Portfolio risk and the quantum majorization of correlation matrices

Andrea Fontanari; Iddo Eliazar; Pasquale Cirillo; Cornelis W. Oosterlee

doi:10.1093/imaman/dpaa011

Portfolio risk and the quantum majorization of correlation matrices

Andrea Fontanari^*, Iddo Eliazar, Pasquale Cirillo, Cornelis W. Oosterlee

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We propose quantum majorization as a way of comparing and ranking correlation matrices, with the aim of assessing portfolio risk in a unified framework. Quantum majorization is a partial order in the space of correlation matrices, which are evaluated through their spectra. We discuss the connections between quantum majorization and an important class of risk functionals, and we define two new risk measures able to capture interesting characteristics of portfolio risk.

Original language	English
Pages (from-to)	257-282
Number of pages	26
Journal	IMA Journal of Management Mathematics
Volume	32
Issue number	3
DOIs	https://doi.org/10.1093/imaman/dpaa011
Publication status	Published - 1 Jul 2021
Externally published	Yes

Keywords

correlation matrix
majorization
portfolio risk

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10.1093/imaman/dpaa011

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title = "Portfolio risk and the quantum majorization of correlation matrices",

abstract = "We propose quantum majorization as a way of comparing and ranking correlation matrices, with the aim of assessing portfolio risk in a unified framework. Quantum majorization is a partial order in the space of correlation matrices, which are evaluated through their spectra. We discuss the connections between quantum majorization and an important class of risk functionals, and we define two new risk measures able to capture interesting characteristics of portfolio risk.",

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AU - Eliazar, Iddo

AU - Cirillo, Pasquale

AU - Oosterlee, Cornelis W.

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Y1 - 2021/7/1

N2 - We propose quantum majorization as a way of comparing and ranking correlation matrices, with the aim of assessing portfolio risk in a unified framework. Quantum majorization is a partial order in the space of correlation matrices, which are evaluated through their spectra. We discuss the connections between quantum majorization and an important class of risk functionals, and we define two new risk measures able to capture interesting characteristics of portfolio risk.

AB - We propose quantum majorization as a way of comparing and ranking correlation matrices, with the aim of assessing portfolio risk in a unified framework. Quantum majorization is a partial order in the space of correlation matrices, which are evaluated through their spectra. We discuss the connections between quantum majorization and an important class of risk functionals, and we define two new risk measures able to capture interesting characteristics of portfolio risk.

KW - correlation matrix

KW - majorization

KW - portfolio risk

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DO - 10.1093/imaman/dpaa011

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JO - IMA Journal of Management Mathematics

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Portfolio risk and the quantum majorization of correlation matrices

Abstract

Keywords

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