Mathematical Finance & Financial Data Science Seminar
James Stein for eigenvectors
Speaker: Lisa Goldberg, University of California, Berkeley
Location: Online Zoom access provided to registrants
Date: Tuesday, March 22, 2022, 5:30 p.m.
Synopsis:
Estimated covariance matrices are widely used to construct portfolios with variance-minimizing optimization, yet the embedded sampling error produces portfolios with systematically underestimated variance. This effect is especially severe when the number of securities greatly exceeds the number of observations. In this high dimension low sample size (HL) regime, we show that a dispersion bias in the leading eigenvector of the estimated covariance matrix is a material source of distortion in the minimum variance portfolio. We correct the bias with the data-driven GPS (Global Positioning System) shrinkage estimator, which improves with the size of the market, and which is structurally identical to the James Stein estimator for a collection of averages. We illustrate the power of the GPS estimator with a numerical example, and conclude with open problems that have emerged from our research.
Bio:
CDAR co-Director Lisa Goldberg is Professor of the Practice of Economics at University of California, Berkeley and Director of Research at Aperio Group. Dr. Goldberg is a mathematician whose research integrates best practices from industry and academia. Her work has touched areas as diverse as topology, dynamical systems, quantitative finance, sports statistics and causal inference. She has published more than 50 articles and is co-author of a book, Portfolio Risk Management, which was published by Princeton University Press in 2010. Dr. Goldberg is inventor on five patents and has been awarded numerous research grants including an Alfred P. Sloan Fellowship and an NSF Visiting Professorship for Women. She has served on the editorial boards of four quantitative finance journals and two Springer book series. She is a member of the Advisory Council for the Museum of Mathematics. She serves as an arXiv moderator and is an expert judge for the Moskowitz Prize for Socially Responsible Investing.
Notes:
This event is free, but requires registration. Please click here to register. You will then receive the Zoom link by email about a day or so before the event.