Question

You are given the following information.The current dollar-pound exchangerate is $1.5 per pound. A U.S. basket that costs $100 would cost 80 poundsin theU.K. For thenext year, theFederal Reserve is predicted to keep U.S. inflation at 2%, and the Bank of England is predicted to keep U.K. inflation at 3%. The speed of convergenceto absolutePPP is 15% per year. a)What is the expected US minus UK inflation differential for coming year?

b)What is the current US real exchange rate qus/uk with the UK?

c) How much is the dollar overvalued/ undervalued?

d)What do you predict the US real exchange rate with UK will be in one year's time?

e)What is the expected rate of real depreciation for US(versus the UK)?

f)What is the expected rate of nominal depreciation for the US(versus the UK)?

g) What do you predict will be the dollar price of one pound a year from now?

Answer 1

Answer:

a) the expected US minus UK inflation differential for coming year is - 1% = 2% - 3%

b) the current US real exchange rate us/uk with the UK 1.25 = 100/80

c) the dollar overvalued 20% = (1.5/1.25-1)

d) the US real exchange rate with UK will be in one year's time is 1.24

e) the expected rate of real depreciation for US (versus the UK) is 1.1

f) the expected rate of nominal depreciation for the US(versus the UK) is 1.24

g) I predict  the dollar price of one pound a year from now will be 1.1

Explanation:

a) The inflation rate differential is the difference between the inflation rate in one country and the inflation rate in another.

b) The real exchange rate can be defined by Purchase Power Parity (PPP)

FX =  P 2 / P  1  

​where:  FX = Exchange rate of currency 1 to currency 2

P  1  = Cost of good X in currency 1

P  2  = Cost of good X in currency 2

c) current quoted rate compared to real exchange rate based on PPP is higher, then USD is overvalued

d) Real exchange rate is defined based on PPP in next 1 year.  In next 1 year, U.S. basket is $102 = 100 x(1+ inflation rate 2%) while this basket in UK is 82.4 pound = 80 x (1+ inflation rate 3%)

thus expected rate us/uk = 102/82.4 = 1.24

e) The speed of convergence to absolute PPP is 15% per year, then US real exchange rate us/uk with the UK 1.1 = current US real exchange rate us/uk with the UK 1.25 - 15%

f) Nominal depreciation is same as real depreciation in item d

d) I used the calculation with convergence to absolute PPP as item e

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