Robust multiperiod portfolio management in the presence of transaction costs

We study the viability of different robust optimization approaches to multiperiod portfolio selection. Robust optimization models treat future asset returns as uncertain coefficients in an optimization problem, and map the level of risk aversion of the investor to the level of tolerance of the total error in asset return forecasts. We suggest robust optimization formulations of the multiperiod portfolio optimization problem that are linear and computationally efficient. The linearity of the optimization problems is an advantage when complex additional requirements need to be imposed on the portfolio structure, e.g., limitations on positions in certain assets or tax constraints. We compare the performance of our robust formulations to the performance of the traditional single period mean-variance formulation frequently employed in the financial industry.     

Models and Simulations for Portfolio Rebalancing

In 1950 Markowitz first formalized the portfolio optimization problem in terms of mean return and variance. Since then, the mean-variance model has played a crucial role in single-period portfolio optimization theory and practice. In this paper we study the optimal portfolio selection problem in a multi-period framework, by considering fixed and proportional transaction costs and evaluating how much they affect a re-investment strategy. Specifically, we modify the single-period portfolio optimization model, based on the Conditional Value at Risk (CVaR) as measure of risk, to introduce portfolio rebalancing. The aim is to provide investors and financial institutions with an effective tool to better exploit new information made available by the market. We then suggest a procedure to use the proposed optimization model in a multi-period framework. Extensive computational results based on different historical data sets from German Stock Exchange Market (XETRA) are presented.     

Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse

Avoiding the possibility of bankruptcy during the investment horizon is very important to multi-period portfolio management. This paper considers a multi-period fuzzy portfolio selection problem with bankruptcy control. A multi-period portfolio optimization model imposed by a bankruptcy control constraint in fuzzy environment is proposed on the basis of credibility theory. In the proposed model, a linearly recourse policy is used to reflect the influence of historical predication basis on current portfolio decision. Three optimization objectives, viz., maximizing the terminal wealth and minimizing the cumulative risk and the cumulative uncertainty of the returns of portfolios over the whole investment horizon, are taken into consideration. For solving the proposed model, a fuzzy programming approach is applied to transform it into a single objective programming model. Then, a hybrid particle swarm optimization algorithm is designed for solution. Finally, an empirical example is presented to illustrate the application of the proposed model and solution comparisons are also given to demonstrate the effectiveness of the designed algorithm.     

基于非正态分布收益率的限制卖空投资组合模型及其优化仿真

针对收益率服从非正态分布的风险资产建立限制卖空的均值-VaR投资组合模型,与马克维兹的均值-方差投资组合模型及收益率服从正态分布的均值-VaR投资组合模型进行比较分析。应用实例显示均值-VaR投资组合模型的投资效果优于均值-方差投资组合模型,基于非正态分布收益率的均值-VaR模型的投资效果略优于基于正态分布收益率的均值-VaR模型。     

Random fuzzy mean-absolute deviation models for portfolio optimization problem with hybrid uncertainty

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. The existing mean-absolute deviation models are devoted to either stochastic portfolio optimization or fuzzy one. However, practical investment decision problems often involve the mixture of randomness and fuzziness such as stochastic returns with fuzzy information. Thus it is necessary to model portfolio selection problem in such a hybrid uncertain environment. In this paper, we employ random fuzzy variable to describe the stochastic return on individual security with ambiguous information. We first define the absolute deviation of random fuzzy variable and then employ it as risk measure to formulate mean-absolute deviation portfolio optimization models. To find the optimal portfolio, we design random fuzzy simulation and simulation-based genetic algorithm to solve the proposed models. Finally, a numerical example for synthetic data is presented to illustrate the validity of the method.     

