1) Assume that one share of the S&P 500 Index can be purchased for 4,100 and that the dividend yield is 2.75% over the holding period and the risk-free rate is 3.20% over the holding period. What should the contract price on a one-year S&P 500 futures be?

2) Imagine you want to put on a short hedge by purchasing the S&P 500 at 4100 (from problem 1), and shorting the futures at 4200. If at the expiration date, the futures contract is valued at 4250, what is the: a. Net Futures Profit b. Net Index Profit c. Dividend d. Net Profit e. What must the risk-free rate be in order to eliminate an arbitrage opportunity?

3) Imagine that you can borrow or lend at a risk-free rate of 3.20% in the US, and you can borrow or lend at a risk-free rate of 4.55% in Europe. You have $500,000 to invest for one-year. The exchange rate is: 1.0000 USD = 0.9372 EUR.

a. Is there a covered interest arbitrage opportunity?

b. If so, how much (in USD) can you profit?

c. Explain what you would do to exploit a mispricing.

d. What would the one-year futures contract FX rate have to be (approximate out to 4 decimals) to eliminate the arbitrage opportunity?