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Capital Budgeting in Banks 249
However, as can be easily seen, in order to do so, we will need to change the
capital structure (i.e., V A,T
/F and hence D/E) as σ A
(the riskiness of the transaction)
changes.
However, as we change the capital structure (D/E as plotted on the x-
axis in Figure 6.1), we also change the return on equity (here denoted as
R_E). Note that D/E = 11.5 represents an equity percentage of 8%, 15.67
represents 6%, and 24.0 represents 4%. So, in the typical areas of bank and
transaction leverage ratios, we experience significant variations in the expected
equity return for relatively small changes in the capital structure. This
may seem to be at odds with the intuition of the M&M propositions at first
sight. 54 However, we are not trying to demonstrate the irrelevance of the
financing decision on the firm value here, but rather the effects when a firm
is trying to fix its default probability. 55
Because the same holds true when the correlation of the asset with the
market portfolio (ρ A,M
) increases, we can plot the following table that summarizes
the results (see Table 6.1)
where E(R A
) = Expected return on asset (which is determined via the
CAPM)
E(R E
) = E(V E,T
)/V E,0
– 1 = The expected return on equity (which
is also determined via the CAPM)
↑ (↓) = Indicate an increase (decrease) in the respective measure.
So, we can conclude from the above discussion that one can either fix
the default probability or R E
h
(the hurdle rate), but not both at the same
time. 56 Before we turn to the consequences of this conclusion in the next
section, we will now define RAROC—using the same modeling context—
so that it can be compared to a CAPM-based hurdle rate.
Let us consider a single one-year investment A of the bank. Let I be the
cost of the investment for asset A, which is an NPV = 0 transaction, and V A,t
be the market value of the investment at time t. It follows that therefore V A,0
= I. Let us further assume that economic capital EC is necessary to set up
a reserve pool that is invested in risk-free bonds to fix the probability of
default at the predetermined confidence level, which is a common assumption
for calculating RAROC in practice.
54 Note that we are using the same assumptions as they do.
55 And hence the effects on R E
rather than on WACC, the weighted average cost of
capital, or on value. Note that R D
is labeled R_D in Figure 6.1.
56 Fixing the default probability (i.e., d 2
) has an effect on the required rate of return
that is of an order of magnitude less than the effect of fixing the required rate of
return on the change in the default probability. See Crouhy et al. (1999), pp. 11–13.