A Comparison of Risk Measures for Portfolio Optimization with Cardinality Constraints

37 Pages Posted: 25 Aug 2022

See all articles by Henrique Ramos

Henrique Ramos

Universidade Federal do Rio Grande do Sul (UFRGS)

Marcelo Righi

Universidade Federal do Rio Grande do Sul (UFRGS)

Pablo Cristini Guedes

Universidade Federal do Rio Grande do Sul (UFRGS)

Fernanda Maria Müller

Universidade Federal do Rio Grande do Sul (UFRGS)

Multiple version iconThere are 2 versions of this paper

Abstract

Ever since the introduction of Markowitz’s classical quadratic programming problem, transforming portfolio optimization into a linear programming (LP) problem has drawn much attention from researchers and practitioners, given the tractability of LP. However, using non-linear risk measures and including real features and frictions may pose a challenge. In this paper, we solve the optimization problem of minimum portfolio risk for seven measures using linear programming under cardinality constraints. The risk measures used are Expected Loss, Expected Loss Deviation, Expected Shortfall, Shortfall Deviation Risk, Expectile Value at Risk, Deviation Expectile Value at Risk, and Maximum Loss. We assess the out-of-sample performance of seven risk-optimized portfolios with a maximum size of 20 assets for S&P 100 components from 2010 to mid-2020. After subtracting transaction costs, the Expected Loss Deviation portfolios have shown superior performance in terms of diversification and risk, the Maximum Loss portfolios have presented higher Sharpe ratio, the Expected Loss portfolios have higher absolute returns, Sortino and STARR ratios, and the Expected Shortfall portfolios have presented lower Beta coefficients than the benchmark and other risk-based portfolios. All portfolios present significant alpha after adjusting for several risk factors. The main results hold for subperiod analysis, different cardinalities, and other rebalancing periods. Our results show that superior performance can be achieved with simple linearized optimization models with lower market exposure measure by the CAPM beta.

Keywords: cardinality constraints, coherent risk measures, Risk, linear portfolio optimization, EVaR

Suggested Citation

Ramos, Henrique and Righi, Marcelo and Guedes, Pablo Cristini and Muller, Fernanda Maria, A Comparison of Risk Measures for Portfolio Optimization with Cardinality Constraints. Available at SSRN: https://ssrn.com/abstract=4173701 or http://dx.doi.org/10.2139/ssrn.4173701

Henrique Ramos (Contact Author)

Universidade Federal do Rio Grande do Sul (UFRGS) ( email )

Av. Carlos Gomes 1111
Porto Alegre, Rio Grande do Sul 90480-004
Brazil

Marcelo Righi

Universidade Federal do Rio Grande do Sul (UFRGS) ( email )

Washington Luis, 855
Porto Alegre, Rio Grande do Sul 90010-460
Brazil

Pablo Cristini Guedes

Universidade Federal do Rio Grande do Sul (UFRGS) ( email )

Fernanda Maria Muller

Universidade Federal do Rio Grande do Sul (UFRGS)

Washington Luiz, 855
Porto Alegre, 90010-460
Brazil

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
48
Abstract Views
390
PlumX Metrics