Question

Due to the integrated nature of their capital markets, investors in both the U.S. and U.K. require the same real interest rate, 2.5%, on their lending. There is a consensus in capital markets that the annual inflation rate is likely to be 3% in the U.S. and 2% in the U.K. for next year. The spot exchange rate is currently E$/£ = 1.4.

a. Compute the nominal interest rate per annum in both the U.S. and U.K., assuming that the Fisher effect holds.

b. Using relative PPP, what is the expected future spot dollar-pound exchange rate in one year from now?

c. Using UIP, what is the expected spot dollar-pound exchange rate in one year from now?

Answer 1

a) Nominal Interest rate in US (R) is given by

1+R = (1 + real rate in US) * (1+inflation rate in US) = 1.025*1.03= 1.05575

So, R = 0.05575 or 5.575%

Nominal Interest rate in UK (Y) is given by

1+Y = (1 + real rate in Uk) * (1+inflation rate in UK) = 1.025*1.02= 1.0455

So, Y = 0.0455 or 4.55%

b) The Cost of Goods in US after one year will be 1.03 times the Cost today

and The Cost of Goods in UK after one year will be 1.02 times the Cost today

So, goods costing $1.4 or 1 pound will be worth $1.4*1.03 and 1*1.02 pound respectively after one year

So, PPP exchange rate = 1.4*1.03 Dollars /(1*1.02) Pound = $1.413725 per Pound

c) Uncovered Interest parity says

Expected Spot rate after one year/Current exchange rate = (1+nominal interest rate in US)/(1+nominal interest rate in UK)

=> Expected Spot rate after one year = 1.4*1.05575/1.0455 = $1.413725 per Pound