Tackling nonlinear price impact with linear strategies

Brokmann, Xavier, Itkin, David ORCID: 0000-0001-8643-574X, Muhle-Karbe, Johannes and Schmidt, Peter (2024) Tackling nonlinear price impact with linear strategies. Mathematical Finance. ISSN 0960-1627

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Abstract

Empirical studies in various contexts find that the price impact of large trades approximately follows a power law with exponent between 0.4 and 0.7. 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 a numerical algorithm proposed by Kolm and Ritter, run at very high accuracy. The effective quadratic cost depends on the portfolio risk and concavity of the impact function, but can be computed without any sophisticated numerics by simply maximizing an explicit scalar function.

Item Type:	Article
Additional Information:	© 2024 The Author(s)
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics H Social Sciences H Social Sciences > HG Finance
JEL classification:	C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice; Investment Decisions
Date Deposited:	25 Oct 2024 09:21
Last Modified:	19 Dec 2024 00:59
URI:	http://eprints.lse.ac.uk/id/eprint/125888

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