Case 031Margin, clearing and risk limitsCore
A desk with a Rs 5 crore one-day VaR limit sits at Rs 4.6 crore, and a client trade would take it to Rs 5.6 crore. It can reject the trade, hedge with index futures to cut VaR by Rs 0.8 crore for Rs 3 lakh, or ask for a temporary limit. What do you do?
1The situation
Ghodbunder Bank's equity derivatives desk runs under a one-day 99% value-at-risk limit of Rs 5.0 crore set by the risk committee. Yesterday's VaR was Rs 4.6 crore. A long-standing institutional client now asks the desk to sell it a large block of index put spreads, and the risk system shows the trade would take VaR to Rs 5.6 crore.
The desk head sees three routes. Decline the trade. Do the trade and sell index futures against it, which the system says cuts VaR by Rs 0.8 crore and costs about Rs 3 lakh in spread and financing over the trade's life. Or do the trade and ask the risk committee for a temporary limit increase. The trade carries an expected margin of about Rs 20 lakh, an illustrative figure for this case.
2Your task
Walk through the three choices, say which you would take and why, and name what you would check before relying on the hedge.
Quick check
The desk hedges with index futures as the system suggests. Where does VaR end up?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Do the trade and hedge: VaR lands at Rs 4.8 crore, inside the Rs 5.0 crore limit, for Rs 3 lakh against about Rs 20 lakh of margin. Rejecting keeps the limit but loses the client and the revenue. A temporary limit costs nothing in cash but puts a breach on record for a trade the desk could have hedged. Before relying on the hedge, check that the Rs 0.8 crore reduction survives a stress, because index futures hedge the market factor and nothing else.
Step 1What is a VaR limit actually for?
Think of a weight limit on a bridge. It is not a prediction that the bridge collapses at one kilo over; it is a line the owner drew so that nobody has to argue about each lorry. A VaR limitThe largest one-day loss, at a stated confidence, that the risk committee has agreed the desk may be exposed to. A cap on size, not a forecast. works the same way: it converts the committee's appetite for loss into a number the desk can test every trade against. One-day 99% VaR of Rs 4.6 crore says that on a normal day the desk should lose more than that about one day in a hundred. The limit of Rs 5.0 crore is the committee saying it does not want that number larger, whatever the opportunity.
Step 2How do the three routes compare?
Lay them side by side with the same three columns: where VaR ends, what it costs, and what it leaves behind. Rejecting leaves VaR at Rs 4.6 crore and costs the Rs 20 lakh of margin plus a client who will remember being turned away; hedging leaves VaR at Rs 4.8 crore, costs Rs 3 lakh, and keeps the client and Rs 17 lakh of margin; the temporary limit leaves VaR at Rs 5.6 crore, costs nothing today, and leaves a breach on the record. The hedge wins on every column but cash cost, and Rs 3 lakh is 15% of the margin. The desk would normally hedge part of the trade's delta anyway, so some of that cost would have been spent regardless.
| Route | VaR after, Rs crore | Against the limit | Cash cost | What it leaves behind |
|---|---|---|---|---|
| Reject | 4.6 | Inside | Nil | Rs 20 lakh of margin forgone, client relationship damaged |
| Hedge with index futures | 4.8 | Inside, Rs 0.2 crore spare | Rs 3 lakh | Basis risk between the put spreads and the futures |
| Temporary limit | 5.6 | Outside, by Rs 0.6 crore | Nil | A breach on record, a precedent for the next request |
Step 3Why is the temporary limit the worst answer, not the free one?
Candidates like it because nothing is spent. A limit that is raised whenever a good client calls is not a limit, and the committee that raised it for this trade will be asked to raise it for the next, so the real cost is the loss of the line the limit exists to draw. There are legitimate uses: a hedge that cannot be executed until tomorrow, or a position that will roll off in two days, where the committee grants a dated and documented exception. A trade that can be hedged for Rs 3 lakh is not one of them. If the desk finds it is at Rs 4.6 crore against Rs 5.0 crore every week, the conversation to have is about the size of the limit, not about one trade.
Step 4What would you check before relying on the hedge?
Two things. First, what the hedge covers. Index futures remove the market-direction exposure the put spreads add, which is why VaR falls Rs 0.8 crore, but they do nothing for the volatility exposure or the gap risk of a short put spread, and the VaR model may be giving the futures more credit than a stress would. Ask the risk team for the stressed loss on the hedged position, a 5% gap with volatility up, and confirm the desk still likes the number. Second, the headroom. After the hedge the desk has Rs 0.2 crore of room, so the next client trade of this size needs the same treatment, and a volatile day can lift VaR on an unchanged book. Close by saying what you would actually do: price the hedge into the client's spread where you can, execute the futures with the trade, and tell the risk team the day's plan before the system flags it.
Where candidates lose it
The common loss is answering with the rulebook alone, reject the trade because the limit says so, which throws away Rs 20 lakh and a client for want of a Rs 3 lakh hedge. The limit constrains risk, not revenue, and the desk's job is to find the route that satisfies both.
The opposite loss is treating the temporary limit as free. It is the most expensive route, because it spends the limit's credibility, and interviewers use this case to see whether a candidate understands that a limit raised on request is no longer a limit.
What the interviewer asks next
- The futures hedge cuts VaR by Rs 0.8 crore on the model but only Rs 0.3 crore in a stress. Does your answer change?
- The client asks the desk to absorb the hedge cost in the price. How do you decide whether to agree?
- What is the difference between a VaR limit and a stress limit, and why does a derivatives desk need both?
- VaR is at Rs 4.9 crore on an unchanged book because volatility rose overnight. What does the desk do?
Company names and figures are illustrative.
