Saving Markowitz: A Risk Parity Approach Based on the Cauchy Interlacing Theorem

25 Pages Posted: 19 Aug 2020

See all articles by Fernando Fernandes

Fernando Fernandes

University of São Paulo

Rogerio Oliveira

Constancia Invest

Rodrigo De-Losso

University of São Paulo (USP) - Department of Economics

Angelo J. D. Soto

affiliation not provided to SSRN

Pedro Delano Cavalcanti

Rio de Janeiro State University - Department of Physics and Astronomy

Gabriel M. S. Campos

affiliation not provided to SSRN

Date Written: May 17, 2020

Abstract

It is well known that Markowitz Portfolio Optimization often leads to unreasonable and unbalanced portfolios that are optimal in-sample but perform very poorly out-of-sample. There is a strong relationship between these poor returns and the fact that covariance matrices that are used within the Markowitz framework are degenerated and ill-posed, leading to unstable results by inverting them, as a consequence of very small eigenvalues. In this paper we circumvent this problem in two steps: the enhancement of traditional risk parity techniques, which consider only volatility, aiming to avoid matrix inversions (including the widespread Naive Risk Parity model) within the Markowitz framework; the preservation of the correlation structure, as much as possible, aiming to isolate a "healthy" portion of the correlation matrix, that can be inverted without generating unstable and risky portfolios, aiming to rescue the original Markowitz framework, by means of using the Cauchy Interlacing Theorem. Using Brazilian and US market data, we show that the discussed framework enables one to build portfolios that outperform the traditional and the newest risk parity techniques.

Keywords: Markowitz, Cauchy Interlacing Theorem, NRP, CIRP

JEL Classification: C38, C61, G11, G17

Suggested Citation

Fernandes, Fernando and Oliveira, Rogerio and De-Losso, Rodrigo and Jonathan Diaz Soto, Angelo and Delano Cavalcanti, Pedro and Moreira da Silva Campos, Gabriel, Saving Markowitz: A Risk Parity Approach Based on the Cauchy Interlacing Theorem (May 17, 2020). Available at SSRN: https://ssrn.com/abstract=3654300 or http://dx.doi.org/10.2139/ssrn.3654300

Fernando Fernandes

University of São Paulo ( email )

Brazil

Rogerio Oliveira

Constancia Invest ( email )

Rua Joaquim Floriano 100
sala 141
São Paulo, São Paulo 04662-002
Brazil

Rodrigo De-Losso (Contact Author)

University of São Paulo (USP) - Department of Economics ( email )

Av. Prof. Luciano Gualberto 908
Sao Paulo SP, 05508-010
Brazil
551130930957 (Phone)

Angelo Jonathan Diaz Soto

affiliation not provided to SSRN

Pedro Delano Cavalcanti

Rio de Janeiro State University - Department of Physics and Astronomy

Brazil

Gabriel Moreira da Silva Campos

affiliation not provided to SSRN

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