Optimal Asset Allocation: A Worst Scenario Expectation Approach

Mean-variance criterion has long been the main stream approach in the optimal portfolio theory. The investors try to balance the risk and the return on their portfolio. In this paper, the deviation of the asset return from the investor’s expectation in the worst scenario is used as the measure of risk for portfolio selection. One important advantage of this approach is that the investors can base on their own knowledge, information, and preference on various risks, in addition to the asset’s volatility, to adjust their exposure to various risks. It also pinpoints one main concern of the investors when they invest, the amount they lose in the worst situation.     

Portfolio performance measurement using differential evolution

The basic problem in finance theory is the selection of an appropriate mix of assets in a portfolio in order to maximize portfolio expected return and subsequently to minimize portfolio risk. Another approach takes into account portfolio performance expressed by various measurement techniques e.g. Sharpe ratio, Treynor ratio, Jensen’s alpha, Information ratio, Sortino ratio, Omega function and Sharpe Omega ratio that are focused on determine the allocation of the available resources in the selected group of assets. This paper presents the alternative approach computing the weights of assets in portfolio assets based on the nonlinear measure techniques: Sortino ratio and Omega function. The proposed alternative includes principle of differential evolution from the group of evolutionary techniques. The experiments are set up on assets included in Dow Jones Industrial Average. Presented original approach enables using also other evolutionary algorithms in the area of portfolio selection based on different measurement techniques.     

Equal Risk Bounding is better than Risk Parity for portfolio selection

Risk Parity (RP), also called equally weighted risk contribution, is a recent approach to risk diversification for portfolio selection. RP is based on the principle that the fractions of the capital invested in each asset should be chosen so as to make the total risk contributions of all assets equal among them. We show here that the Risk Parity approach is theoretically dominated by an alternative similar approach that does not actually require equally weighted risk contribution of all assets but only an equal upper bound on all such risks. This alternative approach, called Equal Risk Bounding (ERB), requires the solution of a nonconvex quadratically constrained optimization problem. The ERB approach, while starting from different requirements, turns out to be strictly linked to the RP approach. Indeed, when short selling is allowed, we prove that an ERB portfolio is actually an RP portfolio with minimum variance. When short selling is not allowed, there is a unique RP portfolio and it contains all assets in the market. In this case, the ERB approach might lead to the RP portfolio or it might lead to portfolios with smaller variance that do not contain all assets, and where the risk contributions of each asset included in the portfolio is strictly smaller than in the RP portfolio. We define a new riskiness index for assets that allows to identify those assets that are more likely to be excluded from the ERB portfolio. With these tools we then provide an exact method for small size nonconvex ERB models and a very efficient and accurate heuristic for larger problems of this type. In the case of a common constant pairwise correlation among all assets, a closed form solution to the ERB model is obtained and used to perform a parametric analysis when varying the level of correlation. The practical advantages of the ERB approach over the RP strategy are illustrated with some numerical examples. Computational experience on real-world and on simulated data confirms accuracy and efficiency of our heuristic approach to the ERB model also in comparison with some state-of-the-art local and global optimization codes.     

A mixed R&D projects and securities portfolio selection model

The business environment is full of uncertainty. Allocating the wealth among various asset classes may lower the risk of overall portfolio and increase the potential for more benefit over the long term. In this paper, we propose a mixed single-stage R&D projects and multi-stage securities portfolio selection model. Specifically, we present a bi-objective mixed-integer stochastic programming model. Moreover, we use semi-absolute deviation risk functions to measure the risk of mixed asset portfolio. Based on the idea of moments approximation method via linear programming, we propose a scenario generation approach for the mixed single-stage R&D projects and multi-stage securities portfolio selection problem. The bi-objective mixed-integer stochastic programming problem can be solved by transforming it into a single objective mixed-integer stochastic programming problem. A numerical example is given to illustrate the behavior of the proposed mixed single stage R&D projects and multi-stage securities portfolio selection model.     

