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

Mikhail Chernov, Bryan T. Kelly, Semyon Malamud and Johannes Schwab
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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)

No 25-26, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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.

Keywords: efficient portfolio; cross-section of stock returns; testing; regularization; random matrix theory (search for similar items in EconPapers)
JEL-codes: C12 C40 C55 C57 G12 (search for similar items in EconPapers)
Pages: 116 pages
Date: 2025-03
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp2526

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