Question

Given the following expectations information on U.S. Treasury instruments:

1-year note yield = 1.83%                       5-year note yield = 2.79%

2-year note yield = 1.99%                       6-year note yield = 3.04%

3-year note yield = 2.21%                       7-year note yield = 3.58%

4-year note yield = 2.42%                       8-year note yield = 4.18%

And non-changing premiums of 0, .11%, .22%, .39%, .52%, .64%, .75%, 88%, & .98%

e. Determine the expectations yield on a 5-year note purchased today.

f. Determine the yield on a 6-year Treasury note purchased today.

Answer 1

e. The expectation yield as per the pure expectation theory is:

((1+2 year yield)^2 *(1+3 years yeild)^3)^(1/5)-1

2 year-note yield + premium = 1.99% + 0.22% = 2.21%

3 year-note yield + premium = 2.21%+0.39% = 2.60%

Expectation of 5 year yield = ((1+0.221)^2*(1+0.026)^3)^(1/5)-1 = ((1.0221)^2*(1.026)^3)^(1/5)-1 = 2.44%

Expectation yield on a 5 year note purchased today = 2.44%

f. Yield on a 6 year note (not expectation) = 6 year note yiled + non- changing preium = 3.04%+0.75% = 3.79%