104 Journal of Financial and Quantitative Analysis greater for the low beta portfolio than for the high beta portfolio. If this were not the case, no investor would hold the low beta portfolio. Thus, the SLB model not only requires the expectation that realized returns for the market will, with some probability, be lower than the risk-free rate, but also requires the expectation that, with some probability, the realized returns for high beta portfolios will be lower than the realized returns for low beta portfolios. The model does not require a direct link between these two relationships. A reasonable inference may, however, be that returns for high beta portfolios are less than returns for low beta portfolios when the realized market return is less than the risk-free rate. Although previous tests of the SLB model have not recognized these relationships when testing the validity of the SLB model, the market model used to calculate beta does imply this relationship B. Empirical Tests Previous tests of the implications of the SLB model have sought to find a positive relationship between realized portfolio returns and portfolio betas. The tests are conducted in stages, with the estimation of beta as shown below, (Rpt -Ra)= B*( Rmut-RA) followed by the test for a positive risk-return tradeoff, 1+*+ Equation(2)estimates the beta risk for each portfolio using realized returns for both the portfolio and the market, thus providing a proxy for the beta in the SLB model. Under the assumption that betas in the estimation period proxy betas in the test period, a test for a positive risk-return relationship utilizes Equation (3) If the value for f1 is greater than zero, a positive risk-return tradeoff is supported This procedure may test the usefulness of beta as a measure of risk, but it does not directly test the validity of the SLB model The SLB model not only requires a direct and unconditional relationship between beta and expected returns, but also requires the expectation that the re- lationship between realized returns and beta will vary. As argued in the previot section, in order for high beta portfolios to have more risk, there must be condi tions under which high beta portfolios earn lower returns than low beta portfolio The SLB model does not directly provide the conditions under which the above relationship will be observed. In contrast, Equation(2), which has been used in previous empirical tests, provides an exact condition under which the realized re turns to high beta portfolios are expected to be lower than the realized returns for low beta portfolios. According to Equation(2), the relationship between the return to high and low beta portfolios is conditional on the relationship between realized market returns and the risk-free return. If Rm Rf, then B *(Rmt-Ra)is <0. In these cases, the predicted portfolio return includes a negative risk premium that is proportionate to beta. Hence, if the realized market return is less than the risk-free return, an inverse relationship exists between beta and predicted return ( i.e., high beta portfolios have predicted returns that are less than the predicted returns for