Investment Decisions under Uncertainty: Application of Estimation Risk in the Hillier Approach

In a seminal paper in 1963, Frederick S. Hillier alerted the finance community to the importance of including probabilistic information in the process of investment decision-making [4]. The method proposed and demonstrated by Hillier introduced the use of additional information regarding the probability distributions governing three measures of investment merit: present worth; internal rate of return; and uniform annual cost. He showed that by assessing investment merit only on the basis of a measure of central tendency, crucial information regarding dispersion, hence risk, was ignored and investments were not evaluated accurately. By incorporating the amount of risk involved in terms of the probability distribution of the present worth, the internal rate of return, or uniform annual cost, a firm's management can make more sound decisions regarding risky investment proposals. Since this important paper was published, a virtual revolution has occurred in finance, particularly in the area of risk assessment. Indeed, under modern capital asset pricing theory, the dispersion in the probability distribution of future cash flows is an irrelevant statistic. Instead, as the theory goes, a project's systematic risk, as indexed by its “beta,†is the only relevant measure of risk. This disparity between modern capital asset pricing theory and the type of analysis that follows from the Hillier approach will be addressed in detail in Section III. We will show that under conditions in which dispersion is regarded as the relevant measure of risk, the Hillier approach provides a reasonable approximation of the dispersion arising from the multiperiod framework.