A multicriteria optimization model of portfolio rebalancing with transaction costs in fuzzy environment

In this paper we propose multicriteria credibilistic framework for portfolio rebalancing (adjusting) problem with fuzzy parameters considering return, risk and liquidity as key financial criteria. The portfolio risk is characterized by a risk curve that represents each likely loss of the portfolio return and the corresponding chance of its occurrence rather than a single pre-set level of the loss. Furthermore, we consider an investment market scenario where, at the end of a typical time period, the investor would like to modify his existing portfolio by buying and/or selling assets in response to changing market conditions. We assume that the investor pays transaction costs based on incremental discount schemes associated with the buying and/or selling of assets, which are adjusted in the net return of the portfolio. A hybrid intelligent algorithm that integrates fuzzy simulation with a real-coded genetic algorithm is developed to solve the portfolio rebalancing (adjusting) problem. The proposed solution approach is useful particularly for the cases where fuzzy parameters of the problem are characterized by general functional forms.     

Multi-objective possibilistic model for portfolio selection with transaction cost

In this paper, we introduce the possibilistic mean value and variance of continuous distribution, rather than probability distributions. We propose a multi-objective Portfolio based model and added another entropy objective function to generate a well diversified asset portfolio within optimal asset allocation. For quantifying any potential return and risk, portfolio liquidity is taken into account and a multi-objective non-linear programming model for portfolio rebalancing with transaction cost is proposed. The models are illustrated with numerical examples.     

Fuzzy turnover rate chance constraints portfolio model

One concern of many investors is to own the assets which can be liquidated easily. Thus, in this paper, we incorporate portfolio liquidity in our proposed model. Liquidity is measured by an index called turnover rate. Since the return of an asset is uncertain, we present it as a trapezoidal fuzzy number and its turnover rate is measured by fuzzy credibility theory. The desired portfolio turnover rate is controlled through a fuzzy chance constraint. Furthermore, to manage the portfolios with asymmetric investment return, other than mean and variance, we also utilize the third central moment, the skewness of portfolio return. In fact, we propose a fuzzy portfolio mean–variance–skewness model with cardinality constraint which combines assets limitations with liquidity requirement. To solve the model, we also develop a hybrid algorithm which is the combination of cardinality constraint, genetic algorithm, and fuzzy simulation, called FCTPM.     

Multiobjective expected value model for portfolio selection in fuzzy environment

In this paper, we propose a credibilistic framework for portfolio selection problem using an expected value multiobjective model with fuzzy parameters. We consider short term return, long term return, risk and liquidity as key financial criteria. A solution procedure comprising fuzzy goal programming and fuzzy simulation based real-coded genetic algorithm is developed to solve the model. The proposed solution approach is considered advantageous particularly for the cases where the fuzzy parameters of the problem may assume any general functional form. An empirical study is included to illustrate the usefulness of the proposed model and solution approach in real-world applications of portfolio selection.     

考虑投资者异质信念和目标优先级的投资组合问题研究

考虑证券市场的模糊不确定性及投资者的模糊决策特征,以资产收益、下方风险及流动性为模糊投资目标,构建考虑投资者异质信念和目标优先级的多目标投资组合模型。进一步,以我国主板、中小板和创业板市场为背景,采用CPT-TOPSIS交互式算法进行实证分析。研究发现:乐观、理性和悲观投资者权衡收益、风险和流动性目标时偏好的优先顺序不同,导致资产配置结构、最优决策和绩效表现存在差别。结果表明模糊多目标模型能够满足不同投资者权衡多目标的差异化投资需求,取得优于基准随机投资组合的投资效果,可作为投资者投资决策的参考依据。     

Uncertain portfolio optimization problem under a minimax risk measure

Portfolio optimization problem is concerned with choosing an optimal portfolio strategy that can strike a balance between maximizing investment return and minimizing investment risk. In many cases, the return rate of risky asset is neither a random variable nor a fuzzy variable. Then, it can be described as an uncertain variable. But, the existing works on uncertain portfolio optimization problem fail to find an analytic solution of optimal portfolio strategy. In this paper, we define a new uncertain risk measure for the modeling of investment risk. Then, an uncertain portfolio optimization model is formulated. By introducing a new variable, we transform it into an equivalent bi-criteria optimization model. Then, we derive a method for the construction of the set of analytic Pareto optimal solutions. Finally, a numerical simulation is carried out to show the applicability of the proposed model and the convenience of finding the analytic solution.     

