Question

The table below shows current and expected future one-year interest rates. Year One-Year Bond Rate 1= 3% 2= 4% 3.=5% 4.= 8% A. Assuming that the expectations theory is the correct theory of the term structure, calculate the current interest rate for a four-year bond (predicted by that theory). Show your work and include a one-sentence explanation. B. Assume now that the liquidity premium theory is the correct theory of the term structure. If the actual interest rate on a four-year bond is currently 9 percent, calculate the liquidity premium for the four-year bond. Show your work and include a one-sentence explanation.

Answer 1

Solution:-

a:
Under expectation theory, predicted rate over long term (0 – t2) is same as rate based on multiple short-term rates such as (0 – t1) and (t1 – t2). In other words, bond traders are indifferent whether they consider long-term or short-term rate on predicting bond price.

1-year rate = 3%

2-year rate = (1.03*1.04)^(1/2) – 1 = 0.034988 = 3.50%

3-year rate = (1.03*1.04*1.05)^(1/3) – 1 = 0.039968 = 4.00%

4-year rate = (1.03*1.04*1.05*1.08)^(1/4) – 1 = 0.049835 = 4.98%

b:

When there is liquidity risk, there will be a liquidity premium.

Liquidity risk adjusted 4-year rate = 9 = 5.97 + liquidity premium