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Equity portfolios generated by functions of ranked market weights


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  • Robert Fernholz

    (INTECH, One Palmer Square, Princeton, NJ 08542, USA Manuscript)

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    Dynamic equity portfolios can be generated by positive twice continuously differentiable functions of the ranked capitalization weights of an equity market. The return on such a portfolio relative to the market follows a stochastic differential equation that decomposes the relative return into two components: the logarithmic change in the value of the generating function, and a drift process that is of bounded variation. The method can be used to construct broad classes of stock portfolios, and has both theoretical and practical applications. Two applications of the method are presented: one offers an explanation for the size effect, the observed tendency of small stocks to have higher long-term returns than large stocks, and the other provides a rigorous analysis of the behavior of diversity-weighted indices, stock indices with weights that lie between capitalization weights and equal weights.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 5 (2001)
    Issue (Month): 4 ()
    Pages: 469-486

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    Handle: RePEc:spr:finsto:v:5:y:2001:i:4:p:469-486

    Note: received: November 1999; final version received: November 2000
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    Related research

    Keywords: Portfolio-generating function; local time; size effect; diversity-weighted index;

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    Cited by:
    1. Diane Wilcox & Tim Gebbie, 2013. "Factorising equity returns in an emerging market through exogenous shocks and capital flows," Papers 1306.5302,, revised Jul 2013.
    2. Attila Herczegh & Vilmos Prokaj & Mikl\'os R\'asonyi, 2013. "Diversity and no arbitrage," Papers 1301.4173,
    3. Raouf Ghomrasni, 2005. "On Local Times of Ranked Continuous Semimartingales;Application to Portfolio Generating Functions," SFB 649 Discussion Papers SFB649DP2005-043, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Francesco Audrino & Robert Fernholz & Roberto Ferretti, 2007. "A Forecasting Model for Stock Market Diversity," Annals of Finance, Springer, vol. 3(2), pages 213-240, March.
    5. Robert Fernholz & Ioannis Karatzas, 2006. "The implied liquidity premium for equities," Annals of Finance, Springer, vol. 2(1), pages 87-99, January.
    6. Constantinos Kardaras & Scott Robertson, 2010. "Robust maximization of asymptotic growth," Papers 1005.3454,, revised Aug 2012.
    7. Constantinos Kardaras & Scott Robertson, 2012. "Robust maximization of asymptotic growth," LSE Research Online Documents on Economics 44994, London School of Economics and Political Science, LSE Library.


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