Estimating the Intertemporal Capital Asset Pricing Model with Cross-Sectional Consistency

Abstract

The intertemporal capital asset pricing model of Merton (1973) states that the expected excess return on an asset is proportional to the expected covariance of the excess return on this asset with the excess return on the market portfolio. The proportionality coefficient measures the average relative risk aversion of investors. When the investment opportunity is stochastic, the expected excess return is also proportional to the covariance of the excess return with the state variables that govern the state of the investment opportunity. The proportionality coefficients on these covariance terms measure the investors' average aversion to unfavorable shifts in these state variables. In this paper, we use GARCH-type models to estimate the conditional covariance of a wide array of industry and Fama-French size/book-to-market portfolios with the market portfolio and with the Fama-French size (SMB) and book-to-market (HML) risk factors. We then estimate the system of simultaneous equations that links the excess returns on these portfolios to the corresponding conditional covariances with the market portfolio and the common risk factors. We obtain a positive and highly significant estimate for the relative risk aversion coefficient. The coefficient is about three for the long sample from July 1926 to December 2002, and is around six for the more recent period from July 1963 to December 2002. Furthermore, the expected excess returns are negatively related to their conditional covariance with the Fama-French size risk factor, suggesting that an increase in the size factor predicts an unfavorable shift in the investment opportunity. However, we do not find any consistent loading on the covariance with the book-to-market risk factor. Our findings are robust to different ways of forming portfolios and estimating conditional covariances. Most of the existing literature estimates the intertemporal risk-return relation using one single series of the market portfolio return. We show that the estimates from a single return series have low statistical significance and large sample variation. Our key contribution here is to direct the attention of the literature to the cross-sectional consistency of the intertemporal asset pricing relation and the universal proportionality underlying the risk-return relation. By exploiting this universal relation, we obtain positive and highly significant estimates on the relative risk aversion coefficient. We also gain a better understanding on how different risk factors predict future movements in investment opportunities.