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Performance Attribution for Portfolio Constraints

Author

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  • Andrew W. Lo

    (Sloan School of Management, Laboratory for Financial Engineering, and Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; and Santa Fe Institute, Santa Fe, New Mexico 87501)

  • Ruixun Zhang

    (School of Mathematical Sciences, Center for Statistical Science, National Engineering Laboratory for Big Data Analysis and Applications, and Laboratory for Mathematical Economics and Quantitative Finance, Peking University, Beijing 100871, China)

Abstract

We propose a new performance attribution framework that decomposes a constrained portfolio’s holdings, expected returns, variance, expected utility, and realized returns into components attributable to (1) the unconstrained mean-variance optimal portfolio; (2) individual static constraints; and (3) information, if any, arising from those constraints. A key contribution of our framework is the recognition that constraints may contain information that is correlated with returns, in which case imposing such constraints can affect performance. We extend our framework to accommodate estimation risk in portfolio construction using Bayesian portfolio analysis, which allows one to select constraints that improve—or are least detrimental to—future performance. We provide simulations and empirical examples involving constraints on environmental, social, and governance portfolios. Under certain scenarios, constraints may improve portfolio performance relative to a passive benchmark that does not account for the information contained in these constraints.

Suggested Citation

  • Andrew W. Lo & Ruixun Zhang, 2025. "Performance Attribution for Portfolio Constraints," Management Science, INFORMS, vol. 71(9), pages 7537-7559, September.
    • Handle: RePEc:inm:ormnsc:v:71:y:2025:i:9:p:7537-7559
    DOI: 10.1287/mnsc.2024.05365
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