produce negative values for 12. The mean value of-00337 is significantly different from zero at the 0.01 level (t=-13.82)6 This result shows that, as expected, high beta portfolios incur lower returns during down markets than low beta portfolios. The mean excess returns for portfolios I through 20 during up markets(periods of positive market excess return) and down markets(periods of negative market excess return) are shown in Figure 1. with minor variations, the figure provides corroborative evidence on the expected association between beta and portfolio returns Table 2 also presents the results for estimates of ?I and 2 for each of the three subperiods. Unlike previous studies, we find a highly significant relationship between beta and returns in each subperiod. For every subperiod, the hypothesis of no relationship between risk and returns during periods of positive excess market returns is rejected in favor of an expected positive relationship at the 0.01 level. 7 Likewise, for every subperiod, the hypothesis of no relationship between risk and returns during periods of negative excess market returns is rejected in favor of an expected negative relationship at the 0.01 level. Previous studies that find inconsistent relationships between beta and returns across subperiods do so because they fail to adjust for the conditional relationship between returns and beta 6Results from Lakonishok and Shapiro(1984) indicate a similar relationship between beta an retums. They find slope coefficients of 0.0333 and -0.0354 for up markets and down markets ients are of the correct sign and significant in each of the subperiods a significant difference does exist in the estimated values of n and m between subperiods