Volatility Expectations and Returns

We provide evidence that agents have slow moving beliefs about stock market volatility. This is supported in survey data and is also reflected in firm level option prices. We embed these expectations into an asset pricing model and show that we jointly explain the following stylized facts (some of which are novel to this paper): when volatility increases the equity and variance risk premiums fall or stay flat at short horizons, despite higher future risk; these premiums appear to rise at longer horizons after future volatility has subsided; strategies that time volatility generate alpha; the variance risk premium forecasts stock returns more strongly than either realized variance or risk-neutral variance (VIX); changes in volatility are negatively correlated with contemporaneous returns. Slow moving expectations about volatility lead agents to initially underreact to volatility news followed by a delayed overreaction. This results in a weak, or even negative, risk-return tradeoff at shorter horizons but a stronger tradeoff at longer horizons (beyond where one can strongly forecast volatility). These dynamics are mirrored in the VIX and variance risk premium which reflect investor expectations about volatility