Question

The Wall Street Journal reports that the rate on 5-year Treasury securities is 6.45 percent and the rate on 6-year Treasury securities is 6.90 percent. The 1-year risk-free rate expected in five years is, E(₆r₁), is 7.50 percent. According to the liquidity premium hypotheses, what is the liquidity premium on the 6-year Treasury security, L₆? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Liquidity premium:______

Answer 1

First, we calculate the rate on the 6-year security without any liquidity premium. Let us say this is R. Then :

(1 + rate on 5-year security)⁵ * (1 + E(₆r₁)) = (1 + R)⁶ (This is because investing at the 5-year for 5 years, and reinvesting the proceeds for 1 year at the expected risk free rate in 5 years, should yield the same as investing at the 6-year rate for 6 years).

(1 + 6.45%)⁵ * (1 + 7.5%)) = (1 + R)⁶

R = ((1 + 6.45%)⁵ * (1 + 7.5%))^1/6 - 1

R = 6.62%

However, the actual 6-year rate is 6.9%. Therefore, the difference is due to liquidity premium.

Liquidity premium = 6.9% - 6.62% = 0.28%