Question

The nominal yield on 6-month T-bills is 4%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 5.5%. In the spot exchange market, 1 yen equals $0.007. If interest rate parity holds, what is the 6-month forward exchange rate? Round the answer to five decimal places. Do not round intermediate calculations.

Answer 1

Solution :

As per the Interest Rate Parity Theory

Exchange rate differential = Interest rate differential

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

Where n = No. of years

As per the Information given in the question we have

Interest rate on T – Bills = 4 % ( annualized )

Interest rate on T – Bills ( 6 months ) :

= 4 % * ( 6/ 12 ) = 2 % for 6 months = 0.02

Interest rate on default-free Japanese bonds = 5.5 % annualized.

Interest rate on default-free Japanese bonds ( 6 months )

= 5.5 % * ( 6 / 12 ) = 2.75 % for 6 months = 0.0275

Spot rate of the Japanese Yen is 1 Yen = $ 0.007

Thus Currency A / Currency B = $ / Yen = $ 0.007

Applying the above values in the formula we have :

( Forward Rate / $ 0.00700 ) = [ ( 1 + 0.02000 ) / ( 1 + 0.02750 ) ]

Forward Rate / $ 0.00700 = [ 1.02000 / 1.02750 ]    

Forward Rate / $ 0.00700 = 0.99270

Forward Rate = 0.99270 * $ 0.00700

= $ 0.00695

Thus if the Interest rate parity holds good,

the 6-month forward exchange rate is 1 Yen = $ 0.00695