A stock index currently has a value of 1,900 and an anticipated dividend of $20

Question

A stock index currently has a value of 1,900 and an anticipated dividend of $20 over the next 6 months. The borrowing rate over the next 6 months is 2% APR, or 1% for the next 6 months. If a futures contract with a settlement date in 6 months currently offers a price of 1,910:

A. Is the futures contract fairly priced? If not, design an arbitrage to take advantage of the mispricing, and calculate the profit.

B. Explain why the arbitrage transaction you designed in Part A is not really an arbitrage (why is it not risk free?).

Explanation / Answer

Fair Future price = Current Index level * (1+Rf) T – Expected Dividend

Fair Future price = $1900 * (1.01)1 - $20

Fair Future price = $1919 - $20

Fair Future price = $1899

Step 2:

Given Price of Future contracts = 1910

No. Future contracts are not fairly priced.

Since the Future contracts are not fairly priced, Arbitrage is possible.

The future contract price being offered is higher than the fair future price. This means that you can enter into a future contract to sell the index in 6 months. To exploit this mispricing, you should buy the index in the spot market, means you have to pay 1900 today. Borrow 1900 from local bank at risk free rate of 1% per 6 months.

After 6 months you have pay 1919 to bank and receive $20 has dividend, so total Outflow is 1899. Next you sell the index at the 1910 that you committed to sell at. You than return the index to the person you borrowed it from and pocket 1910-1899 = 11

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