Question

Utilise the following information. Call option price $5 with strike price $60, put option price $4 with strike price $55. They both expire 90 days from now and are written on the same stock. A client believes the stock price could move substantially in either direction in reaction to an expected court decision involving the company. The client currently owns no stocks.

⦁ Draw the profit and loss graph of long strangle

⦁ Draw the profit and loss graph of short strangle

⦁ What is your advice about implementing a strangle strategy, i.e., choosing a long or a short strangle, to capitalize on the possible stock price movement. (1 mark)

⦁ At expiration, for the appropriate strangle strategy, what is the maximum possible loss per unit of strategy? (1 mark)

⦁ At expiration, for the appropriate strangle strategy, what is the maximum possible gain per unit of strategy? (1 mark)

⦁ What are the break-even stock prices?

Answer 1

Quesition 1 - Profit / Loss graph of long strangle

Step - 1 - Calculation of total premium paid

In a Long Strangle we buy both the call and put options on a stock with different strike price

Therefore we will buy both the 60 Strike call & 55 Strike Put

Total cost of this strategy

Strike Price	Option	Buy/Sell	Premium paid
60	Call	Buy	5
55	Put	Buy	4
		Total Premium paid	9

Therefore to enter into this strategy we have to pay a premium of $ 9

Step 2 - Calculation of payoff and profit

call option will result in a positive payoff when the stock price on expity is above 60, otherwise the option will lapse and the payoff willl be 0

put option will result in a positive payoff when the stock price on expity is below 55, otherwise the option will lapse and the payoff willl be 0

Stock Price	Payoff from call option	Payoff from put option	Total Payoff	Premium paid	Profit
30	0	25	25	9	16
35	0	20	20	9	11
40	0	15	15	9	6
45	0	10	10	9	1
50	0	5	5	9	-4
55	0	0	0	9	-9
60	0	0	0	9	-9
65	5	0	5	9	-4
70	10	0	10	9	1
75	15	0	15	9	6
80	20	0	20	9	11
85	25	0	25	9	16

Quesition 2 - Profit / Loss graph of short strangle

Step - 1 - Calculation of total premium recieved

In a Long Strangle we sell both the call and put options on a stock with different strike price

Therefore we will sell both the 60 Strike call & 55 Strike Put

Total cost of this strategy

Strike Price	Option	Buy/Sell	Premium recieved
60	Call	Sell	5
55	Put	Sell	4
		Total Premium recieved	9

Therefore to enter into this strategy we will recieve a premium of $9

Step 2 - Calculation of payoff and profit

call option will result in a negative payoff when the stock price on expity is above 60, otherwise the option will lapse and the payoff willl be 0

put option will result in a negative payoff when the stock price on expity is below 55, otherwise the option will lapse and the payoff willl be 0

Stock Price	Payoff from call option	Payoff from put option	Total Payoff	Premium received	Profit
30	0	-25	-25	9	-16
35	0	-20	-20	9	-11
40	0	-15	-15	9	-6
45	0	-10	-10	9	-1
50	0	-5	-5	9	4
55	0	0	0	9	9
60	0	0	0	9	9
65	-5	0	-5	9	4
70	-10	0	-10	9	-1
75	-15	0	-15	9	-6
80	-20	0	-20	9	-11
85	-25	0	-25	9	-16

Question 3

Since the client believes the stock price could move substantially in either direction he sholuld go for a long straddle strategy, ie he will make profit when the stock price is above 69 or below 46 as shown in graph in question 1 above

Question 4

The maximum possible loss from the strategy can be $9, ie we will incurr the loss only upto the option premium paid

Question 5

Maximum possible gain is unlimited stock price can go up to any level (100,200,300) and we will make huge profits on call option in that scenario, therefore maximum profit from this strategy is unlimited

Question 6

Stock Price should go either above 60 strike call + $ 9 premium paid = Above 69

OR

Stock Price should go below 55 strike put - $ 9 premium paid = below 46

Therefore breakeven stock prices are 46 on the lower side and 69 on the higher side (Same is shown in graph in question 1 above)