Optimized index tracking using a hybrid genetic algorithm

Assuming the market is efficient, an obvious portfolio management strategy is passive where the challenge is to track a certain benchmark like a stock index such that equal returns and risks are achieved. A tracking portfolio consists of a (usually small) weighted subset of stock funds. The weights are supposed to be positive here which means that short selling is not allowed. We investigate an approach for tracking the Dutch AEX index where an optimal tracking portfolio is determined. The optimal weights of a portfolio are found by minimizing the tracking error for a set of historical returns and covariances. The overall optimal portfolio is found using a hybrid genetic algorithm where each chromosome represents a specific subset of the stocks from the index, the fitness function of each chromosome corresponds to the minimized tracking error achievable with that subset, and the optimal portfolio is the tracking portfolio with highest fitness achievable. We show the experimental setup and the simulation results, including the out-of-sample performance of the optimal tracking portfolio. The hybrid genetic algorithms used appear to be robust in finding the optimal tracking portfolio and the performance of this portfolio on the out-of-sample data set is approximately four times better than that of randomly selected portfolios with optimized stock weights. By choosing a dedicated crossover operator, the hybrid genetic algorithm appears to find the optimal tracking portfolio using, on average, less than 23 generations only.