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A Test of the Efficiency of a Given Portfolio in High Dimensions

Author

Listed:
  • Mikhail Chernov

    (UCLA Anderson)

  • Bryan T. Kelly

    (Yale SOM; AQR Capital Management, LLC; National Bureau of Economic Research (NBER))

  • Semyon Malamud

    (Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute)

  • Johannes Schwab

    (École Polytechnique Fédérale de Lausanne (EPFL))

Abstract

We generalize the seminal Gibbons-Ross-Shanken test to the empirically relevant case where the number of test assets far exceeds the number of observations. In such a setting, one needs to use a regularized estimator of the covariance matrix of test assets, which leads to biases in the original test statistic. Random Matrix Theory allows us to account for these biases and to evaluate the test's power. Power increases with the number of test assets and reaches the maximum for a broad range of local alternatives. These conclusions are supported by an extensive simulation study. We implement the test empirically for state-of-the-art candidate efficient portfolios and test assets.

Suggested Citation

  • Mikhail Chernov & Bryan T. Kelly & Semyon Malamud & Johannes Schwab, 2025. "A Test of the Efficiency of a Given Portfolio in High Dimensions," Swiss Finance Institute Research Paper Series 25-26, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2526
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    More about this item

    Keywords

    efficient portfolio; cross-section of stock returns; testing; regularization; random matrix theory;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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