It is well documented that the volatility of the stock market is stochastic (see Bollerslev, Engle, Nelson (1994) and Ghysels, Harvey, Renault (1996)). In equilibrium settings such as Merton's (1973) ICAPM or the CIR model by Cox, Ingersoll, Ross (1985), shocks to the volatility process become pricing kernel state variables.
The relationship between expected market returns and market volatility is then determined by two forces. From a static point of view, there is the risk-return trade-off: risk-averse investors demand a higher risk premium if volatility is higher. However, from a dynamic point of view, investors price shocks to volatility that are correlated with shocks to the market return.
Only few papers have closely examined volatility as a pricing factor in a cross-sectional pricing context (see, in particular, Ang, Hodrick, Xing, and Zhang (2004)). We extend this analysis by modeling log-volatility as the sum of a short-run and a long-run component, each of which may have its own risk premium. Our equilibrium ICAPM setting predicts that investors hedge volatility risk, and that asset expected returns depend on their covariance with innovations to the short-run and the long-run volatility components as well as the market return.
Intuitively, investors might react differently to volatility shocks that are expected to be short-lived (e.g. news announcements, transitory liquidity events) compared to long-lived shocks (e.g. changes in the economic outlook, structural changes). Our approach makes it possible to identify and analyze long-run volatility shocks that are likely to be most relevant for expected returns.