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071

Case 071Risk measurement and limitsHard

A desk's stress loss hits Rs 42 crore against a Rs 40 crore limit after a volatility spike. Compare cutting positions, buying index puts at a 2.5% premium, and asking for a temporary limit increase, with numbers on each.

1The situation

Pranavika Capital runs a Rs 500 crore gross book on Rs 200 crore of capital, expected to earn about Rs 50 crore a year. Its stress test, an index fall of 20% with credit spreads 150 bps wider and volatility doubled, is limited to Rs 40 crore. Last month it read Rs 34 crore. After this week's volatility spike it reads Rs 42 crore, with no change in positions. Desk policy says a breach must be brought back to 5% inside the limit, Rs 38 crore.

The book has three sleeves: equity longs with index beta (gross Rs 150 crore, stress loss Rs 20 crore, expected edge Rs 15 crore a year), credit carry (Rs 200 crore, Rs 12 crore, Rs 20 crore) and volatility and relative value (Rs 150 crore, Rs 10 crore, Rs 15 crore). Trading in the current market costs about 40 bps round trip. One-month index puts 5% out of the money are offered at 2.5% of notional. The chief risk officer asks for a recommendation by the close.

2Your task

Quantify the three responses: what each does to the stress loss, what each costs, and what each leaves uncovered. Then recommend one and say how you would present the limit question.

Quick check

Which response is cheapest in cash this month, and is that the right way to compare them?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Cut, and cut the equity sleeve: a fifth of it removes the Rs 4 crore for about Rs 37 lakh this month, against Rs 59 lakh for a pro-rata cut and Rs 80 lakh for puts that hedge only the index leg. The breach came from volatility, not new positions, so it may fade, but the limit is set for exactly these weeks. A waiver costs nothing in cash and leaves the fund with 21% of capital in the stress scenario. Ask for one only with a dated plan to come back inside.

Step 1What does the breach actually say?

A household that budgeted Rs 40,000 a month for fuel and finds the bill at Rs 42,000 after a price rise has three choices: drive less, lock in a price, or raise the budget. Pranavika's breach is the same shape: nothing in the book changed, the volatility spike raised the stress loss on the volatility-sensitive and spread-sensitive positions from Rs 34 crore to Rs 42 crore, and the limit is doing what it was designed to do, which is to bind when risk rises. The stress loss is now 21% of capital. Desk policy wants it at Rs 38 crore, so the task is to remove Rs 4 crore of stress loss, and the question is which rupees of stress are cheapest to remove.

Step 2What does cutting positions cost?

A pro-rata cut of 9.5% of everything, Rs 48 crore of gross, removes Rs 4 crore of stress. It costs Rs 19 lakh to trade at 40 bps and gives up 9.5% of the book's edge, about Rs 40 lakh for each month the cut lasts, so around Rs 59 lakh in the first month. A targeted cut is cheaper. The equity sleeve carries 1.33 crore of stress loss per crore of annual edge against 0.60 and 0.67 for the other two, so cutting a fifth of it, Rs 30 crore, removes the same Rs 4 crore for Rs 12 lakh of trading plus Rs 25 lakh of edge a month, about Rs 37 lakh. The cut is permanent until the desk chooses to rebuild, which it can do when volatility settles, paying the trading cost again.

Where to cut: stress loss carried per crore of annual edge, by sleeveEquity longs (index beta)gross 150, stress 20, edge 15 a year1.33 crore of stress per crore of edgeCredit carrygross 200, stress 12, edge 20 a year0.60 crore of stress per crore of edgeVolatility and relative valuegross 150, stress 10, edge 15 a year0.67 crore of stress per crore of edgeCut 20% of the equity sleeve: Rs 30 crore, stress -4, cost Rs 12 lakh to trade + Rs 25 lakh of edge a month = Rs 37 lakh
Pranavika's equity sleeve carries 1.33 crore of stress loss for every crore of annual edge, twice the ratio of the credit and volatility sleeves, so cutting a fifth of it removes the Rs 4 crore of excess stress for about Rs 37 lakh this month against Rs 59 lakh for a pro-rata cut.
Step 3What do the puts do, and what do they miss?

A one-month put 5% out of the money pays 15% of notional in the stress scenario's 20% fall. Net of the 2.5% paid, each crore of puts improves the stress result by 12.5 lakh, so Rs 32 crore of notional removes Rs 4 crore of stress loss for Rs 80 lakh of premium, almost all of which is gone in a month if the index stays put. That is the dearest option in cash, and it is also the narrowest. The puts hedge only the index leg of the stress, Rs 20 crore of the Rs 42; if the next stress is spreads widening with the index flat, the puts pay nothing and the book is still over its limit in the scenario that actually arrives. What the puts keep is the edge: the book stays intact and earns its Rs 417 lakh a month while the cover is in place. They are the right tool when the breach is believed to be short and the edge is worth more than the premium, which here, Rs 417 lakh against Rs 80 lakh, it is not by much.

