Model Comparison Using the Hansen-Jagannathan Distance

Raymond Kan and Cesare Robotti
Working Paper 2007-4
February 2007

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Although it is of interest to empirical researchers to test whether or not a particular asset-pricing model is true, a more useful task 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 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 are nested or nonnested. 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 the same data as in Hodrick and Zhang (2001), we show that the commonly used returns and factors are, for the most part, too noisy to conclude that one model is superior to the other models in terms of Hansen-Jagannathan distance. 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.

JEL classification: G12

Key words: Hansen-Jagannathan distance, asset-pricing models, model misspecification, risk premia

The authors thank Yaxuan Qi, Jay Shanken, Guofu Zhou, seminar participants at the National University of Ireland, and participants at the 2006 All Georgia Finance Conference for helpful discussions and comments. Kan 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. Any remaining errors are the authors’ responsibility.

Please address questions regarding content to Raymond Kan, Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada M5S 3E6, 416-978-4291, 416-978-5433 (fax),, or Cesare Robotti, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30305, 404-498-8543, 404-498-8810 (fax),

For further information, contact the Public Affairs Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, Georgia 30309-4470, 404-498-8020.