Multi-period Portfolio Selection Model Research Articles

The cost of delay as risk measure in target-based multi-period portfolio selection models

Abstract Accepted by: Aris Syntetos Increasingly, in recent years, the fund management industry has evolved towards so-called goal-based investing paradigms, under which investors are assumed to base their portfolio strategies on pre-specified targets to be attained in the future. A similar decision model is common in the wealth management and the life insurance industries where targets may be associated with long-term investment horizons and retirement planning problems. Based on this evidence, we propose in this article a novel risk measure explicitly focusing on the financial cost that may be associated with a delay in reaching those targets. We show that the definition of this risk measure is both rather natural and effective to capture investors’ risk preferences. A dynamic portfolio selection model is developed to assess the effectiveness of the risk measure from financial and risk control perspectives. The introduced risk measure has good properties and it is related to the Value-at-Risk with a given confidence level. Under sufficiently general statistical assumptions, we derive a closed form solution to a mean-risk formulation of the portfolio problem in which the cost of delay is taken as risk measure. Finally, a set of numerical tests validate the proposed portfolio selection model and show a set of comparative results with respect to a classical dynamic mean-variance model.

Responsible Investing: A Multi-period Portfolio Selection Model

Responsible Investing: A Multi-period Portfolio Selection Model

Multi-criteria fuzzy portfolio selection based on three-way decisions and cumulative prospect theory

Portfolio selection is one of the hottest issue in decision-making and management engineering. But due to the capital market natural complexity and investors’ irrational behaviors, it is not easy for investors to achieve their predefined goals. In this study, we propose a novel three-way decisions model based on cumulative prospect theory and outranking relations. Compared with traditional two-way decisions, the introduction of a boundary region into the three-way decisions theory makes it possible to reduce decision risk. By constructing an outranked set for each alternative and a hybrid multi-criteria decision-making matrix, three strategies are proposed by us to design the three-way decisions model. In order to test the effectiveness of the proposed model, we introduce it into a fuzzy multi-period portfolio selection case and design an improved particle swarm optimization as the solution algorithm. Finally, the effectiveness of the algorithm is validated by some test functions. And an experiment based on real market data validates the proposed multi-period portfolio selection model outperforms other compared models in terms of return, risk and risk-adjusted criteria.

Multi-period uncertain portfolio selection model with prospect utility function.

In this paper, we discuss a multi-period portfolio optimization problem based on uncertainty theory and prospect theory. We propose an uncertain multi-period portfolio selection model, in which the return utility and risk of investment are measured by prospect theory utility function and uncertain semivariance. More realistically, the influence of transaction costs and bankruptcy of investor are also considered. Moreover, to solve the portfolio model, this paper designs a new artificial bee colony algorithm by combining sine cosine search method. Finally, a numerical experiment is presented to demonstrate the proposed model and the effectiveness of the designed algorithm.

Multi-period portfolio selection under the coherent fuzzy environment with dynamic risk-tolerance and expected-return levels

We discuss the portfolio selection problems in which the uncertainty of future returns and the heterogeneity of investor attitudes towards the stock market (optimistic–pessimistic–neutral) are captured by coherent fuzzy numbers. Two coherent fuzzy multi-period portfolio selection models are developed from the perspectives of wealth maximization and risk minimization. Given that the constraint levels regarding risk and return of the current period tend to be influenced by the outcome of the previous period, the dynamic risk-tolerance and expected-return levels are integrated into the portfolio modeling. Practical constraints and transaction costs are also taken into account, which enables the models more effective and lifelike in simulating the real-world trading of the stock market. The empirical studies based on two large data sets are presented to illustrate the applicability of the proposed models. To survey the models’ performance, several portfolio evaluation criteria are used to conduct out-of-sample analysis. The results show outstanding performance of the presented models with dynamic strategies over conventional ways (static risk-tolerance and expected-return levels) on most of the indicators. This research offers references for investors with different attitudes to make long-term investment decisions, and is an effective supplement to behavioral portfolio selection research based on bounded rationality under uncertainty.

