An Intertemporal CAPM with Stochastic Volatility

This paper studies the pricing of volatility risk using the first-order conditions of a long-term equity investor who is content to hold the aggregate equity market rather than tilting towards value stocks and other equity portfolios that are attractive to short-term investors. We show that a conservative long-term investor will avoid such tilts in order to hedge against two types of deterioration in investment opportunities: declining expected stock returns, and increasing volatility. Empirically, we present novel evidence that low-frequency movements in equity volatility, tied to the default spread, are priced in the cross-section of stock returns.