Many finance applications require an annual measure of the market premium for equity. Using a long sample combined with a very parsimonious conditional variance function, we find a positive relationship between market risk and expected excess returns. Unlike traditional exponential-smoothing filters, our specification has a well-defined unconditional variance and allows for mean reverting volatility forecasts. Although total volatility is significantly priced, the smooth long-run component in volatility is more important for capturing the dynamics of the premium. This parameterization produces realistic time-varying market equity premium estimates over the entire 1840-2003 period. For example, our results show that the premium was relatively low in the mid-1990s but has recently increased. Results are robust to univariate specifications that condition on either levels or logs of past realized volatility (RV), as well as to a new bivariate risk-return model of returns and RV for which the conditional variance of excess returns is the conditional expectation of the realized volatility process.
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Paper provided by University of Toronto, Department of Economics in its series Working Papers with number
tecipa-204.