An Intertemporal CAPM with Stochastic Volatility

John Y. Campbell, Stefano Giglio, Christopher Polk, and Robert Turley (2018)

The authors show that long-term investors, which includes institutions such as endowments and pension funds, will avoid being overweight in historically high-returning stocks such as value or small caps in order to hedge against declining expected returns and increasing volatility. Previous work involving the intertemporal capital asset pricing model (ICAPM) has shown these hedging assets to offer lower return for long-term investors. The model constructed by the authors constrains investors to be 100% invested in equity.

The risk aversion necessary for an infinitely-lived investor with Epstein-Zin preferences to hold a lower returning market index as opposed a higher returning value stocks is calculated. Epstein-Zin preferences reflect an investor’s consumption, discount factor, risk aversion, and elasticity of intertemporal substitution. They find that investors with a moderate level of risk aversion are sufficiently conservative to prefer holding a market index.

Three dimensions of risk are modeled: betas with unexpected market returns, news about future market returns (such as discount rates or market cash flows), and news about future market volatility. The level of risk aversion of the long-term investor is not calculated separately for each of these risk measures.

In order to concentrate on the time-variation in the volatility of stock returns, the authors estimate a vector autoregressive (VAR) system, which shows low-frequency movements in market volatility to be tied to the default spread. Portfolios are formed by betas to market return, volatility, and characteristics, which are confronted with portfolios of varying equity exposure related to estimates of market variance.

Their findings do not extend to the behavior of short-term investors that would be represented by a single period model. The results also fail to explain the lack of long-term investor equity re-allocation in response to changes in the equity premium that are not in proportion to changes in stock return variances. Consequently, the authors do not believe this model represents market equilibrium.