Analyzing Uncertainty: Probability Distributions and Simulation

14 Pages Posted: 21 Oct 2008

See all articles by Robert L. Carraway

Robert L. Carraway

University of Virginia - Darden School of Business

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Abstract

This note introduces simulation as a tool to analyze uncertainty in business decisions. It first observes the limitations of single point or simple range estimates of key uncertainties, thereby motivating the need to create a risk profile for any alternative that characterizes the full range of possible outcomes and their relative likelihoods. A simple example involving both a discrete and a continuous (triangle) distribution is used. The note is simulation software independent, although output from Crystal Ball is displayed.

Excerpt

UVA-QA-0660

Analyzing Uncertainty:

Probability Distributions and Simulation

When making important business decisions, executives have to rely on both experience and instinct as they consider the consequences of any action they choose. There are many categories of consequences to consider, the relative importance of which may vary with each circumstance, but almost always of interest is the category of economic consequences: how will this course of action affect my company's bottom line? Analyzing economic consequences is a prudent check on intuition, often providing valuable insights that lead to more informed decisions.

Identifying economic consequences is almost always made difficult by the presence of uncertainty in how things will play out. Good economic analysis must somehow deal with this uncertainty. The simplest approach is to just ignore it: make assumptions about the outcome and analyze possible courses of action on this basis. While simple, this approach merely obscures the uncertainty and its resulting risk behind intuition and gut feel. By failing to consider the uncertainty explicitly, we run the risk of (1) improperly valuing the economic consequences of a course of action and (2) exposing ourselves to unacceptable risk that, were we aware of its actual magnitude and likelihood, would have indicated a different course of action. We may also miss opportunities to find better solutions that add value by proactively managing the risk.

A second approach is to determine a likely range of outcomes for individual uncertainties (best case, worst case). This approach enables us to begin to see the impact of uncertainty on the consequences of our actions by generating overall best and worst cases. We often base decisions solely on the worst case: if it is sufficiently bad, we abandon that alternative. While this approach is appealing in its simplicity and better than guessing about important uncertainties, it suffers from its incompleteness. How likely is the worst case? How likely is the best case? And what about all the intermediate possibilities, each more likely than the best or worst cases?

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Keywords: simulation, risk profile, discrete probability distribution, continuous expected value, risk neutral, risk averse, decision analysis, uncertainty

Suggested Citation

Carraway, Robert L., Analyzing Uncertainty: Probability Distributions and Simulation. Darden Case No. UVA-QA-0660, Available at SSRN: https://ssrn.com/abstract=1284242 or http://dx.doi.org/10.2139/ssrn.1284242

Robert L. Carraway (Contact Author)

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States

HOME PAGE: http://www.darden.virginia.edu/faculty/carraway.htm

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