A Capital-Asset Pricing Model with Time-varying Covariances

Abstract

Abstract The capital-asset pricing model provides a theoretical structure for the pricing of assets with uncertain returns. The premium to induce risk averse investors to bear risk is proportional to the nondiversifiable risk, which is measured by the covariance of the asset return with the market portfolio return. In this paper a multivariate generalized autoregressive conditional heteroscedastic process is estimated for returns to bills, bonds, and stocks where the expected return 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 significant determinant of the time-varying risk premia. The implied betas are also time-varying and forecastable. However, there is evidence that other variables including innovations in consumption should also be considered in the investor’s information set when estimating the conditional distribution of returns.