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Gini's Mean Difference and Portfolio Selection: An Empirical Evaluation

Published online by Cambridge University Press:  01 December 2009

Roger P. Bey  and
Keith M. Howe
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Extract

Yitzhaki [19] recently developed two portfolio selection criteria (EG and EΓ) based on the mean and Gini's mean difference. Similar to mean-variance(EV), the EG criterion uses two summary statistics to describe the probability distribution of a risky prospect, the mean and one-half Gini's mean difference. Gini's mean difference is defined as the average of the absolute differences between all possible pairs of observations of a random variable. Yitzhaki's development concentrated on the theoretical aspects of EG and EΓ and the theoretical relationships among EG, EΓ, EV, and stochastic dominance (SD) selection criteria. He did not address either the empirical properties of EG and EΓ or the relationship between the empirical efficient sets of EG and EΓ and other portfolio selection criteria. Yitzhaki suggested that the next step in the development and application of his proposed selection criteria should be an empirical investigation of how the EG and EΓ criteria compare with other selection criteria.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 19 , Issue 3 , September 1984 , pp. 329 - 338
Copyright
Copyright © School of Business Administration, University of Washington 1984

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References

[1]Baumol, William J. “An Expected Gain-Confidence Limit Criterion for Portfolio Selection.” Management Science, Vol. 10 (October 1963), pp. 174–182.CrossRefGoogle Scholar
[2]Bawa, Vijay S. “Optimal Rules for Ordering Uncertain Prospects.” Journal of Financial Economics Vol. 2 (March 1975), pp. 95–121.CrossRefGoogle Scholar
[3]Bey, Roger P. “Estimating the Optimal Stochastic Dominance Efficient Set with a Mean-Semivariance Algorithm.” Journal of Financial and Quantitative Analysis, Vol. 14 (December 1979), pp. 1059–1070.CrossRefGoogle Scholar
[4]Frankfurter, George M., and Phillips, Herbert E.. “Efficient Algorithms for Conducting Stochastic Dominance Tests on Large Numbers of Portfolios: A Comment.” Journal of Financial and Quantitative Analysis, Vol. 10 (March 1975), pp. 177–179.CrossRefGoogle Scholar
[5]Hadar, Joseph, and Russell, William R.. “Rules for Ordering Uncertain Prospects.” American Economic Review, Vol. 59 (March 1969), pp. 25–34.Google Scholar
[6]Hadar, Joseph, “Stochastic Dominance and Diversification.” Journal of Economic Theory. Vol. 3 (September 1971), pp. 288–305.CrossRefGoogle Scholar
[7]Hanoch, Giora, and Levy, Haim. “The Efficiency Analysis of Choices Involving Risk.” Review of Economic Studies, Vol. 36 (July 1969), pp. 335–346.CrossRefGoogle Scholar
[8]Kendall, Maurice, and Stuart, Alan. The Advanced Theory of Statistics, Vol. 1, 4th ed.London: Charles Griffin (1977).Google Scholar
[9]Kroll, Yoram, and Levy, Haim. “Stochastic Dominance: A Review and Some New Evidence.” Research in Finance, Vol. 2, Levy, H.. ed. Greenwich, CT: JAI Press Inc. (1980).Google Scholar
[10]Porter, R. Burr. “An Empirical Comparison of Stochastic Dominance and Mean-Variance Portfolio Choice Criteria.” Journal of Financial and Quantitative Analysis, Vol. 8 (September 1973), pp. 587–608.CrossRefGoogle Scholar
[11]Porter, R. Burr. “Semivariance and Stochastic Dominance: A Comparison.” American Economic Review, Vol. 64 (March 1974), pp. 666–672.Google Scholar
[12]Porter, R. Burr. “Portfolio Applications: Empirical Studies.” In Stochastic Dominance: An Approach to Decision Making under Risk, Whitmore, G. A. and Findlay, M. C., eds. Lexington, MA: Heath (1978).Google Scholar
[13]Porter, R. Burr, and Gaumnitz, Jack. “Stochastic Dominance vs. Mean-Variance Portfolio Analysis: An Empirical Evaluation.” American Economic Review, Vol. 62 (June 1972), pp. 438–446.Google Scholar
[14]Porter, R. Burr, and Pfaffenberger, Roger. “Efficient Algorithms for Conducting Stochastic Dominance Tests on Large Numbers of Portfolios: Reply.” Journal of Financial and Quantitative Analysis, Vol. 10 (March 1975), pp. 181–185.CrossRefGoogle Scholar
[15]Porter, R. Burr; Wart, James R.; and Ferguson, Donald L.. “Efficient Algorithms for Conducting Stochastic Dominance Tests on Large Numbers of Portfolios.” Journal of Financial and Quantitative Analysis, Vol. 8 (January 1973), pp. 71–81.CrossRefGoogle Scholar
[16]Vickson, R. G., and Altman, M.. “On the Relative Effectiveness of Stochastic Dominance Rules: Extension to Decreasing Risk-Averse Utility Functions.” Journal of Financial and Quantitative Analysis, Vol. 12 (March 1977), pp. 73–84.CrossRefGoogle Scholar
[17]Whitmore, G. A. “Third-Degree Stochastic Dominance.” American Economic Review, Vol. 60 (June 1970), pp. 457–459.Google Scholar
[18]Yitzhaki, Shlomo. “On an Extension of the Gini Inequality Index.” International Economic Review, Vol. 24 (October 1983), pp. 617–628.CrossRefGoogle Scholar
[19]Yitzhaki, Shlomo. “Stochastic Dominance, Mean Variance, and Gini's Mean Difference.” American Economic Review, Vol. 72 (March 1982), pp. 178–185.Google Scholar