Characterizing compromise solutions for investors with uncertain risk preferences

[EN] The optimum portfolio selection for an investor with particular preferences was proven to lie on the normalized efficient frontier between two bounds defined by the Ballestero (1998) bounding theorem. A deeper understanding is possible if the decision-maker is provided with visual and quantitative techniques. Here, we derive useful insights as a way to support investor's decision-making through: (i) a new theorem to assess balance of solutions; (ii) a procedure and a new plot to deal with discrete efficient frontiers and uncertain risk preferences; and (iii) two quality metrics useful to predict long-run performance of investors.Work partially funded by projects Collectiveware TIN2015-66863-C2-1-R (MINECO/FEDER) and 2014 SGR 118Salas-Molina, F.; Rodriguez-Aguilar, JA.; Pla Santamaría, D. (2019). Characterizing compromise solutions for investors with uncertain risk preferences. Operational Research. 19(3):661-677. https://doi.org/10.1007/s12351-017-0309-6S661677193Amiri M, Ekhtiari M, Yazdani M (2011) Nadir compromise programming: a model for optimization of multi-objective portfolio problem. Expert Syst Appl 38(6):7222–7226Ballestero E (1998) Approximating the optimum portfolio for an investor with particular preferences. J Oper Res Soc 49:998–1000Ballestero E (2007) Compromise programming: a utility-based linear-quadratic composite metric from the trade-off between achievement and balanced (non-corner) solutions. Eur J Oper Res 182(3):1369–1382Ballestero E, Pla-Santamaria D (2004) Selecting portfolios for mutual funds. Omega 32(5):385–394Ballestero E, Pla-Santamaria D, Garcia-Bernabeu A, Hilario A (2015) Portfolio selection by compromise programming. In: Ballestero E, Pérez-Gladish B, Garcia-Bernabeu A (eds) Socially responsible investment. A multi-criteria decision making approach, vol 219. Springer, Switzerland, pp 177–196Ballestero E, Romero C (1996) Portfolio selection: a compromise programming solution. J Oper Res Soc 47(11):1377–1386Ballestero E, Romero C (1998) Multiple criteria decision making and its applications to economic problems. Kluwer Academic Publishers, BerlinBilbao-Terol A, Pérez-Gladish B, Arenas-Parra M, Rodríguez-Uría MV (2006) Fuzzy compromise programming for portfolio selection. Appl Math Comput 173(1):251–264Bravo M, Ballestero E, Pla-Santamaria D (2012) Evaluating fund performance by compromise programming with linear-quadratic composite metric: an actual case on the caixabank in spain. J Multi-Criteria Decis Anal 19(5–6):247–255Ehrgott M, Klamroth K, Schwehm C (2004) An MCDM approach to portfolio optimization. Eur J Oper Res 155(3):752–770Fawcett T (2006) An introduction to ROC analysis. Pattern Recognit Lett 27(8):861–874Hernández-Orallo J, Flach P, Ferri C (2013) ROC curves in cost space. Mach Learn 93(1):71–91Markowitz H (1952) Portfolio selection. J Finance 7(1):77–91Pla-Santamaria D, Bravo M (2013) Portfolio optimization based on downside risk: a mean-semivariance efficient frontier from dow jones blue chips. Ann Oper Res 205(1):189–201Ringuest JL (1992) Multiobjective optimization: behavioral and computational considerations. Springer Science & Business Media, BerlinSteuer RE, Qi Y, Hirschberger M (2007) Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection. Ann Oper Res 152(1):297–317Xidonas P, Mavrotas G, Krintas T, Psarras J, Zopounidis C (2012) Multicriteria portfolio management. Springer, BerlinYu P-L (1973) A class of solutions for group decision problems. Manag Sci 19(8):936–946Yu P-L (1985) Multiple criteria decision making: concepts, techniques and extensions. Plenum Press, BerlinZeleny M (1982) Multiple criteria decision making. McGraw-Hill, New Yor

A compromise based fuzzy goal programming approach with satisfaction function for multi-objective portfolio optimisation

