Question

If the expected path of one-year interest rates over the next four years is 5 percent, 4 percent, 3 percent, and 2 percent. Draw the yield curve under the expectations theory. Now, assume liquidity premium are 0.25 for 2 year, 0.5 for 3 year and 0.75 for 4 year bonds, draw on the same graph (ideally in different color) the yield curve under the liquidity premium theory.

Answer 1

According to expectations theory, expected interest rates in future for the term of 4 years are the forward rates, that is, 5%, 4%, 3%, 2%. These can be plotted against term to maturity. The graph is as below;

Under expectations theory, yields are calculated using liquidity premiums as below:

Yield for 1st year = 5%

Yield for second year = (5+4)/2 + 0.25 = 4.75%

Yield for third year = (5 +4+ 3) / 3 + 0.5 = 4.5%

Yield for four years = (5 +4+ 3 + 2) / 4 + 0.5 = 4%

The graph for the yields is as below: