Expected and Realized Returns on Volatility

Expected returns on market volatility, which can be obtained from VIX futures in closed form, predict subsequent multi-period realized volatility returns. Expected volatility returns are negative on average, but become more negative after volatility increases. This generates a positive relation with subsequent realized returns on volatility, which are more negative following increases in volatility. Expected volatility returns also predict future index returns, because realized volatility returns are negatively correlated with realized index returns. We show how these results are related to existing results on the predictive power of the market variance risk premium, the slope of the VIX term structure, and the VIX premium. The results are robust to a wide range of variations in the empirical setup.