Portfolio Constraints as Cross-Model Shrinkage: How Inefficient is the 1/M Covariance Combination?

Abstract

Jagannathan and Ma (2003) show that portfolio constraints act as implicit shrinkage on the covariance matrix and help improve out-of-sample performance. We show in this paper that portfolio constraints produce a second regularization effect: they shrink the cross-section of competing covariance estimators. Once weight restrictions are imposed, the mapping from covariance to portfolio becomes increasingly insensitive to the particular choice. As a consequence, covariance combinations that are central in the cloud of competing estimators perform close to the best individual one, without requiring the practitioner to identify it ex-ante. We confirm this mechanism empirically using daily U.S. equity data from 1980 to 2022, implementing ten covariance estimators and five combination strategies in minimum variance portfolios of up to 1,000 assets