JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This content downloaded from 165.123.34.86 on Sat, ABSTRACTIn an intertemporal economy where both risk (stock beta) and expected return are time varying, the authors derive a linear relation between the unconditional beta and the unconditional return under certain stationarity assumptions about the stochastic process of size-portfolio betas. The model suggests the use of long time periods to estimate the unconditional portfolio betas. The authors find that, after controlling for the betas thus estimated, a firm-size proxy, such as the logarithm of the firm size, does not have explanatory power for the averaged returns across the size-ranked portfolios. THE CAPITAL ASSET PRICING Model (CAPM) can be generalized to describe the period-by-period risk-return relation in a multiperiod equilibrium.' The model predicts that an asset's conditional expected return (Eit) is linearly related to its conditional market risk (f3it), both being conditioned on the information available at t -1:2 Eit = Xot + Xtltjit.(1)If we can impose sufficient structures on the stochastic processes of the beta and the expected returns, the model can still be tested in the unconditional form. In this paper, we make assumptions that take into account recent empirical evidence on the movements of the expected returns and betas3 and obtain a linear relation between the unconditional expected returns and the unconditional betas. Consequently, the test presented in this paper is a joint test of the conditional pricing equation and the assumption on the stochastic process of the beta. and UCLA, and the participants at the Symposium for Stock Market Regularities (Brussels), the Western Finance Association Meeting (Colorado Springs), and the European Finance Association Meeting (Dublin, Ireland) for helpful comments and suggestions, as well as the Center for Research in Security Prices for support. 'See, e.g., Fama and MacBeth [161. The additional assumptions are usually sufficient conditions ensuring that the investors on the aggregate do not hedge against stochastic shifts in the investment and consumption opportunity set-e.g., an economy where the stochastic elements cannot be hedged or the investors, consistent with their utility maximizations, behave as if they did not want to hedge on the aggregate. Alternatively, we can consider the conditional pricing equation (1) as a statement regarding the conditional mean-variance efficiency of the selected market index. 2 In the Sharpe [35]-Lintner [24] model, X. = rf, the risk-free rate, and A, = the expected market return over the risk-free rate. In Black's [2] model, Xo = the expected return of a zero-beta portfolio and A, = the expected market return over Ao. 'See, e.g.,...
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