On July 5, a stock index futures contract was at 394.85. The index was at 392.54, the risk free rate was 2.83 percent, the dividend yield was 2.08 percent, and the contract expired on September 20. Determine whether an arbitrage opportunity was available and explain what transactions were executed.

Solution :

Given :

The stock index contracts at = $ 394.85

Index = $ 392.54

Risk fee rate =  2.83 %

Dividend = 2.08 %

Now take long position on the index at $ 392.54 per share

After 75 days, they have to pay $ 392.54 + 392.54 x 2.83 x 75/365

                                                   = $ 394.823

Take s short position on the stock index futures contract on $ 394.85 per share.

Dividends received = $ 392.54 x 2.08%

                                 = $ 8.164

Therefore, there is an  arbitrage opportunity.

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