The table below shows current and expected future one-year...

The table below shows current and expected future one-year interest rates, as well as current interest rates on multiyear bonds. Use the table to calculate the liquidity premium for each multiyear bond. $$\begin{array}{|ccc|} \hline \text { Year } & \begin{array}{l} \text { One-Year } \\ \text { Bond Rate } \end{array} & \begin{array}{l} \text { Multiyear } \\ \text { Bond Rate } \end{array} \\ \hline 1 & 2 \% & 2 \% \\ 2 & 3 \% & 3 \% \\ 3 & 4 \% & 5 \% \\ 4 & 6 \% & 6 \% \\ 5 & 7 \% & 8 \% \\ \hline \end{array}$$

The table below shows current and expected future one-year interest rates, as well as current interest rates on multiyear bonds. Use the table to calculate the liquidity premium for each multiyear bond.
$$\begin{array}{|ccc|}
\hline \text { Year } & \begin{array}{l}
\text { One-Year } \\
\text { Bond Rate }
\end{array} & \begin{array}{l}
\text { Multiyear } \\
\text { Bond Rate }
\end{array} \\
\hline 1 & 2 \% & 2 \% \\
2 & 3 \% & 3 \% \\
3 & 4 \% & 5 \% \\
4 & 6 \% & 6 \% \\
5 & 7 \% & 8 \% \\
\hline
\end{array}$$

Key Concepts

Liquidity Premium

The liquidity premium is the extra yield that investors require to hold a bond that is less liquid or has a longer maturity compared to shorter-term, more liquid bonds. It compensates for the additional risks, such as price volatility and marketability issues, that come with longer investment horizons.

Term Structure of Interest Rates

The term structure of interest rates represents the relationship between the yields on bonds of different maturities. It reflects market expectations about future short-term interest rates, inflation, and the risks associated with holding longer-term securities, and is often visualized as a yield curve.

Expectations Theory

Expectations theory suggests that the yield on a long-term bond is determined by current and expected future short-term interest rates. Differences between the calculated yields from expected short-term rates and the observed long-term yields are often attributed to factors like liquidity premiums or risk premiums that investors demand.

Transcript

00:01 So, before answering our question, let us understand liquidity premium.

00:08 Liquidity premium.

00:14 So liquidity premium in bond valuation seeks to explain the shape of the yield curve.

00:20 This theory assumes that the higher the risk, the amount of return and investor will get is also higher.

00:28 So higher the risk, the return and investor gets will also be higher.

00:39 Higher the return.

00:44 So liquidity of a bond refers to how quickly the investor can sell the bond without having to lower its price.

00:52 Now liquidity premium for a given year in the current rate on a multi -year horizon bond is much more greater than the amount of average one -year interest rate over the over the horizon.

01:07 We will take the average of the one -year interest rate.

01:11 So, basically, basically it is the current rate on a multi -year bond rate of multi -year bond minus the average one year interest rate, average one year interest rate.

01:47 So basically liquided premium is the extra return for holding longer maturity over liquid bond.

01:53 It can be computed as the annual liquidity premium for each year, the bond is held or as the total liquidity premium of the bond.

02:01 So liquidity premium is calculated with the help of the following equation.

02:08 Liquidity premium is calculated with the help of following equation.

02:21 It is interest minus.

02:36 We will first note this down and then we will understand the following equation.

02:44 T plus 1 plus with the help of this equation we will be able to solve the problem associated with the question.

03:17 Now let's understand this...

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