The Wall Street Journal reports that the rate on 5-year Treasury securities is 5.65 percent and the rate on 6-year Treasury securities is 6.00 percent. The 1-year interest rate expected in five years,  E(r16)
  , is 6.60 percent. According to the liquidity premium hypotheses, what is the liquidity premium on the 6-year Treasury security,  L6
  ?

The liquidity premium hypothesis states that the interest rate on a long-term bond is equal to the average of current and expected future short-term interest rates, plus a liquidity premium that compensates investors for holding longer-term securities, which are generally considered riskier due to interest rate fluctuations.

The formula for the yield on a longer-term Treasury security, according to the liquidity premium hypothesis, is:

\[
r_n = \frac{1}{n} \left( r_1 + E(r_2) + E(r_3) + \cdots + E(r_n) \right) + L_n
\]

Where:
- \( r_n \) is the rate on an \( n \)-year Treasury security,
- \( r_1 \) is the current 1-year interest rate,
- \( E(r_i) \) is the expected 1-year rate for year \( i \),
- \( L_n \) is the liquidity premium for an \( n \)-year Treasury security.

For your case, we know the following:
- \( r_5 = 5.65\% \) (5-year Treasury rate),
- \( r_6 = 6.00\% \) (6-year Treasury rate),
- \( E(r_{16}) = 6.60\% \) (expected 1-year interest rate in 5 years).

We can rearrange the equation to solve for the liquidity premium \( L_6 \):

\[
r_6 = \frac{1}{6} \left( r_1 + E(r_2) + E(r_3) + E(r_4) + E(r_5) + E(r_6) \right) + L_6
\]

Since we don't have all of the individual expected interest rates for the first few years, we will approximate them by using the given 5-year and 6-year rates to infer the average future rates.

To compute \( L_6 \), the liquidity premium on the 6-year security, follow these steps:

1. **Calculate the average of the expected future rates** up to 5 years using the information provided.
   
   Given that the average interest rate over 5 years is \( 5.65\% \), we can assume the current 1-year rate and expected rates average out to this value.

2. **Solve for the liquidity premium using the 6-year rate** \( r_6 = 6.00\% \) and expected 1-year rate in year 6 \( E(r_{16}) = 6.60\% \).

Let me calculate this for you.The liquidity premium on the 6-year Treasury security, \( L_6 \), is approximately **0.192%**.

Would you like further details or have any questions? Here are 5 related questions to deepen your understanding:

1. How does the liquidity premium hypothesis differ from the expectations hypothesis?
2. What factors can cause the liquidity premium to change over time?
3. Can the liquidity premium ever be negative? If so, under what conditions?
4. How do short-term interest rate expectations affect long-term bond yields?
5. What other models exist to explain the term structure of interest rates?

**Tip:** The liquidity premium compensates for the additional risk of holding longer-term securities, which can fluctuate more with interest rate changes.

The Wall Street Journal reports that the rate on 5-year Treasury securities is 5.65 percent and the rate on 6-year Treasury securities is 6.00 percent. The 1-year interest rate expected in five years, E(r16), is 6.60 percent. According to the liquidity premium hypotheses, what is the liquidity premium on the 6-year Treasury security, L6?

Discover how to calculate the liquidity premium on a 6-year Treasury security using the liquidity premium hypothesis. This example utilizes current and expected interest rates to solve for L6 with rates provided by The Wall Street Journal. Suitable for finance and economics students.

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