Risk Capital Allocation for RORAC Optimization

Abstract

This paper considers the financial optimization problem of a firm with several sub-businesses striving for its optimal RORAC. An insightful example shows that the implementation of classical gradient capital allocation can be suboptimal if division managers are allowed to venture into all business whose marginal RORAC exceeds the firm's RORAC. The marginal RORAC requirements are refined by adding a risk correction term that takes into account the interdependencies of the risks of different lines of business. It is shown that under certain stationarity conditions this approach can guarantee that the optimal RORAC will eventually be achieved.

Keywords: Risk capital, Economic capital, Capital allocation, Gradient allocation, Euler allocation, RORAC

JEL Classification: C61, D81, D82, G21, G22