A Note on Portfolio Optimization with Quadratic Transaction Costs
This is an incremental improvement for financial portfolio managers, focusing on a specific computational issue in optimization.
The paper tackles the problem of mean-variance portfolio optimization with quadratic transaction costs, showing that it complicates the optimization due to a non-linear budget constraint, and provides numerical algorithms to address this, illustrating significant impacts on expected returns.
In this short note, we consider mean-variance optimized portfolios with transaction costs. We show that introducing quadratic transaction costs makes the optimization problem more difficult than using linear transaction costs. The reason lies in the specification of the budget constraint, which is no longer linear. We provide numerical algorithms for solving this issue and illustrate how transaction costs may considerably impact the expected returns of optimized portfolios.