Risk-Adjusted Values, Timing of Uncertainty Resolution, and the Measurement of Project Worth

Abstract

In the standard setting in which an individual or firm has preferences for probabilistic monetary outcomes that satisfy the Neumann-Morgenstern [10] as? sumptions of rational behavior and has an exponential utility function for money, a popular index for evaluating any proposed single-period probabilistic project is its risk-adjusted (RAV), i.e., its certainty equivalent, the cer? tain amount of money that has the same utility as the expected utility for the project. Since the exponential function is completely characterized by just a single parameter, its risk aversion level, in comparing mutually exclusive proj? ects one can simply plot their RAVs or their expected utilities as a function of this parameter and then, for any given or range of values of the parameter, read off which project is best, i.e., has the highest RAV or, equivalently, the highest expected utility. (See, e.g., [7], p. 203 or [2].) In extending this sort of single-period Neumann-Morgenstern utility analy? sis to the case of multiperiod projects, a traditional approach has been to let the utility be a function of just the single argument, net present value. But, unfortunately, this approach completely fails to take account of potentially important differences in the timing of uncertainty Recently, however, applying a straightforward averaging out and folding back approach to the above-described exponential utility model, Cozzolino [2], [3] has proposed an elegantly simple, multiperiod version of the RAV index that, he asserts, under positive risk aversion, does take proper account of the timing of uncertainty Continuing to assume positive risk aversion, the present analysis explores and extends Cozzolino's interesting approach by stressing further underlying as? sumptions that make the approach applicable and give precise meaning to the value of earlier resolution. An initial application here to the simple but instructive Howard-Matheson lottery appears curiously to show that, even under positive risk aversion, earlier uncertainty resolution has no if the market rate of interest is zero and may even have negative if the risk aversion level