Mean-Gini, Portfolio Theory, and the Pricing of Risky Assets

Haim Shalit · Shlomo Yitzhaki

222 citations0/0 files storedThe Journal of Finance

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Risk and Portfolio Optimization Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

ABSTRACT This paper presents the mean‐Gini (MG) approach to analyze risky prospects and construct optimum portfolios. The proposed method has the simplicity of a mean‐variance model and the main features of stochastic dominance efficiency. Since mean‐Gini is consistent with investor behavior under uncertainty for a wide class of probability distributions, Gini's mean difference is shown to be more adequate than the variance for evaluating the variability of a prospect. The MG approach is then applied to capital markets and the security valuation theorem is derived as a general relationship between average return and risk. This is further extended to include a degree of risk aversion that can be estimated from capital market data. The analysis is concluded with the concentration ratio to allow for the classification of different securities with respect to their relative riskiness.

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References

1964CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*1973Risk, Return, and Equilibrium: Empirical Tests 1952PORTFOLIO SELECTION*1965The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets 1975THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]1970On the measurement of inequality 1966Equilibrium in a Capital Asset Market 1969The Efficiency Analysis of Choices Involving Risk

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