Question

A call option on Santos Limited shares with an exercise price of $7.25 per share, expiry in two months, is currently trading at $0.70. The put option with the same exercise price and date is trading at $0.95.

1. Your friend is very excited. He found an easy way to get rich: “Long a put and a call with the same strike price and one of them will always be in the money!!!!” You can use your pay-off diagram(s) to explain the error in his plan.
2. Beyond which share prices does your friend’s strategy become profitable?

Answer 1

Call option gives right to its buyer to buy underlying at specified price in future. Thus call option will be exercised if price as at expiry is more than the strike price. Hence for seller of call it becomes obligation to sell underlying when buyer enforceses his right. To Buy call option one has to pay premium and hence seller receives the premium

Put option gives right to its buyer to sell underlying at specified price in future. Thus put option will be exercised if price as at expiry is less than the strike price. Hence for seller of put it becomes obligation to buy underlying when buyer enforceses his right. To Buy put option one has to pay premium and hence seller receives the premium

Straddle strategy involves buying put option and call option simultaneously with same expiry and strike price

The Statement Long a put and a call with the same strike price and one of them will always be in the money is false as if stock do not move or moves very less , the premium paid will become loss

Here total cost to buy call and put option = Premium paid for call option + premium paid for put option

= 0.70 + 0.95

= 1.65 $

Thus stock has to move at least by 1.65$ in either direction

Thus if stock moves up, to become profitable it has to move above = strike price + Premium paid = 7.25 + 1.65 = 8.90 $

Thus if stock moves down, to become profitable it has to move below = strike price - Premium paid = 7.25 - 1.65 = 5.60$

Profit table

Price	Profit on call option with Strike price of $ 7.25	Profit on put option with Strike price of $ 7.25	Total profit	Net premium	Net profit
	A	B	C = A + B	D	E = C - D
4.00		3.25	3.25	1.65	1.60
4.25		3.00	3.00	1.65	1.35
4.50		2.75	2.75	1.65	1.10
4.75		2.50	2.50	1.65	0.85
5.00		2.25	2.25	1.65	0.60
5.25		2.00	2.00	1.65	0.35
5.50		1.75	1.75	1.65	0.10
5.75		1.50	1.50	1.65	-0.15
6.00		1.25	1.25	1.65	-0.40
6.25		1.00	1.00	1.65	-0.65
6.50		0.75	0.75	1.65	-0.90
6.75		0.50	0.50	1.65	-1.15
7.00		0.25	0.25	1.65	-1.40
7.25	0.00	0.00	0.00	1.65	-1.65
7.50	0.25		0.25	1.65	-1.40
7.75	0.50		0.50	1.65	-1.15
8.00	0.75		0.75	1.65	-0.90
8.25	1.00		1.00	1.65	-0.65
8.50	1.25		1.25	1.65	-0.40
8.75	1.50		1.50	1.65	-0.15
9.00	1.75		1.75	1.65	0.10
9.25	2.00		2.00	1.65	0.35
9.50	2.25		2.25	1.65	0.60
9.75	2.50		2.50	1.65	0.85
10.00	2.75		2.75	1.65	1.10
10.25	3.00		3.00	1.65	1.35
10.50	3.25		3.25	1.65	1.60

Profit diagram

Thus if stock do not move by 1.65 $ in either direction , strategy will result in loss