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Testing for Alpha in Linear Factor Pricing Models with a Large Number of Securities

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  • M. Hashem Pesaran
  • Takashi Yamagata

Abstract

This paper proposes a novel test of zero pricing errors for the linear factor pricing model when the number of securities, N, can be large relative to the time dimension, T, of the return series. The test is based on Student t tests of individual securities and has a number of advantages over the existing standardised Wald type tests. It allows for non-Gaussianity and general forms of weakly cross correlated errors. It does not require estimation of an invertible error covariance matrix, it is much faster to implement, and is valid even if N is much larger than T. Monte Carlo evidence shows that the proposed test performs remarkably well even when T = 60 and N = 5;000. The test is applied to monthly returns on securities in the S&P 500 at the end of each month in real time, using rolling windows of size 60. Statistically significant evidence against Sharpe-Lintner CAPM and Fama-French three factor models are found mainly during the recent financial crisis. Also we find a significant negative correlation between a twelve-months moving average p-values of the test and excess returns of long/short equity strategies (relative to the return on S&P 500) over the period November 1994 to June 2015, suggesting that abnormal profits are earned during episodes of market inefficiencies.

Suggested Citation

  • M. Hashem Pesaran & Takashi Yamagata, 2017. "Testing for Alpha in Linear Factor Pricing Models with a Large Number of Securities," CESifo Working Paper Series 6432, CESifo.
    • Handle: RePEc:ces:ceswps:_6432
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    References listed on IDEAS

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    1. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    2. Michael R. Harwell & Ronald C. Serlin, 1989. "A Nonparametric Test Statistic for the General Linear Model," Journal of Educational and Behavioral Statistics, , vol. 14(4), pages 351-371, December.
    3. Todd Headrick & Shlomo Sawilowsky, 1999. "Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 251-251, June.
    4. Todd Headrick & Shlomo Sawilowsky, 1999. "Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 25-35, March.
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    Citations

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    Cited by:

    1. Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2021. "Measurement of factor strength: Theory and practice," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 587-613, August.
    2. Victor Chernozhukov & Wolfgang Härdle & Chen Huang & Weining Wang, 2018. "LASSO-driven inference in time and space," CeMMAP working papers CWP36/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. M. Hashem Pesaran & Yimeng Xie, 2021. "A Bias-Corrected CD Test for Error Cross-Sectional Dependence in Panel Data Models with Latent Factors," Papers 2109.00408, arXiv.org, revised Apr 2023.
    4. Chaohua Dong & Jiti Gao & Oliver Linton, 2017. "High dimensional semiparametric moment restriction models," Monash Econometrics and Business Statistics Working Papers 17/17, Monash University, Department of Econometrics and Business Statistics.
    5. Huang, Haitao & Jiang, Lei & Leng, Xuan & Peng, Liang, 2023. "Bootstrap analysis of mutual fund performance," Journal of Econometrics, Elsevier, vol. 235(1), pages 239-255.
    6. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    7. Linton, Oliver & Xiao, Zhijie, 2019. "Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(2), pages 608-631.
    8. Feng, Long & Lan, Wei & Liu, Binghui & Ma, Yanyuan, 2022. "High-dimensional test for alpha in linear factor pricing models with sparse alternatives," Journal of Econometrics, Elsevier, vol. 229(1), pages 152-175.
    9. Im, K S. & Pesaran, M. H. & Shin, Y., 2023. "Reflections on "Testing for Unit Roots in Heterogeneous Panels"," Cambridge Working Papers in Economics 2310, Faculty of Economics, University of Cambridge.
    10. M. Hashem Pesaran & Ron P. Smith, 2019. "The Role of Factor Strength and Pricing Errors for Estimation and Inference in Asset Pricing Models," CESifo Working Paper Series 7919, CESifo.

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    More about this item

    Keywords

    CAPM; testing for alpha; weak and spatial error cross-sectional dependence; S&P 500 securities; long; short equity strategy;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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