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

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

Mean-risk models using two risk measures: A multi-objective approach

This paper proposes a model for portfolio optimisation, in which distributions are characterised and compared on the basis of three statistics: the expected value, the variance and the CVaR at a specified confidence level. The problem is multi-objective and transformed into a single objective problem in which variance is minimised while constraints are imposed on the expected value and CVaR. In the case of discrete random variables, the problem is a quadratic program. The mean-variance (mean-CVaR) efficient solutions that are not dominated with respect to CVaR (variance) are particular efficient solutions of the proposed model. In addition, the model has efficient solutions that are discarded by both mean-variance and mean-CVaR models, although they may improve the return distribution. The model is tested on real data drawn from the FTSE 100 index. An analysis of the return distribution of the chosen portfolios is presented

Processing second-order stochastic dominance models using cutting-plane representations

This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)

Combining Alpha Streams with Costs

We discuss investment allocation to multiple alpha streams traded on the same execution platform with internal crossing of trades and point out differences with allocating investment when alpha streams are traded on separate execution platforms with no crossing. First, in the latter case allocation weights are non-negative, while in the former case they can be negative. Second, the effects of both linear and nonlinear (impact) costs are different in these two cases due to turnover reduction when the trades are crossed. Third, the turnover reduction depends on the universe of traded alpha streams, so if some alpha streams have zero allocations, turnover reduction needs to be recomputed, hence an iterative procedure. We discuss an algorithm for finding allocation weights with crossing and linear costs. We also discuss a simple approximation when nonlinear costs are added, making the allocation problem tractable while still capturing nonlinear portfolio capacity bound effects. We also define "regression with costs" as a limit of optimization with costs, useful in often-occurring cases with singular alpha covariance matrix.Comment: 21 pages; minor misprints corrected; to appear in The Journal of Ris

Portfolio optimisation models and properties of return distributions

Mean-risk models have been widely used in portfolio optimisation. However, such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio which is nondominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties. The problem is multi-objective and is transformed into a single objective problem by using the reference point method, in which target levels, known as aspiration points, are specified for the objective function values. A model is proposed in which the aspiration points relate to ordered return outcomes of the portfolio return. The model is extended by additionally specifying reservation points, which act pre-emptively in the optimisation. The theoretical properties of the models are studied. The performance of the models on real data drawn from the Hang Seng index is also investigated