A Capital Asset Pricing Model with Time-Varying Covariances

Abstract

The capital asset pricing model provides a theoretical structure for the pricing of assets with uncertain returns. The premium to induc e risk-averse investors to bear risk is proportional to the nondivers ifiable risk, which is measured by the covariance of the asset return with the market portfolio return. In this paper, a multivariate, gen eralized-autoregressive, conditional, heteroscedastic process is esti mated for returns to bills, bonds, and stocks where the expected retu rn is proportional to the conditional covariance of each return with that of a fully diversified or market portfolio. It is found that the conditional covariances are quite variable over time and are a signi ficant determinant of the time-varying risk premia. The implied betas are also time varying and forecastable. Copyright 1988 by University of Chicago Press.