IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1212.1877.html
   My bibliography  Save this paper

Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage

Author

Listed:
  • Winslow Strong

Abstract

The theory of functionally generated portfolios (FGPs) is an aspect of the continuous-time, continuous-path Stochastic Portfolio Theory of Robert Fernholz. FGPs have been formulated to yield a master equation - a description of their return relative to a passive (buy-and-hold) benchmark portfolio serving as the num\'eraire. This description has proven to be analytically very useful, as it is both pathwise and free of stochastic integrals. Here we generalize the class of FGPs in several ways: (1) the num\'eraire may be any strictly positive wealth process, not necessarily the market portfolio or even a passive portfolio; (2) generating functions may be stochastically dynamic, adjusting to changing market conditions through an auxiliary continuous-path stochastic argument of finite variation. These generalizations do not forfeit the important tractability properties of the associated master equation. We show how these generalizations can be usefully applied to scenario analysis, statistical arbitrage, portfolio risk immunization, and the theory of mirror portfolios.

Suggested Citation

  • Winslow Strong, 2012. "Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage," Papers 1212.1877, arXiv.org, revised Oct 2013.
    • Handle: RePEc:arx:papers:1212.1877
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1212.1877
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Adrian Banner & Daniel Fernholz, 2008. "Short-term relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 4(4), pages 445-454, October.
    2. Winslow Strong & Jean-Pierre Fouque, 2011. "Diversity and arbitrage in a regulatory breakup model," Annals of Finance, Springer, vol. 7(3), pages 349-374, August.
    3. Robert Fernholz & Ioannis Karatzas & Constantinos Kardaras, 2005. "Diversity and relative arbitrage in equity markets," Finance and Stochastics, Springer, vol. 9(1), pages 1-27, January.
    4. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    5. Fernholz, Robert, 1999. "On the diversity of equity markets," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 393-417, April.
    6. 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..
    7. Robert Fernholz & Ioannis Karatzas, 2005. "Relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 1(2), pages 149-177, November.
    8. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ting-Kam Leonard Wong, 2014. "Optimization of relative arbitrage," Papers 1407.8300, arXiv.org, revised Nov 2014.
    2. Alexander Schied & Leo Speiser & Iryna Voloshchenko, 2016. "Model-free portfolio theory and its functional master formula," Papers 1606.03325, arXiv.org, revised May 2018.
    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. Ting-Kam Wong, 2015. "Optimization of relative arbitrage," Annals of Finance, Springer, vol. 11(3), pages 345-382, November.
    5. Robert Fernholz, 2016. "A new decomposition of portfolio return," Papers 1606.05877, arXiv.org.
    6. 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.
    7. Soumik Pal & Ting-Kam Leonard Wong, 2016. "Exponentially concave functions and a new information geometry," Papers 1605.05819, arXiv.org, revised May 2017.
    8. Kangjianan Xie, 2020. "Leakage of rank-dependent functionally generated trading strategies," Annals of Finance, Springer, vol. 16(4), pages 573-591, December.
    9. Soumik Pal & Ting-Kam Leonard Wong, 2014. "The geometry of relative arbitrage," Papers 1402.3720, arXiv.org, revised Jul 2015.
    10. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988, arXiv.org.
    11. Patrick Mijatovic, 2021. "Beating the Market with Generalized Generating Portfolios," Papers 2101.07084, arXiv.org.
    12. Ioannis Karatzas & Donghan Kim, 2018. "Trading Strategies Generated Pathwise by Functions of Market Weights," Papers 1809.10123, arXiv.org, revised Mar 2019.
    13. 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.
    14. 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.
    15. Qingyin Ge & Yunuo Ma & Yuezhi Liao & Rongyu Li & Tianle Zhu, 2020. "Risk Management and Return Prediction," Papers 2007.01194, arXiv.org.
    16. Yves-Laurent Kom Samo & Alexander Vervuurt, 2016. "Stochastic Portfolio Theory: A Machine Learning Perspective," Papers 1605.02654, arXiv.org.
    17. Johannes Ruf & Kangjianan Xie, 2018. "Generalised Lyapunov Functions and Functionally Generated Trading Strategies," Papers 1801.07817, arXiv.org.

    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. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988, arXiv.org.
    2. Christa Cuchiero, 2017. "Polynomial processes in stochastic portfolio theory," Papers 1705.03647, arXiv.org.
    3. Winslow Strong & Jean-Pierre Fouque, 2011. "Diversity and arbitrage in a regulatory breakup model," Annals of Finance, Springer, vol. 7(3), pages 349-374, August.
    4. Alexander Schied & Leo Speiser & Iryna Voloshchenko, 2016. "Model-free portfolio theory and its functional master formula," Papers 1606.03325, arXiv.org, revised May 2018.
    5. Soumik Pal, 2016. "Exponentially concave functions and high dimensional stochastic portfolio theory," Papers 1603.01865, arXiv.org, revised Mar 2016.
    6. Ting-Kam Leonard Wong, 2017. "On portfolios generated by optimal transport," Papers 1709.03169, arXiv.org, revised Sep 2017.
    7. Andrey Sarantsev, 2014. "On a class of diverse market models," Annals of Finance, Springer, vol. 10(2), pages 291-314, May.
    8. Soumik Pal & Ting-Kam Leonard Wong, 2014. "The geometry of relative arbitrage," Papers 1402.3720, arXiv.org, revised Jul 2015.
    9. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-weighted portfolios with negative parameter," Annals of Finance, Springer, vol. 11(3), pages 411-432, November.
    10. E. Robert Fernholz & Ioannis Karatzas & Johannes Ruf, 2016. "Volatility and Arbitrage," Papers 1608.06121, arXiv.org.
    11. Ting-Kam Leonard Wong, 2014. "Optimization of relative arbitrage," Papers 1407.8300, arXiv.org, revised Nov 2014.
    12. Patrick Mijatovic, 2021. "Beating the Market with Generalized Generating Portfolios," Papers 2101.07084, arXiv.org.
    13. Robert Fernholz, 2015. "An example of short-term relative arbitrage," Papers 1510.02292, arXiv.org.
    14. Soumik Pal & Ting-Kam Leonard Wong, 2016. "Exponentially concave functions and a new information geometry," Papers 1605.05819, arXiv.org, revised May 2017.
    15. Ioannis Karatzas & Johannes Ruf, 2016. "Trading Strategies Generated by Lyapunov Functions," Papers 1603.08245, arXiv.org.
    16. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-Weighted Portfolios with Negative Parameter," Papers 1504.01026, arXiv.org, revised Jul 2015.
    17. 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.
    18. Christiane Goodfellow & Dirk Schiereck & Steffen Wippler, 2013. "Are behavioural finance equity funds a superior investment? A note on fund performance and market efficiency," Journal of Asset Management, Palgrave Macmillan, vol. 14(2), pages 111-119, April.
    19. Frederico Belo & Chen Xue & Lu Zhang, 2010. "Cross-sectional Tobin's Q," NBER Working Papers 16336, National Bureau of Economic Research, Inc.
    20. David Hirshleifer & Danling Jiang, 2010. "A Financing-Based Misvaluation Factor and the Cross-Section of Expected Returns," The Review of Financial Studies, Society for Financial Studies, vol. 23(9), pages 3401-3436.

    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:1212.1877. 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.