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252 RISK MANAGEMENT AND VALUE CREATION IN FINANCIAL INSTITUTIONS
2. EC = V E,0
, that is, economic capital is completely provided by the
shareholders (at least initially). 59
We can then derive:
RAROC = E(V A,T
) + EC( 1 + R ) − ,
( +
f
VD0
1 RD)
−1
EC
= E(V ) ( )
A,T
− V 1 D,
0
+ RD + EC ⋅Rf
(6.13)
EC
Therefore, risk-adjusted net income is defined exactly as shown previously,
60 where V D,0
(1 + R D
) is the cost of funds (including the repayment)
and EC⋅R f
the (nominal) capital benefit, 61 which is the amount of money
made on the investment of economic capital in risk-free assets until the end
of the measurement period.
Only under these conditions will RAROC be an ROE measure that can
be compared to a CAPM-determined hurdle rate R E h .
Wilson (1992) points to the same problem that RAROC is only applicable
under very restrictive assumptions. He claims that RAROC—as currently
defined and used—will only lead to correct results if it is applied to
zero value (i.e., V A,0
= 0 and NPV = 0) self-financing (i.e., I = V D,0
= 0)
portfolios. Applying the above-developed framework under these conditions,
we can show that Wilson is right, but that his assumptions are only a special
case of our framework. 62 It is worthwhile to note however that he is correct
in stating that in his approach “the natural hurdle […] rate […] is the riskfree
rate” 63 as we can show that RAROC reduces then to:
in our framework.
RAROC = V
E,
R 0
( 1 +
f)
− 1 = R f
= R E
(6.14)
V
E,
0
59 See Zaik et al. (1996), p. 84.
60 Note that these are gross amounts and not returns expressed as dollar amounts.
61 The expression capital benefit is introduced by Copeland et al. (1994), pp. 481–
482. In our context, we need to assume either that EC determines the real capital
structure and hence reduces the funding need by debt, so that the capital benefit is
calculated at the interest rate of debt (following the Copeland et al. argument), or
that EC is invested in a(n) (insurance) pool at the risk-free rate of return (as we do
in the RAROC context).
62 Nonetheless, Wilson (1992), p. 114, comes to the conclusion that RAROC would
be biased in an opposite direction, given an incentive to invest in risk-free projects
generating an infinite RAROC (which is true, because RAROC is, like the Sharpe
ratio, not defined for risk-free assets).
63 See Wilson (1992), p. 119.