Question

Problem 5-19
Maturity Risk Premiums

Assume that the real risk-free rate, r*, is 3% and that inflation is expected to be 7% in Year 1, 6% in Year 2, and 4% thereafter. Assume also that all Treasury securities are highly liquid and free of default risk. If 2-year and 5-year Treasury notes both yield 10%, what is the difference in the maturity risk premiums (MRPs) on the two notes; that is, what is MRP₅ minus MRP₂? Round your answer to two decimal places.

Answer 1

The yield on the 2 year security is :

Rf = 3%

Inflation for year 1 : 7%

Inflation for year 2 :6%

Inflation for year 3 and year 4 is = 4%

10% = risk free rate + inflation premium + maturity risk premium

or, 10% = 3% + (7% +6%/2) + MRP

or, MRP 2 = 0.5%

Now, MRP5,

yield on the 5 year treasury security = R f + inflation premium + MRP5

or, 10% = 3% + (7+6+4+4+4/5) + MRP5

MRP5 = 2%

MRP5 -MRP2
= 2 % - 0.5%

= 1.5%