10. Cardinality-Constrained Higher-Order Moment Portfolios Using Particle Swarm Optimization

Particle swarm optimization (PSO) is often used for solving cardinality-constrained portfolio optimization problems. The system invests in at most k out of N possible assets using a binary mapping that enforces compliance with the cardinality constraint. This may lead to sparse solution vectors driving the velocity in PSO algorithm. This sparse-velocity mapping leads to early stagnation in mean-variance-skewness-kurtosis expected utility optimization when k is small compared to N. A continuous-velocity driver addresses this issue. We propose to combine both the continuous- and the sparse-velocity transformation methods so that it updates local and global best positions based on both the drivers. We document the performance gains when k is small compared to N in the case of mean-variance-skewness-kurtosis expected utility optimization of the portfolio.