Pettengill, Sundaram, and Mathur 113 by previous studies. These results support the validity of beta as a measure of risk and its ability to explain the cross-sectional variation in portfolio returns C. Risk vs. Return: A Test for a Positive tradeoff Given the systematic relationship between beta and returns, a positive risk eturn tradeoff requires that i)market excess returns, on average, be positive, and ii)the risk-return relation be consistent during up markets and down markets (i.e periods of positive and negative market excess returns). The following discussion examines the results from the tests of the above requirements To examine if average market excess returns are positive, the mean excess returns for the total sample period and the subperiods are estimated. Table 5 reports an average annualized excess return of 11. 45 percent for the total period, rejecting the null hypothesis of zero excess return at the 0.01 level(t= 3.74). Results for the subperiods show an average annualized excess return of 18.06 percent(t= 2.35)for period 1, and 11 14 percent(t= 3.02)for period 2, rejecting the null hypothesis at the 0.01 level in both cases. The excess return of 7. 02 percent(I= 1. 41) in period 3 allows rejection only at the 10-percent level of significance. These results indicate a significant positive reward for holding market risk during the overall sample period. However, the risk premium during the subperiods, though positive, appears to be infuenced by the general economic conditions during the TABLE 5 Average Market Excess Returns for Sample Periods Total Period Period 1 Period 3 6-1950)(1951-1970)(1971-1990) 11.45% 7.02% 091% 139% 0.57% Monthly Variance 00064 0.0021 0.0039 T-Statistica P-Value 0.0002 aThe t-statistic measures the null hypothesis that mean excess returns equal zero The second condition required for a positive tradeoff is a consistent relation between risk and return during up markets and down markets. This is examined by comparing f1 and i2 from Equation(4) for the total sample period. Table 2 reports the mean values of f1(0.0336)and %2(0.0337)for the total sample period Given the expected difference in signs, these values reflect a strong consistency 9We test for robustness of the results reported in Tables 2 and 4, making two separate modifications n our testing procedures. First, we define a one-factor model as follows: Rp= E(Rp )+Pp*[Rm E(Rm)]+E. We then regress the unexpected portfolio return against beta with up and down markets portfolio betas separately in up and down market periods(see wiggins(1992)). we then regress returns against up or down betas depending on the relationship between market return and the risk- free rate In both cases, results strongly support a significant relationship between beta and retu