On Monday 17 June, 2019, Professor Michael Wolf from the University of Zurich, Switzerland delivered a public lecture at VIASM from 3pm on the topic of portfolio selection in high dimension using shrinkage estimators of covariance matrix of asset returns.

Many econometric and data-science applications require a reliable estimate of the covariance matrix in high dimension, such as Markowitz portfolio selection. 

Markowitz portfolio selection is a well-known problem which attracts interest from investors to propose performant investment strategies. This problem was pioneered by Harry Markowitz in his paper "Portfolio Selection," published in 1952 by the Journal of Finance. He was later awarded a Nobel Prize in Economics in 1990 for developing the Modern Portfolio Theory. Modern Portfolio Theory is a theory on how risk-averse investors can construct portfolios to maximize expected return based on a given level of market risk, emphasizing that risk is an inherent part of higher reward. According to the theory, it's possible to construct an "efficient frontier" of optimal portfolios offering the maximum possible expected return for a given level of risk. Likewise, given a desired level of expected return, an investor can construct a portfolio with the lowest possible risk, based on statistical measures such as variance and covariance matrix. 

When the number of variables is of the same magnitude as the number of observations, this constitutes a difficult estimation problem; the sample covariance matrix certainly will not do. 

In this lecture Professor Michael Wolf reviewed his research works in this area going back more than 15 years. His research team promoted both linear and nonlinear shrinkage estimators. Especially nonlinear shrinkage can deliver a superior level of performance improvement, especially if overlaid with stylized facts such as time-varying co-volatility or factor models.

Michael Wolf is a Professor of Econometrics and Applied Statistics at the University of Zurich, and holds a Ph.D. in Statistics from Stanford University. His research has been published in leading journals in Statistics, Econometrics and Finance, such as The Annals of Statistics, Biometrika, Econometrica, Journal of the American Statistical Association, and The Review of Financial Studies. He also got some consulting experience around the world.

Slides: https://drive.google.com/drive/u/0/folders/1mzaBfzmafXnK9uvj72o_XzXlxHmkuCLV