Minimizing Mean Absolute Deviations to Exactly Solve Expected Utility Problems: Reply

The main purpose of our paper was to show that in many cases when expected utility problems can be transformed into mean-variance problems, they can also be transformed into mean-mean absolute deviation problems. In other words, knowledge of population mean absolute deviations would enable one to solve expected utility problems as accurately as if one had knowledge of the population variances. In that sense, our proof is correct. We believe the main point of the comment is that we did not adequately consider sampling error, which is true. We would like to correct that deficiency and, in so doing, show that the comment is a specific counter-example, not a general refutation of our arguments. Central to that purpose we will argue that a sample statistic may not be the best estimator of the corresponding population parameter. That is, the sample variance may not always be the best estimator of the population variance; and the sample mean absolute deviation, the best estimator of the population mean absolute deviation. Several methods of determining point estimators are available; one which has some optimum properties is the method of maximum likelihood (Mood, Graybill, Boes, p. 358). It is widely known that the quantity