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Specification tests of asset pricing models using excess returns

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  • Raymond Kan
  • Cesare Robotti

Abstract

We discuss the impact of different formulations of asset pricing models on the outcome of specification tests that are performed using excess returns. It is generally believed that when only excess returns are used for testing asset pricing models, the mean of the stochastic discount factor (SDF) does not matter. We show that the mean of the candidate SDF is only irrelevant when the model is correct. When the model is misspecified, the mean of the SDF can be a very important determinant of the specification test statistic, and it also heavily influences the relative rankings of competing asset pricing models. We point out that the popular way of specifying the SDF as a linear function of the factors is problematic because the specification test statistic is not invariant to an affine transformation of the factors and 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 only excess returns are used. 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. We provide asymptotic distributions of the modified HJ distance and of the traditional HJ distance based on the de-meaned SDF under the correctly specified model and the misspecified models. Finally, we propose a simple methodology for computing the standard errors of the estimated SDF parameters that are robust to model misspecification.

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Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2006-10.

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Date of creation: 2006
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Handle: RePEc:fip:fedawp:2006-10

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Citations

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Cited by:
  1. Stefan Nagel, 2013. "Empirical Cross-Sectional Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 167-199, November.
  2. A. Craig Burnside, 2010. "Empirical Asset Pricing and Statistical Power in the Presence of Weak Risk Factors," Working Papers 10-45, Duke University, Department of Economics.
  3. Raymond Kan & Cesare Robotti, 2007. "Model comparison using the Hansen-Jagannathan distance," Working Paper 2007-04, Federal Reserve Bank of Atlanta.
  4. Balduzzi, Pierluigi & Robotti, Cesare, 2010. "Asset pricing models and economic risk premia: A decomposition," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 54-80, January.
  5. Francisco Peñaranda & Enrique Sentana, 2010. "A unifying approach to the empirical evaluation of asset pricing models," Economics Working Papers 1229, Department of Economics and Business, Universitat Pompeu Fabra.
  6. Kroencke, Tim A. & Schindler, Felix & Sebastian, Steffen & Theissen, Erik, 2013. "GDP mimicking portfolios and the cross-section of stock returns," ZEW Discussion Papers 13-026, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  7. Ravi Jagannathan & Srikant Marakani, 2011. "Price Dividend Ratio Factors : Proxies for Long Run Risk," NBER Working Papers 17484, National Bureau of Economic Research, Inc.
  8. Fletcher, Jonathan, 2014. "Benchmark models of expected returns in U.K. portfolio performance: An empirical investigation," International Review of Economics & Finance, Elsevier, vol. 29(C), pages 30-46.
  9. Hammami, Yacine & Lindahl, Anna, 2014. "An intertemporal capital asset pricing model with bank credit growth as a state variable," Journal of Banking & Finance, Elsevier, vol. 39(C), pages 14-28.
  10. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2011. "Chi-squared tests for evaluation and comparison of asset pricing models," Working Paper 2011-08, Federal Reserve Bank of Atlanta.
  11. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2012. "Robust inference in linear asset pricing models," Working Paper 2012-17, Federal Reserve Bank of Atlanta.
  12. Craig Burnside, 2010. "Identification and Inference in Linear Stochastic Discount Factor Models," NBER Working Papers 16634, National Bureau of Economic Research, Inc.
  13. Gospodinov, Nikolay & Kan, Raymond & Robotti, Cesare, 2013. "Misspecification-robust inference in linear asset pricing models with irrelevant risk factors," Working Paper 2013-09, Federal Reserve Bank of Atlanta.

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