Question

Local risk-free rate (r) = 2% annual. Foreign risk-free rate (rf) = 3% annual. Exchange rate = $/euro. The current market exchange rate (S0) = 1.5. Suppose the current market two-year futures price (F0) = 1.4. Is there any arbitrage profit? If there is an arbitrage profit, compute the profit. Assume that you take a loan in Germany. The loan = euro 1000.

A. Yes, the arbitrage profit is higher than $70.
B. Yes, the arbitrage profit is higher than $60 but less than $70

C . No, there is no arbitrage profit
D. Yes, the arbitrage profit is less than $50.

Answer 1

Answer is B. Yes, the arbitrage profit is higher than $60 but less than $70.

First we calculate expected spot exchange rate in two-years.

expected spot exchange rate in two-years = current exchange rate*[(1+Local risk-free rate)no. of years/(1+Foreign risk-free rate)no. of years]

expected spot exchange rate in two-years = 1.5*[(1+0.02)2/(1+0.03)2] = 1.5*(1.022/1.032) = 1.5*(1.0404‬/1.0609‬) = 1.5*0.9807 = 1.47

expected spot exchange rate in two-years is 1.47 dollar per euro where as two-year futures price is 1.4. so, there is a arbitrage profit.

to calculate arbitrage profit, you take a loan in Germany of euro 1000.

total amount to pay back after two-years = loan amount*(1+Local risk-free rate)2 = euro 1000*(1+0.02)2 = euro 1000*1.0404 = euro 1,040.4‬

convert euro 1000 loan into dollars and invest it for 2-years at Foreign risk-free rate.

investment amount = loan amount*current exchange rate = 1,000*1.5 = 1,500‬ dollars

total dollar amount to be received after two-years = investment amount*(1+Foreign risk-free rate)2 = 1,500‬ dollars*(1+0.03)2 = 1,500‬ dollars*1.032 = 1,500‬ dollars*1.0609 = 1,591.35‬ dollars

convert total euro amount to pay back after two-years using expected spot exchange rate in two-years of 1.47 dollar per euro as: euro 1,040.4‬*1.47 = 1,529.39 dollars

arbitrage profit = total dollar amount to be received after two-years - total dollar amount to be paid after two-years

arbitrage profit = 1,591.35‬ dollars - 1,529.39 dollars = 61.96‬ dollars