Conditional Value-at-Risk Vs. Value-at-Risk to Multi-Objective Portfolio Optimization

Bartosz T. Sawik

doi:10.1108/S0276-8976(2012)0000015016

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Applications of Management Science

ISSN: 0276-8976
Series editor(s): Professor Kenneth D. Lawrence

Subject Area: Management Science/Management Studies

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Conditional Value-at-Risk Vs. Value-at-Risk to Multi-Objective Portfolio Optimization

Document Information:
Title:	Conditional Value-at-Risk Vs. Value-at-Risk to Multi-Objective Portfolio Optimization
Author(s):	Bartosz T. Sawik
Volume:	15 Editor(s): Kenneth D. Lawrence, Gary Kleinman ISBN: 978-1-78052-100-8 eISBN: 978-1-78052-101-5
Citation:	Bartosz T. Sawik (2012), Conditional Value-at-Risk Vs. Value-at-Risk to Multi-Objective Portfolio Optimization, in Kenneth D. Lawrence, Gary Kleinman (ed.) Applications of Management Science (Applications of Management Science, Volume 15), Emerald Group Publishing Limited, pp.277-305
DOI:	10.1108/S0276-8976(2012)0000015016 (Permanent URL)
Publisher:	Emerald Group Publishing Limited
Article type:	Chapter Item
Abstract:	This chapter presents a multi-criteria portfolio model with the expected return as a performance measure and the expected worst-case return as a risk measure. The problems are formulated as a single-objective linear program, as a bi-objective linear program, and as a triple-objective mixed integer program. The problem objective is to allocate the wealth on different securities to optimize the portfolio return. The portfolio approach has allowed the two popular financial engineering percentile measures of risk, value-at-risk (VaR) and conditional value-at-risk (CVaR) to be applied. The decision-maker can assess the value of portfolio return, the risk level, and the number of assets, and can decide how to invest in a real-life situation comparing with ideal (optimal) portfolio solutions. The concave efficient frontiers illustrate the trade-off between the conditional value-at-risk and the expected return of the portfolio. Numerical examples based on historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided. The computational experiments prove that both proposed linear and mixed integer programming approaches provide the decision-maker with a simple tool for evaluating the relationship between the expected and the worst-case portfolio return.