Recovering the Variance Premium

This paper generalizes Ross (2015) recovery theory to accommodate growth, including the Black-Scholes and stochastic volatility option models. The new theory recovers information about equity risk premia and variance risk premia from options prices. In the Heston (1993) stochastic volatility model, the theory predicts an exact (negative) value for the variance risk premium as a function of the equity premium. Recovery theory also predicts that the stochastic discount factor is the reciprocal return on a model-free portfolio of index options. This paper tests the theory on returns from one-month VIX and three-month VIX3M option portfolios from 2007-2018. Recovery theory links the equity pre- mium to the values of both conditional and unconditional variance premia. It also predicts how VIX3M option variance is a biased predictor of future one-month VIX variance. Empirically, recovery theory simultaneously matches the average S&P 500 equity premium, the average variance premium, and observed biases in the variance expectations hypothesis. Autocorrelation properties of VIX indices imply a 12% annual equity premium.