Question

Assume that the current interest rate on a 1-year bond is 8 percent, the current rate on a 2-year bond is 15.9 percent, and the current rate on a 3-year bond is 13.9 percent. If the expectations theory of the term structure is correct, what is the difference between the 1-year interest rate expected during Year 3 and the current one year rate?

Answer 1

Given

Current rate of interest on 1 Year bond = 8%

Current rate of interest on 2 Year bond = 15.9%

Current rate of interest on 3 Year bond = 13.9%

We know that

Expectation theory aims to predict what short term interest rate will be in future based on the long term interest rate.

Let the rate of interest in year 3 is x%

( 1+0.159)^2 ( 1+x%) = ( 1+0.139)^3.

( 1.159)^2 ( 1+x%) = ( 1.139)^3

1.343281( 1+x%) =1.477649

( 1+x%) = 1.477649/1.343281

( 1+x%) = 1.100029

x% = 1.100029-1

x% = 0.100029

Hence the rate of interest is 10% in Year 3

The Current rate of interest in Year 1= 8%

The difference between the 1 year interest rate expected during year 3 and Current one year rate is = 10% -8% = 2%.