A new approach to the bi-criteria multi-period fuzzy portfolio selection

The proposed approach to the bi-criteria multi-period fuzzy portfolio selection is based on the observation that the treating the variance as a measure of portfolio risk provides sometimes questionable results. Therefore, the simple criteria of portfolio risk and return are proposed. Based on them and three popular methods for local criteria aggregation, a new fuzzy portfolio selection one-period model has been developed. It is shown that this model provides reasonable results coinciding with common sense. Based on this model, a new two-stage bi-criteria optimization approach to portfolio selection has been developed, tested and used as a main component of proposed multi-period portfolio selection model. A method for obtaining fuzzy distributions of stocks returns based on real market data is developed and used for the optimal portfolio selection. In some cases, to make the presentation of developed methods features more transparent, the problem simplification, when all market decisions (Buy, Sell and Hold) were considered as right ones was used. But finally, the real-world market decisions which are generated using the stock trading expert system based on the real market data were used for the portfolio selection. To do this, the known stock trading expert system has been applied, which was adapted for the conditions of the considered stock markets (NYSE and NASDAQ) providing best results after optimization. Using the real-world examples, it is shown that incorporating the stock signals (decisions) Buy, Sell and Hold in the multi-period portfolio selection models improves strongly the models results making them closer to reality.

Dynamic multi-period sparse portfolio selection model with asymmetric investors’ sentiments

Asymmetric investors’ sentiments on returns and risks play an important role in updating the portfolio strategies in multi-period portfolio selection problems. By introducing the Prospect Theory to measure the asymmetric investors’ sentiments, a dynamic sentiment-adjusted model (DSAM) is proposed to sparse portfolio selection problem over multiple periods, in which the objective is to minimize the risk of the portfolio. As we focus on the sparse portfolio, a l0 constraint is added to our model. The l0 constraint represents that we can only purchase at most k securities from N candidate securities, in which k is a small number compared to N. Since the objective function of the sparse portfolio with l0 constraint is NP-hard, and could not be solved by the Deep Learning algorithms. The stochastic neural networks algorithm with re-parametrisation trick (SNNrP) is introduced to solve the DSAM. The back-testing framework of our paper includes a multi-period portfolio selection model, in which asymmetric investors’ sentiments are modeled to iterate investors’ expected return level each period. In the back-testing framework, we conduct the experiments for different investment periods with different investors’ sentiments. The experimental results for the Nasdaq and CSI 300 data sets show that, on average, compared with the traditional Mean–variance model, the terminal return and risk obtained by the DSAM model outperforms by 9% and 11.75%.

Multiperiod portfolio selection models under uncertain measure and with multiple criteria

This paper explores a multiperiod portfolio optimization problem under uncertain measure involving background risk, liquidity constraints and V-shaped transaction costs. Unlike traditional studies, we establish multiperiod mean-variance portfolio optimization models with multiple criteria in which security returns, background asset returns and turnover rates are assumed to be uncertain variables that can be estimated by experienced experts. When the returns of the securities and background assets follow normal uncertainty distributions, we use the deterministic forms of the multiperiod portfolio optimization model. The uncertain multiperiod portfolio selection models are practical but complicated. Therefore, the models are solved by employing a genetic algorithm. The uncertain multiperiod model with multiple criteria is compared with an uncertain multiperiod model without background risk and an uncertain multiperiod model without liquidity constraint respectively, we discuss how background risk and liquidity affect optimal terminal wealth. Finally, we give two numerical examples to demonstrate the effectiveness of the proposed approach and models.

A multi-period fuzzy mean-minimax risk portfolio model with investor’s risk attitude

This paper deals with a multi-period portfolio selection problem considering investor’s risk attitude in fuzzy environment. We regard the return rate of each risky asset as a fuzzy number and use the expected value and semi-absolute deviation to measure its return and risk, respectively. We adopt an $$l_{\infty }$$ downside risk function to measure the portfolio’s risk, which is represented by the maximum individual risk. Moreover, we formulate a reasonable diversification constraint for the portfolio involving risk-free asset. Then, we propose a multi-period portfolio selection model with the objectives of maximizing the final expected wealth and minimizing the final cumulative risk. Furthermore, we design a multiple particle swarm optimization to solve it. Finally, we illustrate the effectiveness of the model and algorithm by using a real case.

Fuzzy multi-period portfolio selection model with time-varying loss aversion

This paper deals with multi-period portfolio selection problem in a fuzzy environment, in which the effects of investors’ time-varying asymmetric attitudes to losses and gains on portfolio selection are taken into consideration. In the paper, a definition of time-varying loss aversion is presented to describe the aforementioned time-varying asymmetric attitudes to losses and gains. A fuzzy multi-period portfolio selection model based on this new definition of time-varying loss aversion is formulated. Then, an improved co-evolutionary particle swarm optimization (ICPSO) algorithm is designed to solve the proposed model. The comparison analysis between the proposed model and the fixed-parameter loss aversion model is provided to demonstrate the fact that the proposed model can significantly affect the performance of portfolio selection. Finally, a numerical example is given to illustrate the application of the proposed model and the efficiency of the designed algorithm.

