Question

The price of a stock is $40. The price of a 1-year European put on the stock with a strike price of $30 is quoted as $7 and the price of a 1-year European call option on the stock with a strike price of $50 is quoted as $5.

(a) Suppose that an investor buys the stock, shorts the call option, and buys the put option. Calculate the profit function and draw a diagram illustrating how the investor's profit or loss varies with the stock price at expiration. Is the graph similar to any of the strategies covered in class? Identify the prices at which you break even with this strategy. What is the most you can win and the most you can lose?

(b) Calculate also the profit function and the profit/loss diagram assuming the investor buys the stock, shorts 2 call options and buys 2 put options.

Answer 1

The price of a stock is $40. The price of a 1-year European put on the stock with a strike price of $30 is quoted as $7 and the price of a 1-year European call option on the stock with a strike price of $50 is quoted as $5.

Stock price = $40

Price of 30CE = $7

Price of 50PE = $5

(a) Suppose that an investor buys the stock, shorts the call option, and buys the put option.

On Expiry Stock closes	Payoff from Stock (held at 40	Pay off from Shorted 30call at 7	Pay off from Long 50 Put at 5	Net Payoff from Stock, Call & Put
Break Even Price	40	37	45	42
20.00	-20.00	7.00	25.00	12.00
22.50	-17.50	7.00	22.50	12.00
25.00	-15.00	7.00	20.00	12.00
27.50	-12.50	7.00	17.50	12.00
30.00	-10.00	7.00	15.00	12.00
32.50	-7.50	4.50	12.50	9.50
35.00	-5.00	2.00	10.00	7.00
37.50	-2.50	-0.50	7.50	4.50
40.00	0.00	-3.00	5.00	2.00
42.50	2.50	-5.50	2.50	-0.50
45.00	5.00	-8.00	0.00	-3.00
47.50	7.50	-10.50	-2.50	-5.50
50.00	10.00	-13.00	-5.00	-8.00
52.50	12.50	-15.50	-5.00	-8.00
55.00	15.00	-18.00	-5.00	-8.00

Profit / Loss = Profit/ Loss from stock + Profit/ Loss from selling call + Profit/ Loss from buying put

= (Stock Purchase Price - Stock Price at Expiry) + Max(Call Strike + Premium - Expiry price, Premium)

+ Max(Strike - Premium - Expiry, -Premium

Maximum Loss = $8

Maximum Profit = $12

Break even price = $40

The combination appears to be a Bear Put Spread

B) Investor buys the stock, shorts 2 call options and buys 2 put options.

Profit or Loss = Profit/ Loss from stock + Profit/ Loss from selling 2 calls + Profit/ Loss from buying 2 puts

= (Stock Purchase Price - Stock Price at Expiry) + 2 x Max(Call Strike + Premium - Expiry price, Premium)

+ 2 x Max(Strike - Premium - Expiry, -Premium

The Payoff diagram looks like below