Robust multiobjective portfolio optimization: A minimax regret approach

doi:10.1016/j.ejor.2017.03.041

European Journal of Operational Research

Volume 262, Issue 1, 1 October 2017, Pages 299-305

https://doi.org/10.1016/j.ejor.2017.03.041 Get rights and content

Highlights

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A regret-based robustness measure, which can be applied to all Pareto solutions.
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Extension of the minimax regret criterion in multiobjective programming.
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Managerial usability for investment practitioners.
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Out-of-sample empirical testing with historical market data.

Abstract

An efficient frontier in the typical portfolio selection problem provides an illustrative way to express the tradeoffs between return and risk. Following the basic ideas of modern portfolio theory as introduced by Markowitz, security returns are usually extracted from past data. Our purpose in this paper is to incorporate future returns scenarios in the investment decision process. For representative points on the efficient frontier, the minimax regret portfolio is calculated, on the basis of the aforementioned scenarios. These points correspond to specific weight combinations. In this way, the areas of the efficient frontier that are more robust than others are identified. The underlying key-contribution is related to the extension of the conventional minimax regret criterion formulation, in multiobjective programming problems. The validity of the approach is verified through an illustrative empirical testing application on the Eurostoxx 50.

Section snippets

Introduction and problem setting

The classic methodological framework proposed by Markowitz (1952, 1959) has been the primary influence for the majority of financial models designed to provide a solution to the portfolio selection problem. Exclusively based on the criteria of return and risk, investors seek to minimize the expected variance of their portfolio for certain levels of expected return. The crucial assumption for this classic bi-objective approach to work is the accuracy of the estimates of return and covariance

Literature review

Recent developments in the field of portfolio theory imply that the knowledge of future returns and variances, delivered by classic point-estimation techniques, cannot be thoroughly trusted. Since risk and return are characterized by randomness, one should keep in mind that problem data could be described by a set of scenarios. Mulvey, Vanderbei, and Zenios (1995) were the first to work on models of mathematical optimization where data values come in sets of scenarios, while explaining the

Proposed model

It is well known that the minimax regret criterion is among the most popular criteria in decision sciences (Savage, 1954), along with the maximax, maximin, Hurwitz criterion, etc., where different scenarios are present. It actually aims at selecting the solution or alternative which is under the worst case closer to its scenario optimum. The minimax regret criterion provides less conservative solutions than the “pessimistic” approach of the maximin criterion (also used to express “robustness”).

Empirical testing

We use the 50 stocks of the Eurostoxx 50 the Europe's leading blue-chip index for the Eurozone, provides a high capitalization representation of supersector leaders in the Eurozone. The index covers 50 stocks from 12 Eurozone countries. The model is presented in Xidonas and Mavrotas (2014). We use five scenarios of return and risk evolution, all of which conceived in close cooperation with a team of portfolio managers. In the absence of actual decision makers we create 5 scenarios for the

Concluding remarks and discussion

Advances in portfolio management research highlight the growing momentum of robust portfolio optimization. In order to explore the portfolio stability and protect it against input uncertainty, new and effective robust tools need to be deployed and tested. Robust tools may not only be useful in theoretical research, but they also should come in hand for practical investors, as they will allow them to define uncertainty in input portfolio parameters, as they perceive it. In this work we equip the

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View full text

Innovative Applications of O.R.Robust multiobjective portfolio optimization: A minimax regret approach

Highlights

Abstract

Section snippets

Introduction and problem setting

Literature review

Proposed model

Empirical testing

Concluding remarks and discussion

Robust optimization, Princeton Series in Applied Mathematics

Robust multiperiod portfolio management in the presence of transaction costs

Computers & Operations Research

Optimization methods in finance

Robust portfolio optimization with value-at-risk-adjusted Sharpe ratios

Journal of Asset Management

Robustness of optimal portfolios under risk and stochastic dominance constraints

European Journal of Operational Research

Minmax robustness for multi-objective optimization problems

European Journal of Operational Research

Robust portfolios: Contributions from operations research and finance

Annals of Operations Research

Robust portfolio optimization and management

Robust multiobjective optimization & applications in portfolio optimization

European Journal of Operational Research

A practical guide to robust optimization

Omega

Robust optimization and portfolio selection: The cost of robustness

European Journal of Operational Research

Relative robust portfolio optimization

Problems in the application of portfolio selection models

Omega

Robust estimation of covariance and its application to portfolio optimization

Finance Research Letters

Optimisation and quantitative investment management

Journal of Asset Management

Composition of robust equity portfolios

Finance Research Letters

Recent developments in robust portfolios with a worst-case approach

Journal of Optimization Theory and Applications

What do robust equity portfolio models really do

Annals of Operations Research

Robust portfolios that do not tilt factor exposure

European Journal of Operational Research

Innovative Applications of O.R.
Robust multiobjective portfolio optimization: A minimax regret approach