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Testing CAPM with a Large Number of Assets

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  • M Hashem Pesaran
  • Takashi Yamagata

Abstract

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 J_{α,1}, is proposed which is N(0,1) as N→∞, with T fixed. Even when the errors are non-Gaussian we are still able to show that J_{α,1} tends to N(0,1) so long as the errors are cross-sectionally independent and N/T³→0, with N and T→∞, 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 J_{α,1}, denoted by J_{α,2}, 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 J_{α,2} 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 J_{α,2} 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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Bibliographic Info

Paper provided by Department of Economics, University of York in its series Discussion Papers with number 12/05.

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Date of creation: Feb 2012
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Handle: RePEc:yor:yorken:12/05

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Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
Phone: (0)1904 323776
Fax: (0)1904 323759
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Web page: http://www.york.ac.uk/economics/
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Related research

Keywords: CAPM; Testing for alpha; Market e¢ ciency; Long/short equity returns; Large panels; Weak and strong cross-sectional dependence.;

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Cited by:
  1. Bailey, Natalia & Kapetanios, George & Pesaran, M. Hashem, 2012. "Exponent of Cross-sectional Dependence: Estimation and Inference," IZA Discussion Papers 6318, Institute for the Study of Labor (IZA).
  2. Marcelo Bianconi & Joe A. Yoshino, 2012. "Empirical Estimation of the Cost of Equity: An Application to Selected Brazilian Utilities Companies," Discussion Papers Series, Department of Economics, Tufts University 0765, Department of Economics, Tufts University.

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