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Diversity-weighted portfolios with negative parameter

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  • Alexander Vervuurt
  • Ioannis Karatzas

Abstract

We analyze a negative-parameter variant of the diversity-weighted portfolio studied by Fernholz et al. (Finance Stoch 9(1):1–27, 2005 ), which invests in each company a fraction of wealth inversely proportional to the company’s market weight (the ratio of its capitalization to that of the entire market). We show that this strategy outperforms the market with probability one over sufficiently long time-horizons, under a non-degeneracy assumption on the volatility structure and under the assumption that the market weights admit a positive lower bound. Several modifications of this portfolio are put forward, which outperform the market under milder versions of the latter no-failure condition, and one of which is rank-based. An empirical study suggests that such strategies as studied here have indeed the potential to outperform the market and to be preferable investment opportunities, even under realistic proportional transaction costs. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-weighted portfolios with negative parameter," Annals of Finance, Springer, vol. 11(3), pages 411-432, November.
    • Handle: RePEc:kap:annfin:v:11:y:2015:i:3:p:411-432
    DOI: 10.1007/s10436-015-0263-3
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    References listed on IDEAS

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    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. Daniel Fernholz & Ioannis Karatzas, 2010. "On optimal arbitrage," Papers 1010.4987, 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. Banner, Adrian D. & Ghomrasni, Raouf, 2008. "Local times of ranked continuous semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1244-1253, July.
    5. 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.
    6. Ting-Kam Wong, 2015. "Optimization of relative arbitrage," Annals of Finance, Springer, vol. 11(3), pages 345-382, November.
    7. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
    8. Erhan Bayraktar & Yu-Jui Huang & Qingshuo Song, 2010. "Outperforming the market portfolio with a given probability," Papers 1006.3224, arXiv.org, revised Aug 2012.
    9. 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..
    10. Jörg Osterrieder & Thorsten Rheinländer, 2006. "Arbitrage Opportunities in Diverse Markets via a Non-equivalent Measure Change," Annals of Finance, Springer, vol. 2(3), pages 287-301, July.
    11. Robert Fernholz, 2001. "Equity portfolios generated by functions of ranked market weights," Finance and Stochastics, Springer, vol. 5(4), pages 469-486.
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    Citations

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    Cited by:

    1. Aziz Issaka & Indranil SenGupta, 2017. "Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index," Annals of Finance, Springer, vol. 13(4), pages 401-434, November.
    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. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    4. Ting-Kam Leonard Wong, 2017. "On portfolios generated by optimal transport," Papers 1709.03169, arXiv.org, revised Sep 2017.
    5. Patrick Mijatovic, 2021. "Beating the Market with Generalized Generating Portfolios," Papers 2101.07084, arXiv.org.
    6. Donghan Kim, 2019. "Open Markets," Papers 1912.13110, arXiv.org.
    7. Donghan Kim, 2023. "Market-to-book ratio in stochastic portfolio theory," Finance and Stochastics, Springer, vol. 27(2), pages 401-434, April.
    8. 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.
    9. Ricardo T. Fernholz & Caleb Stroup, 2018. "Asset Price Distributions and Efficient Markets," Papers 1810.12840, arXiv.org.
    10. Ioannis Karatzas & Johannes Ruf, 2016. "Trading Strategies Generated by Lyapunov Functions," Papers 1603.08245, arXiv.org.
    11. Ricardo T. Fernholz & Robert Fernholz, 2020. "Permutation-Weighted Portfolios and the Efficiency of Commodity Futures Markets," Papers 2001.06914, arXiv.org, revised Dec 2020.
    12. Yves-Laurent Kom Samo & Alexander Vervuurt, 2016. "Stochastic Portfolio Theory: A Machine Learning Perspective," Papers 1605.02654, arXiv.org.
    13. Donghan Kim, 2022. "Market-to-book Ratio in Stochastic Portfolio Theory," Papers 2206.03742, arXiv.org.
    14. Ioannis Karatzas & Donghan Kim, 2021. "Open markets," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1111-1161, October.

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    More about this item

    Keywords

    Portfolios; Portfolio generating functions; Relative arbitrage; Stochastic Portfolio Theory; Diversity-weighted portfolios; G11;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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