Explain how adopting an economic capital framework helps and changes outcomes in four areas: managing the credit portfolio, pricing for risk, analysing how profitable customers are, and shaping management incentives.
The idea
An economic capital framework gives every exposure a capital cost, which changes decisions in four areas. In credit portfolio management, capital is driven by each loan's contribution to portfolio risk, so concentration and correlation matter, not only the rating. In pricing, the minimum spread covers funding cost, operating cost, expected loss and a charge for the capital used, so riskier loans cost more. In customer profitability, a customer or unit is judged by its RAROC against a hurdle rate. Write EL for expected loss and EC for economic capital. RAROC = (revenue − costs − EL) ÷ EC. A second measure is economic profit, where NI is net income and k is the cost of capital. EP = NI − k × EC. In incentives, rewarding managers on these measures aligns them with shareholders instead of rewarding raw profit or volume. The usual mistake is to rank units on net income or return on assets, ignoring the capital consumed. The exam point is that a unit can be profitable and still destroy value once the capital charge is deducted.
Formulas
Risk-adjusted return on capital
RAROC = (Revenue − Costs − EL) ÷ EC
- Revenue
- the business unit's revenue for the period
- Costs
- its operating costs
- EL
- the expected loss, covered by pricing and provisions
- EC
- the economic capital allocated to the unit
Compared with a hurdle rate. Dividing by exposure instead of economic capital, or leaving out expected loss, overstates the return.
Economic profit of a unit
EP = NI − k × EC
- NI
- the unit's net income
- k
- the cost of capital
- EC
- the economic capital the unit uses
A unit with high net income can have negative economic profit once its capital charge is deducted.
Minimum loan margin above funding cost
Margin = EL + OC + EC × (h − Rf)
- EL
- expected loss as a fraction of the loan
- OC
- operating cost as a fraction of the loan
- EC
- economic capital as a fraction of the loan
- h
- the hurdle rate on capital
- Rf
- the risk-free rate the capital earns when invested
Only the excess of the hurdle over the risk-free rate is charged, because the capital itself earns Rf.
A practice question
Which definition of risk-adjusted return on capital (RAROC) is used in an economic capital framework?
- Net income divided by regulatory capital held against the exposure, with no deduction for expected loss.Why not: Uses regulatory capital and ignores the expected loss deduction; RAROC is built on economic capital.
- Revenue minus costs, divided by the notional amount of the exposure.Why not: Divides by notional exposure instead of capital and does not deduct expected loss.
- Revenue less operating cost less expected loss, divided by economic capital. - correct
- Expected loss divided by economic capital.Why not: Uses a cost as the numerator; RAROC is a return measure built on revenue less costs and expected loss.
RAROC = (revenue - operating cost - expected loss) / economic capital. It is compared with a hurdle rate such as the cost of equity to judge whether a customer or unit creates value.
A harder one
A customer relationship produces revenue of USD 2.4 million, operating costs of USD 0.9 million and expected loss of USD 0.3 million, and uses USD 5 million of economic capital on USD 40 million of exposure. The hurdle rate is 20%. Which statement is correct?
- RAROC is 24%, above the hurdle, so the relationship adds value. - correct
- RAROC is 30%, above the hurdle, so the relationship adds value.Why not: Omits the expected loss deduction: (2.4 - 0.9) / 5.
- RAROC is 3%, below the hurdle, so the relationship destroys value.Why not: Divides by the USD 40 million exposure instead of economic capital.
- RAROC is 48%, far above the hurdle, so the relationship adds value.Why not: Divides revenue alone by economic capital, ignoring both costs and expected loss.
RAROC = (2.4 - 0.9 - 0.3) / 5 = 1.2 / 5 = 24%, above the 20% hurdle. Deducting expected loss and measuring against economic capital, not exposure, is what separates RAROC from simple return measures.
The hardest tier
A bank sets the minimum loan margin above funding cost as expected loss plus operating cost plus a capital charge. Expected loss is 0.60% of the loan, operating cost is 0.70%, economic capital is 8% of the loan, the hurdle rate on capital is 14%, and the capital earns the 3% risk-free rate. The capital charge is economic capital multiplied by (hurdle rate minus risk-free rate). The minimum margin is closest to:
- 2.42%Why not: Charges the full 14% hurdle on capital, ignoring the 3% earned on the capital held.
- 2.18% - correct
- 1.30%Why not: Omits the capital charge and covers only expected loss and operating cost.
- 1.54%Why not: Adds the capital multiplied by the risk-free rate instead of subtracting it from the hurdle, charging 3% instead of 11%.
Capital charge = 8% x (14% - 3%) = 0.88%. Margin = 0.60% + 0.70% + 0.88% = 2.18%. The capital is funded by equity but earns the risk-free rate on its investment, so only the excess return is charged to the borrower.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in Range of practices and issues in economic capital frameworks
- Describe the difficulties met in implementing an economic capital framework when defining and computing risk measures, aggregating risk, validating models, modeling dependency in credit risk, evaluating counterparty credit risk, and assessing interest rate risk in the banking book.
- Set out what the Bank for International Settlements (BIS) recommends supervisors weigh in order to put internal risk measures such as economic capital, which were not built for regulation, to good use.
- Outline good practice in governing an economic capital framework and judge the main concerns that arise.