ALLOCATED CAPITAL VERSUS UTILIZED CAPITAL 199
8.3 Capital Investment versus Capital Allocation
Before discussing the choice among alternative CaR measures for RAP measurement, we
must clarify the difference between capital investment and capital allocation (see Matten
2000). Let us consider a branch making a 100,000 USD 5-year xed-rate loan whose CaR
is equal to 4000 USD. The loan must be entirely funded at a 5-year xed internal transfer
rate by the treasury department. In fact, if instead the loan were assumed to be fi nanced
4% by equity capital and 96% by the treasury department at the 5-year internal transfer
rate, the result of the lending division would be affected by changes in interest rates during
the life of the loan. But if (correctly) the loan is considered funded entirely at the 5-year
internal transfer rate, then the 4000 USD equity capital the loan requires is not invested
in the loan, but is only ideally allocated as a cover for potential unexpected losses the
loan might generate.
The distinction between capital investment and capital allocation has a relevant con-
sequence: If capital at risk is ideally allocated to only a business unit, it could also be
“physically” safely invested somewhere else (e.g., in a risk-free asset). Thus, part of the
target return on equity capital may be produced by capital investment, while the remain-
ing part should be produced by capital allocation. Assuming the target return k
e
on equity
capital were 15% and capital could be invested at the risk-free rate r
f
= 3%, then the return
required on allocated capital in order to obtain the target overall return should be equal
to k
e
r
f
= 12%.
While the assumption to invest equity capital at the risk-free rate is the simplest solu-
tion, a potential alternative is to assume transfering equity capital to the treasury depart-
ment in order to fund assets together with the banks liabilities. In this case, a proper
internal transfer rate for equity (ITR
e
) and a precise maturity should be defi ned. For
instance, the one-year Libor rate at the beginning of the year could be assumed to be the
transfer rate; note that the maturity might also matter when de ning asset and liability
management policies for the treasury department. In theory, the maturity could be either
a one-year rate or a long-term rate; the choice should be made according to how the return
target for the bank has been set. If the target is defi ned as the long-term (short-term) risk-
free rate plus an equity premium, than equity capital should be assumed to be either safely
invested or transferred to the treasury department over the same long (short) horizon.
As a consequence, when evaluating the risk-adjusted profi tability of different business
units, the target level for business unit RAROC (assuming it should be the same for all
units, a topic that is critically discussed in Chapter 9) should be equal to k
e
r
f
rather
than to k
e
only. In fact, a business unit having a RAROC equal to k
e
r
f
implies that by
adding up return on capital investment the overall pro tability target would be met.
Similarly, when calculating EVA the cost of capital should be equal to k
e
r
f
rather than
to k
e
only.
8.4 Choosing the Measure of Capital at Risk: Allocated
Capital versus Utilized Capital
Whenever a business unit is given a VaR/CaR limit as discussed in Chapter 7, there are
two potential CaR measures that could be used in ex post RAP measurement. The fi rst
one is utilized CaR, i.e., the actual, ex post CaR measuring the overall risk accepted by
the business unit during the year. The second one is the CaR limit, representing the
amount of risk that could have been accepted and, most important, the amount of capital

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