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Introduction to Applications of the GMD and the Lorenz Curve in Finance

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Book cover The Gini Methodology

Part of the book series: Springer Series in Statistics ((SSS,volume 272))

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Abstract

The purpose of this part of the book is to expose the reader to applications of the Gini methodology in financial theory. Those applications are relevant whenever one is interested in decision making under risk or in reducing the incompatibility between financial theory and econometric applications. Risky situations are characterized by having to make decisions without knowing what the exact outcome is going to be. This definition covers almost every decision a person makes.

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Notes

  1. 1.

    For example, multivariate normal probability distributions of returns or quadratic utility functions.

  2. 2.

    Yitzhaki and Mayshar (2002) showed that the assumption of continuity in the portfolio space implies that if there is no portfolio that dominates a given portfolio under MCSD, then there will be no other portfolio (among all of portfolios, not just marginal ones) that dominates the given portfolio.

  3. 3.

    Shorrocks (1983) calls these curves generalized Lorenz curves.

  4. 4.

    Yitzhaki (1982a) also shows that the mean-Gini conditions for SSD are sufficient whenever the cumulative probability distributions intersect at most once.

  5. 5.

    LSA coincides with the Yitzhaki and Olkin (1991) line of independence (LOI). Samuelson (1967) shows that independent assets that are not included in the portfolio would be added to it if they have the same expected returns.

  6. 6.

    Whenever the CAPM is mentioned, it is interpreted as the reference portfolio held by the investor and not necessarily the market portfolio.

  7. 7.

    See Aaberge (2000) and Kleiber and Kotz (2002) on additional connections between the Lorenz curve and the extended Gini. Graves and Ringuest (2009) offer a tutorial for stochastic dominance.

  8. 8.

    This topic is dealt in Chap. 18.

  9. 9.

    In general the term market’s return should be interpreted as the portfolio’s return. See Shalit and Yitzhaki (2009) concerning CAPM with heterogeneous risk-averse investors.

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Authors and Affiliations

  1. Department of Economics, The Hebrew University, Mount Scopus, Jerusalem, Israel

    Shlomo Yitzhaki

  2. Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Edna Schechtman

Authors
  1. Shlomo Yitzhaki
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  2. Edna Schechtman
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Yitzhaki, S., Schechtman, E. (2013). Introduction to Applications of the GMD and the Lorenz Curve in Finance. In: The Gini Methodology. Springer Series in Statistics, vol 272. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4720-7_17

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