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Trading strategies generated pathwise by functions of market weights

Author

Listed:
  • Ioannis Karatzas

    (Columbia University
    Intech Investment Management)

  • Donghan Kim

    (Columbia University)

Abstract

Twenty years ago, E.R. Fernholz introduced the notion of “functional generation” to construct a variety of portfolios solely in terms of the individual companies’ market weights. I. Karatzas and J. Ruf recently developed another approach to the functional construction of portfolios which leads to very simple conditions for strong relative arbitrage with respect to the market. Here, both of these notions are generalized in a pathwise, probability-free setting; portfolio-generating functions, possibly less smooth than twice differentiable, involve the current market weights as well as additional bounded-variation functionals of past and present market weights. This leads to a wider class of functionally generated portfolios than was heretofore possible to analyze, to novel methods for dealing with the “size” and “momentum” effects, and to improved conditions for outperforming the market portfolio over suitable time horizons.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:2:d:10.1007_s00780-019-00414-2
    DOI: 10.1007/s00780-019-00414-2
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    References listed on IDEAS

    as
    1. 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.
    2. Winslow Strong, 2014. "Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension," Finance and Stochastics, Springer, vol. 18(3), pages 487-514, July.
    3. Ruf, Johannes & Xie, Kangjianan, 2019. "Generalised Lyapunov functions and functionally generated trading strategies," LSE Research Online Documents on Economics 102424, London School of Economics and Political Science, LSE Library.
    4. Robert Fernholz, 1999. "Portfolio Generating Functions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 15, pages 344-367, World Scientific Publishing Co. Pte. Ltd..
    5. Dieter Sondermann, 2006. "Introduction to Stochastic Calculus for Finance," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-34837-5, December.
    6. Winslow Strong, 2012. "Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage," Papers 1212.1877, arXiv.org, revised Oct 2013.
    7. Alexander Schied & Leo Speiser & Iryna Voloshchenko, 2016. "Model-free portfolio theory and its functional master formula," Papers 1606.03325, arXiv.org, revised May 2018.
    8. Johannes Ruf & Kangjianan Xie, 2019. "Generalised Lyapunov Functions and Functionally Generated Trading Strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(4), pages 293-327, July.
    9. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    10. Nicolas Perkowski & David J. Promel, 2014. "Local times for typical price paths and pathwise Tanaka formulas," Papers 1405.4421, arXiv.org, revised Apr 2015.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Prömel, 2023. "Model‐free portfolio theory: A rough path approach," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 709-765, July.
    2. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2023. "Quantifying dimensional change in stochastic portfolio theory," Papers 2303.00858, arXiv.org, revised Apr 2023.
    3. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Promel, 2021. "Model-free Portfolio Theory: A Rough Path Approach," Papers 2109.01843, arXiv.org, revised Oct 2022.
    4. Jin-Biao Lu & Zhi-Jiang Liu & Dmitry Tulenty & Liudmila Tsvetkova & Sebastian Kot, 2021. "Implementation of Stochastic Analysis in Corporate Decision-Making Models," Mathematics, MDPI, vol. 9(9), pages 1-16, May.
    5. 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.
    6. Patrick Mijatovic, 2021. "Beating the Market with Generalized Generating Portfolios," Papers 2101.07084, arXiv.org.
    7. Donghan Kim, 2022. "Market-to-book Ratio in Stochastic Portfolio Theory," Papers 2206.03742, arXiv.org.
    8. Donghan Kim, 2023. "Market-to-book ratio in stochastic portfolio theory," Finance and Stochastics, Springer, vol. 27(2), pages 401-434, April.
    9. Andrew L. Allan & Chong Liu & David J. Promel, 2021. "A C\`adl\`ag Rough Path Foundation for Robust Finance," Papers 2109.04225, arXiv.org, revised May 2023.

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    More about this item

    Keywords

    Stochastic portfolio theory; Pathwise Itô and Tanaka formulas; Trading strategies; Functional generation; Strong relative arbitrage;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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