You happen to be checking the newspaper and notice an arbitrage opportunity. The
ID: 2739092 • Letter: Y
Question
You happen to be checking the newspaper and notice an arbitrage opportunity. The current stock price of Intrawest is $19 per share and the one-year risk-free interest rate is 5%. A one-year put on Intrawest with a strike price of $16 sells for $4.21, while the identical call sells for $8.28. Explain what you must do to exploit this arbitrage opportunity.
A. The strategy would be to buy the call option, sell the put and the stock, and borrow $15.24. The net benefit is $0.31.
B. The strategy would be to sell the call option, buy the put and the stock, and borrow $15.24. The net benefit is $0.31.
C. The strategy would be to sell the call option, buy the put and the stock, and borrow $16. The net benefit is $0.31.
D. The strategy would be to sell the call option, buy the put and the stock, and borrow $15.24. The net benefit is $1.07
Select the best choice.
Explanation / Answer
The strategy would be to sell the call option, buy the put and the stock, and borrow $15.24. The net benefit is $0.31. (which is Option B).
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Explanation:
The arbitrage opportunity will exist if the selling price of the identical is greater than the sum of selling price of 1 year put, current stock price less present value of strike price of put. The equation can be dervied as follows:
Call Price > 1 Year Put Selling Price + Current Stock Price - Strike Price of Put/(1+Risk Free Interest Rate)
8.28 > 4.21 + 19 - 16/(1+5%)
On calculation, we get,
8.28>7.97
It can be concluded from the above calculations that the call is overpriced when compared to the portfolio having a put, stock and borrowing at risk-free rate. It is, therefore advisable to sell the call option and purchase put, stock and borrow $15.24 (16/(1+5%)) [present value of $15]. The net benefit would be $.31 (8.28 - 7.97).
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