As in Example 3, let’s suppose that the one-year interest rates over the next five years are expected to be 5%, 6%, 7%, 8%, and 9%. Investors’ preferences for holding shortterm bonds have the liquidity premiums for one-year to five-year bonds as 0%, 0.25%,0.5%, 0.75%, and 1.0%, respectively. What

Question

As in Example 3, let’s suppose that the one-year interest rates over the next five years are expected to be 5%, 6%, 7%, 8%, and 9%. Investors’ preferences for holding shortterm bonds have the liquidity premiums for one-year to five-year bonds as 0%, 0.25%, 0.5%, 0.75%, and 1.0%, respectively. What is the interest rate on a two-year bond and a five-year bond? Compare these findings with the answer from Example 5.3 dealing with the pure expectations theory.

Accepted Answer

The interest rate on the two-year bond would be 5.75%.

[latex]i_{nt} =\frac{i_{t}+i^{e}_{t+1} +i^{e}_{t+2} +...+i^{e}_{t+(n-1)} }{n} +l_{nt}[/latex]

where

[latex]i_{t} [/latex]= year 1 interest rate = 5%

[latex]i^{e}_{t+1}[/latex] = year 2 interest rate = 6%

[latex]l_{nt} [/latex]= liquidity premium = 0.25%

[latex]n [/latex]= number of years = 2

Thus,

[latex]i_{2t} =\frac{5\% +6\%}{2}+0.25 =5.75\%[/latex]

The interest rate on the five-year bond would be 8%.

[latex]i_{nt} =\frac{i_{t}+i^{e}_{t+1} +i^{e}_{t+2} +...+i^{e}_{t+(n-1)} }{n} +l_{nt}[/latex]

where

[latex]i_{t}[/latex] = year 1 interest rate = 5%

[latex]i^{e}_{t+1}[/latex] = year 2 interest rate = 6%

[latex]i^{e}_{t+2}[/latex] = year 3 interest rate = 7%

[latex]i^{e}_{t+3}[/latex] = year 4 interest rate = 8%

[latex]i^{e}_{t+4}[/latex] = year 5 interest rate = 9%

[latex]l_{2t}[/latex] = liquidity premium = 1%

[latex]n[/latex] = number of years = 5

Thus,

[latex]i_{5t} =\frac{5\%+6\%+7\%+8\%+9\%}{5} +1\%=8.0\%[/latex]

If you did similar calculations for the one-, three-, and four-year interest rates, the one-year to five-year interest rates would be as follows: 5.0%, 5.75%, 6.5%, 7.25%, and 8.0%, respectively. Comparing these findings with those for the pure expectations theory, we can see that the liquidity preference theory produces yield curves that slope more steeply upward because of investors’ preferences for short-term bonds.

Question 5.4: As in Example 3, let’s suppose that the one-year interest ra...

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