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20 November, 03:33

The real risk-free rate is 2.05%. Inflation is expected to be 3.05% this year, 4.75% next year, and 2.3% thereafter. The maturity risk premium is estimated to be 0.05 (t - 1) %, where t=5 number of years to maturity. What is the yield on a 7-year Treasury note?

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  1. 20 November, 03:57
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    The yield on a 7-year Treasury note is 5.11%.

    Explanation:

    Given

    Real risk-free rate = r * = 2.05%. Inflation Rate = 3.05% this year, 4.75% next year, and 2.3% thereafter.

    Time = 7 years

    Maturity risk premium, MRP = 0.05 (t - 1) %

    First, we'll calculate the average inflation rate for the next 7 years.

    This is given by:

    ((3.05% * 1) + (4.75% * 1) + (2.3% * (7-2))) / 7

    This is so, because the Inflation Rate is 3.05% this year (1 year), 4.75% next year (1 year), and 2.3% thereafter (7-2=5 years).

    So, we have

    (3.05% + 4.75% + 11.5%) / 7

    = 19.3%/7

    = 2.757142857142857%

    = 2.76%

    So, IP7 = 2.76%

    The yield on a 7-year Treasury note is calculated by

    r * + IP7 + MRP

    Yield = 2.05% + 2.76% + 0.05 (t - 1) % where t = 7

    Yield = 4.81% + 0.05 (7-1) %

    Yield = 4.81% + 0.05*6%

    Yield = 4.81% + 0.3%

    Yield = 5.11%
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