Given the following data on US Agency debt instruments 1year

Given the following data on U.S. Agency debt instruments: 1-year note yield = 3.42% 7-year note yield = 4.64% 2-year note yield = 3.69% S-year note yield = 4.70% 3-year note yield = 4.02% 9-year note yield = 4.86% 4-year note yield = 4.02% 10-year note yield = 4.95% 5-year note yield = 4.35% 11-year note yield = 4.90% 6-year note yield = 4.50% 12-year note yield = 4.99% And constant premiums ofO, .17%, .41%, .63%, .82%, .98%, 1.12%, 1.22%, 1.30%, 1.37%, 1.42%, 1.45%, 1.47% Calculate the expected liquidity premium yields for a (1,5,2) path. Calculate the expectations yields for a (3,4,1) path. Calculate the real world yield for a (3,5) path. Calculate the expected pure expectations yield for a 3-year note purchased at the beginning of year 5. Calculate the expected preferred habitat yield on a 6-year note purchased at the beginning of year 3. Determine the expectations yield on a 10-year note purchased today. Determine the market yield on a 12-year note purchased today. Describe the yield curve and provide a general interpretation of what implies about the economy.

Solution

a) According to Liquidity theory, the expected liquidity premium = average return of bond + constant premium

   r = (r1 + r5 + r2)/3 + 3-year bond premium

     = (3.42 + 4.35 + 3.69)/3 + .63 = 4.45%

b) Expected Yield is just the average of the n bonds of different durations or time to maturity

   r = (4.02 + 4.02 + 3.42)/3 = 3.82%

c) Real world yield of a 3-5 path is the return of the average duration or 4-year note yield = 4.02%

d) If expectation hypothesis holds, then a 3 year note at beginning of year 5 will have 1 year left to maturity, According to the hypothesis, yield = discounted forward rate of 1 year note

Yield = 4.35/ 1 + 3.42% = 4.206%