Portfolio rebalancing model using multiple criteria

In order to achieve greater flexibility in portfolio selection, transaction cost, short selling and higher moments should be considered, and actual transactions should be reflected. In this paper, five portfolio rebalancing models, with consideration of transaction cost and consisting of some or all criteria, including risk, return, short selling, skewness, and kurtosis, are compared to determine the important design criteria for a portfolio model. Two examples are used to perform simulated transactions, and the results indicate that the investment strategy of ‘buy and hold’ does not produce better returns for all the portfolios in the first example, and the models with higher moments or adopting short selling strategy perform better while rebalancing in the second example.     

A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs

This paper deals with a multi-period portfolio selection problem with fuzzy returns. A possibilistic mean-semivariance-entropy model for multi-period portfolio selection is presented by taking into account four criteria viz., return, risk, transaction cost and diversification degree of portfolio. In the proposed model, the return level is quantified by the possibilistic mean value of return, the risk level is characterized by the lower possibilistic semivariance of return, and the diversification degree of portfolio is measured by the originally presented possibilistic entropy. Furthermore, a hybrid intelligent algorithm is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis between the possibilistic entropy model and the proportion entropy model is provided by two numerical examples to illustrate the efficiency of the proposed approaches and the designed algorithm.     

Mean-variance portfolio rebalancing with transaction costs and funding changes

Investment portfolios should be rebalanced to take account of changing market conditions and changes in funding. Standard mean-variance (MV) portfolio selection methods are not appropriate for portfolio rebalancing, as the initial portfolio, change in funding and transaction costs are not considered. A quadratic mixed integer programming portfolio rebalancing model, which takes account of these factors is developed in this paper. The transaction costs in this portfolio rebalancing model are composed of fixed charges and variable costs, including the market impact costs associated with large market trades of individual securities, where these variable transaction costs are assumed to be non-linear functions of traded value. The use of this model is demonstrated and it is shown that when initial portfolio, funding changes and transaction costs are taken into account in portfolio construction and rebalancing, MV efficient portfolios that include risk-free lending do not have the structure expected from portfolio theory.     

考虑背景风险和流动性的模糊投资组合模型

利用投资收益率的二阶矩作为风险度量函数,建立了考虑背景风险和流动性的模糊投资组合模型.在满足预设收益率、换手率可能性均值要求水平以及风险资产的投资比例等约束条件下,使投资收益的二阶矩最小.最后选取中证100指数成分股中部分股票的历史数据进行数值分析,证明了该模型符合"高收益、高风险"的规律,说明该模型适用于实际金融市场...     

模糊环境中带交易费用的投资组合策略问题

由于金融市场是波动的,风险资产的预期收益率由于很多不确定性是很难估计的,本文考虑预期收益率是可能性分布(模糊数),并且在此基础上用模糊数的可能性均值表示投资组合的收益,用模糊数的平均绝对偏差表示风险,考虑了交易费用后,得到投资组合模型,最后给出了数值计算的例子.     

基于模糊决策的投资组合优化

基于模糊决策理论研究了带有成比例交易费用的证券投资组合优化问题. 首先,基于半绝对偏差风险函数和极大极小原则提出了一种新的风险函数--极大极小半绝对偏差风险函数;然后, 引入一种非线性隶属函数更加形象地描述了投资者对投资收益和投资风险的满意程度;在此基础上, 进一步提出了非线性满意程度的模糊决策投资组合选择模型;最后, 针对提出的模型,利用中国证券市场的真实数据给出了数值算例.     

Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints

We will propose a branch and bound algorithm for calculating a globally optimal solution of a portfolio construction/rebalancing problem under concave transaction costs and minimal transaction unit constraints. We will employ the absolute deviation of the rate of return of the portfolio as the measure of risk and solve linear programming subproblems by introducing (piecewise) linear underestimating function for concave transaction cost functions. It will be shown by a series of numerical experiments that the algorithm can solve the problem of practical size in an efficient manner. Received: July 15, 1999 / Accepted: October 1, 2000?Published online December 15, 2000     

Tracking error: a multistage portfolio model

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.     

