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The authors introduce the Homoscedastic Gamma [HG] model where the distribution of returns is characterized by its mean, variance and an independent skewness parameter under both measures. The model predicts that the spread between historical and risk-neutral volatilities is a function of the risk premium and of skewness. In fact, the equity premium is twice the ratio of the volatility spread to skewness. They measure skewness from option prices and test these predictions. They find that conditioning on skewness increases the predictive power of the volatility spread and that coefficient estimates accord with theory. In short, the data do not reject the model's implications for the equity premium.
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