Case 038Volatility, options and convertiblesWarm up
A family holds a large stake in Jharna Textiles at Rs 400. A one-year put at Rs 360 costs Rs 20, and a one-year call at Rs 460 can be sold for Rs 20. Compare protecting the stake with the put alone and with a zero-cost collar.
1The situation
A family holds 50 lakh shares of Jharna Textiles, worth Rs 200 crore at today's price of Rs 400. The shares are a large part of the family's wealth and they want protection against a sharp fall over the next year without selling.
The desk quotes a one-year put with a strike of Rs 360 at Rs 20 a share, and a one-year call with a strike of Rs 460 that the family could sell for Rs 20 a share. Both options settle at expiry. Ignore dividends and interest for the comparison.
2Your task
What does each structure pay at expiry across a range of prices, what does each cost, and when is one better than the other?
Quick check
Above what share price does the put alone beat the collar?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
The collar gives the same Rs 360 floor at no cost, but it hands over every rupee above Rs 460. With the put alone the family pays Rs 20 a share, about Rs 10 crore, and its worst outcome is minus Rs 60 a share instead of minus Rs 40. The put alone comes out ahead only if Jharna ends above Rs 480. The choice turns on how much upside the family is willing to give away to avoid paying for protection.
Step 1What does each structure do?
Buying a put is buying insurance: a put optionThe right, not the obligation, to sell a share at a fixed price, the strike, on or before a date. It pays when the share falls below the strike. at Rs 360 lets the family sell at Rs 360 however far Jharna falls, for a premium of Rs 20. A collar pays for that insurance by selling someone else the upside above Rs 460: the call's Rs 20 premium cancels the put's, so the protection costs nothing up front and is paid for in gains the family gives up. It is like a homeowner who pays for flood cover by agreeing that any rise in the house's value above a certain price goes to the insurer.
Step 2How do the payoffs compare at different prices?
| Jharna in a year, Rs | Stake alone | Stake + put | Zero-cost collar |
|---|---|---|---|
| 250 | -150 | -60 | -40 |
| 300 | -100 | -60 | -40 |
| 360 | -40 | -60 | -40 |
| 400 | +0 | -20 | +0 |
| 460 | +60 | +40 | +60 |
| 480 | +80 | +60 | +60 |
| 500 | +100 | +80 | +60 |
| 600 | +200 | +180 | +60 |
Read the table in three zones. Below Rs 360, both structures stop the loss; the collar loses Rs 40 a share and the put Rs 60, the Rs 20 difference being the premium. Between Rs 360 and Rs 460, both simply follow the shares, with the put Rs 20 behind. Above Rs 460 the collar is frozen at plus Rs 60 while the put keeps rising, and the put overtakes at Rs 480. On 50 lakh shares, the put costs Rs 10 crore up front; at Rs 600 the collar's cap costs the family Rs 70 crore of gains it would otherwise have kept.
Step 3What does the equal pricing tell you, and what else matters?
The put is 10% below the price and the call 15% above it, yet they cost the same. Downside puts usually cost more than equally distant calls, because investors pay more for protection against falls than for upside; that volatility skewThe pattern in which options with different strikes on the same share are priced at different implied volatilities, usually with downside puts the most expensive. is why a zero-cost collar normally needs a call closer to the money than the put. Check live quotes rather than assuming symmetry. The family should also know that selling the call can mean delivering shares if Jharna rises, that large holders may face disclosure and trading-window rules on options over their own company, and that tax treatment differs between the structures; confirm the current rules before acting.
Where candidates lose it
The usual loss is calling the collar strictly better because it costs nothing. It is paid for with the upside, and above Rs 480 the family would have been better off with the put alone.
The second is quoting the put's floor as minus Rs 40, the same as the collar's. The premium is part of the cost of the protection, so the put's worst case is minus Rs 60 a share.
What the interviewer asks next
- What call strike would make the collar zero cost if the put cost Rs 25?
- The family is sure the shares will not rise above Rs 460 this year. Which structure suits them?
- How would a put spread, buying the 360 put and selling a 300 put, change the picture?
Company names and figures are illustrative.
