Robust Portfolio Optimization with Multivariate Copulas: A Worst-Case CVaR Approach

20 Pages Posted: 28 Nov 2017 Last revised: 7 Aug 2018

See all articles by Fernando B. Sabino da Silva

Fernando B. Sabino da Silva

Federal University of Rio Grande do Sul (UFRGS) - Statistics Department

Flávio Ziegelman

Flávio Ziegemann

Date Written: November 22, 2017

Abstract

Using data from the S&P 500 stocks from 1990 to 2015, we address the uncertainty of distribution of assets’ returns in Conditional Value-at-Risk (CVaR) minimization model by applying multidimensional mixed Archimedean copula function and obtaining its robust counterpart. We implement a dynamic investing viable strategy where the portfolios are optimized using three different length of rolling calibration windows. The out-of-sample performance is evaluated and compared against two benchmarks: a multidimensional Gaussian copula model and a constant mix portfolio. Our empirical analysis shows that the Mixed Copula-CVaR approach generates portfolios with better downside risk statistics for any rebalancing period and it is more profitable than the Gaussian Copula-CVaR and the 1/N portfolios for daily and weekly rebalancing. To cope with the dimensionality problem we select a set of assets that are the most diversified, in some sense, to the S&P 500 index in the constituent set. The accuracy of the VaR forecasts is determined by how well they minimize a capital requirement loss function. In order to mitigate data-snooping problems, we apply a test for superior predictive ability to determine which model significantly minimizes this expected loss function. We find that the minimum average loss of the mixed Copula-CVaR approach is smaller than the average performance of the Gaussian Copula-CVaR.

Keywords: Asset Allocation; Finance; Gaussian Copula; Linear Programming; Mixed Copula; Risk Management; S&P 500; Scenarios; WCCVaR

JEL Classification: G11, G12, G17

Suggested Citation

B. Sabino da Silva, Fernando and Ziegelmann, Flávio, Robust Portfolio Optimization with Multivariate Copulas: A Worst-Case CVaR Approach (November 22, 2017). Available at SSRN: https://ssrn.com/abstract=3076283 or http://dx.doi.org/10.2139/ssrn.3076283

Fernando B. Sabino da Silva (Contact Author)

Federal University of Rio Grande do Sul (UFRGS) - Statistics Department ( email )

Bento Goncalves, 9500, Ave
Porto Alegre, RS 91509-900
Brazil

Flávio Ziegelmann

Flávio Ziegemann ( email )

Rua Washington Luiz, 855. Centro
Porto Alegre - RS, 90010-460
Brazil

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