Question

current spot exchange rate: $0.0100/yen current 180-day forward exchange rate: $0.0105/yen 180-day U.S. interest rate(on dollar denominated assets): 6.05% 180-day Japanese interest rate(on yen denominated assets): 1.00%

Answer 1

Future Value of 1 Yen after 180 days at 1% annual interest rate =1*((1+0.01)^(180/360))=1.004988

Future Value of $0.0100 US Dollar after 180 days at 6.05% annual interest rate =$0.0100*((1+0.0605)^(180/360))=$0.010298

As per Interest Rate Parity:

The 180 days forward rate should be :

1.004988Yen =0.010298 US Dollar

1 Yen =0.010298/1.004988=$0.010247 US Dollar

Rounded to four digits:

Forward rate should be :

1Yen=$0.0102US Dollar

Actual Forward Rate :

1Yen=$0.0105

You are getting more dollar at forward rate , hence Dollar is cheaper in forward rate

There is opportunity to make profit by Buying US dollars in forward

STRATEGY:

1. Borrow  in US dollar(Say 1million)  at 6.05% interest rate

2. Convert to Yen at current spot rate 1Yen=.0100 US dollar

Total amount received =(1/0.0100)million=100 million Yen

3.Enter into a forward rate contract buy US dollar at Forward Rate : 1 Yen=$0.0105

4. Invest 100 million Yen at 1% interest

5. After 180 days , you will get 100*1.005=100.5 millionYen

6. Convert to US dollar as per forward contract (1Yen=0.0105US dollar)

You will get 100.5*0.0105 million US dollar=$1.05525 million US dollar

7. Amount payable on 1 million US dollar Loan =1*(1+0.03025)=1.03025 million

8. Net Profit =(1.05525-1.03025)Million=0.025million US dollar=

$25,000