Research work · 2021
An impossibility theorem on capital allocation
Yuanying Guan, Andreas Tsanakas, Ruodu Wang
Scandinavian Actuarial Journal
Abstract
Two natural and potentially desirable properties for capital allocation rules are top-downconsistency and shrinking independence. Top-down consistency means that the total capital isdetermined by the aggregate portfolio risk. Shrinking independence means that the risk capitalallocated to a given business line should not be affected by a proportional reduction of exposurein another business line. These two properties are satised by, respectively, the Euler allocationrule and the stress allocation rule. We prove an impossibility theorem which states that these twoproperties jointly lead to the trivial capital allocation based on the mean. When a subadditiverisk measure is used, the same result holds for weaker versions of shrinking independence, whichprevents the increase in risk capital in one line, when exposure to another is reduced. Theimpossibility theorem remains valid even if one assumes strong positive dependence among therisk vectors.