A Note on Portfolio Optimization with Quadratic Transaction Costs

18 Pages Posted: 22 Sep 2020

See all articles by Pierre Chen

Pierre Chen

National School for Statistical and Economic Administration (ENSAE)

Edmond Lezmi

Amundi Asset Management

Thierry Roncalli

Amundi Asset Management; University of Evry

Jiali Xu

Amundi Asset Management

Date Written: November 15, 2019

Abstract

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

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

Pierre Chen

National School for Statistical and Economic Administration (ENSAE) ( email )

92245 Malakoff Cedex
France

Edmond Lezmi

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

Thierry Roncalli (Contact Author)

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

University of Evry ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex
France

Jiali Xu

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

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