Question

Assume that the one-year interest rate in the US is 4% and in the Eurozone is 6%. According to interest rate parity (IRP), What should the one-year forward premium or discount of the euro be (use of approximation is OK)? If the euro’s spot rate is $1.10, what should the one-year forward rate of the euro be?

Answer 1

Solution:

Calculation of Forward Rate:

As per the Interest Rate Parity model

Exchange rate differential = Interest rate differential

( Forward Rate / Spot Rate ) = [ ( 1 + Interest Rate in Currency A) / ( 1 + Interest Rate in Currency B ) ] ⁿ

Where n = No. of years

As per the Information given in the question we have

One year U.S. interest rate = 4 % = 0.04

One Year Eurozone interest rate = 6 % = 0.06

Spot rate of the Euro is $ 1.10

Thus $ / € = $ 1.10

A /B = 1.10

n = 1 years

Applying the above values in the formula / Equation we have

Forward Rate / $ 1.10 = [ ( 1 + 0.04 ) / ( 1 + 0.06 ) ] ¹

Forward Rate = (1.04 / 1.06 ) ¹ * $ 1.10

Forward Rate = (0.981132 ) ¹ * $ 1.10

Forward Rate = 0.981132 * $ 1.10

Forward Rate = $ 1.079245

= $ 1.0792 ( when rounded off to four decimal places )

Thus the Euro exchange rate in Dollars 1 year from now = $ 1.0792

Thus $ / € = 1.0792

Calculation of Forward premium / discount:

The formula for calculating the annualized forward premium / discount is

= [ ( Forward rate – Spot rate ) / Spot rate ] * 100

As per the information given in the question we have

Forward rate of Euro = $ 1.079245     ;   Spot rate of Euro = $ 1.1   ;

Applying the above values in the formula we have

= [ ( 1.079245 – 1.10 ) / 1.10 ] * 100

= [ - 0.020755 / 1.10 ] * 100

= - 0.018868 * 100

= - 1.886792 %

= - 1.8868 %

Since the solution is negative the one year forward rate is at a discount = - 1.8868 %