Question

Acme Corp. is currently trading at $52 per share. Assume the investor buys a put with a strike price of $50 for $1.08 and buys a call for $4.57 with a strike price of $50.

(a) (4 pts) Draw the profit and loss diagram for this strategy (just the options) as a function of the stock price at expiration. In that graph label BOTH the maximum loss and maximum gain possible.

(b) (4 pts) Both options expire in one year and risk free rate is 5 percent. What is the arbitrage opportunity, and what is the profit?

Answer 1

(a)

(b) The put-call parity establishes a fair value of a put option given the price of a call option (with the same strike price, underlying asset, and maturity), the strike price of the option and the current price of the underlying asset. The relationship is as given below:

Call Option Premium + Present Value(Strike Price) = Put Option Premium + Current Stock Price

4.57 + 50 / (1.05) = 1.08 + 52

52.189 (the left-hand side of the equation) is lesser than the right-hand side of the equation. Hence, one must buy the left-hand side of the portfolio (equation) and sell the right-hand side portfolio (equation). The following table depicts the options arbitrage strategy for two situations, first if the price goes below the strike price of $ 50 (say $ 48) and second if the price goes above the strike price of $ 50 (say $ 54).

Stock Price	52	48	54
Short (Sell) Put	1.08	(2)	0
Short Stock	52	(48)	(54)
Long Call	(4.57)	0	4
Lend the remaining cash	(48.51)	50.9355	50.9355
Net Cash Flow	0	0.9355	0.9355