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254 RISK MANAGEMENT AND VALUE CREATION IN FINANCIAL INSTITUTIONS
betas. 70 However, one should keep in mind that the chosen total risk measure
is different from the priced and systematic market risk. Since RAROC
does not use any valuation model to derive the relative ordering of expected
returns, 71 it is not able to provide a consistent relative ranking of transactions.
72
Second, we have already shown that you can either fix the default probability
or the hurdle rate, but not both at the same time. 73 Thus, the following
assumption is not justified: that due to changes in the leverage, which fix
the default probability, we can use a single hurdle rate across all bank transactions.
74
In order to prove that the RAROC analysis generates reliable results
with regard to value creation, one could formulate the following fundamental
hypotheses:
■
■
If we consider a zero NPV project, RAROC should always equal the
(bankwide) hurdle rate R
h
E
and should, thus, indicate that the bank
is indifferent vis-à-vis this transaction.
If we consider a transaction with positive (negative) NPV, RAROC
should always be larger (smaller) than the (bankwide) hurdle rate
R h E
.
However, given the above analysis, we can show that these fundamental
premises do not necessarily hold true.
Let us first consider zero NPV transactions. In the above-defined model,
RAROC changes even for NPV = 0 transactions with a change in the riskiness
of the transactions and with changes in the correlation of the transactions
to the broad market portfolio (as defined in a CAPM world). Figure
6.2 depicts the effects that are derived applying the analysis conducted by
Crouhy et al. (1999).
As can be seen, RAROC increases with increases in the riskiness of a
transaction. RAROC is also higher, the higher the correlation of the transaction
is to the broad market portfolio. Banks applying RAROC as defined
previously, therefore, tend to choose high-risk, high-correlation projects, be-
70 However, this is not true in general.
71 See Crouhy et al. (1999), p. 16.
72 See James (1996), p. 14, and which we will see in more detail below.
73 When the leverage is set so that it matches a fixed equity return, the prespecified
default level will change with changes in the asset risk—or fixing the capital structure
for the default probability results in a change of the equity return with a change
in the asset risk. The same holds true for changes in the correlation. See above and
Crouhy et al. (1999), p. 12.
74 See Crouhy et al. (1999), p. 8.