RFS Advance Access originally published online on November 1, 2008
Review of Financial Studies 2009 22(9):3449-3490; doi:10.1093/rfs/hhn094
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Model Comparison Using the Hansen-Jagannathan Distance
University of Toronto
Federal Reserve Bank of Atlanta
Send correspondence to Raymond Kan, Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada M5S 3E6; telephone: (416) 978-4291; fax: (416) 978-5433. E-mail: kan{at}chass.utoronto.ca.
JEL Classification: G12
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Abstract |
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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.
We thank Fousseni Chabi-Yo, Long Chen, Yufeng Han, Joel Hasbrouck (the editor), Yaxuan Qi, Sergei Sarkissian, Jay Shanken, Halbert White, Hong Zhang, Guofu Zhou, an anonymous referee, seminar participants at the Federal Reserve Bank of Chicago, Hong Kong University of Science and Technology, National University of Ireland, Singapore Management University, Syracuse University, University of Southampton, and participants at the 2006 All Georgia Finance Conference, 2007 Asian Finance Association Conference, 2007 China International Conference in Finance, 2007 Northern Finance Meetings, and 2008 Society for Financial Econometrics Conference for helpful discussions and comments. Kan gratefully acknowledges financial support from the National Bank Financial of Canada. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.