Question

1. With the Expectations Theory, explain what happens to long term interest rates when future short term interest rates are expected to (a) fall and (b) increase.

Answer 1

Solution:

Expectation theory gives the relationship between the short term interest rate in the future and the long-term interest rate. This says that when an investor invests in the long term (eg. 2 Year) maturity then the return should be equal to the consecutive short term( 2 investment of 1-year period) investments.

We are taking the example for 2 years

Forward rate = (1+r2)^2 / ( 1+r1) - 1

When future short term interest rates are expected to fall then the long term interest rate will fall and similarly when short term interest rate increases then the long term interest rate increase.

We can understand this by taking an example.

Suppose 2-year interest rate = 10%

1-year spot rate = 9% then 2nd year spot rate = (1.10)^2 /1.09 -1 = 11.01%

When this rate 11.01% increases to 15% then 2 year rate should be = (1+9%)*(1+15%)^(1/2)- 1 = 16.89%

So we can see that the long term interest rate will increase from 10% to 16.89%