Concentrated portfolio selection models based on historical data

A new risk measure fully based on historical data is proposed, from which we can naturally derive concentrated optimal portfolios rather than imposing cardinality constraints. The new risk measure can be expressed as a quadratics of the introduced greedy matrix, which takes investors' joint behavior into account. We construct distribution‐free portfolio selection models in simple case and realistic case, respectively. The latest techniques for describing transaction cost constraints and solving nonconvex quadratic programs are utilized to obtain the optimal portfolio efficiently. In order to show the practicality, efficiency, and robustness of our new risk measure and corresponding portfolio selection models, a series of empirical studies are carried out with trading data from advanced stock markets and emerging stock markets. Different performance indicators are adopted to comprehensively compare results obtained under our new models with those obtained under the mean‐variance, mean‐semivariance, and mean‐conditional value‐at‐risk models. Out‐of‐sample results sufficiently show that our models outperform the others and provide a simple and practical approach for choosing concentrated, efficient, and robust portfolios. Copyright © 2014 John Wiley & Sons, Ltd.     

Mean-semivariance models for fuzzy portfolio selection

This paper discusses portfolio selection problem in fuzzy environment. In the paper, semivariance is originally presented for fuzzy variable, and three properties of the semivariance are proven. Based on the concept of semivariance of fuzzy variable, two fuzzy mean-semivariance models are proposed. To solve the new models in general cases, a fuzzy simulation based genetic algorithm is presented in the paper. In addition, two numerical examples are also presented to illustrate the modelling idea and the effectiveness of the designed algorithm.     

Bayesian portfolio selection with multi-variate random variance models

We consider multi-period portfolio selection problems for a decision maker with a specified utility function when the variance of security returns is described by a discrete time stochastic model. The solution of these problems involves a dynamic programming formulation and backward induction. We present a simulation-based method to solve these problems adopting an approach which replaces the preposterior analysis by a surface fitting based optimization approach. We provide examples to illustrate the implementation of our approach.     

Probability maximization models for portfolio selection under ambiguity

This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities and decision makers’ predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a portfolio selection problem is provided to compare our proposed models with the basic model.     

Mean-variance models for portfolio selection with fuzzy random returns

This paper develops two novel types of mean-variance models for portfolio selection problems, in which the security returns are assumed to be characterized by fuzzy random variables with known possibility and probability distributions. In the proposed models, we take the expected return of a portfolio as the investment return and the variance of the expected return of a portfolio as the investment risk. We assume that the security returns are triangular fuzzy random variables. To solve the proposed portfolio problems, this paper first presents the variance formulas for triangular fuzzy random variables. Then this paper applies the variance formulas to the proposed models so that the original portfolio problems can be reduced to nonlinear programming ones. Due to the reduced programming problems include standard normal distribution in the objective functions, we cannot employ the conventional solution methods to solve them. To overcome this difficulty, this paper employs genetic algorithm (GA) to solve them, and verify the obtained optimal solutions via Kuhn-Tucker (K-T) conditions. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed models and methods.     

The optimal solution of ESG portfolio selection models that are based on the average ESG score

Recently, various models have been proposed to engage portfolio selection or ESG investments. In this brief report, we solve the problem of optimal portfolio selection of arbitrary ESG utility functions where the ESG preference function is based on the average ESG score. The proposed optimal solution shows that the impact of the ESG score and the expected return vectors on the optimal weights are equal, up to a scalar, regardless of the utility function of the investors.     

An interval portfolio selection problem based on regret function

Recent mergers in the banking industry have often generated disappointing shareholder returns. Delays in implementing potential operating savings and realizing benefits of scale economies may be one reason these mergers have disappointing returns. Using data envelopment analysis (DEA), we analyze a 200-branch network formed in a merger of four banks. The operating efficiency of each branch is benchmarked against “best-practice” branches in the combined merged bank as well as “best practice” branches within each pre-merger bank. This analysis identified opportunities to reduce branch operating costs by 22 percent for the entire merged bank. In contrast, the cost savings opportunity is under seven percent when analyzed within each pre-merger bank.These findings suggest benchmarking across the entire merged bank to identify the best practices bank-wide can generate added savings. However, in this bank merger, these merger benefits were not realized until four years after the merger. Interviews with key players in the merged bank indicate that the bank deferred realizing these benefits because of political pressures, personnel integration issues, system integration issues, and financial components of the merger such as restructuring reserves and the purchase price. These causes suggest areas where shareholders can and should demand more rapid improvement in performance of bank mergers and areas for future corporate merger research.     

Robust portfolio selection based on a multi-stage scenario tree

The aim of this paper is to apply the concept of robust optimization introduced by Bel-Tal and Nemirovski to the portfolio selection problems based on multi-stage scenario trees. The objective of our portfolio selection is to maximize an expected utility function value (or equivalently, to minimize an expected disutility function value) as in a classical stochastic programming problem, except that we allow for ambiguities to exist in the probability distributions along the scenario tree. We show that such a problem can be formulated as a finite convex program in the conic form, on which general convex optimization techniques can be applied. In particular, if there is no short-selling, and the disutility function takes the form of semi-variance downside risk, and all the parameter ambiguity sets are ellipsoidal, then the problem becomes a second order cone program, thus tractable. We use SeDuMi to solve the resulting robust portfolio selection problem, and the simulation results show that the robust consideration helps to reduce the variability of the optimal values caused by the parameter ambiguity.     

