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Diversity-weighted portfolios with negative parameter

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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.

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Acknowledgments

Wharton Research Data Services (WRDS) was used in preparing the data for this paper. This service and the data available thereon constitute valuable intellectual property and trade secrets of WRDS and/or its third-party suppliers.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK

    Alexander Vervuurt

  2. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    Ioannis Karatzas

  3. INTECH Investment Management, One Palmer Square, Suite 441, Princeton, NJ, 08542, USA

    Ioannis Karatzas

Authors
  1. Alexander Vervuurt
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  2. Ioannis Karatzas
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Correspondence to Alexander Vervuurt.

Additional information

The authors are greatly indebted to Adrian Banner, Robert Fernholz, Thibaut Lienart, Michael Monoyios, Vassilios Papathanakos, Julen Rotaetxe, Johannes Ruf, and an anonymous referee for their very careful reading of the manuscript and their many, insightful, and helpful suggestions. Alexander Vervuurt gratefully acknowledges Ph.D. studentships from the Engineering and Physical Sciences Research Council, Nomura and the Oxford-Man Institute of Quantitative Finance. Research supported in part by the National Science Foundation under Grant NSF-DMS-14-05210.

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Vervuurt, A., Karatzas, I. Diversity-weighted portfolios with negative parameter. Ann Finance 11, 411–432 (2015). https://doi.org/10.1007/s10436-015-0263-3

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  • DOI: https://doi.org/10.1007/s10436-015-0263-3

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