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Testing the Capital Asset Pricing Model Efficiently Under Elliptical Symmetry: A Semiparametric Approach

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Author Info
Oliver Linton ()
Douglas J.Hodgson
Keith Vorkink

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Abstract

We develop new tests of the capital asset pricing model that take account of and are valid under the assumption that the distribution generating returns is elliptically symmetric; this assumption is neccessary and sufficient for the validity of the CAPM. Our test is based on semi-parametric efficient estimation procedures for a seemingly unrelated regression model where the multvariate error density is elliptically symmetric, but otherwise unrestricted. The elliptical symmetry assumption allows us to avoid the curse of dimensionality problem that typically arises in multivariate semiparametric estimation procedures, because the multivariate elliptically symmetric density function can be written as a function of a scalar transformation of the observed multivariate data. The elliptically symmetric family includes a number of thick-tailed distributions and so is potentially relevant in financial applications. Our estimated betas are lower than the OLS estimates, and our parametric estimates are much less consistent with the CAPM restrictions than the corresponding OLS estimates.

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Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp382.

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Date of creation: Jun 2001
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Handle: RePEc:fmg:fmgdps:dp382

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References listed on IDEAS
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. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February. [Downloadable!] (restricted)
  2. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-48, May. [Downloadable!] (restricted)
  3. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(04), pages 539-569, August. [Downloadable!]
    Other versions:
  4. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, Blackwell Publishing, vol. 66(1), pages 1-26, January.
    Other versions:
  5. James Tobin, 1956. "Liquidity Preference as Behavior Towards Risk," Cowles Foundation Discussion Papers 14, Cowles Foundation, Yale University. [Downloadable!]
  6. Hodgson, D.J., 1995. "Adaptive Estimation of Error Correlation Models," RCER Working Papers 410, University of Rochester - Center for Economic Research (RCER).
  7. Amsler, Christine E. & Schmidt, Peter, 1985. "A Monte Carlo investigation of the accuracy of multivariate CAPM tests," Journal of Financial Economics, Elsevier, vol. 14(3), pages 359-375, September. [Downloadable!] (restricted)
  8. Douglas J. Hodgson & Keith Vorkink, 2001. "Efficient Estimation of Conditional Asset Pricing Models," Cahiers de recherche CREFE / CREFE Working Papers 144, CREFE, Université du Québec à Montréal. [Downloadable!]
    Other versions:
  9. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
  10. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation, Yale University. [Downloadable!]
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  11. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August. [Downloadable!] (restricted)
  12. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October. [Downloadable!]
  13. repec:cup:etheor:v:11:y:1995:i:5:p:818-87 is not listed on IDEAS
  14. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May. [Downloadable!] (restricted)
  15. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
  16. Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-52, June. [Downloadable!] (restricted)
  17. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September. [Downloadable!] (restricted)
    Other versions:
  18. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June. [Downloadable!]
  19. 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. [Downloadable!] (restricted)
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  21. Hodgson, Douglas J., 1998. "Adaptive Estimation Of Error Correction Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 44-69, February. [Downloadable!]
  22. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March. [Downloadable!] (restricted)
  23. 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 1121-52, September. [Downloadable!] (restricted)
  24. Wesselman, A. M. & Van Praag, B. M. S., 1987. "Elliptical regression operationalized," Economics Letters, Elsevier, vol. 23(3), pages 269-274. [Downloadable!] (restricted)
  25. Gibbons, Michael R., 1982. "Multivariate tests of financial models : A new approach," Journal of Financial Economics, Elsevier, vol. 10(1), pages 3-27, March. [Downloadable!] (restricted)
  26. MacKinlay, A. Craig, 1987. "On multivariate tests of the CAPM," Journal of Financial Economics, Elsevier, vol. 18(2), pages 341-371, June. [Downloadable!] (restricted)
  27. Hodgson, Douglas J., 1998. "Adaptive estimation of cointegrating regressions with ARMA errors," Journal of Econometrics, Elsevier, vol. 85(2), pages 231-267, August. [Downloadable!] (restricted)
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  28. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January. [Downloadable!] (restricted)
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(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. George A. Christodoulakis & Stephen E Satchell, 2006. "Exact Elliptical Distributions for Models of Conditionally Random Financial Volatility," Working Papers 32, Bank of Greece. [Downloadable!]
  2. Douglas J. Hodgson & Oliver Linton & Keith Vorkink, 2004. "Testing forward exchange rate unbiasedness efficiently: a semiparametric approach," Journal of Applied Economics, Universidad del CEMA, vol. 0, pages 325-353, November. [Downloadable!]
  3. Enrique Sentana & Gabriele Fiorentini, 2007. "On The Efficiency And Consistency Of Likelihood Estimation In Multivariate Conditionally Heteroskedastic Dynamic Regression Models," Working Papers wp2007_0713, CEMFI. [Downloadable!]
    Other versions:
  4. Douglas J. Hodgson & Keith Vorkink, 2001. "Efficient Estimation of Conditional Asset Pricing Models," Cahiers de recherche CREFE / CREFE Working Papers 144, CREFE, Université du Québec à Montréal. [Downloadable!]
    Other versions:
  5. Marie-Claude Beaulieu & Jean-Marie Dufour & Lynda Khalaf, 2005. "Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions," CIRANO Working Papers 2005s-03, CIRANO. [Downloadable!]
    Other versions:
  6. Douglas Hodgson & Barrett Slade & Keith Vorkink, 2006. "Constructing Commercial Indices: A Semiparametric Adaptive Estimator Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 32(2), pages 151-168, March. [Downloadable!] (restricted)
  7. Fernando A. Quintana & Pilar L. Iglesias & Manuel Galea-Rojas, 2005. "Bayesian robust estimation of systematic risk using product partition models," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 1(5), pages 313-320, September. [Downloadable!] (restricted)
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