Approximating Expected Utility by a Function of Mean and Variance
1979; American Economic Association; Volume: 69; Issue: 3 Linguagem: Inglês
ISSN
1944-7981
Autores Tópico(s)Financial Markets and Investment Strategies
ResumoSuppose that an investor seeks to maximize the expected value of some utility function U(R), where R is the rate of return this period on his portfolio. Frequently it is more convenient or economical for such an investor to determine the set of mean-variance efficient portfolios than it is to find the portfolio which maximizes EU(R). The central problem considered here is this: would an astute selection from the E,V efficient set yield a portfolio with almost as great an expected utility as the maximum obtainable EU? A number of authors have asserted that the right choice of E, V efficient portfolio will give precisely optimum EU if and only if all distributions are normal or U is quadratic.' A frequently implied but unstated corollary is that a well-selected point from the E, V efficient set can be trusted to yield almost maximum expected utility if and only if the invector's utility function is approximately quadratic, or if his a priori beliefs are approximately normal. Since statisticians frequently reject the hypothesis that return distributions are normal, and John Pratt and Kenneth Arrow have each shwn us absurd implications of a quadratic utility function, some writers have concluded that mean-variance analysis should be rejected as the criterion for portfoliQ selection, no matter how economical it is as compared to alternate formal methods of analysis. Consider, on the other hand, the following evidence to the contrary. Suppose that two investors, let us call them Mr. Bernoulli and Mr. Cramer, have the same probability beliefs about portfolio returns in the forthcoming period; while their utility functions are, respectively,
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