The Fractal Nature of Cost Risk: The Portfolio Effect, Power Laws, and Risk and Uncertainty Properties of Lognormal Distributions

Abstract

Cost risk can be added to the list of the many phenomena in nature that follow a power-law probability distribution. Both the normal and lognormal, neither of which is a power-law distribution, underestimate the probability of extreme cost growth, as shown by comparison with empirical data. This situation puts the widely debated “portfolio effect” into further dispute. However, even though power laws are useful for modeling extreme events, budgets are not typically set at extreme percentiles, such as the 90th. Indeed, budgets are usually set at the 70th percentile or below. In addition, it is shown that the lognormal distribution is also problematic in that region and for percentile funding in general. To model cost risk for an individual program by setting budgets and/or reserves using percentile funding with a percentile chosen at or below the 70th percentile, it appears that the normal distribution may be the best option.