Particle swarm optimization approach to index tracking problem with a cardinality constraint
Xun Zhang · Journal of Natural Science of Heilongjiang University · 2009
With the index derivative production are paid attention to day and day,index portfolio are often used by investor or financial setup,but it is not real that investors invest index according to the proportion of index fund-construction with limited fund in number.So the minimum tracking error of index is becoming increasingly important.The tracking error is defined as the standard deviations of the returns' differences(i.e.the root-mean-squared deviation)between the portfolio and the benchmark of index,and portfolio optimization model of the minimum tracking error is established with cardinality constraints.This portfolio optimization model,with a restriction on the cardinality constraints,is a nonlinear and mixed integer programming problem,for which efficient algorithms do not exist.A particle swarm optimization(PSO)algorithm is proposed to solve the tracking error minimization problem.The numerical results show that PSO approach is successful in portfolio optimization.