114 Journal of Financial and Quantitative Analysis in the relation between beta and returns. A two-population t-test(with the sig adjustment for i2 as described in methodology section)results in at-value of 0.029 which reflects a symmetrical relation between risk and return during positive and negative periods. This result, combined with the finding of positive average excess returns in each period, strongly supports the expectation of a positive reward for holding risk. The hypothesis of a positive risk-return relation is further tested by directly examining the association between betas and portfolio returns. The average return and the corresponding beta for each portfolio are reported in Panel A of Table 6 The reported return is the average from the 660 monthly return observations. The portfolio betas are the average of the betas for each of the ll subperiods. The average betas for portfolio 1(lowest risk) and portfolio 20(highest risk) are found to be 0.49 and 1.50, respectively. Their corresponding average annualized returns are 11.82 percent(portfolio 1)and 18.97 percent(portfolio 20 TABLE 6 est of Risk-Return Tradeoff: Results from Regressing Average Portfolio Beta on Annualized Average Returns Pane/ A. Average Portfolio Betas 7 1.04 1682 20 0.1897 Pane/ B. Regressions Results 70 0.0910 0.0707 8803 132.34 (15.05) (11.50) Significant at the 0.01 level