Multi-period portfolio optimization with linear control policies

This paper is concerned with multi-period sequential decision problems for financial asset allocation. A model is proposed in which periodic optimal portfolio adjustments are determined with the objective of minimizing a cumulative risk measure over the investment horizon, while satisfying portfolio diversity constraints at each period and achieving or exceeding a desired terminal expected wealth target. The proposed solution approach is based on a specific affine parameterization of the recourse policy, which allows us to obtain a sub-optimal but exact and explicit problem formulation in terms of a convex quadratic program.In contrast to the mainstream stochastic programming approach to multi-period optimization, which has the drawback of being computationally intractable, the proposed setup leads to optimization problems that can be solved efficiently with currently available convex quadratic programming solvers, enabling the user to effectively attack multi-stage decision problems with many securities and periods.     

Multistage portfolio optimization with stocks and options

We develop a multistage portfolio optimization model that utilizes options for mitigating market risk in a dynamic setting. Due to the key role of scenarios in the quality of investment decisions, a new scenario generation method is proposed that characterizes the dynamic behavior of asset returns. This methodology takes the dependence structure of different asset returns into account, and also considers serial correlations of each of the asset returns. Moreover, it preserves marginal distributions of asset returns. Also, it precludes arbitrage opportunities. To investigate the role of options, we implement the scenario generation method on a set of stocks selected from the New York Stock Exchange. Results show the high performance of the proposed scenario generation method. Afterwards, the generated set of scenarios is used as the uncertainty set for the multistage portfolio optimization model. Static and dynamic assessments are used for measuring the performance of options in mitigating market risks and generating additional returns. Finally, backtesting simulations are used for assessing different trading strategies of options.     

A hybrid approach for portfolio construction: Combing two-stage ensemble forecasting model with portfolio optimization

Combining the stock prediction with portfolio optimization can improve the performance of the portfolio construction. In this article, we propose a novel portfolio construction approach by utilizing a two-stage ensemble model to forecast stock prices and combining the forecasting results with the portfolio optimization. To be specific, there are two phases in the approach: stock prediction and portfolio optimization. The stock prediction has two stages. In the first stage, three neural networks, that is, multilayer perceptron (MLP), gated recurrent unit (GRU), and long short-term memory (LSTM) are used to integrate the forecasting results of four individual models, that is, LSTM, GRU, deep multilayer perceptron (DMLP), and random forest (RF). In the second stage, the time-varying weight ordinary least square model (OLS) is utilized to combine the first-stage forecasting results to obtain the ultimate forecasting results, and then the stocks having a better potential return on investment are chosen. In the portfolio optimization, a diversified mean-variance with forecasting model named DMVF is proposed, in which an average predictive error term is considered to obtain excess returns, and a 2-norm cost function is introduced to diversify the portfolio. Using the historical data from the Shanghai stock exchange as the study sample, the results of the experiments indicate the DMVF model with two-stage ensemble prediction outperforms benchmarks in terms of return and return-risk characteristics.     

Minimax mean-variance models for fuzzy portfolio selection

This paper discusses fuzzy portfolio selection problem in the situation where each security return belongs to a certain class of fuzzy variables but the exact fuzzy variable cannot be given. Two credibility-based minimax mean-variance models are proposed. The crisp equivalents of the models to linear programming ones are given in three special cases. In addition, a general solution algorithm is also provided. To help understand the modeling idea and to illustrate the effectiveness of the proposed algorithm, one example is presented.     

Risk control over bankruptcy in dynamic portfolio selection: a generalized mean-variance formulation

For an investor to claim his wealth resulted from his multiperiod portfolio policy, he has to sustain a possibility of bankruptcy before reaching the end of an investment horizon. Risk control over bankruptcy is thus an indispensable ingredient of optimal dynamic portfolio selection. We propose in this note a generalized mean-variance model via which an optimal investment policy can be generated to help investors not only achieve an optimal return in the sense of a mean-variance tradeoff, but also have a good risk control over bankruptcy. One key difficulty in solving the proposed generalized mean-variance model is the nonseparability in the associated stochastic control problem in the sense of dynamic programming. A solution scheme using embedding is developed in this note to overcome this difficulty and to obtain an analytical optimal portfolio policy.     