短期趋势判断与投资组合优选

针对股市非常有限的可预测性和投资组合优化时间窗口的选择问题,本文从股指趋势和个股收益率趋势类别两个层次上进行前瞻分析,并依据股指趋势判断和不同时间窗口对应的边际风险收益,提出投资组合优化计算的时间窗口选择规则,动态地进行资产组合优化。通过沪深A股及沪深300成份股两个样本集合的应用研究表明,考虑多层次短期趋势预测的动态投资组合选择方法能有效地改善资产组合绩效,是股市资产风险管理的有效方法之一。     

A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection

This paper presents a new procedure that extends genetic algorithms from their traditional domain of optimization to fuzzy ranking strategy for selecting efficient portfolios of restricted cardinality. The uncertainty of the returns on a given portfolio is modeled using fuzzy quantities and a downside risk function is used to describe the investor's aversion to risk. The fitness functions are based both on the value and the ambiguity of the trapezoidal fuzzy number which represents the uncertainty on the return. The soft-computing approach allows us to consider uncertainty and vagueness in databases and also to incorporate subjective characteristics into the portfolio selection problem. We use a data set from the Spanish stock market to illustrate the performance of our approach to the portfolio selection problem.     

A tail-revisited Markowitz mean-variance approach and a portfolio network centrality

A measure for portfolio risk management is proposed by extending the Markowitz mean-variance approach to include the left-hand tail effects of asset returns. Two risk dimensions are captured: asset covariance risk along risk in left-hand tail similarity and volatility. The key ingredient is an informative set on the left-hand tail distributions of asset returns obtained by an adaptive clustering procedure. This set allows a left tail similarity and left tail volatility to be defined, thereby providing a definition for the left-tail-covariance-like matrix. The convex combination of the two covariance matrices generates a “two-dimensional” risk that, when applied to portfolio selection, provides a measure of its systemic vulnerability due to the asset centrality. This is done by simply associating a suitable node-weighted network with the portfolio. Higher values of this risk indicate an asset allocation suffering from too much exposure to volatile assets whose return dynamics behave too similarly in left-hand tail distributions and/or co-movements, as well as being too connected to each other. Minimizing these combined risks reduces losses and increases profits, with a low variability in the profit and loss distribution. The portfolio selection compares favorably with some competing approaches. An empirical analysis is made using exchange traded fund prices over the period January 2006–February 2018.

     

IPSSIS: An integrated multicriteria decision support system for equity portfolio construction and selection

A fundamental principle of modern portfolio theory is that comparisons between portfolios are generally made using two criteria, corresponding to the first two moments of return distributions, namely the expected return and portfolio variance. According to this model and according to most of the portfolio models derived from the stochastic dominance approach, the group of portfolios open to comparisons is divided into two parts: on the one hand there are the efficient portfolios (those that are not dominated by any other portfolio in the group), and on the other, those that are dominated. In other words, these models do not solve for one optimal portfolio, but rather solve for an efficient set of portfolios, among which the investor must choose, given his preference system. One criticism over these models, which has often been addressed both by practitioners and academics, is that they fail to embody the objectives of the decision maker (DM), through the various stages of the decision process. Our purpose in this article is to present an integrated and innovative methodological approach for the construction and selection of equity portfolios, which will take into account the inherent multidimensional nature of the problem, while allowing the DM to incorporate his preferences in the decision process. The proposed approach, which grounds its basis on the field of multiple criteria decision making (MCDM) and more specifically on multiobjective mathematical programming (MMP), is implemented in the IPSSIS (Integrated Portfolio Synthesis and Selection Information System) decision support system (DSS). The validity of the proposed approach is tested through an illustrative application in the Athens Stock Exchange (ASE).     

Genetic algorithm-based multi-criteria project portfolio selection

Project portfolio selection is one of the most important decision-making problems for most organizations in project management and engineering management. Usually project portfolio decisions are very complicated when project interactions in terms of multiple selection criteria and preference information of decision makers (DMs) in terms of the criteria importance are taken into consideration simultaneously. In order to solve this complex decision-making problem, a multi-criteria project portfolio selection problem considering project interactions in terms of multiple selection criteria and DMs?? preferences is first formulated. Then a genetic algorithm (GA)-based nonlinear integer programming (NIP) approach is used to solve the multi-criteria project portfolio selection problem. Finally, two illustrative examples are presented for demonstration and verification purposes. Experimental results obtained indicate that the GA-based NIP approach can be used as a feasible and effective solution to multi-criteria project portfolio selection problems.     

