Question

.) A currency dealer has good credit and can borrow either $1,000,000 or €800,000 for one year. The one-year interest rate in the U.S. is i$ = 5% and in the euro zone the one-year interest rate is i€ = 4%. The spot exchange rate is $1.25/€ and the one-year forward exchange rate is $1.40/€. a.) Show how to realize a certain profit via covered interest arbitrage.

A) Borrow $1,000,000 at 2%. Trade $1,000,000 for €800,000; invest at i_€=6%; translate proceeds back at forward rate of $1.20 = €1.00, gross proceeds = $1,017,600

B) Borrow €800,000 at i_€=6%. translate to dollars at the spot, invest in the U. S at i_$=2% for one year; translate €848,000 back into euro at the forward rate of $1.20 = €1.00 Net profit $2400

C) Borrow €800,000 at i_€=6%. translate to dollars at the spot, invest in the U. S at i_$=2% for one year; translate €850,000 back into euro at the forward rate of $1.20 = €1.00 Net profit $2000

D) Both C and B.

Answer 1

The question does not fit the options, since the options all refer to a 2% interest rate in US dollars and a 6% interest rate in euros. While the question states that the interest rate in US dollars is 5% and the interest rate in euros is 4%.

The answer to the question is:

If you borrow $1,000,000 today, you will be able to purchase 800,000€. Or if you borrow 800,000€ today, you will be able to purchase $1,000,000.

Since the forward rate is higher, you should borrow dollars, invest in euros and after a year, purchase back dollars and pay back your debt.

Gain:

= 800,000€ x 1.04 = 832,000€ x 1.4 = $1,164,800, then you pay back your loan = $1,164,800 - ($1,000,000 x 1.05) = $1,164,800 - $1,050,000 = $114,800 gain

Options C will also yield gains:

option C = borrow 800,000€ and buy $1,000,000. After one year you will have $1,020,000 which you can use to purchase 850,000€. Your gain = 850,000€ - (800,000€ x 1.06) = 2,000€