Measure how a loan is performing by applying risk-adjusted return on capital (RAROC).

FRM® Part II · Credit Risk Measurement and Management · Introduction to Credit Risk Modeling and Assessment · FRM2.CR.5.g

The idea

RAROC measures the return on the capital a loan consumes. The standard form is RAROC = (revenues − costs − expected loss) ÷ economic capital. Revenues are interest and fees net of funding cost, costs are operating costs, and expected loss is subtracted because it is an expected cost of lending. The denominator is the economic capital held against unexpected loss, not the loan amount. Some versions add the return earned on the economic capital, for instance at the risk-free rate, to the numerator, and a question will say so if it applies. A loan creates value if its RAROC exceeds the hurdle rate, typically the shareholders' required return on equity. Comparing RAROC with the hurdle rate, rather than ranking loans by absolute profit, avoids favouring large, capital-hungry loans. The typical errors are forgetting expected loss and dividing by loan size instead of capital.

Formulas

RAROC of a loan

RAROC = (revenues − costs − expected loss) ÷ economic capital

revenues: interest and fees net of funding cost
costs: operating costs
expected loss: the expected credit loss on the loan
economic capital: the capital held against unexpected loss

Approve if RAROC exceeds the hurdle rate. Dividing by the loan amount or leaving out expected loss are the typical errors.

RAROC crediting a return on the capital

RAROC = (revenues − costs − expected loss + rf × economic capital) ÷ economic capital

revenues: interest and fees net of funding cost
costs: operating costs
expected loss: the expected credit loss on the loan
rf: the rate earned on the capital, for instance the risk-free rate
economic capital: the capital held against unexpected loss

Use only when the question says the capital is credited with a return. The capital benefit is added, and expected loss is still deducted.

A practice question

From the question bank, with the reason each wrong option is wrong.

RAROC for a loan is best defined as:

Risk-adjusted income after expected loss, divided by economic capital - correct
Net income divided by the loan amountWhy not: Divides by loan size rather than by the capital the loan consumes, and ignores expected loss.
Revenue divided by regulatory capitalWhy not: Uses revenue rather than income after costs and expected loss, and regulatory instead of economic capital.
Expected loss divided by economic capitalWhy not: Uses expected loss as the numerator; expected loss is a deduction from income, not the return.

RAROC = (revenues - costs - expected loss) / economic capital. Economic capital is the buffer for unexpected loss, so RAROC is a return on risk capital.

A harder one

A USD 100 million loan generates interest and fee revenue of USD 6.0 million. Funding costs are USD 3.2 million, operating costs are USD 0.8 million and expected loss is USD 0.6 million. Economic capital is USD 8 million. The RAROC is closest to:

25.0%Why not: Leaves out expected loss, which must be deducted from income.
27.5%Why not: Leaves out operating costs.
17.5% - correct
1.4%Why not: Divides by the loan amount instead of economic capital.

Risk-adjusted income = 6.0 - 3.2 - 0.8 - 0.6 = 1.4. RAROC = 1.4 / 8.0 = 17.5%.

The hardest tier

A USD 200 million loan earns a net interest margin m (revenue less funding cost, as a percentage of the loan) and carries an expected loss of 0.5 percent of the loan, operating costs of 0.6 percent of the loan and economic capital of 6 percent of the loan. The bank requires a RAROC of 15 percent. The minimum net interest margin on the loan is closest to:

2.00% - correct
1.50%Why not: Leaves out the expected loss when solving for the required margin.
1.40%Why not: Leaves out the operating costs when solving for the required margin.
0.90%Why not: Includes only the return required on capital and ignores both expected loss and operating costs.

RAROC = (m - 0.5% - 0.6%) / 6% = 15%. So m - 1.1% = 0.9%, giving m = 2.00%. The loan size cancels because every item is a percentage of the loan.

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