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Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977

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BuyFindarrow_forward

Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977
Textbook Problem

MATURITY RISK PREMIUM 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 MRP5 – MRP3?

Summary Introduction

To identify: The difference in maturity risk premiums for 5 years and 3 years.

Maturity Risk Premium:

A premium, which is paid by the borrower to its lender in the form of compensation of interest rate uncertainty in the regards of maturity risk is known as maturity risk premium.

Explanation

Solution:

Year 3:

Given,

The yield is 6.25%.

The risk free rate is 2.75%.

The average inflation premium on 3 year treasury security is 3.1%. (Working note)

Formula to calculate the maturity risk premium derives from the formula of corporate bond yield,

r=r*+IP+MRPMRP=r(r*+IP)

Where,

  • MRP is maturity risk premium.
  • r is corporate bond yield.
  • r* is risk free rate.
  • IP is inflation premium.

Substitute 6.25% for r, 2.75% for r* and 3.1% for IP.

MRP3=6.25%(2.75%+3.1%)=6.25%5.85%=0.4%

The maturity risk premium is on year 3 treasury security is 0.40%.

Year 5

The yield is 6.8%. (Given)

The risk free rate is 2.75%. (Given)

The inflation premium on 5 year treasury security is 3.3%. (Working note)

Substitute 6.8% for r, 2.75% for r* and 3.3% for IP.

MRP5=6.8%(2.75%+3.3%)=6.8%6.05%=0.75%

The maturity risk premium is on year 5 treasury security is 0.75%.

Compute the difference between two maturity risks

Calculated,

MRP3 is 0.40%.

MRP5 is 0.75%.

Formula to calculate the difference between two maturity risks,

DifferencebetweenTwoMaturityRisks=MRP5MRP3

Substitute 0.40% for MRP3 and 0.75% for MRP5.

DifferencebetweenTwoMaturityRisks=0.75%0.40%=0

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