Value at Risk and Bank Capital Management

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 fi xed-rate loan whose CaR

is equal to 4000 USD. The loan must be entirely funded at a 5-year fi 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 bank’s 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 defi 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 profi 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