Cardinality Constrained Portfolio Optimization Research Articles

Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers.

Inspired by sparse learning, the Markowitz mean-variance model with a sparse regularization term is popularly used in sparse portfolio optimization. However, in penalty-based portfolio optimization algorithms, the cardinality level of the resultant portfolio relies on the choice of the regularization parameter. This brief formulates the mean-variance model as a cardinality ( l0 -norm) constrained nonconvex optimization problem, in which we can explicitly specify the number of assets in the portfolio. We then use the alternating direction method of multipliers (ADMMs) concept to develop an algorithm to solve the constrained nonconvex problem. Unlike some existing algorithms, the proposed algorithm can explicitly control the portfolio cardinality. In addition, the dynamic behavior of the proposed algorithm is derived. Numerical results on four real-world datasets demonstrate the superiority of our approach over several state-of-the-art algorithms.

A hybrid level-based learning swarm algorithm with mutation operator for solving large-scale cardinality-constrained portfolio optimization problems

We propose a hybrid variant of the level-based learning swarm optimizer (LLSO) for solving large-scale portfolio optimization problems. This solver fills the gap due to the inadequacy of the particle swarm optimization algorithm for high-dimensional instances. We aim to extend the classical mean-variance formulation by maximizing a modified version of the Sharpe ratio subject to cardinality, box, and budget constraints. The algorithm involves a projection operator to deal with these three constraints simultaneously. Further, we implicitly control transaction costs thanks to a rebalancing constraint handled by a suitable exact penalty function. In addition, we develop an ad hoc mutation operator to modify candidate exemplars in the highest level of the swarm. The experimental results, using three large-scale data sets, show that including this procedure improves the accuracy of the solutions. Then, a comparison with other variants of the LLSO algorithm and two state-of-the-art swarm optimizers points out the outstanding performance of the proposed solver in terms of exploration capabilities and solution quality. Finally, we assess the profitability of the portfolio allocation strategy in the last five years using an investable pool of 1119 constituents from the MSCI World Index.

End-to-End, Decision-based, Cardinality-Constrained Portfolio Optimization

End-to-End, Decision-based, Cardinality-Constrained Portfolio Optimization

Hybrid Enhanced Binary Honey Badger Algorithm with Quadratic Programming for Cardinality Constrained Portfolio Optimization

A portfolio selection problem with cardinality constraints has been proved to be an NP-hard problem, and it is difficult to solve by the traditional optimization methods. This study considers it to be a hybrid of a classical feature selection problem and a standard mean-variance (MV) portfolio selection model. In particular, we propose a new hybrid meta-heuristic algorithm that combines an enhanced binary honey badger algorithm (EBHBA) with quadratic programming to address this issue. First, we employ the proposed EBHBA algorithm to select a portfolio of [Formula: see text] stocks from [Formula: see text] candidate stocks. Second, based on its choice we transform the problem into a mean-variance model, whose objective function could be defined as the fitness function of EBHBA. Finally, the optimal solution to the model could be found with the quadratic programming method. We also test our approach using the benchmark data sets available at the OR-Library involving real capital markets, where indices are derived from major stock markets around the world. Computational results demonstrate that the proposed method can achieve a satisfactory result for portfolio selection with cardinality constraints and perform well in searching non-dominated portfolios with high expected returns.

Cardinality constrained portfolio optimization with a hybrid scheme combining a Genetic Algorithm and Sonar Inspired Optimization

The constraints and the vast solution space of operational research optimization problems make them hard to cope with. However, Computational Intelligence, and especially Nature-Inspired Algorithms, has been a useful tool to tackle hard and large space optimization problems. In this paper, a very consistent and effective hybrid optimization scheme to tackle cardinality constrained portfolio optimization problems is presented. This scheme consists of two nature-inspired algorithms, i.e. Sonar Inspired Optimization algorithm and Genetic Algorithm. Also, the incorporation of heuristic information, i.e. an expert’s knowledge, etc., to the overall performance of the hybrid scheme is tested and compared to previous studies. More specifically, under the framework of a financial portfolio optimization problem, the heuristic information-enhanced hybrid scheme manages to reach a new optimal solution. Additionally, a comparison of the proposed hybrid scheme with other hybrid schemes applied to the same problem with the same data is performed.

Cardinality-constrained portfolio optimization with short selling and risk-neutral interest rate

Short selling strategy leads to a portfolio with significantly better risk-return structure compared to the standard approach. Moreover, investors can use risk-neutral interest rate to increase the return of the portfolio. In this paper, we study the cardinality-constrained mean–variance portfolio optimization model with and without short selling and risk-neutral interest rate. First, to avoid negative investment in stocks with no short selling position, the non-negativeness of the product of each stock’s return to the proportion of investment on it is added to the model as a constraint. Then, we further present an improved model, where instead of determining the term of the short rebate according to the proportion of the total funds invested, it is determined according to the return. Finally, all models are compared using the data set of the S&P 500 index, Communication Service.

