Risk Management puzzles, solved step by step

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  1. 051A bank has CET1 capital of Rs 900 crore and risk-weighted assets of Rs 8,000 crore. It takes a Rs 200 crore loss. What happens to its CET1 ratio?Capital and leverageWarm upBank credit riskRisk GCC

    Try it first

    Before you divide anything: roughly where does the ratio land?

    Show the worked solution

    The CET1 ratio falls from 11.25% to 8.75%, a drop of 2.5 percentage points. The Rs 200 crore loss comes straight out of CET1, taking it from Rs 900 crore to Rs 700 crore, while risk-weighted assets stay close to Rs 8,000 crore. A loss equal to 2.5% of risk-weighted assets wipes out 22% of the capital.

    Why does a loss that looks small against the balance sheet hurt so much?

    Think of a family with a Rs 80 lakh home loan and Rs 9 lakh in savings. A Rs 2 lakh medical bill is a rounding error against the loan and a painful bite out of the savings, because the savings are what pay for it. A bank works the same way. The CET1Common equity tier 1: the shareholders money and retained profits a bank can use to absorb losses while it keeps operating. ratio is capital over risk-weighted assetsThe bank assets, each scaled by a weight that reflects how risky it is, so a safe government bond counts for little and an unsecured loan counts in full.. Losses are paid from the numerator rupee for rupee, while the denominator moves only a little, so a ratio of 11% can lose a quarter of its height in one hit.

    The loss comes out of the top of the fraction; the bottom barely movesBefore the lossCET1 900RWA 8,000=11.25%After a 200 crore lossCET1 700RWA 8,000=8.75%Rs crore. RWA assumed unchanged by the loss.0%4%8%12%11.25%-2.50 pts8.75%BeforeAfter200 / 8,000 = 2.5 points off the ratio
    CET1 of Rs 900 crore over risk-weighted assets of Rs 8,000 crore is 11.25%. A Rs 200 crore loss takes CET1 to Rs 700 crore over the same Rs 8,000 crore, which is 8.75%, so the ratio loses 2.5 points.

    Is there a shortcut for the size of the drop?

    Yes. With the denominator fixed, the ratio falls by the loss divided by risk-weighted assets: 200 over 8,000 is 2.5 points. Every Rs 80 crore of loss costs this bank one full point of CET1 ratio. That is the number a risk manager keeps in their head, because it turns a loss estimate from a stress test straight into a capital headline.

    The relationship
    Δ ratio=−lossRWA=−2008,000=−2.5 pts\Delta\,\text{ratio} = -\frac{\text{loss}}{\text{RWA}} = -\frac{200}{8{,}000} = -2.5\text{ pts}
    lossthe post-tax loss that reduces CET1, here Rs 200 crore
    RWArisk-weighted assets, held at Rs 8,000 crore
    What it says in wordsWith the denominator unchanged, the ratio drops by the loss as a share of risk-weighted assets.

    Say the limitation in one line. The written-off loans do leave the balance sheet, so risk-weighted assets fall a little too, and a tax credit on the loss can soften the hit. Both effects are small next to the Rs 200 crore coming out of capital. Where the result lands against the bank's minimum depends on the current regulatory figure and any buffers, which you would confirm rather than quote from memory.

    Where candidates lose it

    The common slip is to compare the loss with the balance sheet, call it 2.5%, and then shave 2.5% off the ratio to get about 11%. That confuses a fall of 2.5 percentage points with a fall of 2.5 per cent of the ratio, and it misses that the loss lands entirely on the capital line.

    Say 11.25% to 8.75%, then add the shortcut: loss over risk-weighted assets gives the drop in points. It shows you can run a stress number in your head.

    What the interviewer asks next

    • How big a loss takes this bank to an 8% CET1 ratio?
    • The written-off loans carried Rs 300 crore of risk-weighted assets. What is the ratio now?
    • Why do regulators use a risk-weighted denominator rather than total assets?