William H. Jean

Geometric Mean Approximations

In 1959, Henry LatanAi [2] proposed an approximation to the geometric mean that was a simple function of the arithmetic mean and variance, thereby indicating a mathematical relationship between the risky investment choice model of Bernoulli and the Markowitz mean-variance model. In 1969, Young and Trent [4] presented empirical test results of the LatanA© approximation, as well as a set of other approximations to the geometric mean based on moments, and concluded that the Latane formula yielded a quite accurate approximation to the geometric mean. In Jeans 1980 paper [1] relating the geometric mean model to stochastic dominance models, the infinite series representation of the geometric mean used suggests a more accurate approximation with moments of the geometric mean than that contained in the earlier papers may be possible. Various forms of that series expressed in alternate-origin moments are tested empirically below, and the results confirm that this later series does yield the greatest accuracy of the three approaches.

Interest Rate-Independent Present Value Rankings

ABSTRACT In this paper classical mathematical techniques are first used to derive conditions where any interest rate will result in present value rankings between two investment projects, and then a new technique, time dominance, is applied to the ranking situation. In many cases the new procedure only results In the same ranking as with the classical mathematical methods, but sufficient new cases are derived to make the new technique a useful addition to the analysts tool set.

The identification of stochastic dominance efficient sets by moment combination orderings

Abstract A new procedure using algebraic combinations of central moments is derived to identify stochastic dominance efficient sets of security portfolios. The number of computations involved with the moment combinations are significantly smaller than those with regular stochastic dominance tests. The effectiveness of the moment combination procedure is demonstrated with a large-scale empirical study.