Question

1. Suppose the data on today’s and future expected interest rates is given:

Time	Yield on 1-year T-bond
Today	1.2%
Next year	1.2% (expected)
2 years from today	1.6% (expected)
3 years from today	2.0% (expected)

a) Calculate today’s interest rates on 2-year, 3-year and 4-year bonds using the expectations hypothesis. Use these yields to construct a yield curve and plot it. What kind of shape does it have?

b) Now, suppose term premiums for 2-year, 3-year and 4-year bonds are 0.2%, 0.3% and 0.4%, respectively. Recalculate today’s interest rates on 2-year, 3-year and 4-year bonds using the liquidity premium theory. Use the yields to plot the yield curve on the same graph as expectations hypothesis yield curve from part (a). What do you notice?

Answer 1

SOLUTION:-

Given

Time	yield on 1- year T-bond
Today	1.2%
Next years	1.2%
2nd years from today	1.6%
3 years from today	2.0%

Using expectation hypothesis

2^nd year yield = 1.2%

^{3 years yield =} _1.33%

_{4 years yield =1.5%}

Term premimum for 2-years bond = 0.2%

Term premimum for 3-years bond = 0.3%

Term premimum for 4-years bond =0.4%

2 years rate on the bond =

= 0.2%

= 1.2% + 0.2% = 1.4%

3 years rate on the bond = 0.3%

= 1.33% + 0.3% = 1.63%

4 years rate on the bond =0.4%

= 1.5% + 0.4 = 1.9%

Formula for 2-years rate is average of first 2-years yield in the table given + term premium for 2-years bond likewise for 3 and 4 years rate also same formula.

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