Question

Assume that interest rate parity holds. In the spot market 1 Japanese yen = $0.01081, while in the 90-day forward market 1 Japanese yen = $0.01084. In Japan, 90-day risk-free securities yield 2.1%. What is the yield on 90-day risk-free securities in the United States? Round your answer to two decimal places. Do not round intermediate calculations.

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 Foreign Currency ) / ( 1 + Risk free Rate in Home Currency ) ]

As per the Information given in the question we have

Spot rate 1 Japanese Yen = $ 0.01081

Thus we have Spot rate as $ / ¥ = $ 0.01081

90 days Forward rate 1 Japanese Yen = $ 0.01084

Thus we have 90 day Forward rate as $ / ¥ = $ 0.01084

90 days Risk free rate in Japan = 2.1 %   = 0.021 ( Home currency )

90 days Risk free rate in United States = To find ( Foreign Currency ) = x

Applying the above information in the equation we have

( 0.01084 / 0.01081 ) = ( 1 + x ) / ( 1 + 0.021 )

1.002775 = ( 1 + x ) / 1.021

(1 + x ) = 1.002275 * 1.021

(1 + x ) = 1.023833                   

x = 1.023833 – 1 = 0.023833

x = 2.3833 %

= 2.38 % ( when rounded off to two decimal places )

Thus the 90 days United States Risk free rate is = 2.38 %