FRM Part I · FRM Exam Part I · Properties of Options
An investor buys a share at $100, buys a European put with strike $95 for $3, and writes a European call with strike $110 for $2, all with the same expiry. Ignoring discounting, what are the maximum profit and maximum loss per share at expiry?
The maximum profit is $9 and the maximum loss is $6 per share. The collar costs a net $1 in premium. Upside is capped at the $110 strike, so 10 minus 1 is 9. Downside is floored at the $95 strike, so 5 plus 1 is 6.
- AMaximum profit $9; maximum loss $6Correct
- BMaximum profit $10; maximum loss $5
- CMaximum profit $11; maximum loss $7
- DMaximum profit $9; maximum loss $8
Explanation
The net option cost is 3 - 2 = $1. The maximum profit occurs at or above $110: (110 - 100) - 1 = $9. The maximum loss occurs at or below $95: (100 - 95) + 1 = $6. Figures of $10 and $5 come from ignoring the net premium, and $11 and $7 come from applying its sign the wrong way.
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