Math Problem Statement

If 10-year T-bonds have a yield of 6.3%, 10-year corporate bonds yield 8.5%, the maturity risk premium on all 10-year bonds is 1.3%, and corporate bonds have a 0.5% liquidity premium versus a zero liquidity premium for T-bonds, what is the default risk premium on the corporate bond? Question 19Select one:

a. 1.90%

b. 1.70%

c. 2.30%

d. 2.53%

e. 2.78%

Solution

To calculate the default risk premium (DRP) on the corporate bond, we need to use the following relationship for the yield on corporate bonds:

Corporate bond yield=T-bond yield+Default risk premium+Liquidity premium+Maturity risk premium\text{Corporate bond yield} = \text{T-bond yield} + \text{Default risk premium} + \text{Liquidity premium} + \text{Maturity risk premium}

We are given the following dataTo calculate the default risk premium (DRP) on the corporate bond, we need to use the following relationship for the yield on corporate bonds:

Corporate bond yield=T-bond yield+Default risk premium+Liquidity premium+Maturity risk premium\text{Corporate bond yield} = \text{T-bond yield} + \text{Default risk premium} + \text{Liquidity premium} + \text{Maturity risk premium}

We are given the following

  • T-bond yield = 6.3%
  • Corporate bond yield = 8.5%
  • Maturity risk premium (MRP) = 1.3% (same for both T-bonds and corporate bonds)
  • Liquidity premium (LP) on corporate bonds = 0.5%, and for T-bonds = 0% (no liquidity premium)

Now, rearranging the formula to solve for the default risk premium (DRP):

Default risk premium=Corporate bond yieldT-bond yieldLiquidity premiumMaturity risk premium\text{Default risk premium} = \text{Corporate bond yield} - \text{T-bond yield} - \text{Liquidity premium} - \text{Maturity risk premium}

Substituting the given values:

Default risk premium=8.5%6.3%0.5%1.3%\text{Default risk premium} = 8.5\% - 6.3\% - 0.5\% - 1.3\%

Let's calculate that:

Default risk premium=8.5%6.3%0.5%1.3%=0.4%\text{Default risk premium} = 8.5\% - 6.3\% - 0.5\% - 1.3\% = 0.4\%

So, the default risk premium on the corporate bond is 0.4%.

This is quite far from the provided answer choices, so there might be an error. Let me check again or verify...

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Bond Yields
Risk Premiums
Financial Algebra

Formulas

Corporate bond yield = T-bond yield + Default risk premium + Liquidity premium + Maturity risk premium
Default risk premium = Corporate bond yield - T-bond yield - Liquidity premium - Maturity risk premium

Theorems

-

Suitable Grade Level

Undergraduate Finance