The Fractal Geometry of Cost Risk
Smart, C.
MCR

Due to uncertainties in technical parameters, estimating methods, and extrinsic factors such as budget constraints, cost risk is a vital part of a credible estimate. The results of cost risk analyses provide vital information to key decision makers in determining budgets and reserves. Cost risk analyses are often represented as probability density functions. The two most commonly used density functions in cost risk are the Normal and lognormal distributions. However, these commonly used distributions under represent the probability of extreme cost growth, such as that experienced in numerous historical programs. Cost growth is a pervasive phenomenon in space and military programs, and increases in final actual cost from initial budgets in excess of 200% have occurred on a frequent basis. Normal distributions, which have thin tails, are poorly suited to modeling such phenomena. Lognormal distributions are better suited, but still do not are not suitable for adequately assessing the likelihood of excessive cost growth. Historical cost growth patterns follow a power law. Power laws have been found to apply to numerous phenomena across a variety of fields, including physics, biology, and even finance. This indicates that the likelihood of extreme cost risk may be better modeled by a fat-tailed distribution, such as a Pareto distribution. Also, evidence that cost growth follows a power law means that the touted portfolio effect is a myth and should not be used in setting reserve policy.

Conversely, reserves for space and military programs are often set at the 70% or even 65% confidence level. In such cases, a Normal distribution may be the best way to measure cost risk and aid decision makers in setting reserves for individual programs.