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: Using the liquidity premium theory, what is the current rate on a four-year Treasury security?
$$\begin{array} { l l }
R _ { 1 } & = 6.65 \% \
E \left( r _ { 2 } \right) & = 7.75 \% L _ { 2 } = 0.10 \% \
E \left( r _ { 3 } \right) & = 7.85 \% L _ { 3 } = 0.20 \% \
E \left( r _ { 4 } \right) & = 8.15 \% L _ { 4 } = 0.25 \%
\end{array}$$

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: Using the liquidity premium theory, what is the current rate on a four-year Treasury security?
$$\begin{array} { l l } 
R _ { 1 } & = 6.65 \% \
E \left( r _ { 2 } \right) & = 7.75 \% L _ { 2 } = 0.10 \% \
E \left( r _ { 3 } \right) & = 7.85 \% L _ { 3 } = 0.20 \% \
E \left( r _ { 4 } \right) & = 8.15 \% L _ { 4 } = 0.25 \%
\end{array}$$

Quizplus · Accepted Answer

The correct answer is A because the current rate on a four-year Treasury security is 7.736 percent. This is calculated using the liquidity premium theory, which states that the yield on a long-term bond is equal to the average of the expected short-term rates over the life of the bond, plus a liquidity premium. In this case, the average of the expected short-term rates over the next four years is 7.736 percent, and the liquidity premium is 0.10 percent, so the yield on a four-year Treasury security is 7.736 percent.

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