Constrained Portfolio Selection Research Articles

Constrained Dynamic Mean-Variance Portfolio Selection in Continuous-Time

This paper revisits the dynamic MV portfolio selection problem with cone constraints in continuous-time. We first reformulate our constrained MV portfolio selection model into a special constrained LQ optimal control model and develop the optimal portfolio policy of our model. In addition, we provide an alternative method to resolve this dynamic MV portfolio selection problem with cone constraints. More specifically, instead of solving the correspondent HJB equation directly, we develop the optimal solution for this problem by using the special properties of value function induced from its model structure, such as the monotonicity and convexity of value function. Finally, we provide an example to illustrate how to use our solution in real application. The illustrative example demonstrates that our dynamic MV portfolio policy dominates the static MV portfolio policy.

Product Supply Optimization for Crowdfunding Campaigns

Recent years have witnessed the rapid development of Finance Internet platforms, specifically, crowdfunding, which is for creators designing campaigns (projects) to collect funds from the public. Usually, the limited budget of a creator is manually divided into several perks (reward options), which should fit various market demand and further bring different monetary contributions for the campaign. Therefore, it is very challenging for each creator to design an effective allocation of perks when launching a campaign. Indeed, our aim is to enhance the funding performance of newly proposed campaigns, with a focus on optimizing the product supply of perks. In this paper, given the expected budget and the perks of a campaign, we propose a novel solution to automatically recommend the optimal product supply for balancing the expected return of this campaign against the risk. Along this line, we define it as a constrained portfolio selection problem, where the investment volume is measured by a multi-task learning method, and we adopt two kinds of methods for task splitting. Furthermore, we extend the investment volume prediction model with inner competition for capturing the competitive relationship between the perks in one campaign. Finally, extensive experiments on real-world crowdfunding data clearly prove the performance significantly.

Constrained Utility Deviation-Risk Optimization and Time-consistent HJB Equation

In this paper we propose a unified utility deviation-risk model which covers both utility maximization and mean-variance analysis as special cases. We derive the time-consistent Hamilton-Jacobi-Bellman (HJB) equation for the equilibrium value function and significantly reduce the number of state variables, which makes the HJB equation derived in this paper much easier to solve than the extended HJB equation in the literature. We illustrate the usefulness of the time-consistent HJB equation with several examples which recover the known results in the literature and go beyond, including a mean-variance model with stochastic volatility dependent risk aversion, a utility deviation-risk model with state dependent risk aversion and control constraint, and a constrained portfolio selection model. The numerical and statistical tests show that the utility and deviation-risk have a significant impact on the equilibrium control strategy and the distribution of the terminal wealth.

A sparse chance constrained portfolio selection model with multiple constraints

This paper presents a general sparse portfolio selection model with expectation, chance and cardinality constraints. For the sparse portfolio selection model, we derive respectively the sample based reformulation and distributionally robust reformulation with mixture distribution based ambiguity set. These reformulations are mixed-integer programming problem and programming problem with difference of convex functions (DC), respectively. As an application of the general model and its reformulations, we consider the sparse enhanced indexation problem with multiple constraints. Empirical tests are conducted on the real data sets from major international stock markets. The results demonstrate that the proposed model, the reformulations and the solution method can efficiently solve the enhanced indexation problem and our approach can generally achieve sparse tracking portfolios with good out-of-sample excess returns and high robustness.

Constrained Utility Deviation-Risk Optimization and Time-Consistent HJB Equation

In this paper we propose a unified utility deviation-risk model which covers both utility maximization and mean-variance analysis as special cases. We derive the time-consistent Hamilton--Jacobi--Bellman (HJB) equation for the equilibrium value function and significantly reduce the number of state variables, which makes the HJB equation derived in this paper much easier to solve than the extended HJB equation in the literature. We illustrate the usefulness of the time-consistent HJB equation with several examples which recover the known results in the literature and go beyond, including a mean-variance model with stochastic volatility dependent risk aversion, a utility deviation-risk model with state dependent risk aversion and control constraint, and a constrained portfolio selection model. The numerical and statistical tests show that the utility and deviation-risk have a significant impact on the equilibrium control strategy and the distribution of the terminal wealth.

