A Note on Portfolio Optimization with Quadratic Transaction Costs

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.

Keywords: Portfolio allocation, mean-variance optimization, transaction cost, quadratic programming, alternating direction method of multipliers

JEL Classification: C61, G11

Suggested Citation: Suggested Citation

Chen, Pierre and Lezmi, Edmond and Roncalli, Thierry and Xu, Jiali, A Note on Portfolio Optimization with Quadratic Transaction Costs (November 15, 2019). Available at SSRN: https://ssrn.com/abstract=3683466 or http://dx.doi.org/10.2139/ssrn.3683466