Evaluating Asset-Pricing Models Using The Hansen-Jagannathan Bound: A Monte Carlo Investigation

We conduct Monte Carlo experiments to examine whether the bound proposed by Hansen and Jagannathan (1991) is a useful device for evaluating asset pricing models. Specifically, we use recently developed statistical tests, which are based on a 'distance' between the model and the Hansen-Jagannathan bound, to compute the rejection rates of true models. We provide finite-sample critical values for asset pricing models with time separable preferences, and show how they depend upon nuisance parameters—risk aversion and the rate of time preference. Further, we show that the finite-sample distribution of the test statistic associated with the risk-neutral case is extreme, in the sense that critical values based on this distribution will deliver type I errors no larger than intended—regardless of risk aversion or the rate of time preference. Extending the analysis to accommodate other preferences, we show that in the state non-separable case, the small-sample distributions of the test statistics are influenced significantly by the degree of intertemporal substitution, but not by attitudes toward risk. For habit formation preferences, the small-sample distributions are strongly influenced by the habit parameter. However, the maximal-size critical values for time-separable preferences are appropriate for habit formation as well as state non-separable preferences. We conclude that with these critical values the HJ bound is indeed a useful evaluation device. We then use the critical values to evaluate three asset pricing models using U.S. data. We find evidence against the time-separable model and mixed evidence on the remaining two models.