Question

Consider the following term structure of interest rates: 6 month rate 4.2%, twelve month rate 4.1%, eighteen month rate 4.3%, two year rate 4.35%. Using the unbiased expectations theory of interest rate, what is your prediction of the six month interest rate which will apply in six months time? What's is your prediction of the one-year interest rate which will apply in six months time?

Answer 1

As per expectations theory, investing for 1 year at the 1-year rate should result in the same ending value as investing for 6 months at the 6-month rate, and reinvesting the proceeds after 6 months at the 6 month-rate 6 months from now.

 

Let us say the 6 month-rate 6 months from now is R. Then :

(1 + 4.1%)1 = (1 + 4.2%)6/12 * (1 + R)6/12

                 R = (1.041 * 1.0426/12)12/6 - 1

                 R = 4.00%

 

The 6 month-rate 6 months from now is 4.00%

 

As per expectations theory, investing for 18 months at the 18-month rate should result in the same ending value as investing for 6 months at the 6-month rate, and reinvesting the proceeds after 6 months at the 1 year-rate 6 months from now.

 

Let us say the 1 year-rate 6 months from now is R. Then :

(1 + 4.3%)18/12 = (1 + 4.2%)6/12 * (1 + R)1

                         R = (1.04318/12 / 1.0426/12)1 - 1

                         R = 4.35%

 

The 1 year-rate 6 months from now is 4.35%

The 6 month-rate 6 months from now is 4.00%.

The 1 year-rate 6 months from now is 4.35%.