Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/306787 
Year of Publication: 
2024
Series/Report no.: 
Working Paper No. 9/2024
Publisher: 
Örebro University School of Business, Örebro
Abstract: 
This paper examines optimal portfolio selection using quantile-based risk measures such as Valueat-Risk (VaR) and Conditional Value-at-Risk (CVaR). We address the case of a singular covariance matrix of asset returns, which 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 also show that the general solution reduces to the standard optimal portfolio for VaR and CVaR when the covariance matrix is non-singular.
Subjects: 
Minimum VaR portfolio
Minimum CVaR portfolio
Singular covariance matrix
Linear illposed problems
JEL: 
C58
G11
G32
Document Type: 
Working Paper

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