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Journal of Quantitative Economics

, Volume 17, Issue 1, pp 1–9 | Cite as

Ranking Investments Using the Lorenz Curve

  • Doron NisaniEmail author
Original Article
  • 126 Downloads

Abstract

Ranking investments is important for measuring the performance of financial assets over a period of time. The Mean-Variance Model (MV Model) suggests the Reward-to-Variability Index (Sharpe Index) for ranking the performances of investments. However, this model is based on the implicit assumption that the investments’ rate of return is normally distributed. This assumption highlights the importance of a diverse portfolio, but is rarely satisfied. The most accurate method of ranking investments is according to the investor’s preference ratio, described by the stochastic dominance rules (SD Rules). The SD Rules are coherent with the generic properties of the investor’s preference, but their main disadvantage lies in their complex calculations. This paper presents a new method of ranking investments using the Lorenz curve, thus utilizing the investor’s preference ratio ranking and the simplicity of applying the Lorenz curve so as to describe a full order of ranking according to the investor’s behavior.

Keywords

Investment management Stochastic dominance Lorenz curve Gini Index 

JEL Classification

D81 G11 G32 

Notes

Acknowledgements

The author thanks Prof. Haim Shalit for his guidance, and the anonymous reviewers for improving this paper with their helpful comments.

References

  1. Arrow, K.J. 1971. Essays in the Theory of Risk Bearing. Chicago: Markham Publishing Co.Google Scholar
  2. Ekern, S. 1980. Increasing \(\text{ n }^{{\rm th}}\) Degree Risk. Economics Letters 6: 329–333.CrossRefGoogle Scholar
  3. Fisher, L., and J.H. Lorie. 1970. Some Studies of Variability of Returns on Investments in Common Stocks. Journal of Business 43: 99–135.CrossRefGoogle Scholar
  4. Gastwirth, J.L. 1971. A General Definition of the Lorenz Curve. Econometrica 39: 1037–1039.CrossRefGoogle Scholar
  5. Gini, C. 1912. Variabilità e Mutabilità. Studi Economico-Giuridici. Bologna: Università di Cagliari, tipografia di P. Cuppini.Google Scholar
  6. Hadar, J., and W.R. Russell. 1969. Rules for Ordering Uncertain Prospects. American Economic Review 59: 25–34.Google Scholar
  7. Hanoch, G., and H. Levy. 1969. The Efficiency Analysis of Choice Involving Risk. Review of Economic Studies 36: 335–346.CrossRefGoogle Scholar
  8. Jarque, C.M., and A.K. Bera. 1980. Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals. Economics Letters 6: 255–259.CrossRefGoogle Scholar
  9. Kraus, A., and R.H. Litzenberger. 1976. Skewness Preference and the Valuation of Risk Assets. Journal of Finance 31: 1085–1100.Google Scholar
  10. Lorenz, M.O. 1905. Methods of Measuring the Concentration of Wealth. Publications of the American Statistical Association 9: 209–219.CrossRefGoogle Scholar
  11. Markowitz, H. 1952. Portfolio Selection. Journal of Finance 7: 77–91.Google Scholar
  12. Muliere, P., and M. Scarsini. 1989. A Note on Stochastic Dominance and Inequality Measures. Journal of Economic Theory 49: 314–323.CrossRefGoogle Scholar
  13. Pratt, J.W. 1964. Risk Aversion in the Small and in the Large. Econometrica 32: 122–136.CrossRefGoogle Scholar
  14. Ross, S.A. 1976. The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory 13: 341–360.CrossRefGoogle Scholar
  15. Rothschild, M., and J.E. Stiglitz. 1970. Increasing Risk I: A Definition. Journal of Economic Theory 2: 66–84.CrossRefGoogle Scholar
  16. Shalit, H. 2014. Portfolio Risk Management Using the Lorenz Curve. Journal of Portfolio Management 40: 152–159.CrossRefGoogle Scholar
  17. Shalit, H., and S. Yitzhaki. 1984. Mean-Gini, Portfolio Theory, and The Pricing of Risky Assets. Journal of Finance 39: 1449–1468.CrossRefGoogle Scholar
  18. Shalit, H., and S. Yitzhaki. 2005. The Mean-Gini Efficient Frontier. Journal of Financial Research 28: 59–75.CrossRefGoogle Scholar
  19. Sharpe, W.F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance 19: 425–442.Google Scholar
  20. Sharpe, W.F. 1966. Mutual Fund Performance. Journal of Business 39: 119–138.CrossRefGoogle Scholar
  21. Sharpe, W.F. 1994. The Sharpe Ratio. Journal of Portfolio Management 21: 49–58.CrossRefGoogle Scholar
  22. Shorrocks, A.F. 1983. Ranking Income Distributions. Economica 50: 3–17.CrossRefGoogle Scholar
  23. von Neumann, J., and O. Morgenstern. 1944. The Theory of Games and Economic Behavior. Princeton: Princeton University Press.Google Scholar
  24. Whitmore, G.A. 1970. Third-Degree Stochastic Dominance. American Economic Review 60: 457–459.Google Scholar
  25. Yitzhaki, S. 1982. Stochastic Dominance, Mean-Variance, and Gini’s Mean Difference. American Economic Review 72: 178–185.Google Scholar
  26. Yitzhaki, S., and E. Schechtman. 2013. The Gini Methodology. Berlin: Springer.CrossRefGoogle Scholar

Copyright information

© The Indian Econometric Society 2018

Authors and Affiliations

  1. 1.Department of EconomicsBen-Gurion University of the NegevBeer-ShevaIsrael

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