Question

Suppose the inflation rate is expected to be 6% next year, 4.9% the following year, and 2.9% thereafter. Assume that the real risk-free rate, r*, will remain at 1.7% and that maturity risk premiums on Treasury securities rise from zero on very short-term bonds (those that mature in a few days) to 0.2% for 1-year securities. Furthermore, maturity risk premiums increase 0.2% for each year to maturity, up to a limit of 1.0% on 5-year or longer-term T-bonds.

Calculate the interest rate on 1-year Treasury securities. Round your answer to two decimal places. %

Calculate the interest rate on 2-year Treasury securities. Round your answer to two decimal places. %

Calculate the interest rate on 3-year Treasury securities. Round your answer to two decimal places. %

Calculate the interest rate on 4-year Treasury securities. Round your answer to two decimal places. %

Calculate the interest rate on 5-year Treasury securities. Round your answer to two decimal places.%

Calculate the interest rate on 10-year Treasury securities. Round your answer to two decimal places.%

Calculate the interest rate on 20-year Treasury securities. Round your answer to two decimal places.%

Select the correct yield curve based on these data.

1. The correct sketch is -Select-ABCD .
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5. Suppose a AAA-rated company (which is the highest bond rating a firm can have) had bonds with the same maturities as the Treasury bonds. Estimate what you believe a AAA-rated company's yield curve would look like on the same graph with the Treasury bond yield curve. (Hint: Think about the default risk premium on its long-term versus its short-term bonds.)
   
6. The yield risk curve for the AAA-rated corporate bonds will -Select-rise abovefall belowbe the same as the yield curve for the Treasury securities.
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10. What will be the approximate yield curve of a much riskier lower-rated company with a much higher risk of defaulting on its bonds?
    
11. The yield risk curve of a much riskier lower-rated company will be -Select-abovebelowthe same as the yield curve for the Treasury securities and -Select-abovebelowthe same as the yield curve for the AAA-rated corporate bonds.
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13. are you able to show how to calculate these out?
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Answer 1

Given:

Inflation rate next year : 6%

Following year : 4.9%

Thereafter : 2.9%

Real risk-free rate : 1.7%

Maturity risk premium : 0% on very short term bonds to 0.2% for 1 year secuirities.Maturity risk premiums increase 0.2% for each year to maturity, up to a limit of 1.0% on 5-year or longer-term T-bonds.

Formulae for calculation of Nominal Rate :

(1+ nominal rate) = (1+ real rate)(1+ inflation rate)

Calculation of interest rate for various term bonds :

a) Interest on 1 Year Treasury Securities :

Real risk-free rate + maturity risk premium on 1 year treasury bond

1.7% + .2% = 1.9%

Note : No inflation rate given for the current year.

b) Interest rate on 2 Year Treasury Securities :

Step 1 : Calculation of nominal rate :

(1+ nominal rate) = (1+ .017)(1+.06)

1+ nominal rate = 1.07802

nominal rate = 1.07802-1

Nominal Rate = 0.07802 i.e., 7.802%

Step 2 : Calculation of interest rate :

Nominal Rate + Maturity risk premium on 2 year treasury bond

7.802 + (0.2%+0.2%)

=8.202

c) Interest rate on 3 Year Treasury Securities :

Step 1: Calculation of nominal rate :

(1+ nominal rate) = ( 1+.017)(1+.06)(1+.049)

1+ nominal rate = 1.13084

nominal rate = 1.13084-1

Nominal Rate = 0.13084 i.e., 13.084 %

Step 2 : Calculation of interest rate :

Nominal Rate + Maturity risk premium on 3 year treasury bond

13.084% + (0.2%+0.2%+0.2%)

= 13.684%

d) Interest rate on 4 Year Treasury Securities :

Step 1: Calculation of nominal rate :

(1+ nominal rate) = ( 1+.017)(1+.06)(1+.049)(1+.029)

1+ nominal rate = 1.16364

nominal rate = 1.16364-1

Nominal Rate = 0.16364 i.e., 16.364%

Step 2 : Calculation of interest rate :

Nominal Rate + Maturity risk premium on 4 year treasury bond

16.364% + (0.2%+0.2%+0.2%+0.2%)

= 17.164%