Pettengill, Sundaram, and Mathur direct comparison while preserving the effects of slope estimates with unexpected signs(i.e, a negative sign for m1 and a positive sign for 12). After the adjustments, he following hypotheses are tested by using a standard two-population t-test, Ho:71-12=0, Finally, a direct test of the risk-return tradeoff is employed by regressing the average portfolio betas against average portfolio return V. Empirical Results A. Beta vs Realized Returns Previous studies, following Fama and MacBeth, test for a positive linear rela- this relation by estimating the slope coefficients for Equation(3). Results for the total sample period reported in Table I reject the hypothesis of no relation between sk and return at the 0.05 level. However. the results are inconsistent across sub- periods. The null hypothesis is rejected in the first subperiod at the 0.05 level but the null cannot be rejected in the second(t=0.18)or third (t=1.30) subperiods Extant literature cites this weak correlation and the intertemporal inconsistency as evidence against a systematic relationship between risk and return TABLE Estimates of Slope Coefficients(CRSP Equally-Weighted Index) 十 Period T-Statistic P-Value Total Sample 0.0050 00129 (1936-1990) 00111 (1936-1950) 04277 (1951-1970) 00005 0.0975 (1971-1990) We argue that the above results are biased due to the aggregation of positive and negative market excess return periods. Given the conditional relation between risk(beta) and realized returns, we test the dual hypothesis of a positive relation between beta and returns during periods of positive market excess returns and egative relation during periods of negative market excess returns. The hypothesis is tested by examining the regression coefficients f1 and f2 of Equation(4). The regression estimates are presented in Table 2 examination of the estimated regression coefficients provides strong support for a systematic but conditional relationship between beta and realized returns f is estimated in each of the 380 months for which the market excess return is