Question

4. The following table shows the price of $1000 face value 1-year, 2-year, 3-year, 9-year and 10-year US Treasury zero coupon bonds as of March 2018. Use pure expectations hypothesis to determine:

a. the interest rate for the 1-year bond.

b. the expected interest rate on a 1-year bond one year from now, in year 2?

b. the expected interest rate on a 1-year bond two years from now, in year 3?

c. the expected interest rate on a 1-year bond nine years from now, in year 10?

                  

                                                   1-yr     2-yr       3-yr       9-yr        10-yr

U.S. Treasury (March 2018)    982.51   965.31   948.41   783.17   759.11

What is the bond market telling us about the future path of 1-year interest rates?

Answer 1

Expected interest rate in year t = (price of year t-1 bond - price of year t bond) / (price of year t-1 bond)

We can calculate these as follows:

Year = t	Price of year t bond	Expected interest rate in year t
0	1,000.00
1	982.51	1.7490%
2	965.31	1.7506%
3	948.41	1.7507%
9	783.17
10	759.11	3.0721%

b. the expected interest rate on a 1-year bond one year from now, in year 2? 1.7506%

b. the expected interest rate on a 1-year bond two years from now, in year 3? 1.7507%

c. the expected interest rate on a 1-year bond nine years from now, in year 10? 3.0721%

d. since the interest rates are going up, bond market is forecasting some economic uncertainty which will make money more expensive