Measurement without a limit is commentary. A real risk framework attaches a number to each measure and a stated consequence to each breach, and the four kinds of limit are chosen so that they fail in different ways.
- Risk budgets cap a probabilistic measure: a VaR or ES ceiling for the book, often allocated down to desks so the parts sum to something the whole can carry.
- Position limits cap a raw exposure: notional per name, per sector, per currency. Crude, and they bind even when the model says the position is safe, which is the point.
- Scenario limits cap the loss under a named stress: no scenario in the standing set may cost more than a stated amount. This one binds where VaR is silent, because scenarios carry no probability.
- Stop-loss limits cap realised losses: a position or desk down more than a stated amount is cut, regardless of what any model currently says about its prospects.
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What happens when a risk limit is breached?
Work one breach through. A fund with ₹25,00,00,000 of net asset value runs a one-day 99% VaR limit of 2.00% of net asset value, which is ₹5,00,00,000. Its equity sleeve is 42% of the book with a standalone VaR of 4.02% of net asset value, the rest of the book carries 1.21%, and the two sleeves are correlated at 0.35. Portfolio VaR is therefore sqrt((0.42 × 4.02%)² + 1.21%² + 2 × 0.35 × (0.42 × 4.02%) × 1.21%) = 2.396846%, or ₹5,99,21,142. That is a breach of ₹99,21,142, which is 0.3968 percentage points of net asset value and 19.84% over the limit.
The response is a sequence, not a decision. First, verify the number before acting on it, because a breach caused by a stale price file is common and selling into a data error is expensive. Second, notify, on the timetable the policy already specifies, since a breach discovered by the risk committee rather than reported to it is a governance failure independent of the position. Third, size the cure: scaling the equity sleeve by 0.725126 returns portfolio VaR to exactly 2.000000%, which means taking the sleeve from 42.00% of net asset value to 30.46%, a sale of ₹2,88,61,770. Fourth, execute against the limit rather than against a view, because the point of a limit is that it binds when you disagree with it. Fifth, record the cause, since a breach caused by a rising volatility estimate on an unchanged book is a different event from one caused by a trader adding risk, and only the second is a discipline problem.
Note what the arithmetic shows about the cure. The sleeve has to fall by 11.54 percentage points of the book to remove a 0.40-point VaR overage, because VaR combines in quadrature and correlation means the marginal sleeve contributes less than its standalone number suggests. A desk that cuts positions proportionally to the size of the breach will cut far too little and breach again the next day.