(4) (10 POINTS) The table below shows current and expected future one-year inter

Question

(4) (10 POINTS) The table below shows current and expected future one-year interest rates Year One-Year Bond Rate 3% 4% 5% 8% 10% Interest Rates Predicted by the Expectations Theory 2 3 4 5 (a) (5 POINTS) Assuming that the expectations theory is the correct theory of the term structure, calculate the current interest rate for one-year, two-year, three-year, four-year, and five-year bonds (predicted by that theory). Show your work, and include a one-sentence explanation (b) (5 POINTS) Assume now that the liquidity premium theory is the correct theory of the term structure. If the actual interest rate on a five-year bond is currently 9 percent, calculate the liquidity premium for the five-year bond. Show your work, and include a one-sentence explanation.

Explanation / Answer

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%

5-year rate = (1.03*1.04*1.05*1.08*1.10)^(1/5) – 1 = 0.059681 = 5.97%

b:

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

Liquidity risk adjusted 5-year rate = 9 = 5.97 + liquidity premium

Liquidity premium = 3.03%

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