Question

Assume a risk-free asset in the U.S. is currently yielding 1.9 percent while a Canadian risk-free asset is yielding 2.3 percent. The current spot rate is CAD1.361. What is the approximate 2-year forward rate if interest rate parity holds?
CAD1.3688
CAD1.3719
CAD1.3754
CAD1.3786
CAD1.3799

Answer 1

Solution :

As per the Interest rate Parity model

Exchange rate differential = Interest rate differential

( 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 Dollar is = CAD 1.361   ; Thus CAD / $ = A / B = CAD 1.361    ;

Canadian Risk free Interest rate = Risk free Rate in Currency A = 2.3 % = 0.023   ;

U.S. Risk free Interest rate = Risk free Rate in Currency B = 1.9 % = 0.019   ;

n = 2 Years ;

Applying the above values in the formula / Equation we have

Forward Rate / 1.361 = [ ( 1 + 0.023 ) / ( 1 + 0.019 ) ] ²

Forward Rate = [ 1.023 / 1.019 ] ² * 1.361

Forward Rate = [ 1.004 ] ² * 1.361

Forward Rate = 1.008 * 1.361

Forward Rate = 1.3719 CAD

The approximate 2-year forward rate if interest rate parity holds = 1.3719 CAD

The solution is Option 2 = CAD 1.3719

Note : ( 1.004 ) ² is calculated using the excel function =POWER(Number,Power) = POWER(1.004,2) = 1.008