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Permutation-Weighted Portfolios and the Efficiency of Commodity Futures Markets

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  • Ricardo T. Fernholz
  • Robert Fernholz

Abstract

A market portfolio is a portfolio in which each asset is held at a weight proportional to its market value. Functionally generated portfolios are portfolios for which the logarithmic return relative to the market portfolio can be decomposed into a function of the market weights and a process of locally finite variation, and this decomposition is convenient for characterizing the long-term behavior of the portfolio. A permutation-weighted portfolio is a portfolio in which the assets are held at weights proportional to a permutation of their market values, and such a portfolio is functionally generated only for markets with two assets (except for the identity permutation). A reverse-weighted portfolio is a portfolio in which the asset with the greatest market weight is assigned the smallest market weight, the asset with the second-largest weight is assigned the second-smallest, and so forth. Although the reverse-weighted portfolio in a market with four or more assets is not functionally generated, it is still possible to characterize its long-term behavior using rank-based methods. This result is applied to a market of commodity futures, where we show that the reverse price-weighted portfolio substantially outperforms the price-weighted portfolio from 1977-2018.

Suggested Citation

  • Ricardo T. Fernholz & Robert Fernholz, 2020. "Permutation-Weighted Portfolios and the Efficiency of Commodity Futures Markets," Papers 2001.06914, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:2001.06914
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    References listed on IDEAS

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    1. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-Weighted Portfolios with Negative Parameter," Papers 1504.01026, arXiv.org, revised Jul 2015.
    2. 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.
    3. Clifford S. Asness & Tobias J. Moskowitz & Lasse Heje Pedersen, 2013. "Value and Momentum Everywhere," Journal of Finance, American Finance Association, vol. 68(3), pages 929-985, June.
    4. Fernholz, E. Robert & Karatzas, Ioannis & Ruf, Johannes, 2018. "Volatility and arbitrage," LSE Research Online Documents on Economics 75234, London School of Economics and Political Science, LSE Library.
    5. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-weighted portfolios with negative parameter," Annals of Finance, Springer, vol. 11(3), pages 411-432, November.
    6. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
    7. 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..
    8. Ricardo T. Fernholz, 2017. "Nonparametric methods and local†time†based estimation for dynamic power law distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(7), pages 1244-1260, November.
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