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Equity portfolios generated by functions of ranked market weights

Author

Listed:
  • Robert Fernholz

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

Abstract

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.

Suggested Citation

  • Robert Fernholz, 2001. "Equity portfolios generated by functions of ranked market weights," Finance and Stochastics, Springer, vol. 5(4), pages 469-486.
    • 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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    More about this item

    Keywords

    Portfolio-generating function; local time; size effect; diversity-weighted index;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • G19 - Financial Economics - - General Financial Markets - - - Other

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