Uncovering the Risk-Return Relation in the Stock Market

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 e .ect of shocks to expected returns on ex post returns and use implied volatility from aded options to increase estimation e .ciency.As a result,the coe .cient of relative risk aversion is estimated more precisely,and we .nd it to be positive and reasonable in magnitude. Although volatility risk is priced,as theory dictates,it conibutes 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 conadictory and counter-intuitive results in the existing literature.