Portfolio Risk and the Quantum Majorization of Correlation Matrices

22 Pages Posted: 12 Jan 2019 Last revised: 10 Feb 2020

See all articles by Andrea Fontanari

Andrea Fontanari

Delft University of Technology - Delft Institute of Applied Mathematics (DIAM)

Iddo Eliazar

Tel Aviv University

Pasquale Cirillo

ZHAW School of Management and Law

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Date Written: January 3, 2019

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.

Keywords: quantum majorization, portfolio risk, risk measures, order

JEL Classification: B23, C46, D3, G32

Suggested Citation

Fontanari, Andrea and Eliazar, Iddo and Cirillo, Pasquale and Oosterlee, Cornelis W., Portfolio Risk and the Quantum Majorization of Correlation Matrices (January 3, 2019). Available at SSRN: https://ssrn.com/abstract=3309585 or http://dx.doi.org/10.2139/ssrn.3309585

Andrea Fontanari

Delft University of Technology - Delft Institute of Applied Mathematics (DIAM) ( email )

Mekelweg 4
Delft, Holland 2628
Netherlands

Iddo Eliazar

Tel Aviv University ( email )

Pasquale Cirillo (Contact Author)

ZHAW School of Management and Law ( email )

St.-Georgen-Platz 2
Winterthur, 8401
Switzerland

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Vredenburg 138
Utrecht, 3511 BG
Netherlands

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