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Saving Markowitz: A Risk Parity approach based on the Cauchy Interlacing Theorem

Fernando Fernandes () and Rodrigo De Losso, Rogerio Oliveira, Angelo J D Soto, Pedro D Cavalcanti, Gabriel M S Campos
Authors registered in the RePEc Author Service: Rodrigo De-Losso

No 2020_13, Working Papers, Department of Economics from University of São Paulo (FEA-USP)

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 (search for similar items in EconPapers)
JEL-codes: C38 C61 G11 G17 (search for similar items in EconPapers)
Date: 2020-08-18
New Economics Papers: this item is included in nep-ore and nep-rmg
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