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Almost Perfect Shadow Prices

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  • Eberhard Mayerhofer

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 na\"ive shadow price Ansatz for maximizing long term returns given average volatility yields a strategy that is, for small bid-ask-spreads, asymptotically optimal at 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 fourth order. Finally, it is shown that the risk-neutral objective rules out the existence of shadow prices.

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  • Eberhard Mayerhofer, 2024. "Almost Perfect Shadow Prices," Papers 2401.00970, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2401.00970
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    1. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
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    Cited by:

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

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