Based on economists' forecasts and analysis, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows:
$$\begin{array} { l }
R _ { 1 } \quad = \quad 5.95 p e r c e n t \
E \left( r _ { 2 } \right) = 6.25 p \text { ercent } L _ { 2 } = 0.05 \text { percent } \
E \left( r _ { 3 } \right) = 6.75 p \mathrm { percent } \quad L _ { 3 } = 0.10 \text { percent } \
E \left( r _ { 4 } \right) = \quad 7.15 \text { percent } \quad L _ { 4 } = 0.12 p e r c e n t \
\end{array}$$
Using the liquidity premium theory, what should be the current rate on four-year Treasury securities?

Question

Based on economists' forecasts and analysis, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows:
$$\begin{array} { l } 
R _ { 1 } \quad = \quad 5.95 p e r c e n t \
E \left( r _ { 2 } \right) = 6.25 p \text { ercent } L _ { 2 } = 0.05 \text { percent } \
E \left( r _ { 3 } \right) = 6.75 p \mathrm { percent } \quad L _ { 3 } = 0.10 \text { percent } \
E \left( r _ { 4 } \right) = \quad 7.15 \text { percent } \quad L _ { 4 } = 0.12 p e r c e n t \
\end{array}$$
Using the liquidity premium theory, what should be the current rate on four-year Treasury securities?

Quizplus · Accepted Answer

The liquidity premium theory suggests that long-term interest rates reflect expected short-term rates plus a liquidity premium that increases with the term to maturity. To find the current rate on four-year Treasury securities, we calculate the average expected rate over the four years and add the average liquidity premium. The calculation is as follows:$$ \text{Average expected rate} = \frac{5.95\% + 6.25\% + 6.75\% + 7.15\%}{4} = 6.525\% $$$$ \text{Average liquidity premium} = \frac{0\% + 0.05\% + 0.10\% + 0.12\%}{4} = 0.0675\% $$$$ \text{Current rate on four-year Treasury securities} = 6.525\% + 0.0675\% = 6.5925\% $$Rounded to two decimal places, the current rate on four-year Treasury securities is approximately 6.59 percent, which corresponds to choice A.

Based on Economists' Forecasts and Analysis, One-Year Treasury Bill Rates