A bank treasury held Rs 1,500 crore of government bonds with a modified duration of 8 and lost about Rs 180 crore when yields rose 150 basis points. Its PV01 limit was Rs 50 lakh against an actual Rs 1.2 crore. Work out the loss and explain what failed.

The loss is simple: Rs 1,500 crore times a duration of 8 times 1.5% is Rs 180 crore, Rs 1.2 crore for each of 150 basis points. Held at its Rs 50 lakh limit the book would have lost Rs 75 crore, so Rs 105 crore came from the breach. The measure worked and the report showed red every day. What failed was governance: breaches had no consequence, the person breaching approved his own excess, and no stress test tied the position to capital.

Start with the number, because a loss case is easiest to read once you know whether the loss was a surprise. A household on a floating-rate home loan knows that each 1% rise in the rate adds a fixed amount to the instalment; nothing about the rise is mysterious once the loan size is known. Duration does the same job for a bond book: a modified duration of 8 means about 8% of value lost for each 1% rise in yields, so 1.5% costs about 12% of Rs 1,500 crore, Rs 180 crore.

Convexity trims the first-order figure a little. With convexity of about 85, the correction is half of 85 times 0.015 squared times Rs 1,500 crore, about Rs 14 crore, so the precise price loss is nearer Rs 166 crore. Six months of coupons, about Rs 53 crore, softened the total return but not the mark-to-market line the board saw. The point stands either way: there was no hidden risk here, only a known one that was too big.

Compare the actual book with the same book held at its limit. At a PV01 of Rs 50 lakh the 150 basis point rise would have cost Rs 75 crore, about 11.5% of net worth; at Rs 1.2 crore it cost Rs 180 crore, 27.7% of net worth. The Rs 105 crore gap is the price of the breach. Staying inside the limit meant either a book of about Rs 625 crore at duration 8, or the full Rs 1,500 crore at a duration of about 3.3.

The measurement did not fail; the report showed 240% of limit every single day. What failed is that a breach had no consequence: it was marked noted by the same treasury head whose position caused it, and nobody above him was forced to decide. A limit that can be exceeded indefinitely is a reporting line, not a limit. Three further gaps let it run: risk reported to the treasury rather than independently to the board's risk committee, no stress test translating PV01 into a share of net worth, and an incentive that counted the extra coupon from long bonds as profit while the rate risk sat unpriced.

Give every breach a clock and an owner. A breach should force one of two outcomes within a few days: the position is cut back inside the limit, or the board or its risk committee approves a temporary excess in writing, with a date. Add a stress limit tied to capital: a 200 basis point shock on this book costs Rs 240 crore, 37% of net worth, a number no board would sign off if it saw it. Make the risk function report around the treasury, not through it. The limit of all this is that rules only work if someone senior is willing to enforce them against a desk that is making money; say that in the interview.

One caution belongs in the presentation. How such a bank books and values its investments depends on the regulator's current classification and valuation rules for bank investment portfolios, and moving bonds between categories to avoid showing a loss is a known pattern in cases like this. Confirm the rules in force before judging how the loss should have been reported.