Multi-period portfolio selection with mental accounts and realistic constraints based on uncertainty theory

This paper discusses an uncertain multi-period portfolio selection problem in the situation where the future security return rates are given by experts’ estimations instead of historical data. In financial market, investors may have different attitudes towards risk for different goals. In order to reflect these conflicting risk attitudes for different goals, mental accounts are introduced to the investment. In addition, investment strategies may be affected by some realistic constraints such as background risk, liquidity risk, transaction cost and cardinality constraint. Based on uncertainty theory, a nonlinear multi-period portfolio selection model is proposed with consideration of mental accounts and realistic constraints. In the model, indeterminate quantities such as security return rates and turnover rates are assumed to be uncertain variables. Within the framework of uncertainty theory, we discuss the equivalents of the model and show that the nonlinear model can be equivalently transformed into a linear programming model. Finally, a case study is given to illustrate the performance of the proposed model.

A constrained multi-period robust portfolio model with behavioral factors and an interval semi-absolute deviation

In this paper, a multi-period portfolio selection model is presented considering the behavioral factors of investors. The behavioral factors are presented in the form of prospect theory with three main parameters as reference dependence, risk aversion, and diminishing sensitivity; these parameters define the behavioral features of investors that can influence their investing. The future return of assets is regarded according to the interval based on uncertainty. Besides, a criterion of interval semi-absolute deviation is presented to control the risk of investing. The influence of uncertainty exists in the optimal parameters; the final result is controlled by a robust optimization approach. In order to make this model applicable and adapting it to the conditions of the real world, we considered the cardinality constraints, entropy and the possibility of risk-free borrowing and lending with different rates. First, the model is solved by GAMS in small size to check the feasibility, then, due to the NP-hard feature of the model, we used three meta-heuristic algorithms, which are more appropriate for solving large problems, to solve the proposed model. To survey the model’s performance, we used real data from a case study. The results show that the model reflects the behavioral factors of investors in their portfolio and it also maintains the robustness level in accordance with the degree of conservatism. Besides, the sensitivity analysis is performed to show the model’s efficiency. Finally, we compared the results of different meta-heuristic algorithms and benchmark model’s performance.

Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models

There are myriad works that deal with the fuzzy multi-period portfolio selection problem, but when we talk about multi-period portfolio selection in an intuitionistic fuzzy realm, to the best of our knowledge, there is no research work that deals with the same. So, to fill this research gap, we propose an intuitionistic fuzzy multi-period portfolio selection model with the objectives of maximization of the terminal wealth and minimization of the cumulative risk subject to several realistic constraints such as complete capital utilization, no short selling, fixed transaction costs for buying and selling, bounds on the desired returns of each period, cardinality constraint, and bounds on the minimal and the maximal proportion of the capital allocated to an asset. The membership and non-membership of the objectives are modeled using their extreme values. The proposed approach provides avenues for the inclusion and minimization of the hesitation degree into decision making, thereby resulting in a significantly better portfolio. Parameters $$\theta _W$$ and $$\theta _{Va}$$ are used to introduce the hesitation in the model, and, based on their values, the model is further categorized into optimistic and pessimistic intuitionistic fuzzy multi-period portfolio selection models for optimistic and pessimistic investors, respectively. The max–min approach is used to solve the proposed models. Furthermore, a numerical illustration is presented to exhibit the virtues of the proposed model.

损失厌恶下的多期多目标不确定投资组合模型及算法

损失厌恶下的多期多目标不确定投资组合模型及算法

Robust multi-period portfolio selection based on downside risk with asymmetrically distributed uncertainty set

Motivated by the asymmetrical attitudes of investors towards downside losses and upside gains, this paper proposes a robust multi-period portfolio selection model based on downside risk with asymmetrically distributed uncertainty set, in which the downside losses of a portfolio are controlled by the lower partial moment (LPM). A computationally tractable approximation approach based on second-order cone optimization is used for solving the proposed model. We show in theory that the optimal solution of the robust model can generate a given probability guarantee for individual and joint stochastic constraints. The effect of the asymmetrically distributed uncertainty set on performance of the optimal solution is analyzed by the usual comparative static method. Comprehensive numerical comparisons with real market data are reported and indicate that the proposed model can obtain the smaller standard deviation and turnover ratios which reduce the Sharpe ratios of optimal portfolio, compared with some well-known models in the literature.

