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

Mikhail Chernov, Bryan Kelly, Semyon Malamud and Johannes Schwab

No 19999, CEPR Discussion Papers from Centre for Economic Policy Research

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.

JEL-codes: C12 C40 C55 C57 G12 (search for similar items in EconPapers)
Date: 2025-03
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