Case 076Capital and regulationCore

A bank with Rs 2,500 crore of CET1 holds corporate loans, home loans and government bonds at different risk weights. Compute its RWA and CET1 ratio, then show what moving Rs 5,000 crore from corporate to home loans does.

The situation

Oranvi Bank has corporate loans of Rs 20,000 crore at a 100% risk weight, home loans of Rs 15,000 crore at an illustrative 35% and government bonds of Rs 10,000 crore at 0%. On top of the credit risk it carries operational risk RWA of Rs 3,000 crore and market risk RWA of Rs 2,000 crore. Its common equity tier 1 capital is Rs 2,500 crore.

The treasury team proposes letting Rs 5,000 crore of corporate loans run off over the year and replacing them with Rs 5,000 crore of new home loans, so the balance sheet stays the same size. The bank's board runs to an internal CET1 floor of 8.0%, used here as an illustration; the regulatory minimum plus buffers should be confirmed with the regulator.

Your task

What are RWA and the CET1 ratio now, what are they after the shift, and what does the change buy the bank?

Quick check

Capital does not change. Roughly where does the CET1 ratio land after the shift?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

RWA is Rs 30,250 crore and CET1 is 8.3%; after the shift RWA is Rs 27,000 crore and CET1 is 9.3%. Rs 5,000 crore moving from a 100% weight to 35% frees Rs 3,250 crore of RWA. Against an 8.0% floor, headroom rises from Rs 1,000 crore of RWA to Rs 4,250 crore. The ratio improved because the regulator's weights changed, not because the bank raised a rupee of capital.

Step 1How do you get from a balance sheet to RWA?

Multiply each exposure by its risk weight, then add the RWA for risks that do not sit in a loan line. Think of an insurer pricing drivers: the same Rs 10 lakh of car is charged more for a new driver than a veteran. Risk-weighted assetsExposures scaled by a regulator-set weight for how risky each type is, used as the denominator of the capital ratio. count a rupee of corporate loan in full, a rupee of home loan at 35 paise and a rupee of government bond at nothing. Credit RWA is 20,000 plus 5,250 plus zero, Rs 25,250 crore. Add Rs 3,000 crore of operational and Rs 2,000 crore of market RWA and the total is Rs 30,250 crore.

The relationship

\text{CET1 ratio} = \frac{2{,}500}{20{,}000 \times 1.00 + 15{,}000 \times 0.35 + 10{,}000 \times 0 + 3{,}000 + 2{,}000} = \frac{2{,}500}{30{,}250} = 8.26\%

2,500	common equity tier 1 capital, Rs crore
1.00, 0.35, 0	illustrative risk weights for corporate loans, home loans and government bonds
3,000 + 2,000	operational and market risk RWA, added directly

What it says in wordsCapital is divided by exposures weighted for riskiness, so the ratio moves when either the capital or the mix of the book moves.

Step 2What does the Rs 5,000 crore mix shift do?

Only one line of the sum changes. Rs 5,000 crore that used to count at 100% now counts at 35%. RWA falls by 5,000 times 0.65, Rs 3,250 crore, to Rs 27,000 crore, and the same Rs 2,500 crore of capital becomes a 9.3% ratio. The balance sheet is the same size, the capital is the same, and the ratio is a full point higher. That is why capital planning teams talk about RWA density, RWA over total assets, as much as about raising equity.

Moving Rs 5,000 crore from corporate loans at 100% to home loans at 35% cuts RWA from Rs 30,250 crore to Rs 27,000 crore, lifting the CET1 ratio from 8.3% to 9.3% on unchanged capital.

Step 3What does the higher ratio buy, and what does it hide?

Translate the ratio back into lending. At an 8.0% floor, Rs 2,500 crore of capital supports Rs 31,250 crore of RWA. Before the shift the bank had Rs 1,000 crore of RWA headroom; after it, Rs 4,250 crore, enough for another Rs 4,250 crore of corporate loans or about Rs 12,143 crore of home loans. Put the other way, the freed Rs 3,250 crore of RWA could carry Rs 3,250 crore of new corporate lending at the old 8.3% ratio.

Rs crore	Before	After
Corporate loans RWA	20,000	15,000
Home loans RWA	5,250	7,000
Government bonds RWA	0	0
Operational and market RWA	5,000	5,000
Total RWA	30,250	27,000
CET1 ratio	8.26%	9.26%
RWA headroom at an 8.0% floor	1,000	4,250

The mix shift leaves capital at Rs 2,500 crore but cuts RWA by Rs 3,250 crore, raising CET1 from 8.26% to 9.26% and headroom at an 8.0% floor from Rs 1,000 crore to Rs 4,250 crore.

Then say the limit, because a risk interviewer is waiting for it. A risk weight is the regulator's average view, not the risk in this particular book. A 35% weight on home loans assumes sensible loan-to-value ratios; a housing book concentrated in one city or written at high loan-to-value can lose far more than the weight implies. Home loans also earn a thinner margin, so profit per rupee of lending falls. And operational RWA is usually tied to income, so it will not stay at Rs 3,000 crore for ever. The shift is a sound capital move only if the housing book is underwritten as carefully as the corporate book it replaces.

Where candidates lose it

The common slip is to apply the 35% weight to the whole Rs 5,000 crore change instead of to the difference in weights, and conclude RWA falls by Rs 1,750 crore. The exposure leaves a 100% bucket and enters a 35% bucket, so the saving is 65 paise per rupee, Rs 3,250 crore.

The second is stopping at the ratio. A candidate who calls 9.3% safer without asking whether the home loan book is concentrated or written at high loan-to-value has confused a regulatory number with the underlying risk.

What the interviewer asks next

The home loans are all above 80% loan-to-value and carry a higher weight. Redo the ratio at a 50% weight.
How much fresh CET1 would take the ratio to 9.3% without changing the mix?
Why might a regulator add a floor on how low internal-model RWA can go?

Company names and figures are illustrative.