Expected Stock Returns and Variance Risk Premia
TL;DR: This article found that the difference between implied and realized variances, or the variance risk premium, is able to explain more than fifteen percent of the ex-post time series variation in quarterly excess returns on the market portfolio over the 1990 to 2005 sample period, with high premia predicting high (low) future returns.
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Abstract: We find that the difference between implied and realized variances, or the variance risk premium, is able to explain more than fifteen percent of the ex-post time series variation in quarterly excess returns on the market portfolio over the 1990 to 2005 sample period, with high (low) premia predicting high (low) future returns. The magnitude of the return predictability of the variance risk premium easily dominates that afforded by standard predictor variables like the P/E ratio, the dividend yield, the default spread, and the consumption-wealth ratio (CAY). Moreover, combining the variance risk premium with the P/E ratio results in an R 2 for the quarterly returns of more than twenty-five percent. The results depend crucially on the use of “modelfree”, as opposed to standard Black-Scholes, implied variances, and realized variances constructed from high-frequency intraday, as opposed to daily, data. Our findings suggest that temporal variation in risk and risk-aversion both play an important role in determining stock market returns.
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Figures
Table 5 Annual return regressions 
Table 4 Quarterly return regressions 
Figure 1 Model-implied slopes and R2s The figure shows the population slope coefficients and R2s from regressions of the scaled h-period returns on the variance difference implied by the equilibrium model. The four different lines refer to the four different parameter configurations discussed in the main text. 
Table 2 Variance premium return regressions 
Table 3 Monthly return regressions
Citations
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The recovery theorem with application to risk management
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Eugene F. Fama,Kenneth R. French +1 more
TL;DR: In this paper, Bhandari et al. found that the relationship between market/3 and average return is flat, even when 3 is the only explanatory variable, and when the tests allow for variation in 3 that is unrelated to size.
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A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix
TL;DR: In this article, a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction is described.
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A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
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