Risk Management and Value Creation in ... - Arabictrader.com

Capital Budgeting in Banks 251
Table 6.1
Effects of Keeping the Default Probability Constant
σ A
ρ A,M
D/E E(R A
) E(R E
)
↑ Const. ↓ ↑ ↑
Const. ↑ ↑ ↑ ↑
Therefore, in order to finance A, we need to raise funds as follows:
I + EC = V D,0
+ V E,0
(6.9)
For the time being, the split between debt (V D,0
) and equity (V E,0
) financing,
that is, the actual leverage of the transaction does not need to be
determined. Since we invested EC at the risk-free rate, we have additional
funds available in the end of the measurement horizon. Therefore, the probability
of default has a slightly different definition:
p(default) = p[V A,T
≤ F – EC(1 + R f
)] (6.10)
We assume that EC, the required amount of economic capital, is determined
so that the probability of default is kept constant and that it includes
all possible sources of risk, meaning that there are no misspecifications or
omissions leading to an incorrect amount of EC.
Hence, we can model the value of equity at the end of the measurement
horizon as:
V E,T
= V A,T
+ EC(1 + R f
)–V D,T
(6.11)
and the expected return on equity is hence:
E(R E
) = E(V ) ( ) ( )
A,T
+ EC 1+ Rf − VD , 0
1+
RD
– 1 (6.12)
VE
, 0
where R D
= (Promised) yield-to-maturity on the debt (> R f
).
This expression can be transformed into RAROC 57 only if the following
assumptions are met:
1. I = D V,0
, that is, the investment itself is completely financed by debt,
which is common practice in bank transactions. 58
57 Note that E(V A,T
) is assumed to correctly reflect the expenses and expected losses
as defined in the risk-adjusted net income of the RAROC equation. We will discuss
the missing costs of funds and the capital benefit shortly.
58 For 1. and 2., see, for example, Crouhy et al. (1999), pp. 15–16.