Question

"Consider the futures contract written on the S&P 500 index and maturing in one year. The interest rate is 3%, and the future value of dividends expected to be paid over the next year is $35. The current index level is 2,000. Assume that you can short sell the S&P index. a. Suppose the expected rate of return on the market is 8%. What is the expected level of the index in one year? b. What is the theoretical no-arbitrage price for a 1-year futures contract on the S&P 500 stock index? c. Suppose the actual futures price is 2,012. Is there an arbitrage opportunity here? If so, how would you exploit it?"

Answer 1

Answer:

a. $2125

b. $2025

c. there is an arbitrage opportunity.

Explanation:

a. St = So x (1+ rm)-D

So = current index price = 2000

rm = return on market = 8%

D = dividends = $35

inserting into the formula:

2000x(1+0.08)-35

= $2125

b.

So x (1+rf)-D

rf = 3%

2000 x (1+0.03)-35

= $2025

c. yes there is an arbitrage opportunity. the investor should go into contract with an exercise price of 2125dollars then short sell asset in future and after this, buy back after at future market price. since actual future price is 2012 and price expected is 2125.