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Find the yield on a 1-year, 5 - year and 15-year Treasuries if the risk free...

Find the yield on a 1-year, 5 - year and 15-year Treasuries if the risk free rate is 0.25%, inflation rate this year is 3%, 3.2% next year and 4% after that. Maturity risk premium is defined as 0.07*(t-1)%.

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Answer #1

1-year Treasury Bond:

Real Risk-free Rate = 0.25%
Inflation Premium = 3.00%

Maturity Risk Premium = 0.07 * (t - 1)%
Maturity Risk Premium = 0.07 * (1 - 1)%
Maturity Risk Premium = 0.00%

Yield on 1-year Treasury Bond = Real Risk-free Rate + Inflation Premium + Maturity Risk Premium
Yield on 1-year Treasury Bond = 0.25% + 3.00% + 0.00%
Yield on 1-year Treasury Bond = 3.25%

5-year Treasury Bond:

Real Risk-free Rate = 0.25%

Inflation Premium = [3.00% + 3.20% + 3 * 4.00%] / 5
Inflation Premium = 18.20% / 5
Inflation Premium = 3.64%

Maturity Risk Premium = 0.07 * (t - 1)%
Maturity Risk Premium = 0.07 * (5 - 1)%
Maturity Risk Premium = 0.28%

Yield on 1-year Treasury Bond = Real Risk-free Rate + Inflation Premium + Maturity Risk Premium
Yield on 1-year Treasury Bond = 0.25% + 3.64% + 0.28%
Yield on 1-year Treasury Bond = 4.17%

15-year Treasury Bond:

Real Risk-free Rate = 0.25%

Inflation Premium = [3.00% + 3.20% + 13 * 4.00%] / 15
Inflation Premium = 58.20% / 15
Inflation Premium = 3.88%

Maturity Risk Premium = 0.07 * (t - 1)%
Maturity Risk Premium = 0.07 * (15 - 1)%
Maturity Risk Premium = 0.98%

Yield on 1-year Treasury Bond = Real Risk-free Rate + Inflation Premium + Maturity Risk Premium
Yield on 1-year Treasury Bond = 0.25% + 3.88% + 0.98%
Yield on 1-year Treasury Bond = 5.11%

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