An American currency dealer has good credit and can borrow either $1,000,000 or €800,000 for one year. The one-year interest rate is i$ = 2% in the U.S. and i€ = 6% in the euro zone, respectively. The spot exchange rate is $1.25 = €1.00 and the one-year forward exchange rate is $1.20 = €1.00. Show how you can realize a certain dollar profit via covered interest arbitrage.

a. Borrow $1,000,000 at 2%; trade $1,000,000 for €800,000 at the spot rate; invest euros at i€= 6%;translate euro proceeds back to dollars at the forward rate of $1.20 = €1.00. Gross proceeds will be $1,017,600.
b. Borrow $1,000,000 at 2%; trade $1,000,000 for €800,000 at the spot rate; invest euros at i€= 6%;translate euro proceeds back to dollars at the forward rate of $1.20 = €1.00. Net profit will be $17,600.
c. Borrow €800,000 at i€= 6%;translate euros to dollars at the spot rate, invest dollars in the U.S. at i$ = 2% for one year; translate dollars back to €850,000 at the forward rate of $1.20 = €1.00. Net profit will be €2,000.
d. Borrow €800,000 at i€= 6%;translate euros to dollars at the spot rate, invest dollars in the U.S. at i$ = 2% for one year; translate dollars back to €848,000 at the forward rate of $1.20 = €1.00. Net profit will be $2,400.

c. Borrow €800,000 at i€= 6%;translate euros to dollars at the spot rate, invest dollars in the U.S. at i$ = 2% for one year; translate dollars back to €850,000 at the forward rate of $1.20 = €1.00. Net profit will be €2,000.

Explanation:

borrow 800,000€ today and purchase $1,000,000

invest the $1,000,000 and get $1,020,000 in one year

purchase back $1,020,000 / $1.20 = 850,000€

pay your loan resulting in a = 850,000€ - (800,000€ x 1.06) = 850,000€ - 848,000€ = 2,000€ gain

if you borrow $1,000,000 and purchase 800,000€

invest 800,000€ and get 848,000€ in one year

purchase back 848,000€ x 1.2 = $1,017,600

pay your loan back = $1,017,600 - ($1,000,000 x 1.02%) = $1,017,600 - $1,020,000 = -$2,400 loss