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256 RISK MANAGEMENT AND VALUE CREATION IN FINANCIAL INSTITUTIONS
mine what happens to the NPV in a RAROC world. This is a problem
because, on the one hand—as we will show shortly—nonzero NPV projects
lead to further skews in RAROC, 79 and determining the hurdle rate for each
project separately does not fix this problem. On the other hand, one should
keep in mind that the NPV is exactly what we are trying to find out when
we are calculating RAROC, making this discussion a “circular problem.”
We can depict the effects of positive and negative NPV projects on
RAROC as follows (see Figure 6.3).
Given the setup of our model, it is reasonable to assume that, in our
flows-to-equity 80 world, the NPV of a project flows to V E
at time T and
hence eventually to economic capital EC. 81 Additionally, we assume that the
correlation of the asset under consideration to the broad market portfolio
does not change; we are only investigating what happens when the riskiness
of the transaction changes.
RAROC
NPV > 0
NPV = 0
NPV < 0
Risk
Figure 6.3 RAROC and nonzero NPV projects.
Note: Results for plotting this graph are derived similar to Crouhy et al.
(1999), especially Table 4, p. 19.
79 See Crouhy et al. (1999), pp. 16 and 32.
80 Actually, RAROC is a “flows-to-economic capital” approach.
81 However, even though a positive NPV might reduce the equity requirement in a
transaction, it might not decrease the required amount of economic capital to buy
the necessary asset insurance.