Question

Suppose spot rate is $/£ = $1.25/£ and the 1-year forward rate is F1$/£ = $1.20/£. The real interest rate on a risk-free government security is 2 percent in both the United Kingdom and the United States. The U.S. inflation rate is 5 percent.

a. What is the U.K.’s inflation rate if the equilibrium relationships hold

b.What is the U.K's nominal required return on risk-free government securities?

Answer 1

a) If real interest rate in both country is 2% , and if equilibrium holds than, inflation rate in both countries must be 5%

Thus UK's inflation rate = 5%

(1+r)/(1+r) = (1+i)/(1+i)
= (1+2%)/(1+2%) = (1+i)/(1+5%)
=1.02/1.02 = (1+i)/1.05
= 1 =(1+i)/1.05
1.05 = 1+i
i = 5%

b) Real interest rate =(1+ Nominal interest rate)/(1+ inflation rate) - 1
(1+ Nominal rate) = (1+ Real rate of interest)(1+inflatiion rate)
Nominal rate = (1+ Real rate of interest)(1+inflatiion rate) - 1
= (1+2%)(1+5%) - 1
=1.02(1.05) - 1
= 1.071 - 1
= 0.071
i.e. 7.1%