The Department of Finance and Risk Engineering welcomes Alex Shkolnik, Assistant Professor at UC Santa Barbara, to the BQE Lecture Series.
James-Stein Estimation of Minimum Variance Portfolios
In quantitative finance, estimated covariance matrices are routinely used to construct portfolios with mean-variance optimization. It is widely recognized, however, that the embedded sampling error tricks the optimizer into constructing distorted and highly inefficient portfolios. This problem is further amplified when the number of securities vastly exceeds the number of observations. We quantify this inefficiency with a metric we call the optimization bias which depends primarily on the leading eigenvector of a sample covariance matrix. Under a spiked covariance model, we prove that the optimization bias may be completely erased given just two observations of the security return but provided that the number of securities tends to infinity. We illustrate the theory with numerical simulations that provide further insight into the behavior of the proposed estimator in practice. We conclude the talk by establishing rich connections between the Stein paradox in statistics, the beta adjustments commonly used in the financial industry, and the James-Stein estimator of a principal component.
Alex Shkolnik is an Assistant Professor at the Department of Statistics and Applied Probability at the University of California, Santa Barbara, and a Research Fellow at the Consortium for Data Analytics in Risk at the University of California, Berkeley where he was a postdoctoral scholar. Alex received his Ph.D. in computational mathematics and engineering from Stanford University in 2015. His research interests include Monte Carlo simulation, high-dimensional statistics, and quantitative financial risk management.