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Almost Perfect Shadow Prices

Author

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  • Eberhard Mayerhofer

    (Department of Mathematics & Statistics, University of Limerick, V94 T9PX Limerick, Ireland)

Abstract

Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a naïve shadow price ansatz for maximizing long-term returns, given average volatility yields a strategy that is, for small bid–ask spreads, asymptotically optimal at the third order. Considering the second-order impact of transaction costs, such a strategy is essentially optimal. However, for risk aversion different from one, we devise alternative strategies that outperform the shadow market at the fourth order. Finally, it is shown that the risk-neutral objective rules out the existence of shadow prices.

Suggested Citation

  • Eberhard Mayerhofer, 2024. "Almost Perfect Shadow Prices," JRFM, MDPI, vol. 17(2), pages 1-18, February.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:2:p:70-:d:1337166
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    References listed on IDEAS

    as
    1. Richard J Martin, 2016. "Universal trading under proportional transaction costs," Papers 1603.06558, arXiv.org.
    2. S. Gerhold & J. Muhle-Karbe & W. Schachermayer, 2013. "The dual optimizer for the growth-optimal portfolio under transaction costs," Finance and Stochastics, Springer, vol. 17(2), pages 325-354, April.
    3. Czichowsky, Christoph & Schachermayer, Walter, 2016. "Duality theory for portfolio optimisation under transaction costs," LSE Research Online Documents on Economics 63362, London School of Economics and Political Science, LSE Library.
    4. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, vol. 18(1), pages 1-37, January.
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    Cited by:

    1. Eberhard Mayerhofer, 2024. "Asymptotic methods for transaction costs," Papers 2407.07100, arXiv.org.

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