Portfolio optimization under market impact costs

This study presents a methodology for evolving mean-variance efficient portfolios when the agent is facing market impact costs. We use Grammatical Evolution, a form of Genetic Programming, to create portfolio strategies on an artificial market suited to simulate market impact. Classical portfolio selection as introduced by Markowitz is a well-established method to select securities based on their underlying returns and variances. This framework works well in an idealized world, where there are no market frictions and the true returns of the assets are known and normally distributed. In the real world however we face a range of problems such as transaction costs. For an active portfolio manager, transaction costs can consume a substantial amount of information value (also called a manager´s alpha). One part of the transaction costs which are implicit rather than explicit are market impact costs. There has been extensive research which looks at the problem of building or liquefying a given position when facing market impact costs but it might be beneficial to look at the problem at a broader perspective where the decision which assets to include into the portfolio has not been made. We find that on the artificial market, Grammatical Evolution is able to construct portfolio strategies which considerably outperform a linearly built-up Markowitz tangency portfolio by limiting the invested amount and adjusting the portfolio weights.