In: Finance
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 =
ForwardGBP/USD/SpotGBP/USD = (1+iGBP)/(1+iUSD)
ForwardGBP/USD/SpotGBP/USD -1 = (1+iGBP)/(1+iUSD) -1
Calculation:
= -0.34 = iGBP - iUSD / (1+ iUSD)
-0.34 = iGBP/2- 0.0156(180/360) / 1+ 0.0156(180/360)
-0.3427 = iGBP/2- 0.0078
-0.3349 = iGBP/2
iGBP = - 0.3349 x 2 = -0.67 = - 67%
Answer 2.
SpotUSD/AUD = 1.349
ForwardUSD/AUD = 0.75
iUSD = 84%
ForwardUSD/AUD/SpotUSD/AUD = (1+iUSD/2)/(1+iAUD/2)
= 0.75/1.349 = (1 + 0.84/2)/(1 + iAUD/2)
= 0.556 = (1.42)/(1 + iAUD/2)
= (1 + iAUD/2) = 2.554
=iAUD/2 = 1.554
iAUD = 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