Question

Suppose that the annual interest rate is 3.25 percent in the United States and 4 percent in Germany and that the spot exchange rate is $1.50/€ and the forward exchange rate, with one-year maturity, is $1.55/€. Assume that an arbitrager can borrow up to $1,000,000 or its equivalent in Euro. If an astute trader finds an arbitrage, what is the net cash flow in one year in dollar and in Euro?

Answer 1

Fair forward rate as per Interest Rate parity = Spot Rate*(1+Interest Rate Dollar)/(1+Interest Rate Euro)

= 1.50*(1+0.0325)/(1+0.04)

= $1.4892/Euro

Since actual forward rate is different from fair forward rate, arbitrage is possible

Steps:

Borrow Dollar 1,000,000

Convert into Euro at spot rate and get 1,000,000/1.5 = Euro666,666.67

Invest and Get 666,666.67(1.04) = Euro 693,333.34

Convert into Dollar at forward rate = 693,333.34*1.55 = Dollar 1,074,666.67

Pay back loan $1,000,000(1.0325) = $1,032,500

Arbitrage Profit = $42,166.67

Net Cash flow in one year in Dollar = $(1,032,500)

Cash Inflow in Euro = Euro 693,333.34

Net Cash flow in Dollar = $42,166.67 or Equivalent 27,204.30 in Euro