USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The S&P 500 stock index is at 1100. The annualized interest rate is 3.5 percent, and the annualized dividend is 2 percent.
-Refer to Exhibit 15.9. If the futures contract was currently available for 1250, indicate the appropriate strategy that would earn an arbitrage profit.
A) long futures and short the index
B) short futures and long the index
C) long futures and long the index
D) short futures and short the index
E) None of these are correct.

Question

Quizplus · Accepted Answer

To earn an arbitrage profit, we need to compare the fair value of the futures contract with its current price. The fair value of the futures contract is calculated as (Spot price + Cost of Carry), or in this case, (1100 + (0.035-0.02)*1100) = 1138.5. Since the current price of the futures contract is 1250, it is overpriced by (1250-1138.5) = 111.5. 
Therefore, we should short the overpriced futures contract and go long on the underlying index, which is currently undervalued. By doing so, we can earn an arbitrage profit as the futures contract converges to its fair value. 
Hence, the appropriate strategy is to short futures and long the index, which is option B.