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Assume that the real risk-free rate of return, r*, is 1%, and it will remain at...

Assume that the real risk-free rate of return, r*, is 1%, and it will remain at that level far into the future. Also assume that maturity risk premium on Treasury bonds increase from zero for bonds that mature in one year or less to a maximum of 2%, and MRP increases by 0.2% for each year to maturity that is greater than one year – that is, MRP equals 0.2% for two-year bond, 0.4% for a three-year bond, and so forth. Following are the expected inflation rates for the next five years:

Year

Inflation Rate

2018

1%

2019

1.5%

2020

2%

2021

2.5%

Compute the interest rate for 1, 2, 3, and 4-year bond.

If inflation is expected to equal 3% every year after 2021, what should the interest rate be for 5- through 20-year bond?

Draw a graph of the yield curve.

Solutions

Expert Solution

1) Interest rate for 1, 2, 3, and 4-year bond

Bonds maturing year Risk free rate Maturity risk premiun Inflation rate Interest rate
2018 - 1 year bond 1.0% 0.0% 1.0% 2.0%
2019 - 2 year bond 1.0% 0.2% 1.5% 2.7%
2020 -3 year bond 1.0% 0.4% 2.0% 3.4%
2021 - 4 year bond 1.0% 0.6% 2.5% 4.1%

Excel formula:

2) If inflation is 3% after 2021 then interest rate from 2021 to 2036 bonds:

Bonds maturing year Risk free rate Maturity risk premiun Inflation rate Interest rate
2018 - 1 year bond 1.0% 0.0% 1.0% 2.0%
2019 - 2 year bond 1.0% 0.2% 1.5% 2.7%
2020 -3 year bond 1.0% 0.4% 2.0% 3.4%
2021 - 4 year bond 1.0% 0.6% 2.5% 4.1%
2022 1.0% 0.8% 3.0% 4.8%
2023 1.0% 1.0% 3.0% 5.0%
2024 1.0% 1.2% 3.0% 5.2%
2025 1.0% 1.4% 3.0% 5.4%
2026 1.0% 1.6% 3.0% 5.6%
2027 1.0% 1.8% 3.0% 5.8%
2028 1.0% 2.0% 3.0% 6.0%
2029 1.0% 2.0% 3.0% 6.0%
2030 1.0% 2.0% 3.0% 6.0%
2031 1.0% 2.0% 3.0% 6.0%
2032 1.0% 2.0% 3.0% 6.0%
2033 1.0% 2.0% 3.0% 6.0%
2034 1.0% 2.0% 3.0% 6.0%
2035 1.0% 2.0% 3.0% 6.0%
2036 1.0% 2.0% 3.0% 6.0%
2037 1.0% 2.0% 3.0% 6.0%

Graph:

jeff jeffy answered 1 year ago
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