Question

An investor in Treasury securities expects inflation to be 1.6% in Year 1, 3.05% in Year 2, and 3.85% each year thereafter. Assume that the real risk-free rate is 2.35% and that this rate will remain constant. Three-year Treasury securities yield 6.80%, while 5-year Treasury securities yield 8.10%. 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.

Answer 1

The difference between two securities is 0.89%.

Step-by-step explanation:

Inflation premium for the next three and five years:

Inflation premium (3) = (1.6% + 3.05% + 3.85%) ÷ 3

= 2.83%

Inflation premium (5) = (1.6% + 3.05% + 3.85% + 3.85% + 3.85%) ÷ 5

= 3.24%

Real risk-free rate = 2.35%

Since default premium and liquidity premium are zero on treasury bonds, we can now solve for the maturity risk premium:

Three-year Treasury securities = Real risk-free rate + Inflation premium (3) + MRP(3)

6.80% = 2.35% + 2.83% + MRP(3)

MRP (3) = 1.62%

Similarly,

5-year Treasury securities = Real risk-free rate + Inflation premium (5) + MRP(5)

8.10% = 2.35% + 3.24% + MRP(3)

MRP (5) = 2.51%

Thus,

MRP5 - MRP3 = 2.51% - 1.62%

= 0.89%

Therefore, the difference between two securities is 0.89%.