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Stochastic Dominance for Decreasing Absolute Risk Aversion

Published online by Cambridge University Press:  19 October 2009

R. G. Vickson
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Extract

In recent years the expected-utility approach to decision making under risk has gained increasing acceptance among portfolio theorists. On the other hand, the mean-variance (MV) approach of Markowitz [13], which has dominated portfolio theory in the past, continues to enjoy great popularity. In MV theory, the investor is assumed to rank his preferences for risky returns solely in terms of their means and variances, with higher means and lower variances, being preferred. Tobin [20] showed that MV theory is consistent with expected utility theory in the special case of joint-normally distributed asset returns. The MV approach enjoys a ready acceptance among practitioners, and requires only modest informational and computational inputs. Perhaps its most attractive feature is its ability to decompose the overall portfolio problem into a sequence of much simpler problems: first, the “efficient” set of portfolios (which minimize variance for any given mean return) is calculated, and then the investor chooses one of the efficient portfolios in a manner consistent with his personal preferences. This efficient set is the same for all investors having the same mean-variance-covariance estimates of risky-asset returns, and can, in principle, be determined once and for all using parametric quadratic programming [12, 22] Despite these real advantages, the MV theory embodies certain problems of principle in the case of nonnormally distributed asset returns, and this fact has led to increasing emphasis on the presumably more rational expected-utility theory.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 10 , Issue 5 , December 1975 , pp. 799 - 811
Copyright
Copyright © School of Business Administration, University of Washington 1975

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References

REFERENCES

[1]Arrow, K. J.Aspects of the Theory of Risk-Bearing. Helsinki: Yrjö Jahnssonin Säätiö (1965).Google Scholar
[2]Berge, C.Topological Spaces. London: Oliver and Boyd (1963).Google Scholar
[3]Blackwell, D. “Comparison of Experiments.” Proc. Second Berkeley Symp. Math. Statistics and Prob. (1965), pp. 93–102.Google Scholar
[4]Blackwell, D., and Girschick, M. A.. Theory of Games and Statistical Decisions. New York: Wiley (1954).Google Scholar
[5]Brumelle, S., and Vickson, R.. “A Unified Approach to Stochastic Dominance.” Faculty of Commerce, University of British Columbia (May 1973).Google Scholar
[6]Choquet, G.Lectures on Analysis, Vols. 1–3. New York: Benjamin (1969).Google Scholar
[7]Hadar, J., and Russell, W. R.. “Rules for Ordering Uncertain Prospects.” American Economic Review, vol. 59 (1969), pp. 25–34.Google Scholar
[8]Hanoch, G., and Levy, H.. “The Efficiency Analysis of Choices Involving Risk.” Review of Economic Studies, vol. 36 (1969), pp. 335–346.CrossRefGoogle Scholar
[9]Hanoch, G., “Relative Effectiveness of Efficiency Criteria for Portfolio Selection.” Journal of Financial and Quantitative Analysis, vol. 5 (1970), pp. 63–76.Google Scholar
[10]Hardy, G. H.; Littlewood, J. E.; and Polya, G.. Inequalities. Cambridge: Cambridge University Press (1959).Google Scholar
[11]Lehmann, E. “Ordered Families of Distributions.” Annals of Mathematical Statistics, vol. 26 (1955), pp. 399–419.CrossRefGoogle Scholar
[12]Lintner, J. “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” The Review of Economics and Statistics, vol. 47 (1965), pp. 13–37.CrossRefGoogle Scholar
[13]Markowitz, H. M. “Portfolio Selection.” The Journal of Finance, vol. 6 (1952), pp. 77–91.Google Scholar
[14]Meyer, P. A.Probability and Potentials. Waltham, Mass.: Blaisdell (1966).Google Scholar
[15]Phelps, R. R.Lectures on Choquet's Theorem. Princeton, N.J.: Van Nostrand (1966).Google Scholar
[16]Pratt, J. W. “Risk Aversion in the Small and in the Large.” Econometrica, vol. 32 (1964), pp. 122–136.CrossRefGoogle Scholar
[17]Rothschild, M., and Stiglitz, J. E.. “Increasing Risk: I. A Definition.” Journal of Economic Theory, vol. 2 (1970), pp. 225–243.CrossRefGoogle Scholar
[18]Rudin, W.Principles of Mathematical Analysis. New York: McGraw-Hill (1953).Google Scholar
[19]Stoer, J., and Witzgall, C.. Convexity and Optimization in Finite Dimensions I. Heidelberg: Springer-Verlag (1970).CrossRefGoogle Scholar
[20]Tobin, J. “Liquidity Preference as Behavior towards Risk.” Review of Economic Studies, vol. 26 (1958), pp. 65–86.CrossRefGoogle Scholar
[21]Whitmore, G. A. “Third-Degree Stochastic Dominance.” American Economic Review, vol. 60 (1970), pp. 457–459.Google Scholar
[22]Ziemba, W. T.; Brooks-Hill, F. J.; and Parkan, C.. “Calculation of Investment Portfolios with Risk Free Borrowing and Lending.” Management Science Applications, to appear.Google Scholar