Portfolio Selection Problem with Minimax Type Risk Function

The investor's preference in risk estimation of portfolio selection problems is important as it influences investment strategies. In this paper a minimax risk criterion is considered. Specifically, the investor aims to restrict the standard deviation for each of the available stocks. The corresponding portfolio optimization problem is formulated as a linear program. Hence it can be implemented easily. A capital asset pricing model between the market portfolio and each individual return for this model is established using nonsmooth optimization methods. Some numerical examples are given to illustrate our approach for the risk estimation.     

An a posteriori decision support methodology for solving the multi-criteria supplier selection problem

This research presents a novel, state-of-the-art methodology for solving a multi-criteria supplier selection problem considering risk and sustainability. It combines multi-objective optimization with the analytic network process to take into account sustainability requirements of a supplier portfolio configuration. To integrate ‘risk’ into the supplier selection problem, we develop a multi-objective optimization model based on the investment portfolio theory introduced by Markowitz. The proposed model is a non-standard portfolio selection problem with four objectives: (1) minimizing the purchasing costs, (2) selecting the supplier portfolio with the highest logistics service, (3) minimizing the supply risk, and (4) ordering as much as possible from those suppliers with outstanding sustainability performance. The optimization model, which has three linear and one quadratic objective function, is solved by an algorithm that analytically computes a set of efficient solutions and provides graphical decision support through a visualization of the complete and exactly-computed Pareto front (a posteriori approach). The possibility of computing all Pareto-optimal supplier portfolios is beneficial for decision makers as they can compare all optimal solutions at once, identify the trade-offs between the criteria, and study how the different objectives of supplier portfolio configuration may be balanced to finally choose the composition that satisfies the purchasing company's strategy best. The approach has been applied to a real-world supplier portfolio configuration case to demonstrate its applicability and to analyze how the consideration of sustainability requirements may affect the traditional supplier selection and purchasing goals in a real-life setting.     

Regularizing Portfolio Risk Analysis: A Bayesian Approach

It is important for a portfolio manager to estimate and analyze portfolio volatility, to keep the portfolio’s risk within limit. Though the number of financial instruments in the portfolio can be very large, sometimes more than thousands, daily returns considered for analysis are only for a month or even less. In this case rank of portfolio covariance matrix is less than full, hence solution is not unique. It is typically known as the “ill-posed” problem. In this paper we discuss a Bayesian approach to regularize the problem. One of the additional advantages of this approach is to analyze the source of risk by estimating the probability of positive ‘conditional contribution to total risk’ (CCTR). Each source’s CCTR would sum up to the portfolio’s total volatility risk. Existing methods only estimate CCTR of a source, and does not estimate the probability of CCTR to be significantly greater (or less) than zero. This paper presents Bayesian methodology to do so. We propose a simple Monte Carlo (MC) approach to achieve our objective, which can be paralleled. Estimation of various risk measures, such as Value at Risk and Expected Shortfall, becomes a by-product of this Monte-Carlo approach.     

Fuzzy portfolio model with different investor risk attitudes

We propose a fuzzy portfolio model designed for efficient portfolio selection with respect to uncertain or vague returns. Although many researchers have studied the fuzzy portfolio model, no researcher has yet attempted a behavioral analysis of the investor in the fuzzy portfolio model. To address this problem, we examined investor risk attitudes—risk-averse, risk-neutral, or risk-seeking behaviors—to discover an efficient method for fuzzy portfolio selection. In this study, we relied on the advantages of possibilistic mean–standard deviation models that we believed would fit the risk attitudes of investors. Thus, we developed a fuzzy portfolio model that focuses on different investor risk attitudes so that fuzzy portfolio selection for investors who possess different risk attitudes can be achieved more easily. Finally, we presented a numerical example of a portfolio selection problem to illustrate ways to address problems presented by a variety of investor risk attitudes.     

