Question

4. Given the following 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%

a. Calculate the expected expectations yield for a (3,2,1,2) path.

b. Calculate the expected empirical yields for a (2,5,1) path.

c. Calculate the expected expectations yield for a 5-year note purchased at the beginning of year 3.

d. Calculate the expected market yield on a 4-year note purchased at the beginning of year 2.

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

Solution: (W) Given information on Vos Treasury instruments. @ Expected expectations yield for a (3,2,1,2) Path: pure expectation / Expectation theory states that if the 2nd year rate is higher than Iyear rate than short term rate is expected to increase And (1+in) = (1+i) *(1+i2). --Chtin) To for path (3,2,1,2) the expectation gields = = (1+0.0221 ) + (1+0.0199 +0.0039) * (1+ 0.0183+ 0.0064)+ (1+0.0199+0.0075) = (1.0221) (1.0238) 01.0247) (110274) = 1.10165 • Expectation yield for this path = 110.165 © expected Emperical yields for a (2,5,1) path:

= expected Emperical yield for a (2,5,1) path = (1+0.221) (1+0.0279 +0.0022) (1+0.0183+ 0.0088) - = (1.0221) (0301) (1.0271) – = 1.083198-1 = 8.32+6) © Expected expectations yield for a syear note purchased at begining of year 3: » Expected Expectation yield at the begining of 3 years for 5 year note = 2.74 +0.64 = 3.43-10) year note purchased @ expected market yield on a at the begining of year 2: >>> = 2.42 +0.52 = 19.94-41

@ The expectations yield on syear note purchated today : The expectation yield as per pure expectation theory 18: ((1+2year yield); CH3 years yeild??)"5_1 Qyear note yield + premimum = 1.994.70.22-). = 2.214 Byear note yeild + premim = 2:21.4. + 0.594. = 7.601. Expectation syear yield = ((1+0.921)?# [1+0.02613 =((1.022134(1.026)3395, = qrunt:7 6 yield on a byear Treasury note porchased today: → = 6year note yeild then changing preium = 3.04.1. +0.7571 = (3.79 to]