A stock index is valued at $800 and pays a continuous dividend at the rate of 3% per year. The 6-month futures contract on that index is trading at $758. The continuously compounded risk free rate is 2.5% per year. There are no transaction costs or taxes. Is the futures contract priced so that there is an arbitrage opportunity? If yes, which of the following numbers comes closest to the arbitrage profit you could realize by taking a position in one futures contract?

Question

Business

Cortez

25 October, 15:42

A stock index is valued at $800 and pays a continuous dividend at the rate of 3% per year. The 6-month futures contract on that index is trading at $758. The continuously compounded risk free rate is 2.5% per year. There are no transaction costs or taxes. Is the futures contract priced so that there is an arbitrage opportunity? If yes, which of the following numbers comes closest to the arbitrage profit you could realize by taking a position in one futures contract?

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Answers (1)

Know the Answer?

Howie · Answer 1

Possible options:

A. 38

B. 40

C. 42

D. There is no arbitrage opportunity.

Answer is B

Explanation:

With the given data, the no-arbitrage futures price should be; 800e (0.025-0.03) * 0.50 = 798-Since the market price of the futures contract is lower than this price there is an arbitrage opportunity. The futures-contract could be purchased and the index sold.-

Arbitrage profit is 798 - 758 = 40