A bond-futures basis desk with a 99% VaR of Rs 8 crore loses Rs 14 crore in one day. The VaR model maps cash bonds and futures to the same yield curve. Explain the loss and fix the measurement.

The VaR could not see the loss because the risk that caused it was not in the model. Mapping cash bonds and futures to one curve makes a Rs 1.4 crore DV01 long and short cancel, so the basis has no volatility. The basis widened about 10 basis points, costing Rs 14 crore. Add the basis as its own risk factor, measured on stressed history, and cap gross DV01.

Picture holding a fixed deposit and owing exactly the same amount on a loan at the same rate. Rates move and you do not care. Now suppose the loan reprices and the deposit does not. A hedge protects you only against the risk both legs share; the gap between the legs is a separate risk that stays with you. Kelvora's legs share the level of government yields. They do not share the spread between cash bonds and futures, the basisThe difference between the price of a cash bond and the price implied by the futures contract on it; it moves with funding costs, delivery options and demand for each., and that spread is what moved.

The arithmetic is short. Cash bonds cheapened about 10 basis points relative to futures. The desk is long Rs 1.4 crore per basis point of cash bonds, so 10 basis points of basis widening costs Rs 14 crore, with the futures leg offering nothing back because futures yields did not move with the cash bonds.

A VaR model only measures the risk factors it has. Mapping both legs to one curve is an assumption that the basis never moves, so the model reports zero risk for exactly the position that carries it. This is not a bad day for a good model; it is a gap in the model, and the loss would not have shown up even with a thousand years of history. Risk teams keep a list of such gaps, called risks not in VaRAn inventory of exposures the VaR model does not capture, each measured separately and covered by limits or capital., for exactly this reason.

Map the cash bonds to their own bond-specific yields and the futures to the futures price, so the spread between them becomes a risk factor with its own history. At a calm-period basis volatility of 1.5 basis points a day, 99% basis VaR is about Rs 4.9 crore; on a stressed window with 4 basis points it is about Rs 13.0 crore, close to the actual loss. Use the stressed figure for limits, because basis trades earn small amounts in calm markets and lose large ones in stress.

Add two controls that do not depend on any model: a gross DV01 limit on each leg, so the desk cannot scale the trade just because its net risk looks small, and a basis stress test, such as the widest one-week basis move on record, reported beside the VaR. The limitation to say: even a separate basis factor relies on history, and a basis driven by a funding squeeze can move further than it ever has.