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9 June, 11:26

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.

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  1. 9 June, 11:42
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    The difference between two securities is 0.89%.

    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%.
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