| Summary: | The problem of portfolio selection has always been a key concern for investors. The early
work of Markowitz (1959), known as the Mean-Variance model, has been widely adopted
as the basis for solving the portfolio selection problem. In real-world scenarios, investors
would normally impose certain constraints on their portfolio solution in order to
customise it to meet their investment needs. Incorporating these constraints into the
portfolio selection problem makes the problem nonlinear which unveils the inability of the
Mean-Variance model for solving the nonlinear portfolio selection problem.
In this study, a portfolio optimisation system (POPT) is developed. POPT incorporates
three heuristic methods based on Simulated Annealing (SA), Tabu Search (TS) and
Variable Neighbourhood Search (VNS), which are applied to the optimisation of realistic
portfolios. The optimisation model used is based on the classical Mean-Variance
approach but enhanced with cardinality, proportion and pre-assignment constraints. The
model is flexible enough to accommodate any objective function without relying on any
assumed or restrictive features of the model.
In evaluating the model, several cases are considered under varying conditions such as
portfolio size, constraints and neighbourhood size. For example, the number of assets in
a portfolio invariably increases the search space. This study evaluates the model portfolio
problems containing up to 150 assets. SA, TS and VNS are applied to each case and
comparisons of the results are examined. In all cases, the ability of VNS to produce the
best objective value in its first few iterations makes it outperform SA and TS. In order of
performance, VNS is found to be the best, followed by TS and lastly SA.
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