How should the cost of joint risk capital be allocated for performance measurement?

We consider the problem of allocating the cost of risk capital based on value-at-risk (VaR) for performance measurement in a decentralized organization with several divisions. The focus of the analysis is on fair risk capital allocation schemes. To this end, we analyze several well-known allocation schemes in the context of a model based on cooperative game theory using the core concept. We provide theoretical evidence that two allocation schemes, the beta method and the nucleolus method, turn out to perform best in allocating the cost of risk capital. A simulation study shows that another allocation method, the cost gap method, shows similar results. However, within an experiment we obtain empirical evidence that the core concept is of minor importance with respect to individually perceived fairness. Subjects tend to favor simple allocation rules such as the activity-level method and the beta method. In summary only the beta method can be considered to be fair both from a normative and a descriptive point of view.