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Specification tests of asset pricing models using excess returns

Author

Listed:
  • 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.

Suggested Citation

  • Raymond Kan & Cesare Robotti, 2006. "Specification tests of asset pricing models using excess returns," FRB Atlanta Working Paper 2006-10, Federal Reserve Bank of Atlanta.
    • Handle: RePEc:fip:fedawp:2006-10
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Jagannathan, Ravi & Wang, Zhenyu, 1996. "The Conditional CAPM and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 51(1), pages 3-53, March.
    3. Raymond Kan & Chu Zhang, 1999. "Two‐Pass Tests of Asset Pricing Models with Useless Factors," Journal of Finance, American Finance Association, vol. 54(1), pages 203-235, February.
    4. Berndt, Ernst R & Savin, N Eugene, 1977. "Conflict among Criteria for Testing Hypotheses in the Multivariate Linear Regression Model," Econometrica, Econometric Society, vol. 45(5), pages 1263-1277, July.
    5. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
    6. John Y. Campbell & John H. Cochrane, 2000. "Explaining the Poor Performance of Consumption‐based Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(6), pages 2863-2878, December.
    7. Ravi Jagannathan & Yong Wang, 2007. "Lazy Investors, Discretionary Consumption, and the Cross‐Section of Stock Returns," Journal of Finance, American Finance Association, vol. 62(4), pages 1623-1661, August.
    8. Shanken, Jay, 1985. "Multivariate tests of the zero-beta CAPM," Journal of Financial Economics, Elsevier, vol. 14(3), pages 327-348, September.
    9. Ferson, Wayne E & Foerster, Stephen R & Keim, Donald B, 1993. "General Tests of Latent Variable Models and Mean-Variance Spanning," Journal of Finance, American Finance Association, vol. 48(1), pages 131-156, March.
    10. Hansen, Lars Peter & Heaton, John & Luttmer, Erzo G J, 1995. "Econometric Evaluation of Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 237-274.
    11. Hodrick, Robert J. & Zhang, Xiaoyan, 2001. "Evaluating the specification errors of asset pricing models," Journal of Financial Economics, Elsevier, vol. 62(2), pages 327-376, November.
    12. Ravi Jagannathan & Zhenyu Wang, 2002. "Empirical Evaluation of Asset‐Pricing Models: A Comparison of the SDF and Beta Methods," Journal of Finance, American Finance Association, vol. 57(5), pages 2337-2367, October.
    13. Martin Lettau & Sydney Ludvigson, 2001. "Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia Are Time-Varying," Journal of Political Economy, University of Chicago Press, vol. 109(6), pages 1238-1287, December.
    14. 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.
    15. Hansen, Lars Peter & Jagannathan, Ravi, 1997. "Assessing Specification Errors in Stochastic Discount Factor Models," Journal of Finance, American Finance Association, vol. 52(2), pages 557-590, June.
    16. Jagannathan, Ravi & Kubota, Keiichi & Takehara, Hitoshi, 1998. "Relationship between Labor-Income Risk and Average Return: Empirical Evidence from the Japanese Stock Market," The Journal of Business, University of Chicago Press, vol. 71(3), pages 319-347, July.
    17. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    18. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    19. Shanken, Jay & Zhou, Guofu, 2007. "Estimating and testing beta pricing models: Alternative methods and their performance in simulations," Journal of Financial Economics, Elsevier, vol. 84(1), pages 40-86, April.
    20. Campbell, John Y., 2003. "Consumption-based asset pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 13, pages 803-887, Elsevier.
    21. Heber Farnsworth & Wayne E. Ferson & David Jackson & Steven Todd, 2002. "Performance Evaluation with Stochastic Discount Factors," NBER Working Papers 8791, National Bureau of Economic Research, Inc.
    22. Balduzzi, Pierluigi & Kallal, Hedi, 1997. "Risk Premia and Variance Bounds," Journal of Finance, American Finance Association, vol. 52(5), pages 1913-1949, December.
    23. Raymond Kan & Guofu Zhou, 1999. "A Critique of the Stochastic Discount Factor Methodology," Journal of Finance, American Finance Association, vol. 54(4), pages 1221-1248, August.
    24. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    25. 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.
    26. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, February.
    27. 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.
    28. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    29. Kevin Q. Wang, 2003. "Asset Pricing with Conditioning Information: A New Test," Journal of Finance, American Finance Association, vol. 58(1), pages 161-196, February.
    30. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    31. Kirby, Chris, 1998. "The Restrictions on Predictability Implied by Rational Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 11(2), pages 343-382.
    32. Kan, Raymond & Zhang, Chu, 1999. "GMM tests of stochastic discount factor models with useless factors," Journal of Financial Economics, Elsevier, vol. 54(1), pages 103-127, October.
    33. Heber Farnsworth, 2002. "Performance Evaluation with Stochastic Discount Factors," The Journal of Business, University of Chicago Press, vol. 75(3), pages 473-504, July.
    34. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    35. Michael W. Brandt & David A. Chapman, 2006. "Linear Approximations and Tests of Conditional Pricing Models," NBER Working Papers 12513, National Bureau of Economic Research, Inc.
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