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A large-dimensional test for cross-sectional anomalies:Efficient sorting revisited

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  • De Nard, Gianluca
  • Zhao, Zhao
Abstract
Many researchers seek factors that predict the cross-section of stock returns. In finance, the key is to replicate anomalies by long–short portfolios based on their firm characteristics, with microcap biases alleviated via New York Stock Exchange (NYSE) breakpoints and value-weighted returns. In econometrics, the key is to include a covariance matrix estimator of stock returns for (mimicking) the portfolio construction. This paper marries these two strands of literature in order to test the zoo of cross-sectional anomalies by injecting size controls, basically NYSE breakpoints and value-weighted returns, into efficient sorting. We propose to use a covariance matrix estimator for ultra-high dimensions (up to 5,000) taking into account large, small and microcap stocks. We demonstrate that using a nonlinear shrinkage estimator of the covariance matrix substantially enhances the power of tests for cross-sectional anomalies: On average, t-statistics more than double. Furthermore, the proposed revisited efficient sorting method computes even highly significant factor portfolios net of transaction costs.

Suggested Citation

  • De Nard, Gianluca & Zhao, Zhao, 2022. "A large-dimensional test for cross-sectional anomalies:Efficient sorting revisited," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 654-676.
    • Handle: RePEc:eee:reveco:v:80:y:2022:i:c:p:654-676
    DOI: 10.1016/j.iref.2022.02.049
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    Keywords

    Anomalies; Cross-section of returns; Efficient sorting; Large dimensions; Markowitz portfolio selection; Nonlinear shrinkage;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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