Applying Particle Swarm Optimization: New Solutions and Cases for Optimized Portfolios

Optimization is to find the best-performing solution under the constraints given. It can be something better by optimization process. Heuristic algorithm is an optimization algorithm which depends on natural events. The algorithms are simple and easy to implement for the researcher. The portfolio optimization is a process to find a solution to select the most appropriate combination between all financial assets under certain expectations and constraints. While solving portfolio optimization problems, the aim is to create portfolios by selecting the assets that provide the highest return from huge numbers of financial assets at a certain risk level or provide the lowest risk at a certain level of return. This chapter aims to examine the optimum portfolio with minimum risk by using the particle swarm optimization (PSO) technique, for the stocks in the BIST-30 index. Logarithmic returns are calculated using the price data of the stocks. By using these returns, the optimum portfolio with minimum risk is created with PSO and nonlinear GRG (generalized reduced gradient) techniques. The empirical results obtained indicate that both methods give similar results