Index fund rebalancing using probabilistic model-building genetic algorithm with narrower width histograms

The portfolio optimization/rebalancing problem is to determine a proportion-weighted combination in a portfolio in order to achieve certain investment targets. For this problem, many researchers have used various evolutionary methods and models such as genetic algorithms and simulated annealing. On the other hand, the portfolio optimization/rebalancing problem can be viewed as a multi-dimensional problem because its solution is a proportion-weighted combination for the given assets. The previous works, however, have not taken into account the multi-dimensional aspect of the problem. In order to approach this problem from the multi-dimensional aspect, we propose a model based on the probabilistic model-building genetic algorithm with narrower width histograms (PMBGA-NWH), and then apply it to optimize the constrained index funds with the given rebalancing cost in this paper. In the numerical experiments, we show that our model has better ability to make optimal index funds than the traditional genetic algorithm (GA).