Suppose the inflation rate is expected to be 7% next year, 5% the followingyear, and 3% thereafter. Assume that the real risk-free rate, r*, will remain at 2% and thatmaturity 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 riskpremiums increase 0.2% for each year to maturity, up to a limit of 1.0% on 5-year or longer termT-bonds.a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities andplot the yield curve.b. 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 and plot whatyou believe a AAA-rated company’s yield curve would look like on the same graphwith the Treasury bond yield curve. (Hint: Think about the default risk premium on itslong-term versus its short-term bonds.)c. On the same graph, plot the approximate yield curve of a much riskier lower-ratedcompany with a much higher risk of defaulting on its bonds.
Suppose the inflation rate is expected to be 7% next year, 5% the following
year, and 3% thereafter. Assume that the real risk-free rate, r*, will remain at 2% 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.
a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities and
plot the yield curve.
b. 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 and plot 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.)
c. On the same graph, plot the approximate yield curve of a much riskier lower-rated
company with a much higher risk of defaulting on its bonds.
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