Modelling of multiple constraints portfolio optimization using modified particle swarm optimization

Abstract

In finance, the portfolio is the set of investment in the assets. Meanwhile, its optimization leads towards the best selection and diversification of investments. Portfolio optimization involves the objectives (mean, variance or Sharp Ratio (SR)) and constraints (budget, short sell, outliers, cardinality, lot and transaction cost, liquidity), as well as some others which makes it more complex, dynamic and intractable. The SR function is considered to be the measuring tool for best portfolio selection and optimization. At present, the area of portfolio optimization lacks in having multiple constraints with the SR as the objective function. This research focuses on a two-stage portfolio selection, diversification, and optimization. The normality tests have been performed from the data considered and it is found that the data is nonlinear and stochastic. The two selection criterion (mean and variance) have been introduced in this research. Furthermore, several constraints have been considered for the problem of Multiple Constraints Portfolio Optimization (MCPO). A metaheuristic technique needs to be developed with the financial toolbox inMATLAB and the Particle SwarmOptimization (PSO) for portfolio construction, diversification, and optimization, namely, the Modified PSO (MPSO). The simulation on the benchmark model for restriction on the short sale was performed. Also, the diversification phenomenon for having the 10, 50 and 150 assets collection has been observed. The obtained results for the benchmark model are 42.51% and 84.20% increment in Maximum of Maximum Sharp Ratio (MMSR), whereas 39.88% and 84.30% increment in Average of Maximum Sharp Ratio (AMSR). The results of the models having mean of return selection criteria have increments of 2.58%, 21.10%, 16.41%, 11.67%, and 6.42%; whereas, models M3 and M4 for MMSR values have decrement of 3.52% in comparison with the model having the variance of return selection criteria. This research will be beneficial for those involved such as in mathematical finance modeling, asset portfolio optimization and financial model optimization using metaheuristic techniques.