Testing CAPM with a Large Number of Assets (Updated 28th March 2012)
This paper is concerned with testing the time series implications of the capital asset pricing model (CAPM) due to Sharpe (1964) and Lintner (1965), when the number of securities, N , is large relative to the time dimension, T , of the return series. Two new tests of CAPM are proposed that exploit recent advances on the analysis of large panel data models, and are valid even if N > T . When the errors are Gaussian and cross sectionally independent, a test, denoted by , is proposed which is N(0; 1) as , with T fixed. Even when the errors are non-Gaussian we are still able to show that tends to N (0; 1) so long as the errors are cross-sectionally independent and , with N and T ! 1, jointly. In the case of cross sectionally correlated errors, using a threshold estimator of the average squares of pair-wise error correlations, a modified version of , denoted by , is proposed. Small sample properties of the tests are compared using Monte Carlo experiments designed specifically to match the correlations, volatilities, and other distributional features of the residuals of Fama-French three factor regressions of individual securities in the Standard & Poor 500 index. Overall, the proposed tests perform best in terms of power, with empirical sizes very close to the chosen nominal value even in cases where N is much larger than T. The test (which allows for non-Gaussian and weakly cross correlated errors) is applied to all securities in the S&P 500 index with 60 months of return data at the end of each month over the period September 1989-September 2011. Statistically significant evidence against Sharpe-Lintner CAPM is found mainly during the recent financial crisis. Furthermore, a strong negative correlation is found between a twelve-month moving average p-values of the test and the returns of long/short equity strategies relative to the return on S&P 500 over the period December 2006 to September 2011, suggesting that abnormal profits are earned during episodes of market inefficiencies.
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- C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer, vol. 48(3), pages 465-471, September.
- Affleck-Graves, John & McDonald, Bill, 1990. "Multivariate Tests of Asset Pricing: The Comparative Power of Alternative Statistics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(02), pages 163-185, June.
- Pasaran, M.H. & Im, K.S. & Shin, Y., 1995.
"Testing for Unit Roots in Heterogeneous Panels,"
Cambridge Working Papers in Economics
9526, Faculty of Economics, University of Cambridge.
- Peter Bossaerts & Charles Plott & William R. Zame, 2007.
"Prices and Portfolio Choices in Financial Markets: Theory, Econometrics, Experiments,"
Econometric Society, vol. 75(4), pages 993-1038, 07.
- Peter Bossaerts & Charles Plott & William R. Zame, 2003. "Prices and Portfolio Choices in Financial Markets: Theory, Econometrics, Experiments," Swiss Finance Institute Research Paper Series 07-05, Swiss Finance Institute, revised Mar 2007.
- Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2009.
"Weak and Strong Cross Section Dependence and Estimation of Large Panels,"
CESifo Working Paper Series
2689, CESifo Group Munich.
- Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14, pages C45-C90, 02.
- Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages C45-C90, February.
- Chudik, A. & Pesaran, M.H. & Tosetti, E., 2009. "Weak and Strong Cross Section Dependence and Estimation of Large Panels," Cambridge Working Papers in Economics 0924, Faculty of Economics, University of Cambridge.
- Chudik, Alexander & Pesaran, Hashem & Tosetti, Elisa, 2009. "Weak and strong cross section dependence and estimation of large panels," Working Paper Series 1100, European Central Bank.
- Sermin Gungor & Richard Luger, 2013. "Testing Linear Factor Pricing Models With Large Cross Sections: A Distribution-Free Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 66-77, January.
- Todd Headrick & Shlomo Sawilowsky, 1999. "Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method," Psychometrika, Springer, vol. 64(1), pages 25-35, March.
- Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer, vol. 43(4), pages 521-532, December.
- 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.
- Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
- Frederick Wong, 2003. "Efficient estimation of covariance selection models," Biometrika, Biometrika Trust, vol. 90(4), pages 809-830, December.
- Todd Headrick & Shlomo Sawilowsky, 1999. "Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method," Psychometrika, Springer, vol. 64(2), pages 251-251, June.
- Affleck-Graves, John & McDonald, Bill, 1989. " Nonnormalities and Tests of Asset Pricing Theories," Journal of Finance, American Finance Association, vol. 44(4), pages 889-908, September.
- Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-36, May-June.
- Eugene F. Fama & Kenneth R. French, 2004. "The Capital Asset Pricing Model: Theory and Evidence," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 25-46, Summer.
- H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
- Gungor, Sermin & Luger, Richard, 2009. "Exact distribution-free tests of mean-variance efficiency," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 816-829, December.
- 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.
- Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, edition 1, number 9780198774488, July.
- Ullah, Aman, 1974. "On the sampling distribution of improved estimators for coefficients in linear regression," Journal of Econometrics, Elsevier, vol. 2(2), pages 143-150, July.
- Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
- Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
- Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2007. "Multivariate Tests of MeanVariance Efficiency With Possibly Non-Gaussian Errors: An Exact Simulation-Based Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 398-410, October.
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