The Estimation–Efficiency Frontier in Portfolio Complexity

How complex should a portfolio be in high-dimensional markets? We show that even in frictionless settings, portfolio complexity has diminishing returns and an interior optimum. Holding more assets improves diversification but magnifies estimation error when return histories are short. We formalize this tradeoff through an estimation–efficiency frontier that decomposes Sharpe-ratio losses into efficiency losses from restricting the investable span and estimation losses from learning portfolio weights. Under an approximate factor structure, these forces yield a sharp scaling law for the optimal number of active positions as a function of sample size, universe size, and factor strength.

Bio

Ming Yuan is a Professor of Statistics at Columbia University. He was previously a Senior Investigator in Virology at Morgridge Institute for Research and a Professor of Statistics at University of Wisconsin at Madison, and prior to that Coca-Cola Junior Professor of Industrial and Systems Engineering at Georgia Institute of Technology. His research and teaching interests lie broadly in statistics and its interface with other quantitative and computational fields such as optimization, machine learning, computational biology, and financial engineering. He has served as the program secretary of the Institute for Mathematical Statistics (IMS), and a member of the advisory board for the Quality, Statistics and Reliability section of the Institute for Operations Research and the Management Sciences (INFORMS). He was also a co-Editor of The Annals of Statistics and has served on numerous editorial boards. He was named a Senior Fellow of the Institute for Theoretical Research at ETH Zurich (2020), a Medallion Lecturer of IMS (2018), and a recipient of the William F. Sharpe Award (2024; JFQA), Leo Breiman Junior Researcher Award (2017; American Statistical Association), the Guy Medal in Bronze (2014; Royal Statistical Society), and CAREER Award (2009; US National Science Foundation).

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Day 1:    14:20-15:10  –  The Estimation–Efficiency Frontier in Portfolio Complexity