Portfolio Optimization with Transaction Costs

When buying and selling assets on the markets, the investors incur in payment of commissions and other costs, globally defined transaction costs, that are charged by the brokers or the financial institutions playing the role of intermediary. Transaction costs represent the most important feature to account for when selecting a real portfolio, since they diminish net returns and reduce the amount of capital available for future investments. In this chapter, we show that transaction costs may have different structures and that we need for a specific use of variables and constraints to express the transaction costs in linear form. We specify that a model may account for transaction costs in different ways. Transaction costs may be treated separately in a constraint imposing they should not exceed a predefined amount or be deducted from the expected portfolio return and/or diminish the capital available for the actual investment. When a complete portfolio optimization model is defined, some of the constraints on the definition of the transaction costs may be relaxed without affecting the correctness of the model as the optimization ’pushes’ the transaction costs to the minimum value allowed by the constraints. In this chapter, we first present the most common structures of transaction costs including fixed, proportional, with minimum charge, convex and concave piecewise linear costs, and see how to model them. We then discuss the different ways to account for transaction costs in a portfolio optimization model. Finally, we present, as an example, a complete portfolio optimization model using CVaR as objective function.