Tackling Nonlinear Price Impact with Linear Strategies

15 Pages Posted: 25 Oct 2023

See all articles by Xavier Brokmann

Xavier Brokmann

Qube Research & Technologies

David Itkin

Imperial College London - Department of Mathematics

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

Peter Schmidt

Qube Research & Technologies

Date Written: September 26, 2023

Abstract

Empirical studies consistently find that the price impact of large trades approximately follows a nonlinear power law. Yet, tractable formulas for the portfolios that trade off predictive trading signals, risk, and trading costs in an optimal manner are only available for quadratic costs corresponding to linear price impact. In this paper, we show that the resulting linear strategies allow to achieve virtually optimal performance also for realistic nonlinear price impact, if the “effective” quadratic cost parameter is chosen appropriately. To wit, for a wide range of risk levels, this leads to performance losses below 2% compared to the numerical Viterbi algorithm of Kolm and Ritter (2014) run at very high accuracy. The effective quadratic cost depends on the portfolio risk, but can be computed without any sophisticated numerics by simply maximizing an explicit scalar function.

Keywords: Nonlinear price impact, portfolio choice

JEL Classification: C51, C61, G11

Suggested Citation

Brokmann, Xavier and Itkin, David and Muhle-Karbe, Johannes and Schmidt, Peter, Tackling Nonlinear Price Impact with Linear Strategies (September 26, 2023). Available at SSRN: https://ssrn.com/abstract=4584448 or http://dx.doi.org/10.2139/ssrn.4584448

Xavier Brokmann

Qube Research & Technologies ( email )

David Itkin

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Johannes Muhle-Karbe (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 1NE
United Kingdom

HOME PAGE: http://www.ma.imperial.ac.uk/~jmuhleka/

Peter Schmidt

Qube Research & Technologies ( email )

London
United Kingdom

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