IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2507.09196.html
   My bibliography  Save this paper

Functionally Generated Portfolios Under Stochastic Transaction Costs: Theory and Empirical Evidence

Author

Listed:
  • Nader Karimi
  • Erfan Salavati

Abstract

Assuming frictionless trading, classical stochastic portfolio theory (SPT) provides relative arbitrage strategies. However, the costs associated with real-world execution are state-dependent, volatile, and under increasing stress during liquidity shocks. Using an Ito diffusion that may be connected with asset prices, we extend SPT to a continuous-time equity market with proportional, stochastic transaction costs. We derive closed-form lower bounds on cost-adjusted relative wealth for a large class of functionally generated portfolios; these bounds provide sufficient conditions for relative arbitrage to survive random costs. A limit-order-book cost proxy in conjunction with a Milstein scheme validates the theoretical order-of-magnitude estimates. Finally, we use intraday bid-ask spreads as a stand-in for cost volatility in a back-test of CRSP small-cap data (1994--2024). Despite experiencing larger declines during the 2008 and 2020 liquidity crises, diversity- and entropy-weighted portfolios continue to beat the value-weighted benchmark by 3.6 and 2.9 percentage points annually, respectively, after cost deduction.

Suggested Citation

  • Nader Karimi & Erfan Salavati, 2025. "Functionally Generated Portfolios Under Stochastic Transaction Costs: Theory and Empirical Evidence," Papers 2507.09196, arXiv.org.
    • Handle: RePEc:arx:papers:2507.09196
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2507.09196
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Thierry Foucault & Ohad Kadan & Eugene Kandel, 2005. "Limit Order Book as a Market for Liquidity," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1171-1217.
    2. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    3. Ruf, Johannes & Xie, Kangjianan, 2020. "Impact of proportional transaction costs on systematically generated portfolios," LSE Research Online Documents on Economics 104696, London School of Economics and Political Science, LSE Library.
    4. Karatzas, Ioannis & Ruf, Johannes, 2017. "Trading strategies generated by Lyapunov functions," LSE Research Online Documents on Economics 69177, London School of Economics and Political Science, LSE Library.
    5. Nicolae Gârleanu & Lasse Heje Pedersen, 2013. "Dynamic Trading with Predictable Returns and Transaction Costs," Journal of Finance, American Finance Association, vol. 68(6), pages 2309-2340, December.
    6. Ananth Madhavan, 2012. "Exchange-Traded Funds, Market Structure, and the Flash Crash," Financial Analysts Journal, Taylor & Francis Journals, vol. 68(4), pages 20-35, July.
    7. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    8. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2013. "How efficiency shapes market impact," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1743-1758, November.
    9. Heikki Marjosola, 2021. "The problem of regulatory arbitrage: A transaction cost economics perspective," Regulation & Governance, John Wiley & Sons, vol. 15(2), pages 388-407, April.
    10. Patrick O'Sullivan & David Edelman, 2015. "Adaptive universal portfolios," The European Journal of Finance, Taylor & Francis Journals, vol. 21(4), pages 337-351, March.
    11. Koutmos, Dimitrios, 2018. "Liquidity uncertainty and Bitcoin’s market microstructure," Economics Letters, Elsevier, vol. 172(C), pages 97-101.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David Itkin, 2025. "Stochastic portfolio theory with price impact," Papers 2506.07993, arXiv.org, revised Jun 2025.
    2. Johannes Ruf & Kangjianan Xie, 2019. "The impact of proportional transaction costs on systematically generated portfolios," Papers 1904.08925, arXiv.org.
    3. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2024. "Quantifying dimensional change in stochastic portfolio theory," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 977-1021, July.
    4. Patrick Mijatovic, 2021. "Beating the Market with Generalized Generating Portfolios," Papers 2101.07084, arXiv.org.
    5. Adrian Buss & Bernard Dumas, 2019. "The Dynamic Properties of Financial‐Market Equilibrium with Trading Fees," Journal of Finance, American Finance Association, vol. 74(2), pages 795-844, April.
    6. Ruf, Johannes & Xie, Kangjianan, 2020. "Impact of proportional transaction costs on systematically generated portfolios," LSE Research Online Documents on Economics 104696, London School of Economics and Political Science, LSE Library.
    7. Christa Cuchiero & Janka Moller, 2023. "Signature Methods in Stochastic Portfolio Theory," Papers 2310.02322, arXiv.org, revised Oct 2024.
    8. David Itkin & Benedikt Koch & Martin Larsson & Josef Teichmann, 2022. "Ergodic robust maximization of asymptotic growth under stochastic volatility," Papers 2211.15628, arXiv.org.
    9. James S. Ang & Kenneth J. Hunsader & Shaojun Zhang, 2019. "Order dynamics during the flash crash," Journal of Asset Management, Palgrave Macmillan, vol. 20(5), pages 365-383, September.
    10. Yamamoto, Ryuichi, 2019. "Dynamic Predictor Selection And Order Splitting In A Limit Order Market," Macroeconomic Dynamics, Cambridge University Press, vol. 23(5), pages 1757-1792, July.
    11. Johannes Ruf & Kangjianan Xie, 2018. "Generalised Lyapunov Functions and Functionally Generated Trading Strategies," Papers 1801.07817, arXiv.org.
    12. Ricardo T. Fernholz & Robert Fernholz, 2022. "Permutation-weighted portfolios and the efficiency of commodity futures markets," Annals of Finance, Springer, vol. 18(1), pages 81-108, March.
    13. Clarence Simard & Bruno Rémillard, 2019. "Pricing European Options in a Discrete Time Model for the Limit Order Book," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 985-1005, September.
    14. Ioannis Karatzas & Donghan Kim, 2020. "Trading strategies generated pathwise by functions of market weights," Finance and Stochastics, Springer, vol. 24(2), pages 423-463, April.
    15. Qianhui Lai & Qiang Yang, 2025. "Deep Learning Strategies for Intraday Optimal Carbon Options Trading with Price Impact Considerations," Mathematics, MDPI, vol. 13(7), pages 1-20, March.
    16. Black, Jeffrey R. & Stock, Duane & Yadav, Pradeep K., 2016. "The pricing of different dimensions of liquidity: Evidence from government guaranteed bonds," Journal of Banking & Finance, Elsevier, vol. 71(C), pages 119-132.
    17. Jonathan A. Chávez Casillas, 2024. "A Time-Dependent Markovian Model of a Limit Order Book," Computational Economics, Springer;Society for Computational Economics, vol. 63(2), pages 679-709, February.
    18. Donghan Kim, 2022. "Market-to-book Ratio in Stochastic Portfolio Theory," Papers 2206.03742, arXiv.org.
    19. O’Sullivan, Conall & Papavassiliou, Vassilios G. & Wafula, Ronald Wekesa & Boubaker, Sabri, 2024. "New insights into liquidity resiliency," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 90(C).
    20. Hai-Chuan Xu & Wei Chen & Xiong Xiong & Wei Zhang & Wei-Xing Zhou & H Eugene Stanley, 2016. "Limit-order book resiliency after effective market orders: Spread, depth and intensity," Papers 1602.00731, arXiv.org, revised Feb 2017.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2507.09196. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.