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

IF 1.4 Q2 MATHEMATICS, APPLIED
Mårten Gulliksson , Stepan Mazur , Anna Oleynik
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引用次数: 0

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 L2-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.
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来源期刊
Results in Applied Mathematics
Results in Applied Mathematics Mathematics-Applied Mathematics
CiteScore
3.20
自引率
10.00%
发文量
50
审稿时长
23 days
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