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Tackling nonlinear price impact with linear strategies

Author

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  • Brokmann, Xavier
  • Itkin, David
  • Muhle-Karbe, Johannes
  • Schmidt, Peter

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.

Suggested Citation

  • Brokmann, Xavier & Itkin, David & Muhle-Karbe, Johannes & Schmidt, Peter, 2024. "Tackling nonlinear price impact with linear strategies," LSE Research Online Documents on Economics 125888, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:125888
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    File URL: http://eprints.lse.ac.uk/125888/
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    More about this item

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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