Pettengill,Sundaram,and Mathur115 The risk-return relation is tested by regressing the average portfolio betas on annualized average portfolio returns. The results reported in Panel B of Table 6 provide strong evidence that investors are paid for holding beta risk. Changes in beta explain 88 percent of the variation in average portfolio returns. The estimated slope coefficient of 0.0707(t= 11. 50)indicates a market risk premium of 7.07 percent, and the intercept of 0.091(t= 15.05)reflects a risk-free rate of 9. 1 percent over the testing period, 1936-1990. These results strongly support the presence of a positive tradeoff between risk(beta)and return VI. Summary and Conclusion Previous studies testing for a systematic relationship between risk(as mea sured by beta)and returns find weak and intertemporally inconsistent results These test results are biased due to the conditional relation between beta and re- ositive relation is always predicted be returns, but this relation is conditional on the market excess returns when realized returns are used for tests. In this study, a methodology that considers the posi tive relation between beta and returns during up markets and the negative relation during down markets is employed. This method yields the following finding i)a systematic relation exists between beta and returns for the total sample period and is consistent across subperiods and across months in a year, and ii)a positive tradeoff between beta and average portfolio returns is observed Since the concerns regarding the weak correlation between beta and the cross- section of returns appear to be unfounded, the results support the continued use of The market risk premium of 7. 07 percent is consistent with the findings of Lakonishok and Shapiro (984), who estimated the risk premium to be 7. 7 percent annually