A Relaxed Optimization Approach for Cardinality-Constrained Portfolio Optimization

A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client preferences as they seek to maximize return and limit risk. We develop a new approach to solve cardinality-constrained portfolio optimization problems, extending both Markowitz and conditional value at risk (CVaR) optimization models with cardinality constraints. We derive a continuous relaxation method for the NP-hard objective, which allows for very efficient algorithms with standard convergence guarantees for nonconvex problems. For smaller cases, where brute force search is feasible to compute the globally optimal cardinality-constrained portfolio, the new approach finds the best portfolio for the cardinality-constrained Markowitz model and a very good local minimum for the cardinality-constrained CVaR model. For higher dimensions, where brute-force search is prohibitively expensive, we find feasible portfolios that are nearly as efficient as their non-cardinality constrained counterparts.

A GRASP based solution approach to solve cardinality constrained portfolio optimization problems

In the current work, a solution methodology which combines a meta-heuristic algorithm with an exact solution approach is presented to solve cardinality constrained portfolio optimization (CCPO) problem. The proposed method is comprised of two levels, namely, stock selection and proportion determination. In stock selection level, a greedy randomized adaptive search procedure (GRASP) is developed. Once the stocks are selected the problem reduces to a quadratic programming problem. As GRASP ensures cardinality constraints by selecting predetermined number of stocks and quadratic programming model ensures the remaining problem constraints, no further constraint handling procedures are required. On the other hand, as the problem is decomposed into two sub-problems, total computational burden on the algorithm is considerably reduced. Furthermore, the performance of the proposed algorithm is evaluated by using benchmark data sets available in the OR Library. Computational results reveal that the proposed algorithm is competitive with the state of the art algorithms in the related literature.

A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs

A memetic approach that combines a genetic algorithm (GA) and quadratic programming is used to address the problem of optimal portfolio selection with cardinality constraints and piecewise linear transaction costs. The framework used is an extension of the standard Markowitz mean–variance model that incorporates realistic constraints, such as upper and lower bounds for investment in individual assets and/or groups of assets, and minimum trading restrictions. The inclusion of constraints that limit the number of assets in the final portfolio and piecewise linear transaction costs transforms the selection of optimal portfolios into a mixed-integer quadratic problem, which cannot be solved by standard optimization techniques. We propose to use a genetic algorithm in which the candidate portfolios are encoded using a set representation to handle the combinatorial aspect of the optimization problem. Besides specifying which assets are included in the portfolio, this representation includes attributes that encode the trading operation (sell/hold/buy) performed when the portfolio is rebalanced. The results of this hybrid method are benchmarked against a range of investment strategies (passive management, the equally weighted portfolio, the minimum variance portfolio, optimal portfolios without cardinality constraints, ignoring transaction costs or obtained with L1 regularization) using publicly available data. The transaction costs and the cardinality constraints provide regularization mechanisms that generally improve the out-of-sample performance of the selected portfolios.

Решение задачи оптимального портфельного инвестирования с ограничением на кардинальность методами эвристического поиска

Решение задачи оптимального портфельного инвестирования с ограничением на кардинальность методами эвристического поиска

Cardinality Constrained Portfolio Optimization Using a Hybrid Approach Based on Particle Swarm Optimization and Hopfield Neural Network

Cardinality Constrained Portfolio Optimization Using a Hybrid Approach Based on Particle Swarm Optimization and Hopfield Neural Network

A Local Relaxation Method for Cardinality Constrained Portfolio Optimization Problem

The NP-hard nature of cardinality constrained mean-variance portfolio optimization problems has led to a variety of different algorithms with varying degrees of success in reaching optimality given limited computational resources and under the presence of strict time constraints in practice. The proposed local relaxation algorithm exploits the inherent structure of the objective function. It solves a sequence of small, local, quadratic-programs by first projecting asset returns onto a reduced metric space, followed by clustering in this space to identify sub-groups of assets that best accentuate a suitable measure of similarity amongst different assets. The algorithm can either be cold started using the centroids of initial clusters or be warm started based on the output of a previous result. Empirical result, using baskets of up to 3,000 stocks and with different cardinality constraints, indicates that the proposed algorithm is able to achieve significant performance gain over a sophisticated branch-and-cut method. One key application of this algorithm is in dealing with large scale cardinality constrained portfolio optimization under tight time constraint, such as for the purpose of index tracking or index arbitrage at high frequency

Lagrangian relaxation procedure for cardinality-constrained portfolio optimization

This paper studies a portfolio-selection problem subject to a cardinality constraint, that is, the number of securities in a portfolio is restricted to a certain limit. The problem is formulated as a cardinality-constrained quadratic programming problem, and a dedicated Lagrangian relaxation method is developed. In contrast to many existing Lagrangian relaxation methods, the approach presented in the paper is able to take advantage of the special structure of the objective function rather than the special structure of the constraints. The algorithm developed here has been applied to track the major market indices, such as the S&P 500, S&P 100, FTSE 100, and FTSE 250, using real data, and the computational results are promising.