Question

Assume a risk-free asset in the U.S. is currently yielding 2.2 percent while a Canadian risk-free asset is yielding 2.5 percent. The current spot rate is CAD1.328. What is the approximate 2-year forward rate if interest rate parity holds?

Answer 1

Solution :

As per the Interest rate Parity model

Exchange rate differential = Interest rate differential

Thus we have

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

Where n = No. of years

As per the Information given in the question we have

Spot rate of the US Dollar is = 1.328 CAD

1 USD = 1.328 CAD

Thus CAD / USD = A / B = 1.328 CAD

A /B = 1.328 CAD

Canada Interest rate = 2.5 % = 0.025   ( Risk free Rate in Currency A )

U.S. Interest rate = 2.2 % = 0.022 ( Risk free Rate in Currency B )

n = 2 years

Applying the above values in the formula / Equation we have the 2 year forward exchange rate as follows :

Forward Rate / 1.328 = [ ( 1 + 0.025 ) / ( 1 + 0.022 ) ] 2

Forward Rate = [ 1.025 / 1.022 ] 2 * 1.328

Forward Rate = ( 1.002935 ) 2 * 1.328

Forward Rate = 1.005879 * 1.328

Forward Rate = CAD 1.335808

= CAD 1.336 ( when rounded off to three decimal places )

Thus the 2 year forward exchange rate for the US Dollar = CAD 1.336

Note : = (1.002935 ) 2 is calculated using the excel formula =POWER(Number, Power)

= POWER(1.002935,2) = 1.005879