108 Journal of Financial and Quantitative Analysis Ho:作=0, Ha:1>0. Since y2 is estimated in periods with negative market excess returns, the expected sign of this coefficient is negative. Hence, the following hypotheses are Ho:2=0, 0. ported if, in both cases, the null hypothesis is rejected in favor of the alternate A systematic conditional relationship between beta and realized returns is st C. Subsample Procedures The sample period of 1926 through 1990 allows for the creation of 1l distinct 15-year subsamples. The first subsample extends from 1926 through 1940, the second from 1931 through 1945, and so on. In the first subsample, the first five- year period (1926-1930)is the portfolio formation period, the second(1931 1935)and third( 1936-1940)five-year periods are the portfolio beta estimation period and the test period, respectively. Each subsample includes all securities available from the CRSP monthly returns file that have at least 45 observations in each of the three periods within the subsample. The number of securities in the 11 subsamples ranged from a low of 366(first subsample)to a high of 1350 (penultimate subsample). The entire three-step procedure is conducted separately for each subperiod Equation(4)is first examined using all 660 monthly observations. In addition, the data are divided into three approximately equal subperiods: 1936 through 1950, 1951 through 1970, and 1971 through 1990. Separately, the data are divided by months in a year. Applying Equation(4)to each of these subperiods tests whether intertemporal inconsistencies and seasonality observed by previous studies result from the conditional nature of the relationship between beta and realized returns D. A Test of the Positive Risk-Return Tradeoff The second goal of the study is to determine if a systematic relationship between beta and return translates into a positive reward for holding risk (i.e, do high beta assets, on average, earn higher returns than low beta assets? ) If a systematic, conditional relationship between beta risk and returns exists, a positive reward for holding beta risk will occur if two conditions are met: i)market excess returns are, on average, positive; and ii)the risk-return relationship is symmetrical etween periods of positive and negative excess market returns. We test each of these conditions and then provide a direct test of a positive risk-return tradeoff. The average market excess return for the total sample period and the various subperiods are calculated to test for the first condition. A standard t-test is used to determine if market excess returns are, on average, positive. The risk premiums during up and down markets, as captured by f1 and f2, are compared to test for symmetry. Since the expected signs of these coefficients differ, a direct comparison of their average values would be inappropriate. To facilitate comparisons, the sign for i2 is reversed and its mean value is reestimated. These adjustments allow a