What should the trader do?

A trader finds that a stock index is trading at 1000, and a six month futures contract on the same index is available at 1020. The risk free rate is 2% per annum, and the dividend rate is 1% per annum.

What should the trader do?
A . Buy the index spot and sell the futures contract
B . Buy the futures contract and sell the index spot
C . Buy the index spot and buy the futures contract
D . Sell the futures contract

Answer: A

Explanation:

The fair price for the futures contract should be [1000 x ( 1 + (2%-1%)/2)] = 1005. This means the futures contract is ‘rich’ at 1020. The trader should therefore short the futures contract, and buy the index spot. To buy the spot index, he will incur a borrowing cost of 2%, which will be partly offset by the dividend yield of 1%, and at the end of six months he will owe a net amount of 1005 and hold the index. At the same time the futures contract would expire too, and he would be able to sell at the agreed price of 1020, making a risk free profit of 15.