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074

Case 074Option strategies and trade ideasHard

A stock at Rs 1,200 reports results tomorrow, and the at-the-money straddle expiring in a week costs Rs 84. Its last eight results-day moves were 5%, 3%, 9%, 4%, 6%, 2%, 7% and 4%. Buy the straddle, sell it, or sell an iron fly with wings at 1,100 and 1,300 for Rs 60?

1The situation

Brahmagiri Software, a mid-cap IT services company, reports quarterly results after the close tomorrow. The stock is at Rs 1,200. The 1,200 call and put expiring in a week together cost Rs 84, so the at-the-money straddle prices a move of about 7% by expiry.

A derivatives desk pulls the stock's last eight results-day moves, ignoring direction: 5%, 3%, 9%, 4%, 6%, 2%, 7% and 4%. It considers three trades: buy the straddle for Rs 84, sell it for Rs 84, or sell an iron fly, short the 1,200 straddle and long the 1,100 put and the 1,300 call, for a net credit of Rs 60.

2Your task

Compare the priced move with the historical moves, work out what each trade would have made on the eight past results, and reach a view on which trade, if any, the desk should put on and in what form.

Quick check

Before working it: on the eight past results, the iron fly at Rs 60 would have made, on average, about:

Worked solution

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

30-second answerThe answer to give first

Do not buy: the straddle prices a 7% move against a 5% average, and buying it would have lost about Rs 24 a share on average. Selling it would have earned Rs 24 on average with no cap on a surprise. The iron fly caps the loss at Rs 40, but its break-evens sit at the 5% average move, so on history it earns about Rs 1: the wings cost the whole edge. Sell premium only in a capped form, at a better credit or with cheaper, wider wings.

Step 1What move is the straddle pricing, and how does that compare with history?

An umbrella seller who doubles his price on the morning of a forecast storm is pricing the rain he expects. If storms here usually bring less rain than he charges for, buying his umbrella is a poor bet and selling umbrellas alongside him is a good one, until the one storm that floods the street. A straddle at Rs 84 on a Rs 1,200 stock prices a move of about 7% by expiry; Brahmagiri's last eight results moves average 5%, about Rs 60 a share, so the straddle looks rich. Only one of the eight moves, 9%, beat 7%, and one, 7%, matched it.

The straddle prices a 7% move; Brahmagiri has averaged 5%2%4%6%8%5%Q13%Q29%Q34%Q46%Q52%Q67%Q74%Q87%: priced5%: averageRs 60 a shareResults-day moves, oldest first. Green: below the priced move. Grey: equal to it. Red: above it.
Of Brahmagiri's last eight results-day moves only one, 9%, exceeded the 7% the Rs 84 straddle prices, and the average was 5%, about Rs 60 a share, so the market is charging for a larger move than the stock has usually delivered.
Step 2What would each trade have made on the eight past results?

At expiry the straddle is worth the size of the move in rupees: 12 rupees for each 1%. Bought at Rs 84, it would have made 24 on the 9% move, broken even on the 7% and lost on the other six, an average loss of Rs 24; sold, it would have earned that Rs 24 on average and lost Rs 24 in its worst quarter. The iron fly collects Rs 60 and its loss stops at Rs 40 once the stock is beyond a wing, so its outcomes are narrower on both sides.

Past moveStraddle value at expiryBuy straddle, 84Sell straddle, 84Sell iron fly, 60
5%60-24+24+0
3%36-48+48+24
9%108+24-24-40
4%48-36+36+12
6%72-12+12-12
2%24-60+60+36
7%84+0-0-24
4%48-36+36+12
Average60-24+24+1
Rupees a share at expiry on each of the eight past moves. Buying the straddle would have averaged -24, selling it +24, and selling the iron fly +1, with its worst case floored at minus 40.
Step 3Why does the iron fly earn so little of the edge?

Because the wings are not free. Selling the straddle collects Rs 84; buying the 1,100 put and the 1,300 call costs Rs 24, leaving Rs 60. The iron fly's break-evens are 1,140 and 1,260, a 5% move, which is the stock's average move, so on history it roughly breaks even: the Rs 24 spent on the wings is almost exactly the Rs 24 average edge from selling. What the wings buy is the floor: on a 15% surprise the short straddle loses Rs 96 a share, while the iron fly loses Rs 40.

Selling the straddle against selling the iron fly: the wings cap the loss and cost the edge-80-40+40+8001,1001,2001,300Brahmagiri at expiry, Rsfloor -40+84+60straddle keeps losingshort straddle, 84iron fly, 60past moves, up sideOn the eight movesShort straddle: +24Iron fly: +1Wings cost Rs 24
The short straddle peaks at Rs 84 and keeps losing beyond its break-evens of 1,116 and 1,284, while the iron fly peaks at Rs 60, breaks even at 1,140 and 1,260 and is floored at minus Rs 40; on the eight past moves the iron fly averages about +1 against +24 for the straddle.
Step 4So which trade, and in what form?

Not the long straddle: it needs a move larger than all but one of the last eight. The edge is in selling, but a naked short straddle into results is a bet that this quarter looks like the last eight, with no limit if it does not. The defensible trade is short premium with a capped loss, sized so that the Rs 40 worst case is affordable, and only at a credit that leaves an edge: the Rs 60 iron fly does not, so the desk should ask for a better price or look at wider wings, which cost less and keep more of the Rs 84. Three limits belong in the pitch. Eight results are a small sample, and a guidance cut or a large deal can produce a move the history never showed. After results the options still have days to expiry, so closing the next morning costs a little more than the expiry values in the table. And a market pricing 7% may know something about this quarter that the history does not.

Where candidates lose it

Candidates see that the straddle is rich and sell the iron fly, assuming the capped version keeps the edge. Work the eight outcomes and the iron fly averages about Rs 1: the wings cost Rs 24 and the average edge is Rs 24.

The second miss is comparing the straddle price with the average move in per cent without converting: 7% of Rs 1,200 is Rs 84, and 5% is Rs 60. Put both in rupees before deciding.

What the interviewer asks next

  • What credit would the iron fly need to earn Rs 10 a share on the eight past moves?
  • How would you use the 1,050 put and 1,350 call instead, and what would you need to know about their prices?
  • Implied volatility will collapse the morning after results. How does that help the seller even if the stock moves 6%?
← Case 073A market maker quotes a stock's 500 call at 12.00 bid, 12.40 offered, lot 100. Over the day it buys 600 contracts on the bid and sells 400 on the offer; the option's delta is 0.5. What spread did it earn, what inventory is left, and how does it hedge it?Case 075 →A stock is at Rs 900 and pays a Rs 10 dividend in one month. The three-month 900 call is 48 and the 900 put 30, rate 7% continuous. Check put-call parity, and if it fails, build the arbitrage.

Company names and figures are illustrative.

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