One-year T-bill rates over the next five years are expected to be 4%, 5%, 6%, 6.5%, and 7%. If five year T-bonds are yielding 9.5%, what is the liquidity premium on this bond?

To determine the liquidity premium on the five-year T-bond, we use the following method:

### Step 1: Calculate the Average Expected One-Year T-Bill Rates

The expected one-year T-bill rates over the next five years are given as: 4%, 5%, 6%, 6.5%, and 7%. The average of these rates is calculated as:

\[
\text{Average Expected Rate} = \frac{4\% + 5\% + 6\% + 6.5\% + 7\%}{5} = \frac{28.5\%}{5} = 5.7\%
\]

### Step 2: Compare with the Yield on the Five-Year T-Bond

The yield on the five-year T-bond is given as 9.5%. We compare this yield with the average expected one-year T-bill rates. The difference between the T-bond yield and the average expected T-bill rate represents both the liquidity premium and any risk premium that might be present.

\[
\text{Liquidity Premium} = \text{T-Bond Yield} - \text{Average Expected Rate}
\]
\[
\text{Liquidity Premium} = 9.5\% - 5.7\% = 3.8\%
\]

Thus, the liquidity premium on this bond is **3.8%**.

Would you like more details or have any questions? Here are some related questions:

1. How do liquidity premiums impact bond prices in general?
2. Why might long-term bonds have higher liquidity premiums than short-term bonds?
3. How does the expectation theory relate to T-bond yields?
4. What is the significance of the average expected T-bill rate in bond yield calculations?
5. How does inflation risk influence the yield on bonds?

**Tip**: Long-term bonds typically carry higher liquidity premiums because investors demand compensation for the increased uncertainty over a longer investment period.

One-year T-bill rates over the next five years are expected to be 4%, 5%, 6%, 6.5%, and 7%. If five-year T-bonds are yielding 9.5%, what is the liquidity premium on this bond?

Learn how to calculate the liquidity premium on a five-year T-bond given expected one-year T-bill rates of 4%, 5%, 6%, 6.5%, and 7%, and a T-bond yield of 9.5%. This solution explains the key financial concepts and formulas required to determine the liquidity premium. Suitable for college and university-level finance students.

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