Question

Below shows the information for exchange rates, interest rates and inflation rates in the US and
Germany. Answer the following questions

Current spot rate: $1.60/€
One-year forward rate: $1.58/€
Interest rate in the US: 2%
Interest rate in Germany: 4%
Inflation rate in the US: 2%
Inflation rate in Germany: 3%

(a) If you borrowed $1,000 for 1 year, how much money would you owe at maturity?
(b) Find the 1-year forward exchange rate in $ per € that satisfies IRP from the perspective of a customer
that borrowed $1000 traded for € at the spot and invested in Germany.
(c) There is one profitable arbitrage at these prices. How to conduct the covered interest arbitrage if you can
either borrow $1000 in the US or €1000 in Germany? What would be the profit?
(d) Explain how the IRP will be restored as a result of covered arbitrage activities.
(e) A fund manager uses the concepts of purchasing power parity (PPP) to forecast spot exchange rates
using the financial information. Calculate the future euro spot rate in dollar after one year that would be
forecast by relative PPP.
(Numbers should be rounded to at least 3 decimal places. Please include currency symbols $, € in
your answer)

Answer 1

a) Amount borrowed=$1,000 at 2% for 1 year. So money owed at maturity=$(1,000*1.02)=$1,020

b) As per IRP,

  

c) Since actual forward rate is higher than forward rate as per IRP , arbitrage opportunity exists.

If we borrow $1,000 in US, the arbitrage is by borrowing for 1 year whose outflow is $1,020 as par part (a).

Now we sell dollar spot to receive euro. Euro received=1,000/1.6 euro=625 euro

We deposit euro at 4% for 1 year. So euro receivable at end of 1 year=(625*1.04) euro = 650 euro

Now we sell euro one year forward at 1.58 to get back dollars. Dollars received=$(650*1.58)=$1,027

So arbitrage profit = $(1,027-1,020)=$7.

But if euro was borrowed, there would not be arbitrage profit.

d) As a result of covered interest arbitrage, the dollar interest rate will rise, the euro interest rate will fall, the spot exchange rate will rise and forward exchange rate will fall. This adjustements will continue till IRP holds.

e) As per PPP,

  

Given inflation rate in US=2% and in Germany=3%, Thus,