Incorporating Value-at-Risk in Portfolio Selection: An Evolutionary Approach

Controller design is performed to meet some performance criteria. Some of them are the gain and phase margins, control effort, settling time, overshoot, amongst other indexes. Obtaining a controller or compensator that fits all these criteria (or some of them) for a closed loop control is done in both empirical and analytical procedures. The most of these procedures assumes the plant to be controlled could be modelled as first or second-order system. This paper aims to show a way to find the controller parameters based on the multi-objective optimization with a evolutionary approach. The systems to be controlled must be the type SISO (Single Input Single Output) whose transfer functions may have order higher than second order.

Modern Portfolio Theory (MPT) is based upon the classical Markowitz model which uses variance as a risk measure. A generalization of this approach leads to mean‐risk models, in which a return distribution is characterized by the expected value of return (desired to be large) and a “risk” value (desired to be kept small). Portfolio choice is made by solving an optimization problem, in which the portfolio risk is minimized and a desired level of expected return is specified as a constraint. The need to penalize different undesirable aspects of the return distribution led to the proposal of alternative risk measures, notably those penalizing only the downside part (adverse) and not the upside (potential). The downside risk considerations constitute the basis of the Post Modern Portfolio Theory (PMPT). Examples of such risk measures are lower partial moments, Value‐at‐Risk (VaR) and Conditional Value‐at‐Risk (CVaR). We revisit these risk measures and the resulting mean‐risk models. We discuss alternative models for portfolio selection, their choice criteria and the evolution of MPT to PMPT which incorporates: utility maximization and stochastic dominance. Copyright © 2009 Wilmott Magazine Ltd

This paper describes the development and application of a new multi-objective evolutionary optimization approach for the design and upgrading of water distribution systems with multiple pumps and service reservoirs. The optimization model employs a pressure-driven analysis simulator that accounts for the minimum node pressure constraints and conservation of mass and energy. Pump scheduling, tank siting and tank design are integrated seamlessly in the optimization without introducing additional heuristic procedures. The computational solution of the optimization problem is entirely penalty-free, thanks to pressure-driven analysis and the inclusion of explicit criteria for tank depletion and replenishment. The model was applied to the Anytown network that is a benchmark optimization problem. Many new solutions were achieved that are cheaper and offer superior performance compared to previous solutions in the literature. Detailed and extensive simulations of the solutions achieved were carried out. Spatial and temporal variations in water quality were investigated by simulating the chlorine residual and disinfection by-products in addition to water age. The hydraulic requirements were satisfied; efficiency of pumps was consistently high; effective operation of the new and existing tanks was achieved; water quality was improved; and overall computational efficiency was high. The formulation is entirely generic.

With the nor-normal distribution and nor-binomial utility function of investors, higher-order moments should be taken into consideration with portfolio selection. So far, studies on portfolio selection with higher-order moments are mainly conducted under the framework of mean-variance-skewness while kurtosis is seldom taken into account. But many literatures have pointed out kurtosis play more important role in portfolio selection than variance and skewness. So, in order to fill up the study gap, portfolio selection with higher-order moments will be studied, under the framework of mean-variance-skewness-kurtosis, in this paper. Firstly, the optimization model of portfolio selection with kurtosis minimization is set up. Then, semidefinite programming relaxation is suggested based on research results of Lasserre and Waki to resolve the difficulty of model solution from the higher order and non-convexity of objective function and the efficient frontier of portfolio selection model minimizing kurtosis is deduced theoretically. Finally, the theoretical efficient frontier and the effectiveness of semidefinite programming relaxation are verified through empirical analysis.

Marginal risk that represents the risk contribution of an individual asset is an important criterion in portfolio selection and risk management. In the literature, however, the measure of marginal risk has been only employed in ex post analysis of a portfolio policy, and the control of marginal risk is achieved usually via position diversification that simply imposes upper bounds on the portfolio position without considering the effect of correlations of asset returns in risk diversification. We investigate in this paper a new optimal portfolio selection problem with direct (relative) marginal risk control in the mean-variance framework, accounting for the correlations of asset returns. The resulting optimization model, however, is a notorious non-convex quadratically constrained quadratic programming problem. By exploiting the special structure of the problems, we propose an efficient branch-and-bound solution method to achieve a global optimality in which convex quadratic relaxation subproblems with second-order cone constraints are formulated to generate a tight lower bound. Empirical study shows that the model with marginal risk control is a suitable analytical tool for active portfolio risk management and demonstrates several preferable features of this new model to the traditional mean-variance model in risk management. The method is tested and compared with the commercial global optimization solver BARON for portfolio optimization problems with up to hundreds of assets and tens of marginal risk constraints.

A mathematical framework for passenger screening optimization via a multi-objective evolutionary approach

In this article we present a technique for implementing large-scale optimal portfolio selection. We use high-frequency daily data to capture valuable statistical information in asset returns. We describe several statistical issues involved in quantitative approaches to portfolio selection. Our methodology applies to large-scale portfolio-selection problems in which the number of possible holdings is large relative to the estimation period provided by historical data. We illustrate our approach on an equity database that consists of stocks from the Standard and Poor's index, and we compare our portfolios to this benchmark index. Our methodology differs from the usual quadratic programming approach to portfolio selection in three ways: (1) We employ informative priors on the expected returns and variance-covariance matrices, (2) we use daily data for estimation purposes, with upper and lower holding limits for individual securities, and (3) we use a dynamic asset-allocation approach that is based on reestimating and then rebalancing the portfolio weights on a prespecified time window. The key inputs to the optimization process are the predictive distributions of expected returns and the predictive variance-covariance matrix. We describe the statistical issues involved in modeling these inputs for high-dimensional portfolio problems in which our data frequency is daily. In our application, we find that our optimal portfolio outperforms the underlying benchmark.

