Empirical Tests of Stochastic Dominance in Capital Investment Planning: A Spreadsheet Framework

Abstract

The empirical inadequacy of direct application of stochastic dominance rules and their variants has led to the development of statistical tests for making dominance inferences. Yet very little is known about their application in capital investment planning, and the algorithms for their implementation are not readily available to the analyst who uses spreadsheets for capital investment planning. Therefore, this article develops a spreadsheet framework for conducting empirical tests of stochastic dominance when comparing alternative capital investment plans under uncertainty. It uses bootstrap and simulation methodology to compute the p-values required for making first- and second-order dominance inferences. Results from numerical examples show that empirical tests yield robust inferences when the structure of risk profiles and their integrals is such that dominance inferences by visual inspection are difficult. Therefore, analysts should model and empirically test for these relationships if they want to make defensible decisions when comparing risky capital investments.

Notes

The limited scope to FSD and SSD is due to the prevalence of their use in the literature. The framework can easily be extended to higher order dominance relationships if necessary.

Under special conditions, p-values for testing SD₁ can be computed using exp ( − 2D²_ij); see Barrett and Donald (2003, p. 78) and Heathcote et al. (2010, p. 456).

Additional information

Notes on contributors

Emmanuel A. Donkor

Emmanuel A. Donkor, M.S., is a doctoral candidate in the Engineering Management and Systems Engineering Department at George Washington University, where he specializes in the application of OR/MS tools to support quantitative modeling in risk and decision analysis. Specific research interests include parametric cost modeling; design, simulation, and optimization of spreadsheet models for decision making; and capital investment planning. He is a student member of INFORMS, ASCE, and AWWA.