Question

A U.S.-based currency dealer has good credit and can borrow $2,000,000 for one year. The one-year interest rate in the U.S. is i $ = 2% and in the euro zone the one-year interest rate is i € = 6%. The spot exchange rate is $1.25 = €1.00 and the one-year forward exchange rate is $1.20 = €1.00. Show how to realize a certain dollar profit via covered interest arbitrage.

Answer 1

According to Interest Rate parity,

Forward Rate = Spot Rate * (1+Hi) / (1+Fi)

Hi = Home currency i.e., USD

Fi = Foreign currency i.e., Euro

Forward Rate = 1.25 * ( 1+0.02) / (1+0.06)

= 1.25 * ( 1.02) / (1.06)

= 1.25 * 0.9626

= 1.2028

Actual forward rate is not equal to IRPT forward rate, hence arbitrage exists

Assumption Euro 1,600,000 is borrowed. ( Equivalent to USD 2,000,000 )

Step 1:

Take Loan of 1600000 Euro

Step 2:

Convert into USD using spot Rate.

Amount in USD = 1600000 * 1.25

= USD 2000000

Step 3: Deposit in US for 1 Year and realize the maturity after1 year.

Maturity value after 1 Year = Deposit * (1+r)

= $ 2000000 * ( 1+ 0.02)

= USD 2000000 (1.02)

= USD 2040000

Step 4:

COnvert Into Euro Using, Actual Forward Rate

Amount in Euro = 2040000 /1.20

= Euro 1700000

Step 5:

Repay the loan in Euro

Maturity value of Euro Loan = 1600000 * 1.06

= Euro 1696000

Step 6 :

Profit = Euro 1700000 - Euro 1696000

= Euro 4000

Convert profit into USD using actual forward Rate :

Profit in USD = 4000 * 1.20

'= USD 4800

Pls comment, if any further assistance is required.