Case 026Capital and regulationCore
A bank's internal models produce far lower risk-weighted assets than the standardised approach. Apply an output floor, recompute the CET1 ratio and explain what the floor protects against.
1The situation
Harnavi Bank uses approved internal models for credit risk. They put its risk-weighted assets (RWA) at Rs 30,000 crore. Running the same book through the regulator's standardised approach, which uses fixed risk weights by exposure type, gives Rs 50,000 crore. Harnavi's common equity tier 1 (CET1) capital is Rs 4,200 crore.
For this case the regulator applies an output floor of 72.5%: the RWA the bank reports can be no lower than 72.5% of the standardised figure. Treat 72.5% as an illustration of how the rule works; confirm the level and phase-in timetable your regulator applies.
2Your task
What RWA does Harnavi report, what is its CET1 ratio before and after the floor, how much capital would it need to keep its old ratio, and what is the floor there to prevent?
Quick check
Once the floor applies, what is Harnavi's CET1 ratio?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Harnavi reports RWA of Rs 36,250 crore and its CET1 ratio falls from 14.0% to 11.6%. The floor, 72.5% of Rs 50,000 crore, is above the modelled Rs 30,000 crore, so it binds. Keeping a 14.0% ratio would need Rs 875 crore more capital. The floor exists because models can understate risk, and it caps how far any bank's own numbers can cut its capital.
Step 1How does the floor decide which RWA number counts?
Think of a car insurer that gives careful drivers a discount based on a tracking device, but never lets the premium fall below 72.5% of the standard price, however good the data looks. The discount is real until it hits that line, and then it stops. The floored RWA is the higher of the modelled figure and 72.5% of the standardised figure. For Harnavi that is the higher of Rs 30,000 crore and Rs 36,250 crore, so the floor wins by Rs 6,250 crore.
| Measure | RWA, Rs crore | CET1 ratio |
|---|---|---|
| Internal models | 30,000 | 14.0% |
| Floor: 72.5% of standardised | 36,250 | 11.6% |
| Standardised approach | 50,000 | 8.4% |
| Reported: the higher of models and floor | 36,250 | 11.6% |
Step 2How much capital does the floor cost Harnavi?
Hold the ratio the bank showed investors, 14.0%, and ask what capital it now needs. 14.0% of Rs 36,250 crore is Rs 5,075 crore, so Harnavi is Rs 875 crore short of its old ratio, about 21% more equity for the same loans. It could raise equity, retain profit, or shrink the exposures where its models and the standardised weights differ most, since those are the ones the floor now prices at the standardised rate.
Step 3Why would a regulator distrust a bank's own models?
Harnavi's models say its book is 40% less risky than the standard weights assume. That may be true. But risk-weighted assetsExposures scaled by a weight for how risky each one is, so that a secured home loan needs less capital than an unsecured business loan. built from a bank's own default and loss estimates depend on short data histories, few defaults in safe portfolios, and choices the bank makes about its own capital. Studies of banks holding similar portfolios found their modelled RWA differed widely, which is hard to explain by risk alone. The floor does not say the model is wrong. It says the cut a model can deliver is capped at 27.5%, so an optimistic model, an honest error or a gamed input can only do limited damage.
Say the limitation as well. The floor is blunt: a bank whose low RWA is genuinely earned, say from well-collateralised lending, is charged as if it were not. And because it is set against the standardised approach, the floor inherits that approach's crude weights. A good answer calls the floor a backstop against model risk, not a better measure of risk.
Where candidates lose it
The common slip is to replace the modelled RWA with the full standardised Rs 50,000 crore and report 8.4%. The floor is a percentage of the standardised figure, not the figure itself, and it only matters when the model falls below it.
The second is to treat the lower ratio as a sign that Harnavi has become riskier. Nothing in the book changed; the denominator did. Saying that clearly, and then explaining why the regulator wants it that way, is what earns the mark.
What the interviewer asks next
- Harnavi's models are revised and now give RWA of Rs 38,000 crore. What does it report?
- Which kinds of lending would a bank shrink first once the floor binds?
- Why might a floor be applied to the whole bank's RWA rather than portfolio by portfolio?
- How does the leverage ratio differ from the output floor as a backstop?
Company names and figures are illustrative.