Fuzzy portfolio selection model with real features and different decision behaviors

In the ever changing financial markets, investor’s decision behaviors may change from time to time. In this paper, we consider the effect of investor’s different decision behaviors on portfolio selection in fuzzy environment. We present a possibilistic mean-semivariance model for fuzzy portfolio selection by considering some real investment features including proportional transaction cost, fixed transaction cost, cardinality constraint, investment threshold constraints, decision dependency constraints and minimum transaction lots. To describe investor’s different decision behaviors, we characterize the return rates on securities by LR fuzzy numbers with different shape parameters in the left- and right-hand reference functions. Then, we design a novel hybrid differential evolution algorithm to solve the proposed model. Finally, we provide a numerical example to illustrate the application of our model and the effectiveness of the designed algorithm.     

具有不确定交易价格的指数跟踪资产组合再平衡问题

本文考虑具有某种不确定性的交易费用及预算约束的指数跟踪资产组合的再平衡问题。在已有的模型中,预算约束中使用的交易价格通常是一个确定值。而在再平衡过程中,股票的实际交易价格是不确定的。本文使用有限状态的离散时间马尔柯夫链模型处理交易价格的不确定性,并基于情景分析方法建立了具有不确定预算关系式的再平衡模型,然后使用股票市场的实际样本数据进行了数值实验,模拟结果说明本文的模型是可行的。     

Forecasting portfolio returns using weighted fuzzy time series methods

We propose using weighted fuzzy time series (FTS) methods to forecast the future performance of returns on portfolios. We model the uncertain parameters of the fuzzy portfolio selection models using a possibilistic interval-valued mean approach, and approximate the uncertain future return on a given portfolio by means of a trapezoidal fuzzy number. Introducing some modifications into the classical models of fuzzy time series, based on weighted operators, enables us to generate trapezoidal numbers as forecasts of the future performance of the portfolio returns. This fuzzy forecast makes it possible to approximate both the expected return and the risk of the investment through the value and ambiguity of a fuzzy number.We incorporate our proposals into classical fuzzy time series methods and analyze their effectiveness compared with classical weighted fuzzy time series models, using historical returns on assets from the Spanish stock market. When our weighted FTS proposals are used to point-wise forecast portfolio returns the one-step ahead accuracy is improved, also with respect to non-fuzzy forecasting methods.     

多约束的多阶段积极投资组合模型及实证研究

构建投资组合时需要衡量其风险, 除了考虑组合本身的风险暴露, 还需考虑其相对基准组合的风险暴露. 再者, 确定组合权重时需要根据市场的规则加入合适的约束. 基于此, 为了较为完整地考虑现实投资组合面临的风险及交易约束, 将绝对风险(CVaR)和相对风险(跟踪误差)作为风险约束, 将交易成本、卖空限制和多元权值作为交易限制约束, 构建一个新的多阶段投资组合模型, 并利用动态规划和非线性优化方法进行求解. 最后, 利用上证50成分股中41只股票构建投资组合进行实证研究. 实证结果表明构建的多阶段投资组合模型能持续战胜基准组合且优于单阶段投资组合, 同时也表明模型考虑多元权值约束具有现实意义.     

Portfolio selection based on fuzzy cross-entropy

In this paper, the Kapur cross-entropy minimization model for portfolio selection problem is discussed under fuzzy environment, which minimizes the divergence of the fuzzy investment return from a priori one. First, three mathematical models are proposed by defining divergence as cross-entropy, average return as expected value and risk as variance, semivariance and chance of bad outcome, respectively. In order to solve these models under fuzzy environment, a hybrid intelligent algorithm is designed by integrating numerical integration, fuzzy simulation and genetic algorithm. Finally, several numerical examples are given to illustrate the modeling idea and the effectiveness of the proposed algorithm.     

具有熵约束的多阶段均值—绝对偏差模糊投资组合决策

文章运用可能性绝对偏差和比例熵分别度量风险和分散化程度,提出了具有风险控制和线性交易成本的终期财富最大化的多阶段模糊投资组合模型。运用可能理论,将该模型转化为显示的非线性动态优化问题。由于投资过程存在交易成本,上述模型为具有路径依赖性的动态优化问题。文章提出了前向动态规划方法求解。最后, 通过实证研究比较了不同熵的取值投资组合最优投资比例和最终财富的变化。