The Fractal Nature of Cost Risk: The Portfolio Effect, Power Laws, and Risk and Uncertainty Properties of Lognormal Distributions
Journal of Cost Analysis and Parametrics
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.
Christian Smart, Ph.D., is the Director for Cost Estimating at the Missile Defense Agency. In this capacity, he is responsible for overseeing all cost estimating activities developed and produced by the agency, and directs the work of a 100-person team. In 2010, he received an Exceptional Public Service Medal from NASA for his contributions to the Ares I Joint Cost Schedule Confidence Level Analysis and his support for the Human Space Flight Review Panel led by Norm Augustine. In 2009, he was awarded the Parametrician of the Year award by the International Society of Parametric Analysts. He has won several best paper awards at the annual International Society of Parametric Analysts and the Society of Cost Estimating and Analysis annual conferences. One of these conference papers was the basis for this journal article.