Question

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

Current spot rate: $1.35/€

One-year forward rate: $1.30/€ Interest rate in the US: 4%

Interest rate in Germany: 5% Inflation rate in the US: 3% Inflation rate in Germany: 3.5%

(a) If you borrowed $1,000 for 1 year, how much money would you owe at maturity? (2 mark)

(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.

Answer 1

?Solution:

Given,

spot rate: $1.35/€

One-year forward rate: $1.30/€

Interest rate in the US: 4%

Interest rate in Germany: 5%

Inflation rate in the US: 3%

Inflation rate in Germany: 3.5%

a) Borrowed amount = $1000, time= 1 Year

First, we have to calculate nominal interest rate

Nominal interest rate= inflation + Real interest rate

= 4+3 = 7%

So, after 1-year amount owed = 1000 + (1000*.07*1) = 1000 + 70 = $ 1070

b) Spot rate, S= $1.35/€

Forward exchange rate, F =?

Interest rate in the US I_$: 4%

Interest rate in Germany I€: 5%

Given that the $ per € that satisfies IRP

So,

1+ I_$ = (1 + I€) F/ S

1+0.04= (1+0.05) F/1.35

1.04= 1.05F/1.35

F= 1.04*1.35/1.05 = 1.3371

c) Borrow €1000; repayment will be $1085

Buy $1350 spot using $1000 as the spot rate is

Invest $1350 at the dollar interest rate of 7%; maturity value will be $1444.5

Sell $1444.5 forward for €1111.15

Arbitrage profit will be € 1111.15 - €1085 = € 26.15

d) Given that the spot rate is dollar interest rate will rise; The pound interest rate will fall or vice a versa. This will result in the rise in spot exchange rate thus, the forward exchange rate will fall. These adjustments will continue until IRP holds.

e)

E(e) = E ($) - E (€)

= 3% - 3.5%

= -0.5%

The future spot rate will be

E(ST) = So (1 + E(e))

= (R$1.35/€) (1 + 0.005)

= R$ 1.35675/€