SEM 217: Alec Kercheval, Florida State University: The James-Stein estimator for eigenvectors

Tuesday, October 4th @ 11:00-12:30 PM (ONLINE)

Portfolio risk forecasts require an estimate of the covariance matrix of asset returns, often for a large number of assets. When only a small number of observations are available, we are in the high-dimension-low-sample-size (HL) regime in which estimation error dominates. Factor models are used to decrease the dimension, but the factors still need to be estimated. We describe a shrinkage estimator for the first principal component, called James-Stein for Eigenvectors (JSE), that is parallel to the famous James-Stein estimator for a collection of averages. In the context of a 1-factor model, JSE substantially improves optimization-based metrics for the minimum variance portfolio. With certain extra information, JSE is a consistent estimator of the leading eigenvector. This is based on joint work with Lisa Goldberg, Hubeyb Gurdogan, and Alex Shkolnik.