Uncovering the Risk-Return Relation in the Stock Market

TLDR

There is an ongoing debate about the weak or negative relation between risk (conditional variance) and return in the aggregate stock market. The study develops an ICAPM‑based empirical model to investigate this risk–return relation. The model jointly estimates the risk component and the hedge‑component of expected returns, incorporates shocks to expected returns on ex post returns, and uses implied volatility from options to improve estimation efficiency. The estimated relative risk aversion is positive and precise, volatility risk is priced but explains only a small share of return variation, and expected returns are mainly driven by the hedge component, whose omission explains prior contradictory findings.

Abstract

There is an ongoing debate in the literature about the apparent weak or negative relation between risk (conditional variance) and return (expected returns) in the aggregate stock market. We develop and estimate an empirical model based on the ICAPM to investigate this relation. Our primary innovation is to model and identify empirically the two components of expected returns--the risk component and the component due to the desire to hedge changes in investment opportunities. We also explicitly model the effect of shocks to expected returns on ex post returns and use implied volatility from traded options to increase estimation efficiency. As a result, the coefficient of relative risk aversion is estimated more precisely, and we find it to be positive and reasonable in magnitude. Although volatility risk is priced, as theory dictates, it contributes only a small amount to the time-variation in expected returns. Expected returns are driven primarily by the desire to hedge changes in investment opportunities. It is the omission of this hedge component that is responsible for the contradictory and counter-intuitive results in the existing literature.