The real risk-free rate is 2.5% and inflation is expected to be 2.75% for the next 2 years. A 2-year Treasury security yields 6.25%. What is the maturity risk premium for the 2-year security? Round your answer to one decimal place.
The real risk-free rate is 2.5% and inflation is expected to be 2.75% for the next 2 years. A 2-year Treasury security yields 6.25%. What is the maturity risk premium for the 2-year security? Round your answer to one decimal place.
Intermediate Financial Management (MindTap Course List)
13th Edition
ISBN:9781337395083
Author:Eugene F. Brigham, Phillip R. Daves
Publisher:Eugene F. Brigham, Phillip R. Daves
Chapter4: Bond Valuation
Section: Chapter Questions
Problem 18P
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![**Title: Calculating Maturity Risk Premium for a 2-Year Treasury Security**
**Question:**
The real risk-free rate is 2.5% and inflation is expected to be 2.75% for the next 2 years. A 2-year Treasury security yields 6.25%. What is the maturity risk premium for the 2-year security? Round your answer to one decimal place.
**Instructions:**
Calculate the maturity risk premium based on the given data. Follow the steps below to understand the components and arrive at the correct answer.
**Key Terms:**
- **Real Risk-Free Rate:** The rate of return on an investment with no risk of financial loss, excluding inflation.
- **Inflation Rate:** The expected percentage increase in prices over a set period.
- **Treasury Security Yield:** The return on investment for a government debt instrument.
- **Maturity Risk Premium:** The extra yield that investors require to hold a longer-term security.
**Calculation Steps:**
1. **Nominal Rate Calculation:**
- Use the Fisher equation to combine the real risk-free rate and expected inflation:
\[
\text{Nominal Rate} = \text{Real Risk-Free Rate} + \text{Inflation Rate} + (\text{Real Risk-Free Rate} \times \text{Inflation Rate})
\]
- Since the product of the real risk-free rate and inflation is typically small, it’s often ignored for simplicity:
\[
\text{Nominal Rate} \approx \text{Real Risk-Free Rate} + \text{Inflation Rate} = 2.5\% + 2.75\% = 5.25\%
\]
2. **Calculate Maturity Risk Premium:**
- The maturity risk premium is the difference between the Treasury security yield and the calculated nominal rate:
\[
\text{Maturity Risk Premium} = \text{Treasury Yield} - \text{Nominal Rate} = 6.25\% - 5.25\% = 1.0\%
\]
**Conclusion:**
The maturity risk premium for the 2-year Treasury security is **1.0%**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37e2f913-30b2-4c8c-98d5-339163057ff1%2Fd45975cd-01f5-46f6-a4ee-4aa5c1e9a4cc%2Fj4hscts_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Maturity Risk Premium for a 2-Year Treasury Security**
**Question:**
The real risk-free rate is 2.5% and inflation is expected to be 2.75% for the next 2 years. A 2-year Treasury security yields 6.25%. What is the maturity risk premium for the 2-year security? Round your answer to one decimal place.
**Instructions:**
Calculate the maturity risk premium based on the given data. Follow the steps below to understand the components and arrive at the correct answer.
**Key Terms:**
- **Real Risk-Free Rate:** The rate of return on an investment with no risk of financial loss, excluding inflation.
- **Inflation Rate:** The expected percentage increase in prices over a set period.
- **Treasury Security Yield:** The return on investment for a government debt instrument.
- **Maturity Risk Premium:** The extra yield that investors require to hold a longer-term security.
**Calculation Steps:**
1. **Nominal Rate Calculation:**
- Use the Fisher equation to combine the real risk-free rate and expected inflation:
\[
\text{Nominal Rate} = \text{Real Risk-Free Rate} + \text{Inflation Rate} + (\text{Real Risk-Free Rate} \times \text{Inflation Rate})
\]
- Since the product of the real risk-free rate and inflation is typically small, it’s often ignored for simplicity:
\[
\text{Nominal Rate} \approx \text{Real Risk-Free Rate} + \text{Inflation Rate} = 2.5\% + 2.75\% = 5.25\%
\]
2. **Calculate Maturity Risk Premium:**
- The maturity risk premium is the difference between the Treasury security yield and the calculated nominal rate:
\[
\text{Maturity Risk Premium} = \text{Treasury Yield} - \text{Nominal Rate} = 6.25\% - 5.25\% = 1.0\%
\]
**Conclusion:**
The maturity risk premium for the 2-year Treasury security is **1.0%**.
Expert Solution
Step 1
Information Provided:
- Real risk-free rate = 2.5%
- Inflation = 2.75%
- Return on Treasury security (yield) = 6.25%
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