Work

Minimum VaR and minimum CVaR optimal portfolios: The case of singular covariance matrix

Year: 2025

Type: article

Abstract: This paper examines optimal portfolio selection using quantile-based risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We address the case of a singular covariance matrix of asset returns, which may arise due to potential multicollinearity and strong correlations. This leads to an optimization problem with infinitely many solutions. An analytical form for a general solution is derived, along with a unique solution that minimizes the L 2 -norm. We show that the general solution reduces to the standard optimal portfolio for VaR and CVaR when the covariance matrix is non-singular. We also provide a brief discussion of the efficient frontier in this context. Finally, we present a real-data example based on the weekly log returns of assets included in the S&P 500 index.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2025.100557

Authors: Mårten Gulliksson, Stepan Mazur, Anna Oleynik

Institutions: Örebro University, University of Bergen

Language: English

Topic: Risk and Portfolio Optimization

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $1,770

Funders: Equinor, Örebro Universitet, Universitetet i Bergen