James-Stein for eigenvectors: reducing the optimization bias in Markowitz portfolios

Abstract:

We identify and reduce bias in the leading sample eigenvector of a high-dimensional covariance matrix of correlated variables. Our analysis illuminates how error in an estimated covariance matrix corrupts optimization. It may be applicable in finance, machine learning and genomics.

Biography:

Lisa Goldberg is Head of Research at Aperio and Managing Director at BlackRock.  She is Professor of the Practice of Economics at University of California, Berkeley, where she co-directs the Center for Data Analysis in Risk, an industry partnership that supports research at the intersection of financial economics and data science. Lisa is a mathematician whose research has touched topology, dynamical systems, quantitative finance, sports analytics, personalized investing and high-dimensional statistics.  She is the co-author of Portfolio Risk Management,  published by Princeton University Press in 2010, and inventor on five patents. Lisa is on track to complete a swim around the equator, roughly 40,000km, in 2036.