Mean-chance model for portfolio selection based on uncertain measure

This paper discusses a portfolio selection problem in which security returns are given by experts’ evaluations instead of historical data. A factor method for evaluating security returns based on experts’ judgment is proposed and a mean-chance model for optimal portfolio selection is developed taking transaction costs and investors’ preference on diversification and investment limitations on certain securities into account. The factor method of evaluation can make good use of experts’ knowledge on the effects of economic environment and the companies’ unique characteristics on security returns and incorporate the contemporary relationship of security returns in the portfolio. The use of chance of portfolio return failing to reach the threshold can help investors easily tell their tolerance toward risk and thus facilitate a decision making. To solve the proposed nonlinear programming problem, a genetic algorithm is provided. To illustrate the application of the proposed method, a numerical example is also presented.     

Mean-risk-skewness models for portfolio optimization based on uncertain measure

Numerous empirical studies show that portfolio returns are generally asymmetric. In this paper, skewness is considered to measure the asymmetry of portfolio returns and a mean-risk-skewness model for portfolio selection will be proposed in uncertain environment. Here, the returns of the securities are regarded as uncertain variables which are estimated by experienced experts instead of historical data. Furthermore, the corresponding variations and crisp forms of the model are considered. To solve the proposed optimization models, a hybrid intelligent algorithm is designed. Finally, the feasibility and necessity of the hybrid intelligent algorithm and the application of the proposed models are illustrated by two numerical examples.     

工件具有任意尺寸的混合分批平行机排序问题的近似算法

本文考虑了工件具有任意尺寸且机器有容量限制的混合分批平行机排序问题。在该问题中, 一个待加工的工件集需在多台平行批处理机上进行加工。每个工件有它的加工时间和尺寸, 每台机器可以同时处理多个工件, 称为一个批, 只要这些工件尺寸之和不超过其容量; 一个批的加工时间等于该批中工件的最大加工时间和总加工时间的加权和; 目标函数是极小化最大完工时间。该问题包含一维装箱问题为其特殊情形, 为强NP-困难的。对此给出了一个$\left( {2 + 2\alpha+\alpha^{2}}\right)$-近似算法, 其中$\alpha$为给定的权重参数, 满足考虑了不同于Goldfarb和Iyengar （2003）的因子模型,通过横截面回归分析以及Fama-MacBeth估计构造了关于资产的平均收益向量和协方差矩阵的不确定性集合（置信区域）。基于这些不确定性集合以及Markowitz“均值-方差模型”的鲁棒投资组合问题,提出了多个鲁棒投资组合问题,并对应的推导出其等价的半正定规划形式,使得问题可以在多项式时间内求解。     

Convergence rates for rank-based models with applications to portfolio theory

We determine rates of convergence of rank-based interacting diffusions and semimartingale reflecting Brownian motions to equilibrium. Bounds on fluctuations of additive functionals are obtained using Transportation Cost-Information inequalities for Markov processes. We work out various applications to the rank-based abstract equity markets used in Stochastic Portfolio Theory. For example, we produce quantitative bounds, including constants, for fluctuations of market weights and occupation times of various ranks for individual coordinates. Another important application is the comparison of performance between symmetric functionally generated portfolios and the market portfolio. This produces estimates of probabilities of “beating the market”.     

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.     

Expanded models of the project portfolio selection problem with loss in divisibility

This research develops three new models for the project portfolio selection problem with multiple periods. To reflect some real situations, three loss assumptions are considered for the interruption of project execution for the first time. The mathematical representations of the loss assumptions are provided and proved. Besides, the workload constraint, capital flow constraint, cardinality constraint, and precedence relationship are incorporated into the models. One benchmark example and one real-world application case are used to demonstrate the capability and characteristics of the proposed models.     

Two new models for portfolio selection with stochastic returns taking fuzzy information

This paper proposes two new models for portfolio selection in which the security returns are stochastic variables with fuzzy information. A hybrid intelligent algorithm is designed to solve the optimization problem which is otherwise hard to solve with the existing algorithms due to the complexity of the return variables. To illustrate the modelling idea and to show the effectiveness of the proposed approach, two numerical examples are provided.     

Robust portfolio selection based on asymmetric measures of variability of stock returns

This paper addresses a new uncertainty set—interval random uncertainty set for robust optimization. The form of interval random uncertainty set makes it suitable for capturing the downside and upside deviations of real-world data. These deviation measures capture distributional asymmetry and lead to better optimization results. We also apply our interval random chance-constrained programming to robust mean-variance portfolio selection under interval random uncertainty sets in the elements of mean vector and covariance matrix. Numerical experiments with real market data indicate that our approach results in better portfolio performance.     

Indeterminacy in portfolio selection

This paper develops the indeterminacy in “portfolio selection” putting together a modification of a device of measure theory used in our previous papers [Atti del XXI Convegno Annuale AMASES, 1997, pp. 635–647; Soft Computing in Financial Engineering, 1999, pp. 425–432] and Shannon's entropy of information. We obtain an expectation, variance and indeterminacy (E–V–I) functional which is a generalization of the expectation quadratic utility. If I=0 our model is more coherent with the expectation–variance (E–V) model than the classical model and if I≠0 our model yields a warning about the risk from indeterminacy that expectation quadratic utility model does not. A numerical method and its statistical application with Italian data illustrates the results.     

Quantile-based optimal portfolio selection

Computational Management Science - In this paper the concept of quantile-based optimal portfolio selection is introduced and a specific portfolio connected to it, the conditional value-of-return...