Generating effective defined-contribution pension plan using simulation optimization approach

This paper presents an optimization approach to analyze the problems of portfolio selection for long-term investments, taking into consideration the specific target replacement ratio for defined-contribution (DC) pension scheme; the purpose is to generate an effective multi-period asset allocation that reaches an amount matching the target liability at retirement date and reduce the downside risk of the investment. A multi-period asset liability simulation model was used to generate 4000 asset return predictions, and an evolutionary algorithm, evolution strategies, was incorporated into the model to generate multi-period asset allocations under four conditions, considering different weights for measuring the importance of matching the target liability and different periods of downside risk measurement. Computational results showed that the evolutionary algorithm, evolution strategies, is a very robust and effective approach to generate promising asset allocations under all the four cases. In addition, computational results showed that the promising asset allocations revealed valuable information, which is able to help fund managers or investors achieve a higher average investment return or a lower level of volatility under different conditions.     

Selection of a dynamic supply portfolio in make-to-order environment withrisks

The problem of a multi-period supplier selection and order allocation in make-to-order environment in the presence of supply chain disruption and delay risks is considered. Given a set of customer orders for finished products, the decision maker needs to decide from which supplier and when to purchase product-specific parts required for each customer order to meet customer requested due date at a low cost and to mitigate the impact of supply chain risks. The selection of suppliers and the allocation of orders over time is based on price and quality of purchased parts and reliability of supplies. For selection of dynamic supply portfolio a mixed integer programming approach is proposed to incorporate risk that uses conditional value-at-risk via scenario analysis. In the scenario analysis, the low-probability and high-impact supply disruptions are combined with the high probability and low impact supply delays. The proposed approach is capable of optimizing the dynamic supply portfolio by calculating value-at-risk of cost per part and minimizing expected worst-case cost per part simultaneously. Numerical examples are presented and some computational results are reported.     

基于QPSO-SA混合算法的多目标投资组合优化

多目标投资组合优化就是决定每个具有特定风险、回报、交易费用等特征的资产在总投资价值中的投资比例,即选择那些资产投资以及寻找每个投资资产的最佳投资比例,使得总投资的风险最小、交易费用最小、回报最大等等。该问题是典型的NP难解问题,通常方法很难达到全局最优。研究如何把基于量子行为的微粒群优化算法（QPSO算法）和模拟退火算法(SA算法)结合起来解决多目标投资组合优化问题。利用美国标准普尔指数100的股票历史数据进行验证,纯QPSO算法与QPSO-SA混合算法的运行结果比较表明在解决多目标投资组优化问题中,QPSO-SA混合算法是一种高效的、可靠的优化算法,具有一定的实用价值。     

Asset portfolio optimization using fuzzy mathematical programming

By morphing mean-variance optimization (MVO) portfolio model into semi-absolute deviation (SAD) model, we apply multi criteria decision making (MCDM) via fuzzy mathematical programming to develop comprehensive models of asset portfolio optimization (APO) for the investors’ pursuing either of the aggressive or conservative strategies.     

Mean-variance model for portfolio optimization with background risk based on uncertainty theory

The aim of this paper is to develop a mean-variance model for portfolio optimization considering the background risk, liquidity and transaction cost based on uncertainty theory. In portfolio selection problem, returns of securities and assets liquidity are assumed as uncertain variables because of incidents or lacking of historical data, which are common in economic and social environment. We provide crisp forms of the model and a hybrid intelligent algorithm to solve it. Under a mean-variance framework, we analyze the portfolio frontier characteristic considering independently additive background risk. In addition, we discuss some effects of background risk and liquidity constraint on the portfolio selection. Finally, we demonstrate the proposed models by numerical simulations.     

风险资产收益序列相关的多阶段均值-方差投资组合选择

基于多阶段均值-方差框架, 研究任意多种风险资产存在一般收益序列相关时的投资组合选择问题. 首先, 采用Lagrange 对偶原理与动态规划相结合的方法对模型进行求解, 得到多阶段均值-方差模型的有效投资策略和有效边界的解析表达式; 然后, 证明在含有无风险资产的情形下有效边界仍为均值-标准差平面上的一条射线; 最后, 应用所得结论给出一个具体的实例分析.

