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Preference-based evolutionary multi-objective optimization for portfolio selection: a new credibilistic model under investor preferences

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Abstract

We propose a new credibility portfolio selection model, in which a measure of loss aversion is introduced as an objective function, joint to the expected value of the returns and the below-mean absolute semi-deviation as a risk measure. The uncertainty of the future returns is directly approximated using the historical returns on the portfolios, so the uncertain return on a given portfolio is modeled as an LR-power fuzzy variable. Quantifying the uncertainty by means of a credibility distribution allows us to measure the investors’ loss aversion as the credibility of achieving a non-positive return, which is better perceived by investors than other measures of risk. Furthermore, we analyze the relationships between the three objective functions, showing that the risk measure and the loss aversion function are practically uncorrelated. Thus, the information provided by these criteria do not overlap each other. In order to generate several non-dominated portfolios taking into account the investor’s preferences and that the problem is non-linear and non-convex, we apply up to three preference-based EMO algorithms. These algorithms allow to approximate a part of the Pareto optimal front called region of interest. We analyze three investor profiles taking into account their loss-adverse attitudes: conservative, cautious and aggressive. A computational study is performed with data of the Spanish stock market, showing the important role played by the loss aversion function to generate a diversified set of non-dominated portfolios fitting the expectations of each investor.

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Notes

  1. Although IBEX35 has 35 assets, there were two assets which were not included in the index through all the time window considered.

  2. jMetal is an open source object-oriented Java-based framework for multi-objective optimization using meta-heuristic algorithms. It can be downloaded at http://jmetal.sourceforge.net/.

  3. In our computational tests, \({\mathbf {r}}\) has been set as follows. If the reference point used \({\mathbf {q}}\) is achievable, then \({\mathbf {r}} = {\mathbf {q}}\). Providing that \({\mathbf {q}}\) is unachievable, \({\mathbf {r}}\) is obtained using the worst objective function values achieved by all the solutions found in the region of interest by the algorithms in all runs.

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Acknowledgements

Ana B. Ruiz is recipient of a Post-Doctoral fellowship of “Captación de Talento para la Investigación” at Universidad de Málaga (Spain). Rubén Saborido is a Post-Doctoral fellow at Concordia University (Canada).

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Authors and Affiliations

  1. Department of Applied Economics (Mathematics), Universidad de Málaga, Málaga, Spain

    Ana B. Ruiz & Mariano Luque

  2. Department of Computer Science and Software Engineering, Concordia University, Montreal, Canada

    Rubén Saborido

  3. Department of Statistics and Operational Research, Universitat de València, Valencia, Spain

    José D. Bermúdez & Enriqueta Vercher

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  1. Ana B. Ruiz
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Correspondence to Enriqueta Vercher.

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This work has been supported by the Spanish Ministry of Economy and Competitiveness (Projects ECO2017-88883-R and MTM2017-83850-P), co-financed by FEDER funds.

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Ruiz, A.B., Saborido, R., Bermúdez, J.D. et al. Preference-based evolutionary multi-objective optimization for portfolio selection: a new credibilistic model under investor preferences. J Glob Optim 76, 295–315 (2020). https://doi.org/10.1007/s10898-019-00782-1

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