1 A particular securitys equilibrium rate of return is 8 per

1- A particular security’s equilibrium rate of return is 8 percent. For all securities, the inflation risk premium is 3.35 percent and the real risk-free rate is 2.2 percent. The security’s liquidity risk premium is 0.55 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the security’s default risk premium. (Round your answer to 2 decimal places. (e.g., 32.16))

Default risk premium %

2- Suppose we observe the following rates: ₁R₁ = 5.2%, ₁R₂ = 6.1%, and E(₂r₁) = 5.2%. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2? (Round your intermediate calculations to 5 decimal places and final answer to 2 decimal places. (e.g., 32.16))

Solution

Question 1

Equilibrium rate of return = Real Risk free rate + Inflation risk premium + Liquidity risk premium + Maturity risk premium + Default risk premium

Default risk premium = 8% - 2.2% - 3.35% - 0.55% - 0.85%

Default risk premium = 1.05%

Question 2

Let the Liquidity premium in Year 2 be L2

Based on the pure expectations theory, return earned in a 2 year bond should be equal to return earned in a 1 year bond and post its maturity again invested in a one year bond (such that investment duration is still 2 years).

1 + 1R2 = {(1 + 1R1)(1 + E(2r1) + L2)}^1/2

1.061 = {(1.052)(1.052 + L2)}^1/2

1.1257 = (1.052)(1.052 + L2)

1.0701 = (1.052 + L2)

L2 = 1.81%