1.The real risk-free rate is 4%. Inflation is expected to be 3% this year, 5% ne

Question

1.The real risk-free rate is 4%. Inflation is expected to be 3% this year, 5% next year, and then 5% thereafter. The maturity risk premium is estimated to be 0.0003 x (t - 1), where t = number of years to maturity. What is the nominal interest rate on a 7-year Treasury security?

2.

Assume that the real risk-free rate, r*, is 2% and that inflation is expected to be 8% in Year 1, 5% in Year 2, and 4% thereafter. Assume also that all Treasury securities are highly liquid and free of default risk. If 2-year and 5-year Treasury notes both yield 10%, what is the difference in the maturity risk premiums (MRPs) on the two notes; that is, what is MRP5 minus MRP2? Round your answer to two decimal places.

3.

Because of a recession, the inflation rate expected for the coming year is only 3%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3%. Assume that the real risk-free rate is r* = 2% for all maturities and that there are no maturity premiums. If 3-year Treasury notes yield 2 percentage points more than 1-year notes, what inflation rate is expected after Year 1?

Explanation / Answer

1.The real risk-free rate is 4%. Inflation is expected to be 3% this year, 5% next year, and then 5% thereafter. The maturity risk premium is estimated to be 0.0003 x (t - 1), where t = number of years to maturity. What is the nominal interest rate on a 7-year Treasury security?

Inflation for 7 years = (3%+ 5%*6)/7= 4.71%

nominal interest rate on a 7-year Treasury security = 4% + 4.71% + 0.0003 * (7 - 1)= 8.89%

2. Assume that the real risk-free rate, r*, is 2% and that inflation is expected to be 8% in Year 1, 5% in Year 2, and 4% thereafter. Assume also that all Treasury securities are highly liquid and free of default risk. If 2-year and 5-year Treasury notes both yield 10%, what is the difference in the maturity risk premiums (MRPs) on the two notes; that is, what is MRP5 minus MRP2? Round your answer to two decimal places.

Inflation for 2 year note = (8%+5%)/2= 6.5%

Inflation for 5 year note = (8%+5% + 4%*3)/5= 5%

Yield on 2 year note = 2%+ 6.5%+ MRP2 = 8.5%+ MRP2

Yield on 5 year note = 2%+ 5%+ MRP5= 7%+ MRP5

8.5%+ MRP2 = 7%+ MRP5

MRP5- MRP2 = 8.5%-7% = 1.5%

3. Because of a recession, the inflation rate expected for the coming year is only 3%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3%. Assume that the real risk-free rate is r* = 2% for all maturities and that there are no maturity premiums. If 3-year Treasury notes yield 2 percentage points more than 1-year notes, what inflation rate is expected after Year 1?

Let inflation rate is expected after Year 1 = i

3-year Treasury notes yield = 2% + (3%+ i+i)/3

1-year Treasury notes yield = 2% + (3%)

2% + (3%+ i+i)/3 = 2% + 2% + (3%)

(3%+ i+i)/3 = 5%

2i = 12%

i= 6%

inflation rate is expected after Year 1 = 6%

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