Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities

We examine the behavior of measured variances from the options market and the underlying stock market. Under the joint hypotheses that markets are informationally efficient and that option prices are explained by a particular asset pricing model, forecasts from time-series models of the stock return process should not have predictive content given the market forecast as embodied in option prices. Both in-sample and out-of-sample tests suggest that this hypothesis can be rejected. Using simulations, we show that biases inherent in the procedure we use to imply variances cannot explain this result. Thus, we provide evidence inconsistent with the orthogonality restrictions of option pricing models that assume that variance risk is unpriced. These results also have implications for optimum variance forecast rules.