A constrained portfolio selection model at considering risk-adjusted measure by using hybrid meta-heuristic algorithms

Portfolio selection is a key issue in the business world and financial fields. This article presents a new decision making method of portfolio optimization (PO) issues in different risk measures by using new evolutionary computing method and cardinality constrains which is mentioned as hybrid meta-heuristic algorithms. Based on mean–variance (MV) Method by Markowitz we collected three risk levels; mean absolute deviation (MAD), semi variance (SV) and variance with skewness (VWS). The developed algorithms are Electromagnetism-like algorithm (EM), particle swarm optimization (PSO), genetic algorithm (GA), genetic network programming (GNP) and simulated annealing (SA). Also a diversification mechanism strategy is implemented and hybridized with the developed algorithms to increase the diversity and overcome local optimality. The sustainability of this proposed model is verified by 50 factories on the Iranian stock exchange. Finally, experimental results of proposed algorithms with cardinality constraint are compared with each other by four effective metrics in which the algorithms performance for achieving the optimal solution discussed. In addition, we have done the analysis of variance technique to confirm the validity and accurately analyze of the results which the success of this method was proved.

Estimation of cardinality constrained portfolio efficiency via segmented DEA

The cardinality constrained portfolio selection problem arises due to the empirical findings that investors tend to hold a limited number of assets. Yet the lack of fast computational methods for frontier of cardinality constrained portfolio investments makes the performance evaluation of this problem a long-standing challenge. Classic Data Envelopment Analysis (DEA) models have been justified valid in evaluating and ranking portfolio performance. Unfortunately, when it comes to the cardinality constrained portfolio selection problem, the DEA models fail to approximate the portfolio efficiency (PE) since the real frontier is discontinuous and not concave. To solve this problem, we propose a segmented DEA approach based on data segment points. A searching algorithm is introduced to approach the real segment points and proved to be valid. In each segment, the frontier is continuous and concave; hence, classic DEA models can be applied to evaluate the PE. The simulation results further indicate that the segmented DEA approach proposed in this paper is effective and practical in evaluating the cardinality constrained portfolio performance.

Improved Constrained Portfolio Selection Model using Particle Swarm Optimization

Improved Constrained Portfolio Selection Model using Particle Swarm Optimization

Efficiency impact of convergence bidding in the california electricity market

The California Independent System Operator (CAISO) has implemented Convergence Bidding (CB) on February 1, 2011 under Federal Energy Regulatory Commission’s September 21, 2006 Market Redesign and Technology Upgrade Order. CB is a financial mechanism that allows market participants, including electricity suppliers, consumers and virtual traders, to arbitrage price differences between the day-ahead (DA) market and the real-time (RT) market without physically consuming or producing energy. In this paper, market efficiency is defined in terms of trading profitability, where a zero-profit competitive equilibrium implies market efficiency (Jensen in, J Financial Econ 6(2):95–101, 1978). We analyze market data in the CAISO electric power markets, and empirically test for market efficiency by assessing the performance of trading strategies from the perspective of virtual traders. By viewing DA–RT spreads as payoffs from a basket of correlated assets, we can formulate a chance constrained portfolio selection problem, where the chance constraint takes two different forms as a value-at-risk constraint and a conditional value-at-risk constraint, to find the optimal trading strategy. A hidden Markov model (HMM) is further proposed to capture the presence of the time-varying forward premium. This is meant to be a contribution to the modeling of regime shifts in the electricity forward premium with unobservable states. Our backtesting results cast doubt on the efficiency of the CAISO electric power markets, as the trading strategy generates consistent profits after the introduction of CB, even in the presence of transaction costs. Nevertheless, by comparing with the performance before the introduction of CB, we find that the profitability decreases significantly, which enables us to identify the efficiency gain brought about by CB. Convincing evidence for the improvement of market efficiency in the presence of CB is further provided by the test for the Bessembinder and Lemmon (J Finance 57(3):1347–1382, 2002) model.

