Question

An investor in Treasury securities expects inflation to be 2.4% in Year 1, 3.1% in Year 2, and 3.75% each year thereafter. Assume that the real risk-free rate is 1.65% and that this rate will remain constant. Three-year Treasury securities yield 6.60%, while 5-year Treasury securities yield 8.00%. What is the difference in the maturity risk premiums (MRPs) on the two securities; that is, what is MRP₅ - MRP₃? Do not round intermediate calculations. Round your answer to two decimal places.

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Answer 1

IP3 = (2.4% + 3.1% + 3.75%) / 3 = 9.25% / 3 = 3.0833%

IP5 = (2.4% + 3.1% + 3.75% + 3.75% + 3.75%) / 5 = 16.75% / 5 = 3.35%

3 year treasury security yield = Real risk free rate + IP3 + MRP3
6.60% = 1.65% + 3.0833% + MRP3
MRP3 = 6.60% - (1.65% + 3.0833%)
MRP3 = 1.8667%

5 year treasury security yield = Real risk free rate + IP5 + MRP5
8% = 1.65% + 3.35% + MRP5
MRP5 = 8% - (1.65% + 3.35%)
MRP5 = 3%

Difference in the maturity risk premiums (MRPs) on the two securities = MRP5 - MRP3
= 3% - 1.8667%
= 1.1333% or 1.13%

Difference in the maturity risk premiums (MRPs) on the two securities = 1.13%