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A Treasury bond that matures in 10 years has a yield of 6\%. A 10-year corporate bond has a yield of \(8 \%\). Assume that the liquidity premium on the corporate bond is \(0.5 \%\). What is the default risk premium on the corporate bond?

Short Answer

Expert verified
The default risk premium on the corporate bond is 1.5%.

Step by step solution

01

Understanding the Problem

A Treasury bond and a corporate bond both mature in 10 years. The Treasury bond has a yield of 6%, while the corporate bond yields 8%. We assume the corporate bond has an additional 0.5% liquidity premium. We need to find the default risk premium on the corporate bond.
02

Formula Setup

To find the default risk premium, we need to use this relation: \( \text{Corporate Bond Yield} = \text{Treasury Bond Yield} + \text{Default Risk Premium} + \text{Liquidity Premium} \). We need to solve for the Default Risk Premium.
03

Plug in the Values

The Treasury Bond Yield is 6%, the Corporate Bond Yield is 8%, and the Liquidity Premium is 0.5%. Substituting these into the equation, we have:\[ 8\% = 6\% + \text{Default Risk Premium} + 0.5\% \].
04

Solving the Equation

Re-order the equation to solve for the Default Risk Premium:\[ \text{Default Risk Premium} = 8\% - 6\% - 0.5\% \].
05

Calculate Default Risk Premium

Subtract to find the Default Risk Premium:\[ \text{Default Risk Premium} = 1.5\% \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Treasury Bond Yield
The treasury bond yield represents the return investors can expect from holding a government-issued treasury bond until maturity. Since treasury bonds are backed by the government, they are considered risk-free investments. This makes their yield an essential benchmark for evaluating other investments.
Treasury bonds are attractive because they offer stable returns while minimizing risk. Investors often compare the yields of treasury bonds with those of other securities to decide where to allocate their funds. Treasury bond yields can also reflect the general economic conditions, such as inflation expectations and interest rate movements.
  • If inflation is expected to rise, treasury bond yields might increase to compensate investors for decreasing purchasing power.
  • Conversely, if inflation is expected to be low, yields may decrease.
This yield provides a baseline against which other bond yields, such as corporate bond yields, are measured.
Corporate Bond Yield
Corporate bond yield is the return investors earn from buying a company's bond and holding it until it matures. It includes compensation for the additional risks associated with corporate bonds, compared to treasury bonds.
Corporate bonds are considered riskier than treasury bonds due to the potential for a company's financial instability or bankruptcy, which might lead to default on their interest or principal payments.
  • The yield on a corporate bond is usually higher than that on a treasury bond to attract investors to take on these inherent risks.
  • The corporate bond yield is influenced by the company's creditworthiness, market conditions, and the business environment.
The difference in yield between corporate and treasury bonds is partly due to the default risk premium and liquidity premium, which investors need to weigh in their investment decision-making process.
Liquidity Premium
The liquidity premium compensates investors for the risk associated with holding less-liquid or harder-to-trade bonds. Liquidity refers to how quickly and easily an asset can be converted into cash without significantly affecting its price. If a bond or security is liquid, selling it quickly will not greatly impact its price.
Corporate bonds often carry a liquidity premium because:
  • They might not be as easy to sell as treasury bonds, especially if they're issued by smaller or less-known companies.
  • It compensates investors for this potential inconvenience and risk.
In our exercise, a liquidity premium of 0.5% is factored into the yield of the corporate bond. When analyzing bonds, investors must consider this premium along with other factors like default risk to make informed decisions.
Bond Yield Calculation
Bond yield calculation involves adding various premiums to the "risk-free" rate of treasury bonds. To calculate the yield on a corporate bond, you need to consider multiple components.

Components of Bond Yield:

  • Treasury Bond Yield: The foundational "risk-free" rate.
  • Default Risk Premium: Compensation for the chance that a company may fail to make payments.
  • Liquidity Premium: Compensation for potential difficulties in trading the bond.
The sum of these factors gives the total yield on a corporate bond.
Given the calculated formula:\[ \text{Corporate Bond Yield} = \text{Treasury Bond Yield} + \text{Default Risk Premium} + \text{Liquidity Premium} \]One can solve for any missing component as demonstrated in our problem by substituting known values to find the unknown default risk premium.

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Most popular questions from this chapter

INFLATION Due to a recession, expected inflation this year is only \(3 \%\). However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above \(3 \%\) Assume that the expectations theory holds and the real risk-free rate is \(\mathrm{r}^{*}=2 \% .\) If the yield on 3 -year Treasury bonds equals the 1 -year yield plus \(2 \%,\) what inflation rate is expected after Year 1?

An investor in Treasury securities expects inflation to be \(2.5 \%\) in Year \(1,3.2 \%\) in Year \(2,\) and \(3.6 \%\) each year thereafter. Assume that the real risk-free rate is \(2.75 \%\) and that this rate will remain constant. Three-year Treasury securities yield \(6.25 \%\) while 5 -year Treasury securities yield \(6.80 \% .\) What is the difference in the maturity risk premiums (MRPs) on the two securities; that is, what is \(\mathrm{MRP}_{5}-\mathrm{MRP}_{3} ?\)

The real risk-free rate, r", is 2.5\%. Inflation is expected to average \(2.8 \%\) a year for the next 4 years, after which time inflation is expected to average \(3.75 \%\) a year. Assume that there is no maturity risk premium. An 8 -year corporate bond has a yield of \(8.3 \%,\) which includes a liquidity premium of \(0.75 \% .\) What is its default risk premium?

Interest rates on 4-year Treasury securities are currently \(7 \%\) while 6 -year Treasury securities yield \(7.5 \%\). If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now?

The following yields on U.S. Treasury securities were taken from a recent financial publication: $$\begin{array}{ll} \text { Term } & \text { Rate } \\ \hline 6 \text { months } & 5.1 \% \\ \text { 1 year } & 5.5 \\ \text { 2 years } & 5.6 \\ \text { 3 years } & 5.7 \\ \text { 4 years } & 5.8 \\ \text { 5 years } & 6.0 \\ \text { 10 years } & 6.1 \\ \text { 20 years } & 6.5 \\ \text { 30 years } & 6.3 \end{array}$$ a. Plot a yield curve based on these data. b. What type of yield curve is shown? c. What information does this graph tell you? d. Based on this yield curve, if you needed to borrow money for longer than 1 year, would it make sense for you to borrow short-term and renew the loan or borrow long-term? Explain.

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