Allocation of Risk Capital in Financial Institutions

Financial Management (Financial Management Association), Autumn, 1999 by Francesco Saita

However attractive either solution may be in providing a measure of each unit's performance, a substantial objection can be raised. Imagine using a RAROC measure based on marginal CaR to assign bonuses to individuals and teams throughout the bank. In this case, the main problem is not represented by the existence of unallocated CaR: in fact, higher RAROC targets on marginal CaR could compensate for this effect. Rather, the real problem is that the use of marginal CaR will make each unit's performance vary according to a variable outside its control, i.e., the magnitude of the diversification benefits.

A simple example can clarify this point. Consider the hypothetical results of the four business units reported in Table 6.

Let us now imagine that, due to relatively poor performance--in terms of return on marginal CaR--by units A and D, capital is partially reallocated at the end of year 1 to units B and C, as shown in Table 7. The marginal capital-at-risk for each unit is obviously going to change as a result of the reallocation.

At the end of year 2, each of the units obtains exactly the same return on unit CaR as in year 1 (i.e., it has exactly the same performance in managing its core business risks). But due to the changes in the distribution of diversification benefits, results in terms of return on marginal CaR are completely different (see Table 8).

Thus, even though each unit has maintained its performance in terms of individual capital-at-risk, profitability rankings in terms of marginal CaR have completely changed. In fact, the least profitable units, A and D, have become the best performing ones. This has not been due to any improvement in the management of unit-specific risks, but is due solely to a redistribution of diversification benefits across business units.

It is clear that a similar conclusion also applies when measures based on internal betas are used. In fact, when the mix of businesses changes, correlations of returns between individual business units and the bank as a whole change as well. Therefore, any RAROC measure based on "diversified" CaR, no matter which method is used to determine it, is by definition influenced by the correlation structure among existing businesses returns. This i a fundamental advantage from the viewpoint of top management decisions, but a substantial pitfall from the perspective of measuring individual unit performance (and consequently of bonus definition). The conclusion is straightforward: the choice of the "best" CaR measure depends on the purpose for which it is intended. In fact, performance measures can be generally created for two very different purposes: [22]

* to support top management decisions (by raising attention to key problems; by supporting problem-solving, e.g., pricing or strategic entry/exit, or capital budgeting decisions; or by enabling "scorekeeping" across business units); and

* to standardize the measure of output for each organizational unit and, in this way, to coordinate actions.