Question

The table below shows current and expected future one-year interest rates, as well as current interest rates on multi-year bonds. Use the table to calculate the liquidity premium for each multiyear bond.

Short answer

The multiyear bond rate is subtracted from the average of the one-year bond rates for each of the years considered.

Step-by-step solution

Definition

A liquidity premium is an additional return expected by investors for instruments that are not easily traded. It could not be easily converted into cash by selling at a fair price in the financial market. Long-term interest rates include a premium for holding a bond for an extended period of time.

Explanation

The liquidity premium could be calculated as:

For each year, the given multiyear bond rate is being subtracted from the average of one-year bond rates of each of the years is taken into consideration.

$$\begin{gathered} {\text{I}}_{11}=2-\frac{2}{1} \\ =0 \\ {I}_{21}=4-\frac{2+4}{2} \\ =1\% \\ {I}_{31}=6-\frac{2+4+5}{3} \\ =2.33\% \\ {I}_{41}=9-\frac{2+4+5+8}{4} \\ =4.25\% \\ {I}_{51}=12-\frac{2+4+5+8+11}{5} \\ =6\% \\ \text{Hence,theliquiditypremiumsare}{I}_{11}=0\%,I_{21}=1\%,I_{31}=2.33\%,I_{41}=4.25\%,I_{51}=6\% \end{gathered}$$