What it means
Standard profit figures can flatter risky activity. A lending desk that makes loans to weak borrowers can report a big interest income, while the losses only show up later.
RAROC corrects this by charging each activity for the losses it is expected to cause and for the capital it needs to survive a bad outcome. The numerator is income after costs and after expected losses.
The denominator is economic capital, an estimate of the cushion needed to cover losses that are unlikely but severe, usually set by risk models to a chosen confidence level. Together they show the return earned per dollar of capital at risk.
The measure is then compared with a hurdle rate, the minimum return shareholders require. If RAROC is above the hurdle, the activity creates value, and if it is below, it destroys value even if it reports an accounting profit.
This allows a bank to rank mortgages, corporate loans and trading desks on one scale. RAROC is also used for pricing.
If a loan to a risky borrower would produce a RAROC below the hurdle at the market interest rate, the bank can raise the rate, ask for collateral or decline. This links the price to the risk rather than to the competition alone.
The nuance is that the answer depends on how economic capital is estimated, and that estimate involves judgement. Two banks could compute different RAROC figures for the same loan, so the ratio is best used for ranking within one consistent framework.
Finally, RAROC is useful in setting limits. Credit committees can cap the capital allocated to a business with a low ratio and expand the capital given to one with a high ratio.
Over time this steers the whole organisation towards activities that earn their keep after risk.
In practice
Real-world examples.
Example
A bank compares its credit card business and its corporate lending business. The card business reports higher profit, but it needs much more capital to cover losses. After calculating RAROC, the corporate lending business turns out to earn the better return on capital.
Example
A relationship manager proposes a $20,000,000 loan at a thin margin to win a client's wider business. The credit team runs the numbers and finds that the RAROC falls below the hurdle rate. The manager must raise the price or bring in other fee income to justify it.
Example
An insurance group applies the same idea to its product lines, comparing the profit from each line with the capital it ties up. A line with large but volatile claims needs more capital and so shows a lower RAROC. Management shifts capital towards the steadier line.
Formula
Calculation
RAROC = (revenue - operating costs - expected losses) / economic capital
A commercial lending division earns $9,000,000 of net revenue after funding costs, has operating costs of $3,000,000 and expects credit losses of $1,500,000. Profit after expected losses is 9,000,000 - 3,000,000 - 1,500,000 = $4,500,000. The division needs $30,000,000 of economic capital, so RAROC = 4,500,000 / 30,000,000 = 0.15, or 15%. If the shareholders' hurdle rate is 12%, the division clears it.Case study
Seen in the real world.
Northgate Bank is an illustrative, fictional lender with two divisions: a mortgage division and a leveraged-lending division. The leveraged-lending division reported twice the profit of the mortgage division and was celebrated at the annual meeting.
The new chief risk officer calculated RAROC for both. The mortgage division earned $6,000,000 after expected losses on $40,000,000 of capital, a RAROC of 15%. The leveraged-lending division earned $12,000,000 after expected losses but needed $120,000,000 of capital, a RAROC of 10%.
With a hurdle rate of 12%, the second division was destroying value despite its large profits. Management moved $40,000,000 of capital from the second division towards mortgages over the following year. The change lifted the blended RAROC of the bank without any increase in total risk. The illustrative lesson is that profit alone is not a measure of performance until it is set against the capital that risk requires.
Watch out
Common mistakes.
- Comparing RAROC figures from different banks or models as if the capital estimates were calculated the same way.
- Forgetting to deduct expected losses, which turns RAROC into an ordinary return on capital.
- Using RAROC without a hurdle rate, which leaves no benchmark for deciding what counts as good.
Questions
People also ask.
How is RAROC different from return on equity?
Return on equity uses accounting capital, whereas RAROC uses economic capital based on the riskiness of each activity.
Who uses RAROC?
Mainly banks and insurers, though any business with distinct risky activities can adapt it.
What is a good RAROC?
It should exceed the firm's cost of equity or hurdle rate, which varies by institution and risk appetite, so there is no single number that is good for every lender.
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