Question

A Euro based currency dealer has good credit and can borrow $2,250,000 for one year or its equivalent in Euro. The one-year interest rate in the U.S. is i$ = 2.15% and in the euro zone the one-year interest rate is i€ = 5.58%. The spot exchange rate is $1.35 = €1.00 and the one-year forward exchange rate is $1.29 = €1.00. Show how to realize a certain Euro profit via covered interest arbitrage. Convert it into dollars as well.

Answer #1

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

= 1.35*(1+0.0215)/(1+0.0558)

= $1.3061/Euro

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

Steps:

Borrow Euro 1,666,666.67

Convert into dollar at spot rate and get $2,250,000

Invest and Get 2,250,000(1.0215) = $2,298,375

Convert into Euro at forward rate = 2,298,375/1.29 = Euro1,781,686.05

Pay back loan Euro 1,666,666.67(1.0558) = Euro 1,759,666.67

Arbitrage Profit = Euro 22,019.38

Arbitrage Profits in Dollars = 22,019.38*1.29 = $28,405

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