In this paper we investigate a multi-objective portfolio selection model with three criteria: risk, return and liquidity for investors. Non-probabilistic uncertainty factors in the market, such as imprecision and vagueness of investors’ preference and judgement are simulated in the portfolio selection process. The liquidity of portfolio cannot be accurately predicted in the market, and thus is measured by fuzzy set theory. Invertors’ individual preference and judgement are cooperated in the decision making process by using satisfaction functions to measure the objectives. A compromise based goal programming approach is applied to find compromised solutions. By this approach, not only can we obtain quality solutions in a reasonable computational time, but also we can achieve a trade-off between the objectives according to investors’ preference and judgement to enable a better decision making. We analyse the portfolio strategies obtained by using the proposed simulation approach subject to different settings in the satisfaction functions

FUZZY LOGIC AND COMPROMISE PROGRAMMING IN PORTFOLIO MANAGEMENT

The objective of this paper is to develop a portfolio optimization technique that is simple enough for an individual with little knowledge of economic theory to systematically determine his own optimized portfolio. A compromise programming approach and a fuzzy logic approach are developed as alternatives to the traditional EV model.Agricultural Finance,

Strict Solution Method for Linear Programming Problem with Ellipsoidal Distributions under Fuzziness

This paper considers a linear programming problem with ellipsoidal distributions including fuzziness. Since this problem is not well-defined due to randomness and fuzziness, it is hard to solve it directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed model is transformed into the deterministic equivalent problems. Furthermore, since it is difficult to solve the main problem analytically and efficiently due to nonlinear programming, the solution method is constructed introducing an appropriate parameter and performing the equivalent transformations

Multi crteria decision making and its applications : a literature review

This paper presents current techniques used in Multi Criteria Decision Making (MCDM) and their applications. Two basic approaches for MCDM, namely Artificial Intelligence MCDM (AIMCDM) and Classical MCDM (CMCDM) are discussed and investigated. Recent articles from international journals related to MCDM are collected and analyzed to find which approach is more common than the other in MCDM. Also, which area these techniques are applied to. Those articles are appearing in journals for the year 2008 only. This paper provides evidence that currently, both AIMCDM and CMCDM are equally common in MCDM

Encompassing statistically unquantifiable randomness in goal programming: an application to portfolio selection

[EN] Random events make multiobjective programming solutions vulnerable to changes in input data. In many cases statistically quantifiable information on variability of relevant parameters may not be available for decision making. This situation gives rise to the problem of obtaining solutions based on subjective beliefs and a priori risk aversion to random changes. To solve this problem, we propose to replace the traditional weighted goal programming achievement function with a new function that considers the decision maker's perception of the randomness associated with implementing the solution through the use of a penalty term. This new function also implements the level of a priori risk aversion based around the decision maker's beliefs and perceptions. The proposed new formulation is illustrated by means of a variant of the mean absolute deviation portfolio selection model. As a result, difficulties imposed by the absence of statistical information about random events can be encompassed by a modification of the achievement function to pragmatically consider subjective beliefs.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. s This work is devoted to the memory of Professor Enrique Ballestero for his selfess dedication to it.Bravo Selles, M.; Jones, D.; Pla Santamaría, D.; Salas-Molina, F. (2022). Encompassing statistically unquantifiable randomness in goal programming: an application to portfolio selection. Operational Research (Online). 22(5):5685-5706. https://doi.org/10.1007/s12351-022-00713-156855706225Abdelaziz FB, Aouni B, El Fayedh R (2007) Multi-objective stochastic programming for portfolio selection. Eur J Oper Res 177(3):1811–1823Abdelaziz FB, El Fayedh R, Rao A (2009) A discrete stochastic goal program for portfolio selection: the case of united arab emirates equity market. 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Multi-objective portfolio optimization of mutual funds under downside risk measure using fuzzy theory

Mutual fund is one of the most popular techniques for many people to invest their funds where a professional fund manager invests people's funds based on some special predefined objectives; therefore, performance evaluation of mutual funds is an important problem. This paper proposes a multi-objective portfolio optimization to offer asset allocation. The proposed model clusters mutual funds with two methods based on six characteristics including rate of return, variance, semivariance, turnover rate, Treynor index and Sharpe index. Semivariance is used as a downside risk measure. The proposed model of this paper uses fuzzy variables for return rate and semivariance. A multi-objective fuzzy mean-semivariance portfolio optimization model is implemented and fuzzy programming technique is adopted to solve the resulted problem. The proposed model of this paper has gathered the information of mutual fund traded on Nasdaq from 2007 to 2009 and Pareto optimal solutions are obtained considering different weights for objective functions. The results of asset allocation, rate of return and risk of each cluster are also determined and they are compared with the results of two clustering methods