EURO 2024 Copenhagen
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2936. Achieving robustness by searching for the right amount of shrinkage in minimum variance portfolios

Invited abstract in session WC-63: Applications to Economics and Finance, stream OR in Banking, Finance and Insurance: New Tools for Risk Management.

Wednesday, 12:30-14:00
Room: S14 (building: 101)

Authors (first author is the speaker)

1. Xiang Zhao
School of Mathematical Sciences, University of Southampton
2. Selin Ahipasaoglu
University of Southampton

Abstract

We study the minimum variance portfolio optimisation problem, wherein the covariance matrix is subject to a degree of uncertainty, possibly due to estimation errors and the presence of outliers. Classic solutions mitigate such errors through a rank-one shrinkage matrix, constructed using dual variables from a related constrained optimisation problem. Inspired by this, we propose a model that permits varying degrees of matrix shrinkage and identifies the most effective shrinkage scale based on the in-sample performance.Moreover, we identify sufficient conditions that guarantee that the updated (shrunk) covariance matrix remains positive semi-definite, and obtain a practical range for the scale of the shrinkage.
Our numerical experiments on out-of-sample data demonstrate that portfolios generated by our model typically exhibit lower levels of short selling and higher Sharpe ratios compared to existing methods. Additionally, they outperform in key risk metrics, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). This highlights our approach's effectiveness in addressing estimation uncertainties and its potential to redefine investment strategies in volatile markets.

Keywords

Status: accepted

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