Question

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Chapter 10: Futures Contract and Swaps Exercise: 5, 6, 12, 15, and 20 5.Consider the futures contract written on the S&P 500 index and maturing in 6 months. The interest rate is 3% per 6-month period, and the future value of dividends expected to be paid over the next 6 months is $15. The current index level is 1,425. Assume that you can short sell the S&P index. a. Suppose the expected rate of return on the market is 6% per 6-month period. What is the expected level of the index in 6 months? b. What is the theoretical no-arbitrage price for a 6-month futures contract on the S&P 500 stock index? c. Suppose the futures price is 1,422. Is there an arbitrage opportunity here? If so, how would you exploit it? I level

Answer 1

a. Expected rate of return = Current index level * (1+ return) - dividends paid

= 1425 * ( 1+6%) - 15

= 1495.5

b. Expected rate of return = Current index level * (1+ no arbitrage return) - dividends paid

= 1425 * ( 1+3%) - 15

= 1452.75

c. The arbitrage opportunity is as below:

Buy index future at $1422

Short the index dividends $15

Invest the proceeds in T bills at $1467.15 ( 1452. 75 + 15)

Net gain from the arbitrage = 1467.15 - 1422 - 15 = $30.75