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Testing CAPM with a Large Number of Assets (Updated 28th March 2012)

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  • Pesaran, M. H.
  • Yamagata, T.

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 , 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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Bibliographic Info

Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 1210.

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Date of creation: 28 Feb 2012
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Handle: RePEc:cam:camdae:1210

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Web page: http://www.econ.cam.ac.uk/index.htm

Related research

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

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