Abstract Recent empirical evidence suggests that the variance risk premium predicts aggregate stock market returns. We demonstrate that statistical finite sample biases cannot “explain” this apparent predictability. Further corroborating the existing evidence of the United States, we show that country-specific regressions for France, Germany, Japan, Switzerland, the Netherlands, Belgium, and the United Kingdom result in quite similar patterns. Defining a “global” variance risk premium, we uncover even stronger predictability and almost identical cross-country patterns through the use of panel regressions.

We propose a decomposition of the realized covariance matrix into components based on the signs of the underlying high‐frequency returns, and we derive the asymptotic properties of the resulting realized semicovariance measures as the sampling interval goes to zero. The first‐order asymptotic results highlight how the same‐sign and mixed‐sign components load differently on economic information related to stochastic correlation and jumps. The second‐order asymptotic results reveal the structure underlying the same‐sign semicovariances, as manifested in the form of co‐drifting and dynamic “leverage” effects. In line with this anatomy, we use data on a large cross‐section of individual stocks to empirically document distinct dynamic dependencies in the different realized semicovariance components. We show that the accuracy of portfolio return variance forecasts may be significantly improved by exploiting the information in realized semicovariances.

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.