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On the cross-sectional distribution of portfolio returns

Author

Listed:
  • Calès, Ludovic

    (European Commission)

  • Chalkis, Apostolos

    (National and Kapodistrian University of Athens)

  • Emiris, Ioannis Z.

    (National and Kapodistrian University of Athens)

Abstract

The aim of this paper is to study the distribution of portfolio returns across portfolios and for given asset returns. We focus on the most common type of investment considering portfolios whose weights are non-negative and sum up to 1. We provide algorithms and formulas from computational geometry and the literature on splines to compute the exact values of the probability density function, and of the cumulative distribution function at any point. We also provide closed-form solutions for the computation of its first four moments, and an algorithm to compute the higher moments. All algorithms and formulas allow for equal asset returns.

Suggested Citation

  • Calès, Ludovic & Chalkis, Apostolos & Emiris, Ioannis Z., 2019. "On the cross-sectional distribution of portfolio returns," JRC Working Papers in Economics and Finance 2019-11, Joint Research Centre, European Commission.
    • Handle: RePEc:jrs:wpaper:201911
    as

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    File URL: http://publications.jrc.ec.europa.eu/repository/bitstream/JRC116554/paper_csptfret_final.pdf
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    References listed on IDEAS

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    2. J. Bradford De Long & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1989. "The Size and Incidence of the Losses from Noise Trading," Journal of Finance, American Finance Association, vol. 44(3), pages 681-696, July.
    3. Banerjee, Anurag & Hung, Chi-Hsiou, 2011. "Informed momentum trading versus uninformed "naive" investors strategies," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 3077-3089, November.
    4. Boehmer, Ekkehart & Masumeci, Jim & Poulsen, Annette B., 1991. "Event-study methodology under conditions of event-induced variance," Journal of Financial Economics, Elsevier, vol. 30(2), pages 253-272, December.
    5. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    6. Winfried G. Hallerback & Igor Pouchkarev, 2016. "Active Portfolio Management with Conditional Tracking Error," Bankers, Markets & Investors, ESKA Publishing, issue 143, pages 18-25, July-Augu.
    7. Thanos Verousis & Nikolaos Voukelatos, 2018. "Cross-sectional dispersion and expected returns," Quantitative Finance, Taylor & Francis Journals, vol. 18(5), pages 813-826, May.
    8. Bhootra, Ajay, 2011. "Are momentum profits driven by the cross-sectional dispersion in expected stock returns?," Journal of Financial Markets, Elsevier, vol. 14(3), pages 494-513, August.
    9. Stivers, Chris & Sun, Licheng, 2010. "Cross-Sectional Return Dispersion and Time Variation in Value and Momentum Premiums," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(4), pages 987-1014, August.
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    Cited by:

    1. Apostolos Chalkis & Emmanouil Christoforou & Ioannis Z. Emiris & Theodore Dalamagas, 2020. "Modeling asset allocation strategies and a new portfolio performance score," Papers 2012.05088, arXiv.org, revised Sep 2021.

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    More about this item

    Keywords

    Cross-section of portfolios; Finance; Geometry; B-spline;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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