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Specification tests of asset pricing models using excess returns

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Author Info
Kan, Raymond
Robotti, Cesare

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Abstract

In this paper, we discuss the impact of different formulations of asset pricing models on the outcome of specification tests that are performed using excess returns. We point out that the popular way of specifying the stochastic discount factor (SDF) as a linear function of the factors is problematic because (1) the specification test statistic is not invariant to an affine transformation of the factors, and (2) the SDFs of competing models can have very different means. In contrast, an alternative specification that defines the SDF as a linear function of the de-meaned factors is free from these two problems and is more appropriate for model comparison. In addition, we suggest that a modification of the traditional Hansen-Jagannathan distance (HJ-distance) is needed when we use the de-meaned factors. The modified HJ-distance uses the inverse of the covariance matrix (instead of the second moment matrix) of excess returns as the weighting matrix to aggregate pricing errors. Asymptotic distributions of the modified HJ-distance and of the traditional HJ-distance based on the de-meaned SDF under correctly specified and misspecified models are provided. Finally, we propose a simple methodology for computing the standard errors of the estimated SDF parameters that are robust to model misspecification. We show that failure to take model misspecification into account is likely to understate the standard errors of the estimates of the SDF parameters and lead us to erroneously conclude that certain factors are priced.

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Publisher Info
Article provided by Elsevier in its journal Journal of Empirical Finance.

Volume (Year): 15 (2008)
Issue (Month): 5 (December)
Pages: 816-838
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Handle: RePEc:eee:empfin:v:15:y:2008:i:5:p:816-838

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Web page: http://www.elsevier.com/locate/jempfin

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Keywords: Asset pricing models Specification tests Modified Hansen-Jagannathan distance Misspecification robust standard errors De-meaned stochastic discount factor;

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  2. Balduzzi, Pierluigi & Yao, Tong, 2007. "Testing heterogeneous-agent models: an alternative aggregation approach," Journal of Monetary Economics, Elsevier, vol. 54(2), pages 369-412, March. [Downloadable!] (restricted)
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  6. Hansen, Lars Peter & Heaton, John & Luttmer, Erzo G J, 1995. "Econometric Evaluation of Asset Pricing Models," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 8(2), pages 237-74. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. A. Craig Burnside, 2007. "Empirical Asset Pricing and Statistical Power in the Presence of Weak Risk Factors," NBER Working Papers 13357, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Raymond Kan & Cesare Robotti, 2007. "Model comparison using the Hansen-Jagannathan distance," Working Paper 2007-04, Federal Reserve Bank of Atlanta. [Downloadable!]
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