3. S&P 500 index futures are the most popular stock futures contracts in the market. The contract multiplier is $250, which means that the contract size of these derivatives is 250 times the value of the S&P 500 index. (Note that while this multiplier makes the positions too large for many small investors, E-Minis are also available in the market, which are contracts that use the contract multiplier of $125).

Assume that the value of the S&P 500 is 1330 points currently, the risk free rate of interest is 4% annually, and the dividend yield for the index is 2%. The price of a June S&P 500 futures contract for delivery in three months is $336,250.

(a) Is there an arbitrage opportunity? How much money can you make per contract?

(b) What must be the fair price of the December contract?