Model Comparison Using the Hansen-Jagannathan Distance

Abstract

Although it is of interest to test whether or not a particular asset pricing model is literally true, a more useful task for empirical researchers is to determine how wrong a model is and to compare the performance of competing asset pricing models. In this paper, we propose a new methodology to test whether or not two competing linear asset pricing models have the same Hansen-Jagannathan distance. We show that the asymptotic distribution of the test statistic depends on whether the competing models are correctly specified or misspecified, and on whether the competing models are nested or non-nested. In addition, given the increasing interest in misspecified models, we propose a simple methodology for computing the standard errors of the estimated stochastic discount factor parameters that are robust to model misspecification. Using monthly data on 25 size and book-to-market ranked portfolios and the one-month T-bill, we show that the commonly used returns and factors are, for the most part, too noisy for us to conclude that one model is superior to the other models in terms of Hansen-Jagannathan distance. Specifically, there is little evidence that conditional and intertemporal capital asset pricing model (CAPM)-type specifications outperform the simple unconditional CAPM. In addition, we show that many of the macroeconomic factors commonly used in the literature are no longer priced once potential model misspecification is taken into account.

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