Suppose interest rate parity holds, and the current risk-free rate in the United

Question

Suppose interest rate parity holds, and the current risk-free rate in the United States is 4 percent per six months. Use the approximate interest rate parity equation to answer the following questions.

What must the six-month risk-free rate be in Australia? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What must the six-month risk-free rate be in Japan? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What must the six-month risk-free rate be in Great Britain? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation / Answer

Answer:

We know that:

Forward Rate = Spot rate x (1 + Interest rate in overseas) / (1 + Interest rate in domestic)

Requirement-1

the risk free rate in US = 4% ; this is rate in domestic market

and 6-month forward rate of Australian dollar (AUD) is:

1 USD = 1.2349 AUD

Also the spot rate of AUD is:

1 USD = 1.2384 AUD

Now by using interest rate parity equation we get:

1.2349 = 1.2384 x (1 + Rf) / (1+4%)

1 + Rf = 1.03706

Hence Rf (in Australia) = 0.03706 or 3.71%

Requirement-2

the risk free rate in US = 4% ; this is rate in domestic market

and 6-month forward rate of Japanese Yen (JPY) is:

1 USD = 99.98 JPY

Also the spot rate of JPY is:

1 USD = 100.4 JPY

Now by using interest rate parity equation we get:

99.98 = 100.4 x (1 + Rf) / (1+4%)

1 + Rf = 1.03564

Hence Rf (in Japan) = 0.03564 or 3.56%

Requirement-3

the risk free rate in US = 4% ; this is rate in domestic market

and 6-month forward rate of Great Britain (GBP) is:

1 USD = 0.6781 GBP

Also the spot rate of GBP is:

1 USD = 0.6792GBP

Now by using interest rate parity equation we get:

0.6781 = 0.6792 x (1 + Rf) / (1+4%)

1 + Rf = 1.03831

Hence Rf (in Great Britain) = 0.03831 or 3.83%

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