The following information is available: Spot rate for Euro: $1.4/€; 511-days futures rate for Euro: $1.50/€ (assume 365-day year); U.S. risk-free rate: 3%; Euro risk-free rate: 5%.
a. A U.S. investor who can borrow in dollars (look at it from U.S. perspective) is looking at the above quotes. Find for this U.S. investor the correct futures price for the 511-days futures on $/€ exchange rate using continuous compounding, and then list the specific transactions in the spot, futures, and credit markets needed to avail an arbitrage opportunity if possible, and calculate the arbitrage profit per Euro. For arbitrage transactions, assume that U.S. investor can borrow $1,000 at 3%.
b. Now think of a European investor who can borrow in Euros. He treats the U.S. risk-free rate as the foreign interest rate (q variable) and his spot and futures rates are €0.7143/$ and €0.6667/$, respectively (i.e., inverse of the above $/€ exchange rates). Find for this European investor the correct futures price for the 511-days futures €/$ exchange rate using continuous compounding and show possible arbitrage transactions (Assume that European investor can borrow €714.30 at 5%.).