Question

A call option with a strike price of $50 costs $2. A put option with a strike price of $45 costs $3. Explain how a strangle can be created from these two options. Construct a table that shows the payoff and profits of the strangle.

Answer 1

1. A strangle strategy is created by holding a call and put position having different exercise price but having the same expiry date and on the same underlying asset. There are 2 ways to create a strangle.

1. Long the strangle

Premium on call option = $2
Premium on put option = $3

Total Premium paid = Premium on call option + Premium on put option
                                       = $2 + $3
                                     = $5

PROFIT AND PAYOFF FOR THE LONG STRANGLE :

STOCK PRICE	PAYOFF FROM C+ AT $50	PAYOFF FROM P+ AT $45	TOTAL PAYOFF	PROFIT = TOTAL PAYOFF - NET INITIAL PREMIUM
ST ≥ 50	S - 50	0	S - 50	S - 50 – 5 = S - 55
50 < ST < 45	0	0	0	-5
ST ≤ 45	0	45 – S	45 – S	45 – S – 5 = 40 - S

Range of Stock Price at maturity for which strategy is profitable :

If Stock Price is more than 55, this strategy will always be profitable.
If Stock Price is more than 45 but less than 50, this strategy will always have a loss equal to the net premium paid = 5.
If Stock Price is less than 40, this strategy will always be profitable.

So the breakeven price is 55 and 40.

2. Short the strangle

Premium on call option = $2
Premium on put option = $3

Total Premium Received = Premium on call option + Premium on put option
                                       = $2 + $3
                                     = $5

PROFIT AND PAYOFF FOR THE LONG STRANGLE :

STOCK PRICE	PAYOFF FROM C- AT $50	PAYOFF FROM P- AT $45	TOTAL PAYOFF	PROFIT = TOTAL PAYOFF + NET INITIAL PREMIUM RECEIVED
ST ≥ 50	-(S – 50)	0	-(S – 50)	-(S – 50) + 5 = 55 - S
50 < ST < 45	0	0	0	5
ST ≤ 45	0	-(45 – S)	-(45 – S)	-(45 – S) + 5 = S – 40

Range of Stock Price at maturity for which strategy is profitable :

If Stock Price is more than 55, this strategy will always give loss.
If Stock Price is more than 45 but less than 50, this strategy will always have a profit equal to the net premium received = 5.
If Stock Price is less than 40, this strategy will always give loss.
So the strategy will be profitable if stock price is more than 40 but less than 55.

So the breakeven price is 55 and 40.