Title: Minimising value-at-risk in a portfolio optimisation problem using a multi-objective genetic algorithm

Authors: Eva Alfaro-Cid; J. Samuel Baixauli-Soler; Matilde O. Fernandez-Blanco

Addresses: Instituto Tecnológico de Informática, Camino de Vera s/n, 46022 Valencia, Spain. ' Department of Management and Finance, University of Murcia, Campus de Espinardo, 30100 Murcia, Spain. ' Department of Business Finance, University of Valencia, Avda Tarongers s/n, 46022 Valencia, Spain

Abstract: In this paper, we develop a general framework for market risk optimisation that focuses on VaR. The reason for this choice is the complexity and problems associated with risk return optimisation (non-convex and non-differential objective function). Our purpose is to obtain VaR efficient frontiers using a multi-objective genetic algorithm (GA) and to show the potential utility of the algorithm to obtain efficient portfolios when the risk measure does not allow calculating an optimal solution. Furthermore, we measure differences between VaR efficient frontiers and variance efficient frontiers in VaR-return space and we evaluate out-sample capacity of portfolios on both bullish and bearish markets. The results indicate the reliability of VaR-efficient portfolios on both bullish and bearish markets and a significant improvement over Markowitz efficient portfolios in the VaR-return space. The improvement decreases as the portfolios level of risk increases. In this particular case, efficient portfolios do not depend on the risk measure minimised.

Keywords: artificial intelligence; investment criteria; portfolio selection; genetic algorithms; value at risk; VaR; market risk; risk minimisation; portfolio optimisation; multi-objective algorithms; complexity; risk return; on-convex objective functions; non-differential objective functions; efficient portfolios; optimal solutions; variance efficient frontiers; bull markets; bear markets; Harry Markowitz; stock indices; United States; USA; Canada; Japan; UK; United Kingdom; France; Germany; Spain; Netherlands; Holland; Sweden; risk assessment; risk management.

DOI: 10.1504/IJRAM.2011.043701

International Journal of Risk Assessment and Management, 2011 Vol.15 No.5/6, pp.453 - 477

Received: 22 Oct 2010
Accepted: 21 Jun 2011

Published online: 28 Feb 2015 *

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