     

A new Chance-Variance optimization criterion for portfolio selection in uncertain decision systems

The Markowitz’s mean-variance (M-V) model has received widespread acceptance as a practical tool for portfolio optimization, and his seminal work has been widely extended in the literature. The aim of this article is to extend the M-V method in hybrid decision systems. We suggest a new Chance-Variance (C-V) criterion to model the returns characterized by fuzzy random variables. For this purpose, we develop two types of C-V models for portfolio selection problems in hybrid uncertain decision systems. Type I C-V model is to minimize the variance of total expected return rate subject to chance constraint; while type II C-V model is to maximize the chance of achieving a prescribed return level subject to variance constraint. Hence the two types of C-V models reflect investors’ different attitudes toward risk. The issues about the computation of variance and chance distribution are considered. For general fuzzy random returns, we suggest an approximation method of computing variance and chance distribution so that C-V models can be turned into their approximating models. When the returns are characterized by trapezoidal fuzzy random variables, we employ the variance and chance distribution formulas to turn C-V models into their equivalent stochastic programming problems. Since the equivalent stochastic programming problems include a number of probability distribution functions in their objective and constraint functions, conventional solution methods cannot be used to solve them directly. In this paper, we design a heuristic algorithm to solve them. The developed algorithm combines Monte Carlo (MC) method and particle swarm optimization (PSO) algorithm, in which MC method is used to compute probability distribution functions, and PSO algorithm is used to solve stochastic programming problems. Finally, we present one portfolio selection problem to demonstrate the developed modeling ideas and the effectiveness of the designed algorithm. We also compare the proposed C-V method with M-V one for our portfolio selection problem via numerical experiments.     

Evaluating methods of investment project and optimizing models of portfolio selection in fuzzy uncertainty

This paper deals with the problems of both project valuation and portfolio selection under the assumption that the investment capitals and the net cash flows of the projects are fuzzy variables. Using the credibilistic expected value and the credibilistic lower semivariance of fuzzy variables, this paper proposes both the credibilistic return index and the credibilistic risk index, which are measures of investment return and investment risk with annuity form for evaluating single project. Moreover, a composite risk-return index for selecting the optimal investment strategy is also presented. Then, we set up a general project portfolio optimization model with fuzzy returns and two specific models: triangle and interval fuzzy returns. Furthermore, we provide two algorithms: the improved heuristic rules based on genetic algorithm and the traversal algorithm. Finally, two numerical examples are presented to illustrate the efficiency and the effectiveness of these proposed optimization methods.     

Polyhedral Coherent Risk Measures in the Case of Imprecise Scenario Estimates

Polyhedral coherent risk measures are extended to the case of imprecise scenario estimates of random variables. Optimization problems under uncertainty are considered that cover a wide class of stochastic programming and robust optimization problems. It is shown how they are reduced to linear programming problems in the linear case. Problems of portfolio optimization by the reward-to-risk ratio are considered.     

Tail mean and related robust solution concepts

Robust optimisation might be viewed as a multicriteria optimisation problem where objectives correspond to the scenarios although their probabilities are unknown or imprecise. The simplest robust solution concept represents a conservative approach focused on the worst-case scenario results optimisation. A softer concept allows one to optimise the tail mean thus combining performances under multiple worst scenarios. We show that while considering robust models allowing the probabilities to vary only within given intervals, the tail mean represents the robust solution for only upper bounded probabilities. For any arbitrary intervals of probabilities the corresponding robust solution may be expressed by the optimisation of appropriately combined mean and tail mean criteria thus remaining easily implementable with auxiliary linear inequalities. Moreover, we use the tail mean concept to develope linear programming implementable robust solution concepts related to risk averse optimisation criteria.