ELLIPTICAL SYMMETRY, EXPECTED UTILITY, AND MEAN-VARIANCE ANALYSIS

Mean-variance analysis in the form of risk programming has a long, productive history in agricultural economics research. And risk programming continues to be used despite well known theoretical results that choices based on mean-variance analysis are not consistent with choices based on expected utility maximization. This paper demonstrates that the multivariate distribution of returns used in risk programming must be elliptically symmetric in order for mean-variance analysis to be consistent with expected utility choices. Then a statistical test for elliptical symmetry is developed and demonstrated. This test enables researchers to determine when data will produce significant differences between risk programming choices and expected utility choices.