Equality constrained long-short portfolio replication by using probabilistic model-building GA

Abstract

Portfolio replication problem is to optimize the portfolio such that its proportion-weighted combination is the same as the given benchmark portfolio. However, the benchmark portfolio generally opens only the return to the public but other information such as the assets included in the portfolio, the proportion-weighted combination, the rebalancing date and the investment strategies is closed to the public. In order to optimize such portfolios, we propose an optimization method based on the probabilistic model-building GA in this paper. On the other hand, we are focusing on the long-short portfolio optimization. The long-short portfolio consists of the assets with long positions in which they have bought and been held and with short positions in which they have been borrowed and sold. While applying any optimization method to the long-short portfolios, the portfolio as a feasible solution must be satisfied an equality constraint. In order to make the feasible solutions effectively, we propose two techniques and then apply them to our optimization method. In the numerical experiments, we show that our method has better ability to replicate the long-short portfolios with good fitness values. We found that, however, some portfolios were not replicated though our method worked well. We also discuss this problem in this paper.