ResponseStress loss after, Rs croreCash cost this month, Rs lakhEdge given up, Rs lakh a monthLeft uncovered
Cut pro rata381940Nothing; the book is smaller everywhere
Cut the equity sleeve381225Nothing; the cut lands where stress per edge is worst
Buy Rs 32 crore of puts38800A spread or volatility stress with the index flat
Limit raised to 45 for a month4200Rs 2 crore more loss in the stress; the limit's credibility
The targeted cut brings the stress loss to Rs 38 crore for about Rs 37 lakh all in, the puts do the same for Rs 80 lakh and cover only an index fall, and the waiver costs nothing in cash while leaving the full Rs 42 crore in place.
Step 4What does a temporary limit increase really cost?

In cash, nothing, and the argument for it sounds reasonable: the breach is a volatility artefact, the positions have not changed, and the spike will pass. Price it anyway. The extra Rs 2 crore of stress loss is carried for a month; if the scenario is a one-in-ten-year event it has about a 0.8% chance of arriving in any month, and perhaps three times that in the month after a volatility spike, so the expected cost is only about Rs 5 lakh, which is the number a desk will quote to you. It is the wrong number. Limits are not set on expected loss; they are set on what the fund can survive, and 21% of capital in one scenario is a decision for the people who own the capital. A limit that is raised whenever volatility rises is not a limit, because volatility rising is the only time it binds. The honest version of the request is a dated one: raise the limit for two weeks while the equity sleeve is cut in an orderly way, with the cut starting now.

Three ways out of a breach, with the stress loss and the cost of eachCut positionsstress loss, Rs crorenow 42after 38limit 40cost: Rs 37 lakh targeted,Rs 59 lakh pro rata, this monthedge given up while cutStops the breach for good;costs edge every month it lastsBuy index putsstress loss, Rs crorenow 42after 38limit 40cost: Rs 80 lakh premiumfor one month of coverpays only if the index fallsKeeps the edge; dearest in cash;misses a spread or vol stressRaise the limit to 45stress loss, Rs crorenow 42after 42limit 45old 40cost: nothing in cash;Rs 2 crore more in the tailand a limit that moves when hitCheapest today; the fundhas decided to run more risk
Cutting brings Pranavika's stress loss to Rs 38 crore for about Rs 37 lakh of cost this month, puts do the same for Rs 80 lakh and cover only an index fall, and a limit increase to Rs 45 crore costs nothing today while leaving Rs 42 crore of stress loss, 21% of capital, in place.
Step 5What would you recommend by the close?

Cut a fifth of the equity sleeve, starting today and spread over three or four sessions to hold the trading cost near the Rs 12 lakh estimate, and report the stress loss daily until it reads Rs 38 crore. The reason to choose the cut over the puts is that the breach is not an index-only problem: the stress loss rose because volatility and spread sensitivity grew, and a put does nothing for those. The limitation to state is that the stress scenario is one point in a space of bad outcomes; the ranking of the sleeves by stress per edge depends on that scenario, and a different one, say spreads 300 bps wider, would point at the credit sleeve. Run the cut against two or three scenarios before the orders go out, and tell the risk officer which scenario drove the choice.

Where candidates lose it

The common answer recites the rule, cut until under the limit, without numbers. The interviewer wants the cost of each branch: trading cost and edge for the cut, premium and basis for the puts, tail loss and credibility for the waiver, and then a choice.

The second miss is pricing the waiver at its expected cost and calling it free. Limits exist for survival, not for expected loss, and a limit that moves whenever it binds protects nothing.

What the interviewer asks next

  • How would the comparison change if the index puts were offered at 1% of notional?
  • The volatility spike reverses next week and the stress loss falls to Rs 36 crore. Do you rebuild the equity sleeve?
  • Why might a stress limit be set as a share of capital rather than a rupee figure, and what would change here?
← Case 070A desk has two even-money bets, each winning 55% of the time. Size them with Kelly alone, then jointly when they are independent, and then when their outcomes have correlation 0.5.Case 072 →A stock will join a benchmark tracked by Rs 20,000 crore of passive money at a 0.8% weight, and it trades Rs 60 crore a day. Estimate the passive demand in days of volume and the likely price pressure around the effective date.

Company names and figures are illustrative.

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