证券投资组合理论的一种新模型及其应用

马科维茨(Markowitz)以证券收益率的方差作为投资风险的测度建立了组合证券投资模型，本基于熵的概念，在研究马科维茨(Markowitz)证券投资组合模型的基础上，分析了该模型用方差度量风险的不足，进而提出一种新的证券投资组合优化模型，并以实例作了说明。     

Multiple criteria linear programming model for portfolio selection

The portfolio selection problem is usually considered as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model the risk is measured with variance, thus generating a quadratic programming model. The Markowitz model is frequently criticized as not consistent with axiomatic models of preferences for choice under risk. Models consistent with the preference axioms are based on the relation of stochastic dominance or on expected utility theory. The former is quite easy to implement for pairwise comparisons of given portfolios whereas it does not offer any computational tool to analyze the portfolio selection problem. The latter, when used for the portfolio selection problem, is restrictive in modeling preferences of investors. In this paper, a multiple criteria linear programming model of the portfolio selection problem is developed. The model is based on the preference axioms for choice under risk. Nevertheless, it allows one to employ the standard multiple criteria procedures to analyze the portfolio selection problem. It is shown that the classical mean-risk approaches resulting in linear programming models correspond to specific solution techniques applied to our multiple criteria model. This revised version was published online in June 2006 with corrections to the Cover Date.     

Portfolio selection based on upper and lower exponential possibility distributions

In this paper, two kinds of possibility distributions, namely, upper and lower possibility distributions are identified to reflect experts' knowledge in portfolio selection problems. Portfolio selection models based on these two kinds of distributions are formulated by quadratic programming problems. It can be said that a portfolio return based on the lower possibility distribution has smaller possibility spread than the one on the upper possibility distribution. In addition, a possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower possibility distributions to reflect the uncertainty in real investment problems. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches.     

Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming

This paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example.     

Importance sampling for integrated market and credit portfolio models

A sophisticated approach for computing the total economic capital needed for various stochastically dependent risk types is the bottom-up approach. In this approach, usually, market and credit risks of financial instruments are modeled simultaneously. As integrating market risk factors into standard credit portfolio models increases the computational burden of calculating risk measures, it is analyzed to which extent importance sampling techniques previously developed either for pure market portfolio models or for pure credit portfolio models can be successfully applied to integrated market and credit portfolio models. Specific problems which arise in this context are discussed. The effectiveness of these techniques is tested by numerical experiments for linear and non-linear portfolios.     

Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market

We propose a way of using DEA cross-efficiency evaluation in portfolio selection. While cross efficiency is an approach developed for peer evaluation, we improve its use in portfolio selection. In addition to (average) cross-efficiency scores, we suggest to examine the variations of cross-efficiencies, and to incorporate two statistics of cross-efficiencies into the mean-variance formulation of portfolio selection. Two benefits are attained by our proposed approach. One is selection of portfolios well-diversified in terms of their performance on multiple evaluation criteria, and the other is alleviation of the so-called “ganging together” phenomenon of DEA cross-efficiency evaluation in portfolio selection. We apply the proposed approach to stock portfolio selection in the Korean stock market, and demonstrate that the proposed approach can be a promising tool for stock portfolio selection by showing that the selected portfolio yields higher risk-adjusted returns than other benchmark portfolios for a 9-year sample period from 2002 to 2011.     

Multi-objective stochastic programming for portfolio selection

Generally, in the portfolio selection problem the Decision Maker (DM) considers simultaneously conflicting objectives such as rate of return, liquidity and risk. Multi-objective programming techniques such as goal programming (GP) and compromise programming (CP) are used to choose the portfolio best satisfying the DM’s aspirations and preferences. In this article, we assume that the parameters associated with the objectives are random and normally distributed. We propose a chance constrained compromise programming model (CCCP) as a deterministic transformation to multi-objective stochastic programming portfolio model. CCCP is based on CP and chance constrained programming (CCP) models. The proposed program is illustrated by means of a portfolio selection problem from the Tunisian stock exchange market.