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/€.

1. Show how to realize a certain profit via covered interest arbitrage.
2. How do interest rates, the spot currency market, and the forward currency market adjust to produce an equilibrium?

Answer 1

By use of concept of interest rate differential and exchange rate concept ,

F = 1.25 * (1+0.05)/(1+0.04) = $ 1.26 / €

There is differential in actual forward rate and calculated forward rate by use of interest rate concept with create a arbitrage opportunity.

Answer A)

• Borrow $ 1,000,000 @ 5% , the total loan repayment a year would be $ 1,050,000.
• Convert $ 1,000,000 in € 800,000 at spot rate 1.25$/€
• Lock 4% rate on € 800,000 to get € 832,000 and same time create forward contract to convert the maturity amount in $ at rate = 1.40 $/€
• settle the forward contract after one year value in 832,000 *1.40 = $1,164,800
• Repay the loan amount of $ 1,050,000 and pocket the difference of .$ 114,800

Answer B) Simple a relation has been established between , SPOT rate , Interest rate and forward rate to establish a equilibrium .