Improved Constrained Portfolio Selection Model using Particle Swarm Optimization

Objective: The main objective of this study is to improve the extended Markowitz mean-variance portfolio selection model by introducing a new constraint known as expert opinion practicable for portfolio selection in real-life situation. Methods: This new extended model consists of four constraints namely: bounds on holdings, cardinality, minimum transaction lots, and expert opinion. The first three constraints have been presented in other researches in literature. The fourth constraint introduced in this study is an essential parameter in making and guiding a realistic portfolio selection. To solve this new extended model an efficient heuristic method of Particle Swarm Optimization (PSO) was engaged with existing benchmark data in the literature. Results: The outcome of the computational results obtained in this study with the new extended Markowitz mean-variance portfolio selection model proposed in this study and solved with PSO showed an improved performance over existing algorithm in particular GA in different instances of the data set used. Conclusion: The study evolves a new extended portfolio selection model and the findings demonstrate the superiority of PSO performance in solving portfolio selection problem in comparison with GA algorithm.

Portfolio Selection with Multiple Spectral Risk Constraints

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value-at-risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In each step, the algorithm solves very simple separable convex quadratic programs; hence, we show that the spectral risk constrained portfolio selection problem can be solved using the technology developed for solving mean-variance problems. The algorithm extends to the case where the objective is a weighted sum of the mean return and either a weighted combination or the maximum of a set of spectral risk measures. We report numerical results that show that our proposed algorithm is very efficient; it is at least one order of magnitude faster than the state-of-the-art general purpose solver for all practical instances. One can leverage this efficiency to be robust against model risk by including constraints with respect to several different risk models.

Factor Model Based Clustering Approach for Cardinality Constrained Portfolio Selection

Portfolio selection concerns identifying an optimal composition of various risky assets and their corresponding holding amounts such that the corresponding investment strategy strikes a balance between maximizing the expected investment return and minimizing investment risk. While market frictions make full diversification impractical, cardinality constrained mean-variance (CCMV) portfolio selection problem emerges as a natural remedy: Given an asset pool with total n assets and a given cardinality s < n , optimally choose s assets from the entire asset pool such as to achieve a mean-variance efficiency. Unfortunately, CCMV has been proved to be NP hard and has been posted in front of optimization society as a long-standing challenge. By invoking structural market information and utilizing fast clustering algorithm for classification, we develop in this paper an effective heuristic scheme to identify approximate solutions for large-scale CCMV problems. More specifically, by constructing grouping constraints generated from factor-model based clustering algorithm and attaching them to the mixed integer programming formulation associated with the CCMV problem, we are able to significantly reduce the computational complexity, thus offering a fast algorithm with relatively high quality solution.

In This Issue

In This Issue

Optimal Cardinality Constrained Portfolio Selection

One long-standing challenge in both the optimization and investment communities is to devise an efficient algorithm to select a small number of assets from an asset pool such that a portfolio objective is optimized. This cardinality constrained investment situation naturally arises due to the presence of various forms of market friction, such as transaction costs and management fees, or even due to the consideration of mental cost. Unfortunately, the combinatorial nature of such a portfolio selection problem formulation makes the exact solution process NP-hard in general. We focus in this paper on the cardinality constrained mean-variance portfolio selection problem. Instead of tailoring such a difficult problem into the general solution framework of mixed-integer programming formulation, we explore the special structures and rich geometric properties behind the mathematical formulation. Applying the Lagrangian relaxation to the primal problem results in a pure cardinality constrained portfolio selection problem, which possesses a symmetric property, and to which geometric approaches can be developed. Different from the existing literature that has primarily focused on some direct relaxations of the cardinality constraint, we consider modifying the objective function to some separable relaxations, which are immune to the hard cardinality constraint. More specifically, we develop efficient lower bounding schemes by using the circumscribed box, the circumscribed ball, and the circumscribed axis-aligned ellipsoid to approximate the objective contour of the problem. In particular, all these cardinality constrained relaxation problems can be solved analytically. Furthermore, we derive efficient polynomial-time algorithms for the corresponding dual search problems. Most promisingly, the lower bounding scheme using the circumscribed axis-aligned ellipsoid leads to a semidefinite programming (SDP) formulation and offers a sharp bound and high-quality feasible solution. By integrating these lower bounding schemes into a branch-and-bound algorithm (BnB), our solution scheme outperforms CPLEX significantly in identifying the exact optimal portfolio.

