Ebook 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. In this context, capital allocation is a crucial task which is very similar to a portfolio management problem. More precisely, a top-down approach consists in disaggregating a bank's portfolio into different business lines with different ratios of expected return and different risks. Then the capital should be allocated in order to balance the portfolio in an optimal way.
According to the portfolio theory, 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. In most cases, the bank has a good knowledge of its expected returns and risks. As for the correlation matrix, the problem is more complex: the bank does not have enough internal data and information to estimate it accurately. In this respect, we develop an approach based on a Market Factor Model: we estimate an implied correlation matrix using the returns of a panel of banks. The second section presents this model.
The third section deals with the allocation problem. An asset allocation problem cannot exactly stand for a capital allocation problem. Nevertheless the portfolio theory can be adapted so that it takes capital allocation's specific issues into account. For example, a bank has to abide by some solvency rules, it also has to reach some implicit objectives fixed by its shareholders. Besides, capital allocation could be viewed as an optimisation problem or an economic utility function problem under specific constraints.
Actually, the allocation problem is not exactly the problem a bank has to cope with. A bank is caracterised by its initial allocation. Moving to a new and better allocation generates costs that can be taken into account by penalizing the utility function. Nonetheless, if such a method determines the position of the optimum, it does not exhibit any path going from the initial allocation to the optimal one. Then, we introduce reallocation signals allowing a dynamic policy that leads to the optimum.
This paper is based on two works made at the Operational Research Group of Crédit Lyonnais ([7], [15]). The findings being confidential, this paper is not extensively illustrated by figures. Moreover, we have decided to conceal any reference to particular financial institutions. Yet, the main lines have been preserved.
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