990 research outputs found
Cardinality constrained portfolio optimisation
Copyright © 2004 Springer-Verlag Berlin Heidelberg. The final publication is available at link.springer.comBook title: Intelligent Data Engineering and Automated Learning – IDEAL 20045th International Conference on Intelligent Data Engineering and Automated Learning (IDEAL 2004), Exeter, UK. August 25-27, 2004The traditional quadratic programming approach to portfolio optimisation is difficult to implement when there are cardinality constraints. Recent approaches to resolving this have used heuristic algorithms to search for points on the cardinality constrained frontier. However, these can be computationally expensive when the practitioner does not know a priori exactly how many assets they may desire in a portfolio, or what level of return/risk they wish to be exposed to without recourse to analysing the actual trade-off frontier.This study introduces a parallel solution to this problem. By extending techniques developed in the multi-objective evolutionary optimisation domain, a set of portfolios representing estimates of all possible cardinality constrained frontiers can be found in a single search process, for a range of portfolio sizes and constraints. Empirical results are provided on emerging markets and US asset data, and compared to unconstrained frontiers found by quadratic programming
Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation
A financial portfolio contains assets that offer a return with a certain
level of risk. To maximise returns or minimise risk, the portfolio must be
optimised - the ideal combination of optimal quantities of assets must be
found. The number of possible combinations is vast. Furthermore, to make the
problem realistic, constraints can be imposed on the number of assets held in
the portfolio and the maximum proportion of the portfolio that can be allocated
to an asset. This problem is unsolvable using quadratic programming, which
means that the optimal solution cannot be calculated. A group of algorithms,
called metaheuristics, can find near-optimal solutions in a practical computing
time. These algorithms have been successfully used in constrained portfolio
optimisation. However, in past studies the computation time of metaheuristics
is not limited, which means that the results differ in both quality and
computation time, and cannot be easily compared. This study proposes a
different way of testing metaheuristics, limiting their computation time to a
certain duration, yielding results that differ only in quality. Given that in
some use cases the priority is the quality of the solution and in others the
speed, time limits of 1, 5 and 25 seconds were tested. Three metaheuristics -
simulated annealing, tabu search, and genetic algorithm - were evaluated on
five sets of historical market data with different numbers of assets. Although
the metaheuristics could not find a competitive solution in 1 second, simulated
annealing found a near-optimal solution in 5 seconds in all but one dataset.
The lowest quality solutions were obtained by genetic algorithm.Comment: 51 pages, 8 tables, 3 figure
Portfolio selection using neural networks
In this paper we apply a heuristic method based on artificial neural networks
in order to trace out the efficient frontier associated to the portfolio
selection problem. We consider a generalization of the standard Markowitz
mean-variance model which includes cardinality and bounding constraints. These
constraints ensure the investment in a given number of different assets and
limit the amount of capital to be invested in each asset. We present some
experimental results obtained with the neural network heuristic and we compare
them to those obtained with three previous heuristic methods.Comment: 12 pages; submitted to "Computers & Operations Research
Constrained portfolio optimisation: the state-of-the-art Markowitz models
This paper studies the state-of-art constrained portfolio optimisation models, using exact solver to identify the optimal solutions or lower bound for the benchmark instances at the OR-library with extended constraints. The effects of pre-assignment, round-lot, and class constraints based on the quantity and cardinality constrained Markowitz model are firstly investigated to gain insights of increased problem difficulty, followed by the analysis of various constraint settings including those mostly studied in the literature. The study aims to provide useful guidance for future investigations in computational algorithm
Constrained Portfolio Optimisation
Portfolio optimisation is an important problem in finance; it allows investors to manage
their investments effectively. This paper considers finding the efficient frontier associated
with the mean-variance portfolio optimisation (unconstrained) problem. We then
extend the mean-variance model to include cardinality constraints (resulting in an NPHard
problem) that limits the number of assets in a portfolio. We discuss different
types of algorithms that one can use for finding the optimal portfolios, implementing a
meta-heuristic genetic algorithm technique to solve the unconstrained and cardinality
constrained problems. Finally, we improve our solutions by altering the crossover and
mutation probabilities in the genetic algorithm method. For finding the efficient frontier
associated with both problems, we examine a dataset involving 55 assets from the US
stock exchange
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Solving cardinality constrained portfolio optimisation problem using genetic algorithms and ant colony optimisation
This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonIn this thesis we consider solution approaches for the index tacking problem, in which we aim to reproduces the performance of a market index without purchasing all of the stocks that constitute the index. We solve the problem using three different solution approaches: Mixed Integer Programming (MIP), Genetic Algorithms (GAs), and Ant-colony Optimization (ACO) Algorithm by limiting the number of stocks that can be held. Each index is also assigned with different cardinalities to examine the change to the solution values. All of the solution approaches are tested by considering eight market indices. The smallest data set only consists of 31 stocks whereas the largest data set includes over 2000 stocks. The computational results from the MIP are used as the benchmark to measure the performance of the other solution approaches. The Computational results are presented for different solution approaches and conclusions are given. Finally, we implement post analysis and investigate the best tracking portfolios achieved from the three solution approaches. We summarise the findings of the investigation, and in turn, we further improve some of the algorithms. As the formulations of these problems are mixed-integer linear programs, we use the solver ‘Cplex’ to solve the problems. All of the programming is coded in AMPL
Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması
Mean-variance portfolio optimization model, introduced by Markowitz, provides a fundamental answer to the problem of portfolio management. This model seeks an efficient frontier with the best trade-offs between two conflicting objectives of maximizing return and minimizing risk. The problem of determining an efficient frontier is known to be NP-hard. Due to the complexity of the problem, genetic algorithms have been widely employed by a growing number of researchers to solve this problem. In this study, a literature review of genetic algorithms implementations on mean-variance portfolio optimization is examined from the recent published literature. Main specifications of the problems studied and the specifications of suggested genetic algorithms have been summarized
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