A hybrid algorithm for constrained portfolio selection problems

Since Markowitz's seminal work on the mean-variance model in modern portfolio theory, many studies have been conducted on computational techniques and recently meta-heuristics for portfolio selection problems. In this work, we propose and investigate a new hybrid algorithm integrating the population based incremental learning and differential evolution algorithms for the portfolio selection problem. We consider the extended mean-variance model with practical trading constraints including the cardinality, floor and ceiling constraints. The proposed hybrid algorithm adopts a partially guided mutation and an elitist strategy to promote the quality of solution. The performance of the proposed hybrid algorithm has been evaluated on the extended benchmark datasets in the OR Library. The computational results demonstrate that the proposed hybrid algorithm is not only effective but also efficient in solving the mean-variance model with real world constraints.

Portfolio Selection with Multiple Spectral Risk Constraints

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In each step, the algorithm solves very simple separable convex quadratic programs; hence, we show that the spectral risk constrained portfolio selection problem can be solved using the technology developed for solving mean-variance problems. The algorithm extends to the case where the objective is a weighted sum of the mean return and either a weighted combination or the maximum of a set of spectral risk measures. We report numerical results that show that our proposed algorithm is very efficient; it is at least one order of magnitude faster than the state-of-the-art general purpose solver for all practical instances. One can leverage this efficiency to be robust against model risk by including constraints with respect to several different risk models.

Hybrid metaheuristics for constrained portfolio selection problems

Portfolio selection is a problem arising in finance and economics. While its basic formulations can be efficiently solved using linear or quadratic programming, its more practical and realistic variants, which include various kinds of constraints and objectives, have in many cases to be tackled by heuristics. In this work, we present a hybrid technique that combines a local search metaheuristic, as master solver, with a quadratic programming procedure, as slave solver. Experimental results show that the approach is very promising, as it regularly provides the optimal solution and thus achieves results comparable, or superior, to state-of-the-art solvers, including widespread commercial software tools (CPLEX 11.0.1 and MOSEK 5). The paper reports a detailed analysis of the behavior of the technique in various constraint settings, thus demonstrating how the performance is dependent on the features of the instance.

A Class of Chance Constrained Multi-objective Portfolio Selection Model Under Fuzzy Random Environment

This paper deals with a class of chance constrained portfolio selection problems in the fuzzy random decision making system. An integrated fuzzy random portfolio selection model with a chance constraint is proposed on the basis of the mean-variance model and the safety-first model. According to different definitions of chance, we consider two types of fuzzy random portfolio selection models: one is for the optimistic investors and the other is for the pessimistic investors. In order to deal with the fuzzy random models, we develop a few theorems on the variances of fuzzy random returns and the equivalent partitions of two types of chance constraints. We then transform the fuzzy random portfolio selection models into their equivalent crisp models. We further employ the e-constraint method to obtain the efficient frontier. Finally, we apply the proposed models and approaches to the Chinese stock market as an illustration.

A new particle swarm optimisation based on MATLAB for portfolio selection problem

This paper focuses on the constrained portfolio selection problem and develops an improved particle swarm optimisation (IPSO) algorithm to solve it. As an alternative and extension to the standard Markowitz model, a constrained portfolio selection model with transaction costs and quantity limit is formulated for selecting portfolios. Due to these complex constraints, the process becomes a high-dimensional constrained optimisation problem. Traditional optimisation algorithms fail to work efficiently and heuristic algorithms with effective searching ability can be the best choice for the problem, so we design an IPSO to solve our problem. In order to prevent premature convergence to local minima, we design a new definition for global point. Finally, a numerical example of a portfolio selection problem is given to illustrate our proposed method; the simulation results demonstrate good performance of the IPSO in solving the complex constrained portfolio selection problem.

Risk Constrained Portfolio Selection of Renewable Sources in Hydrothermal Electricity Markets

Renewable sources have recently emerged as a generation option for many countries in order to promote clean energy development. In the case of Brazil, small hydro plants and cogeneration from sugarcane waste (bagasse) have been attractive alternatives during the past years, with hundreds of MW installed since 2004. Despite their advantages, both alternatives are hindered by seasonal yet complementary availability. This forces producers to discount (or price) the risks faced when selling firm energy contracts and may ultimately lead to projects being commercially unattractive. We propose a stochastic optimization model that defines the optimal composition of a portfolio based on these two renewable sources in order to maximize the revenue of an energy trading company. At the same time, this model mitigates hydrological and fuel unavailability risks, thus allowing the participation of both sources in the forward market environment in a competitive manner. A case study is presented, based on data from the Brazilian system.