Universal Portfolio Shrinkage

Bryan T. Kelly; Semyon Malamud; Mohammad Pourmohammadi; Fabio Trojani

doi:10.3386/w32004

Universal Portfolio Shrinkage

Bryan T. Kelly, Semyon Malamud, Mohammad Pourmohammadi & Fabio Trojani

Working Paper 32004

DOI 10.3386/w32004

Issue Date December 2023

Revision Date May 2026

We introduce a nonlinear covariance shrinkage method for building optimal portfolios. Our universal portfolio shrinkage approximator (UPSA) is given in closed-form, is cheap to implement, and improves upon existing shrinkage methods. Rather than uniformly penalizing all principal components of returns or discarding low-variance ones, UPSA instead reweights components to explicitly optimize expected out-of-sample portfolio performance. In empirical applications using a large cross-section of anomaly factors, it delivers robust improvements over alternative shrinkage methods in the literature.

AQR Capital Management is a global investment management firm that may or may not apply similar investment techniques or methods of analysis as described herein. The views expressed here are those of the authors and not necessarily those of AQR. Semyon Malamud gratefully acknowledges the financial support of the Swiss National Science Foundation (Grant 100018-228042) and the Swiss Finance Institute. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.

Bryan T. Kelly
I have received consulting income from AQR Capital Management exceeding $10,000 over the past three years. AQR Capital Management is a global investment management firm, which may or may not apply similar investment techniques or methods of analysis as described herein. The views expressed here are those of the authors and not necessarily those of AQR.

Semyon Malamud
Semyon Malamud gratefully acknowledges support from the Swiss Finance Institute.

Mohammad Pourmohammadi
Mohammad Pourmohammadi gratefully acknowledges support from the Swiss Finance Institute.

Fabio Trojani
Fabio Trojani gratefully acknowledges support from the Swiss Financial Institute and the AXA chair in socioeconomic risks of financial markets at the University of Turin.
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Bryan T. Kelly, Semyon Malamud, Mohammad Pourmohammadi, and Fabio Trojani, "Universal Portfolio Shrinkage," NBER Working Paper 32004 (2023), https://doi.org/10.3386/w32004.

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Universal Portfolio Shrinkage

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