A Capital Asset Pricing Model with Time-Varying Covariances

TLDR

The CAPM provides a theoretical framework for asset pricing, linking risk premium to nondiversifiable risk measured by covariance with the market, though other variables such as consumption innovations may also influence the conditional distribution of returns. The study estimates a multivariate GARCH model for bills, bonds, and stock returns, linking expected return to the conditional covariance with a fully diversified market portfolio. Using this multivariate GARCH framework, the authors model returns and compute conditional covariances with the market to derive time‑varying betas. The results show that conditional covariances vary over time and significantly determine time‑varying risk premia, while the implied betas are also time‑varying and forecastable.

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 stock where the expected return is proportional to the conditional convariance 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 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.