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On Robustness of Double Linear Trading with Transaction Costs

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  • Chung-Han Hsieh

Abstract

A trading system is said to be {robust} if it generates a robust return regardless of market direction. To this end, a consistently positive expected trading gain is often used as a robustness metric for a trading system. In this paper, we propose a new class of trading policies called the {double linear policy} in an asset trading scenario when the transaction costs are involved. Unlike many existing papers, we first show that the desired robust positive expected gain may disappear when transaction costs are involved. Then we quantify under what conditions the desired positivity can still be preserved. In addition, we conduct heavy Monte-Carlo simulations for an underlying asset whose prices are governed by a geometric Brownian motion with jumps to validate our theory. A more realistic backtesting example involving historical data for cryptocurrency Bitcoin-USD is also studied.

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  • Chung-Han Hsieh, 2022. "On Robustness of Double Linear Trading with Transaction Costs," Papers 2209.12383, arXiv.org.
    • Handle: RePEc:arx:papers:2209.12383
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    References listed on IDEAS

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    1. Chung-Han Hsieh, 2020. "Necessary and Sufficient Conditions for Frequency-Based Kelly Optimal Portfolio," Papers 2004.12099, arXiv.org.
    2. Etheridge,Alison, 2002. "A Course in Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521890779.
    3. Chung-Han Hsieh & B. Ross Barmish & John A. Gubner, 2019. "On Positive Solutions of a Delay Equation Arising When Trading in Financial Markets," Papers 1901.02480, arXiv.org, revised Oct 2019.
    4. Atul Deshpande & B. Ross Barmish, 2018. "A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control," Papers 1803.04591, arXiv.org.
    5. Jingzhi Tie & Hanqin Zhang & Qing Zhang, 2018. "An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 654-675, November.
    6. Kim, Thomas, 2017. "On the transaction cost of Bitcoin," Finance Research Letters, Elsevier, vol. 23(C), pages 300-305.
    7. Joseph D. O'Brien & Mark E. Burke & Kevin Burke, 2018. "A Generalized Framework for Simultaneous Long-Short Feedback Trading," Papers 1806.05561, arXiv.org, revised Aug 2020.
    8. Jaksa Cvitanic & Fernando Zapatero, 2004. "Introduction to the Economics and Mathematics of Financial Markets," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262532654, April.
    9. Etheridge,Alison, 2002. "A Course in Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521813853.
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    Cited by:

    1. Chung-Han Hsieh, 2023. "On Data-Driven Drawdown Control with Restart Mechanism in Trading," Papers 2303.02613, arXiv.org.
    2. Xin-Yu Wang & Chung-Han Hsieh, 2023. "On Robustness of Double Linear Policy with Time-Varying Weights," Papers 2303.10806, arXiv.org.

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