Portfolio selection in discrete time with transaction costs and power utility function: a perturbation analysis

ABSTRACTIn this article, we study a multi-period portfolio selection model in which a generic class of probability distributions is assumed for the returns of the risky asset. An investor with a power utility function rebalances a portfolio comprising a risk-free and risky asset at the beginning of each time period in order to maximize expected utility of terminal wealth. Trading the risky asset incurs a cost that is proportional to the value of the transaction. At each time period, the optimal investment strategy involves buying or selling the risky asset to reach the boundaries of a certain no-transaction region. In the limit of small transaction costs, dynamic programming and perturbation analysis are applied to obtain explicit approximations to the optimal boundaries and optimal value function of the portfolio at each stage of a multi-period investment process of any length.

Multi-period portfolio selection with dynamic risk/expected-return level under fuzzy random uncertainty

In this study, we discuss multi-period portfolio selection problems when security returns are described as fuzzy random variables. The main concern of this work is to apply dynamic risk tolerance and expected return levels in mathematical modeling; i.e., these two indices of each period are influenced by the investment result of the previous period as well as human risk attitudes instead of static values over the entire investment horizon. Essentially, this assumption is based on the reality that investors tend to update targets when their wealth changes. In addition, fuzzy random variables are employed here to incorporate historical data with expert knowledge when estimating security future returns. Based on the above considerations, two multi-period portfolio selection models are built in light of the different risk attitudes. We then provide property analysis on complicated nonlinear optimization problems and derive several equivalents of the models, which can be solved by the existing dynamic programming. In general situations, a fuzzy random simulation-based particle swarm optimization algorithm is developed to search for approximate optima. The performance of this research is exemplified by a real market data-based case study in which the superiority of the dynamic strategy is demonstrated by a comparison with conventional approaches.

Dynamic and Cross-Platform Optimal Financial Transaction Taxation

This paper analyzes the welfare implications of a linear financial transactions tax in a multi-period portfolio selection model with heterogeneous agents. Under certain conditions over the redistribution of government revenues, with no Pigouvian motives, I find such a tax may induce first-order losses due to the distortion of idiosyncratic risk-sharing. A transaction tax induces both a contemporaneous inaction region and intertemporal shifting of transaction realizations. Given a segmented market over multiple trading platforms and the choice of at least two different tax instruments, I develop sufficient statistic formulas that differ from standard optimal commodity tax theory in that they account for untaxed capital accumulation, market structure rents, and uncertain returns.

Robust Multi-Period Portfolio Selection with Asymmetrically Distributed Uncertainty Set and Return Predictability

This paper considers a robust multi-period portfolio selection problem with asymmetrically distributed uncertainty set. We introduce the mean-LPM (lower partial moment) risk measure and establish a multi-period portfolio selection model, in which the mean-LPM is used to limit the loss of portfolio. To add practicality, we allow the uncertainty set to be asymmetric and include transaction cost in the model. A computationally tractable approximation approach based on second order cone optimization is used for solving the proposed model. Comprehensive numerical comparisons with simulated data and real market data are reported. The numerical results indicate that the proposed model can obtain better expected returns and Sharpe ratios, while reduce the standard deviation and turnover ratios, compared with some well-known models in the literature.

Fuzzy multi-period portfolio selection model with discounted transaction costs

In this paper, we discuss a multi-period portfolio selection with discounted transaction costs in a fuzzy uncertain investment environment, which has not been given much attention before. We assume that an investor’s motivation is to find the portfolio with maximizing terminal wealth and the cumulative skewness on portfolios, and minimizing the cumulative risk on portfolios. We consider the major criteria including wealth, risk, skewness, transaction costs, proportion entropy, transaction lots, the maximum holding number of assets in the portfolio and budge constraint. We propose a possbilistic mean-semivariance-skewness model with discounted transaction costs for multi-period fuzzy portfolio selection. To solve the multi-objective portfolio selection model, we first introduce a weighted max–min fuzzy goal programming approach to take investor’s different investment preferences into account and transform it into a single-objective programming problem and then design a dynamic differential evolution algorithm for solution. Finally, we provide an empirical study with the sample data from Chinese stock market to analyze the application of the model and the performance of the solution algorithm.