Question

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5 pts)The 6-month forward discount for converting the U.S. dollar into the British pound is 34%...

5 pts)The 6-month forward discount for converting the U.S. dollar into the British pound is 34% and 6-month U.S. Treasury bills yield 1.56%. Based on interest rate parity, what should be the 6-month British Treasury bill yield?

(10 pts)The current exchange rate is one Australian dollar (AUD) equal to 1.349 USD. In the United States, the 6 months T-bill rate is 84%. The 6-month forward rate for AUD is .75 USD/AUD. Assuming that interest rate parity exists, what is the implied interest rate for Australia?

(15 pts)Suppose the following conditions exist between the U.S. and Canada. 6 month U.S. interest rate = 4.5%. Canadian interest rate = 4%. Spot rate: 1 CAD = .9537 USD. 6 month forward rate: 1 CAD = .9612 USD. Are the conditions of interest rate parity violated? If so, what would be our profit if we engaged in covered interest arbitrage by borrowing $2M in the U.S.?

Expert Solution

Answer 1.

Forward discount = USD is trading weaker relative to British pound since it is trading at a discount, means USD interest rate is higher than the British pound

Interest rate parity formula =

Forward_GBP/USD/Spot_{GBP/USD =} (1+i_GBP)/(1+i_USD)

Forward_GBP/USD/Spot_GBP/USD -1 ₌ (1+i_GBP)/(1+i_USD) -1

Calculation:

= -0.34 = i_GBP - i_USD / (1+ i_USD)

-0.34 = i_GBP/2- 0.0156(180/360) / 1+ 0.0156(180/360)

-0.3427 = i_GBP/2- 0.0078

-0.3349 = i_GBP/2

i_{GBP =} - 0.3349 x 2 = -0.67 = - 67%

Answer 2.

Spot_USD/AUD = 1.349

Forward_USD/AUD = 0.75

i_{USD =} 84%

Forward_USD/AUD/Spot_{USD/AUD =} (1+i_USD/2)/(1+i_AUD/2)

= 0.75/1.349 = (1 + 0.84/2)/(1 + i_AUD/2)

= 0.556 = (1.42)/(1 + i_AUD/2)

= (1 + i_AUD/2) = 2.554

=i_AUD/2 ₌ 1.554

i_{AUD =} 3.108 ~ 310.8%

Answer 3.

Forward rate according to interest rate parity

0.9537 (1+0.0225)/1+0.02)

= 0.9560375

Yes, interest rate parity condition is violated

Strategy to follow:

a) Borrow $2M at 4.5% and convert it into CAD at spot price of 1.0485(1/0.9537). = CAD 20,97,000

b) Invest the amount at Canadian interest rate at 4%,

c) take a position in forward position to convert it at forward rate of 0.9612 USD.

Final output:

Interest to be paid in USD = 2,000,000 X 0.0225 = $45,000

Final amount to be paid after 6 months = $2,045,000

Canadian final amount received = CAD 2,097,000 (1+0.02) = CAD 2,138,940

Convert it at Forward rate and receive USD= 2,138,000 X 0.9612 = $2,055,045.6

Arbitrage profit = $2,055,045.6 - $2,045,000 = $10,045.6

jeff jeffy answered 7 months ago

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