Return Prediction and Portfolio Selection: A Distributional Approach

Portfolio Selection with a Systematic Skewness Constraint

Public data sharing is utilized in a number of businesses to facilitate the exchange of information. Privacy constraints are usually enforced to prevent unwanted inference of information, specially when the shared data contain sensitive personal attributes. This, however, has an adverse effect on the utility of the data for statistical studies. Thus, a requirement while modifying the data is to minimize the information loss. Existing methods employ the notion of minimal distortion where the data is modified only to the extent necessary to satisfy the privacy constraint, thereby asserting that the information loss has been minimized. However, given the subjective nature of information loss, it is often difficult to justify this assertion. In this paper, we propose an evolutionary algorithm to explicitly minimize an achievement function given constraints on the privacy level of the transformed data. Privacy constraints specified in terms of anonymity models are modeled as additional objectives and an evolutionary multi-objective approach is proposed. We highlight the requirement to minimize any bias induced by the anonymity model and present a scalarization incorporating preferences in information loss and privacy bias as the achievement function.

This research provides a possible variant of the basic framework of portfolio selection. First, for the return estimation, considering Asian exchange-traded funds as the selection pool for the investment, regression analysis is applied to generate future return scenarios. Second, for the assignment of weights, the likelihood of these scenarios are assumed to be equally likely. Third, for the portfolio selection model, the safety-first model is utilized with consideration of 5 different diversification factors. The proposed procedure is modeled as a linear programming model into AIMMS optimization software where the resulting portfolios show that safety-first portfolios can outperform the benchmark. These observations can pave the way to a new generic portfolio selection framework that can possibly help investors and may lead to alternative investment instruments.

Purpose This paper aims to propose two portfolio selection models with hesitant value-at-risk (HVaR) – HVaR fuzzy portfolio selection model (HVaR-FPSM) and HVaR-score fuzzy portfolio selection model (HVaR-S-FPSM) – to help investors solve the problem that how bad a portfolio can be under probabilistic hesitant fuzzy environment. Design/methodology/approach It is strictly proved that the higher the probability threshold, the higher the HVaR in HVaR-S-FPSM. Numerical examples and a case study are used to illustrate the steps of building the proposed models and the importance of the HVaR and score constraint. In case study, the authors conduct a sensitivity analysis and compare the proposed models with decision-making models and hesitant fuzzy portfolio models. Findings The score constraint can make sure that the portfolio selected is profitable, but will not cause the HVaR to decrease dramatically. The investment proportions of stocks are mainly affected by their HVaRs, which is consistent with the fact that the stock having good performance is usually desirable in portfolio selection. The HVaR-S-FPSM can find portfolios with higher HVaR than each single stock and has little sacrifice of extreme returns. Originality/value This paper fulfills a need to construct portfolio selection models with HVaR under probabilistic hesitant fuzzy environment. As a downside risk, the HVaR is more consistent with investors’ intuitions about risks. Moreover, the score constraint makes sure that undesirable portfolios will not be selected.

Dividends, taxes, and normative portfolio theory

This paper presents an application of a constrained multiobjective evolutionary algorithm for the design of active suspension controllers for light rail vehicles with the aim of providing superior ride comfort within the suspension's stroke limitation. A multibody dynamic model of a three‐car train is derived and the control parameters are optimized. Force cancellation, skyhook damper, and track‐following are used to synthesize the active controller. Selection of the active suspension parameters is aided by an evolutionary computation algorithm to get the best compromise between ride quality and suspension deflections due to irregular gradient tracks. An evolutionary multiobjective optimization approach accompanied with the Pareto set is proposed to deal with the complicated control design problem.

This research aims to explore the selection and optimization of stocks from two Eastern European markets, Romania and Poland, starting from the maximum return criterion, downside risk, and Sortino ratio when building a portfolio. The Post-Modern Portfolio Theory (PMPT) serves as the main methodological framework to achieve our primary objective, ‘Building portfolios of stocks on the two markets in Eastern Europe, Romania and Poland, starting from the maximum return criterion’. The research focused on stocks from the flagship indexes of the Bucharest Stock Exchange (BSE) and the Warsaw Stock Exchange (WSE), namely the BET Index and the WIG20 Index. The data was collected for 40 companies, 20 companies in each stock market, for the period June 2020 until June 2025, 5 ‘stock years’, with daily close prices, government 10-year bonds as risk-free rates, and equity risk premiums for Romanian and Polish markets. Two portfolios were built, one from the BSE and another from the WSE. The results indicate, through PMPT and Sortino ratio as a performance indicator, that indeed the potential loss of a stock (downside risk) and the expected return play a crucial role in building portfolios, especially in volatile markets.