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Cost Risk Allocation Theory and Practice

Risk Track

RS13A_Cost Risk Allocation Theory and Practice



Risk allocation is the assignment of risk reserves from a total project or portfolio level to individual constituent elements. For example, cost risk at the total project level is often allocated to individual work breakdown structure (WBS) elements. This is a non-trivial exercise in most instances because of issues related to the aggregation of risks, such as the fact that percentiles do not add. For example if a project is funded at a 70% confidence level then one cannot simply allocate that funding to WBS elements by assigning each its 70% confidence level estimate. This is because the resulting sum may (but not necessarily will) be larger than the total 70% confidence estimate for the entire project. One method for allocating risk that has commonly been used in practice and has been implemented in a cost estimating integration software package is to assign risk by assigning the element’s standard deviation as a proportion of the sum of the standard deviations for all WBS elements. Another method proposed as an improvement over this notes that risk is typically not symmetric, and looks at the relative contribution of the element’s variation above the mean or other reference estimate. This technique, based on the concept of “need,” has been implemented in the NASA/Air Force Cost Model. These contributions represent the current state-of-the-practice in cost analysis. The notion of considering positive semi-variance as an alternative to the needs method was brought forth by Sandberg. A new method proposed by Hermann introduces the concept of optimality in risk allocation and proposes a one-sided moment method objective function for calculating the optimal allocation. Aside from Hermann’s paper, cost risk allocation has typically not been associated with optimality, so neither the proportional standard deviation method nor the needs method guarantees the allocation scheme will be optimal or even necessarily desirable. Indeed, the twin topics of risk measurement and risk allocation have either been treated independently, or they have been treated as one and the same. Regardless the current situation is muddled, with no clear delineation between the two. In this paper, the author introduces to cost analysis the concept of gradient risk allocation, which has been recently used in the areas of finance and insurance. Gradient allocation clearly illustrates that the notions of risk measure and risk allocation are distinct but intrinsically linked. This principle is shown to be an optimal method for allocation using three distinct arguments – axiomatic, game-theoretic, and economic. It is also shown that the gradient risk allocation method is intrinsically tied to the method used to measure risk, a concept not heretofore considered in cost analysis. Gradient allocation is applied to five risk measures, resulting in five different allocation methods, each optimal for the risk measure from which they are derived. Considerations on when the proportional standard deviation and needs method are optimal are discussed, and a link between Hermann’s method and the proportional standard deviation method is demonstrated.


Christian Smart
Missile Defense Agency
Dr. Christian Smart is currently employed as the director for cost estimating and analysis at the Missile Defense Agency (MDA). 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. Prior to joining MDA, Dr. Smart worked as a senior parametric cost analyst and program manager with Science Applications International Corporation. An experienced estimator and analyst, he was responsible for risk analysis and cost integration for NASA’s Ares launch vehicles. Dr. Smart spent several years overseeing improvements and updates to the NASA/Air Force Cost Model and has developed numerous cost models and techniques that are used by Goddard Space Flight Center, Marshall Space Flight Center, and NASA HQ. 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. He has given numerous presentations on cost modeling and risk analysis both in the U.S. and abroad. He was awarded best of conference paper at the 2008 Annual Joint ISPA-SCEA conference in Noordwijk for “The Fractal Geometry of Cost Risk,” best of conference paper at the 2009 Annual Joint ISPA-SCEA conference in St. Louis for “The Portfolio Effect and the Free Lunch” and best of conference paper at the 2010 Annual Joint ISPA-SCEA conference in San Diego for “Here, There Be Dragons: Considering the Right Tail in Risk Management.” Dr. Smart was named the 2009 Parametrician of the Year by ISPA. He is a SCEA certified cost estimator/analyst (CCEA), a member of the Society for Cost Estimating and Analysis (SCEA) and the International Society of Parametric Analysts (ISPA). Dr. Smart is a past president of the Greater Alabama Chapter of SCEA, is the managing editor for The Journal of Cost Analysis and Parametrics, and serves as the Region III VP on the SCEA national board of directors. Dr. Smart earned bachelors degrees in Economics and Mathematics from Jacksonville State University, and a Ph.D. in Applied Mathematics from the University of Alabama in Huntsville.