Case 058Concentrated positions and liquidity eventsCore

A client holds Rs 10 crore of one stock at Rs 2,000. He buys a Rs 1,800 put for Rs 60 and sells a Rs 2,300 call for Rs 60. What is his position worth if the stock goes to Rs 1,500, and if it goes to Rs 2,600?

The situation

Gaurav Sabharwal holds 50,000 shares of the company he used to run, worth Rs 10 crore at Rs 2,000. He cannot sell for a year under a lock-in agreed at his exit, and the shares are most of his wealth.

His banker proposes a one-year collar: buy a put with a strike of Rs 1,800 for Rs 60 a share and sell a call with a strike of Rs 2,300 for Rs 60 a share, on all 50,000 shares. The premiums cancel, so the structure costs nothing up front. Ignore dealing costs and tax for the numbers, and assume the options settle at expiry.

Your task

What is the position worth at Rs 1,500 and at Rs 2,600, and what has Gaurav given up for the protection?

Quick check

At expiry the stock is Rs 2,600. What is Gaurav's whole position worth?

Worked solution

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

30-second answerThe answer to give first

Rs 9 crore at Rs 1,500, and Rs 11.5 crore at Rs 2,600. At Rs 1,500 the put pays Rs 300 a share, lifting each share to Rs 1,800, against Rs 7.5 crore unhedged. At Rs 2,600 the sold call costs Rs 300 a share, capping each at Rs 2,300, against Rs 13 crore unhedged. The collar costs nothing in cash; its price is the upside above Rs 2,300.

Step 1What does each leg of the collar do?

Think of buying home insurance and paying the premium by agreeing to hand the insurer any rise in your house's value above a set price. The putAn option that gives the holder the right to sell at a fixed strike price, so it pays out when the price falls below that strike. sets a floor at Rs 1,800; the sold call sets a ceiling at Rs 2,300; the Rs 60 received for the call pays the Rs 60 for the put. Between the two strikes nothing happens and Gaurav simply owns the stock. The premium on each leg is Rs 60 on 50,000 shares, Rs 30 lakh, and the two cancel.

Step 2What is the position worth at each price?

Work it per share, then multiply. At Rs 1,500 the put pays Rs 300, so every share is worth Rs 1,800 and the position is Rs 9 crore, Rs 1.5 crore better than the bare stock's Rs 7.5 crore. At Rs 2,600 the call he sold is exercised against him for Rs 300, so every share nets Rs 2,300 and the position is Rs 11.5 crore, Rs 1.5 crore less than the bare stock's Rs 13 crore.

Gaurav's collared position is worth at least Rs 9 crore below a price of Rs 1,800 and at most Rs 11.5 crore above Rs 2,300, so at Rs 1,500 it beats the bare stock by Rs 1.5 crore and at Rs 2,600 it trails it by Rs 1.5 crore.

Price at expiry, Rs	Put pays	Call costs	Collared, Rs crore	Unhedged, Rs crore
1,200	600	0	9.00	6.00
1,500	300	0	9.00	7.50
1,800	0	0	9.00	9.00
2,000	0	0	10.00	10.00
2,300	0	0	11.50	11.50
2,600	0	300	11.50	13.00
3,000	0	700	11.50	15.00

Below Rs 1,800 the collared position is always Rs 9 crore and above Rs 2,300 always Rs 11.5 crore; between the strikes it moves one for one with the stock, from Rs 9 crore to Rs 11.5 crore.

Step 3Is a zero-cost collar really free?

No, and saying so is what the interviewer is listening for. The cost is paid in upside: every rupee above Rs 2,300 now belongs to the buyer of the call. For a client whose problem is concentration, that trade is usually sensible, because a 25% fall on most of his wealth matters far more than a 30% rise. The limits: the floor is Rs 1,800, not Rs 2,000, so he still carries the first 10% of any fall; the protection lasts a year; and dealing costs, the tax treatment of each leg and whether the options settle in cash or shares all need checking with the desk before the trade.

Where candidates lose it

The common slip at Rs 2,600 is to answer Rs 13 crore, forgetting that the sold call is a liability. Candidates remember the put because it is the reason for the trade, and lose track of the leg that paid for it.

The second miss is calling the structure free. Zero premium is not zero cost; the price is the upside above Rs 2,300, and the interviewer wants you to name it.

What the interviewer asks next

How would you make the floor Rs 1,900 while keeping the cost at zero?
The lock-in ends in a year. What should the collar's expiry be, and why?
Why might a lender give Gaurav better terms against collared shares?

Company names and figures are illustrative.