3. S&P 500 index futures are the most popular stock futures contracts in the mar

Question

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?

Explanation / Answer

A)Calculation of arbitrage opportunity

Current S&P 500 Contract price = 1330*$250

=$332500

Fair price of S&P 500 = 1330 * e (0.04-0.02)*3/12

= 1330 * e 0.005

= 1330 * 1.00501252 (e 0.005=1.00501252)

= 1336.67

Fair value of contract = $250 * 1336.67

= $334166.66

Yes arbitrage opportunity exists,  

Amount we can make per contract = $334166.66 - $332500

= $1666.66

B) Calculation of fair price of december contract :

= 1330* e (0.04-0.02)9/12

= 1330 * 1.01511306

Value of S&P 500 Index = 1350.10

Fair price of the december contract =1350.10*$250

= $337525

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