An Analysis Framework for Bank Capital Allocation

Capital allocation within a bank is getting more important as the regulatory requirements are moving towards economic-based measures of risk. Banks are urged to build sound internal measures of credit and market risks for all their activities. Internal models for credit, market and operational risks are fundamental for bank capital allocation in a bottom-up approach. But this approach has to be completed by a top-down approach in order to give to bank managers a more comprehensive (but less detailed) vision of the allocation efficiency.From a top-down viewpoint, we are considering the different business lines of a bank as assets. Then the capital has to be allocated in order to balance a portfolio in an optimal way. In this respect, a bank has to evaluate not only the expected return and the risk of every business line, but also the correlation matrix of these business lines returns. If a bank usually has a good knowledge of its expected returns and risks, the problem is more complex in the case of the correlation matrix: to cope with the lack of internal data and information, we develop an approach based on a Market Factor Model and estimate an implied correlation matrix using the returns of a panel of banks.The allocation problem is not exactly the problem a bank is confronted to. It more precisely deals with capital reallocation. Moving from an allocation to a new one generates costs that have to be taken into account to ensure that the new allocation is better than the former one. That is why reallocation signals are more interesting: they do not point out the optimal allocation but they allow the implementation of a dynamic policy that leads to an optimal situation.