What would you estimate is the percentage difference between the inflation rates
ID: 2613173 • Letter: W
Question
What would you estimate is the percentage difference between the inflation rates of the United States and Japan?
What is the cross-rate for Canadian dollars in terms of British pounds? (Do not include the Canadian dollar sign (C$). Round your answer to 4 decimal places (e.g., 32.1616).)
What is the cross-rate for British pounds in terms of Canadian dollars? (Do not include the pound sign (£). Round your answer to 4 decimal places (e.g., 32.1616).)
What would you estimate is the difference between the inflation rates of the United States and Japan?(Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)
Suppose the spot and three-month forward rates for the yen are ¥85.14 and ¥84.61, respectively. (Enter your answer as directed, but do not round intermediate calculations.)Explanation / Answer
JPY/USD
Spot Rate S = Y 85.14 / 1 USD
3 month forward rate F = Y 84.61 / 1 USD
period d = 3 months or 90 days (3*30)
Answer (a)
Calculation of forward premium / discount P can be calculated using the formula
P = (F/S) - 1
P = (84.61/85.14) - 1 = 0.9938 - 1 = - 0.0062
Annualised premium = ((F/S)-1)*360/d = ((84.61/85.14)-1)*360/90 = -0.0062 * 4 = - 0.0248 or -2.48%
That if USD 1 is sold today we will be getting Y 85.14 where as the amount received after 3 months will be Y 84.61 a decrease of Y 0.53 in three month period.
This indicates that the Yen is expected to strengthen over the 3 month period.
Answer (b)
P = (84.61/85.14) - 1 = 0.9938 - 1 = - 0.0062
Annualised premium = ((F/S)-1)*360/d = ((84.61/85.14)-1)*360/90 = -0.0062 * 4 = - 0.0248 or -2.48%
Forward exchange rate can be calculated using the formula
F = S {(1+ru)/(1+rj)} where ru and rj represent interest rates in US and Japan respectively
As per the international Fisher effect which is an extention of Fisher effect, if E(ru) is the inflation rate and inu is the real interst rate then
E(r) = iu - inu (approximately) that is iu = inu+E(ru)
similarly ij = inj+E(rj)
As per the international Fisher Effect, a change country's inflation rate will result in a proportionate change in country's interest rates. The change in interest rates in turn reflects as differential between the spot and forward exchange rates. The change will be in the order that the country with higher interest rates will depreciate while that with lower interest rates will appreciate.
As per the above, USD is expected to decline by -2.48% against Yen in 3 month period while the Yen is expected to appreciate against USD by same percentage.
Thus the difference between the inflation rates of United States and Japan would be -2.48%
Answers to Requirement 1, 2, 3
Requirement (1)
$100 = $100 * 0.6265 = GBP 62.65
GBP 100 = 100 * 1.5961 = $ 159.61
Based strictly on exchange rates it is better to have GBP 100.
Requirement (2)
Canadian Dollars 100 = 100 * 1.0057 = USD 100.57
GBP 100 = 100 * 1.5961 = $ 159.61
Based on the above it is better to have GBP 100
Requirement (3)(a)
Buy USD at 1.5961 and convert to Candian Dollar at 0.9943
GBP 1 = 1*1.5961 * 0.9943 = Candian Dollars 1.5870
Cross rate - 1.5870 / GBP
Requirement (3)(b)
The conversion can be done in two steps
Buy USD at USD 1.0057 per Canandian Dollar
Sell USD at GBP 0.6265 per USD
Canadian Dollar 1 = 1*1.0057 *0.6265 = GBP 0.6301
Cross rate = 0.6301 / Canadian Dolla
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