Maturity Risk Premiums 1. Assume that the real risk-free rate, r*, is 2% and tha
ID: 2742723 • Letter: M
Question
Maturity Risk Premiums
1. Assume that the real risk-free rate, r*, is 2% and that inflation is expected to be 7% in Year 1, 5% in Year 2, and 3% 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.
Yeild to Call, Yeild to Maturity and Market Rates
2. Absalom Motors' 11% coupon rate, semiannual payment, $1,000 par value bonds that mature in 10 years are callable 8 years from now at a price of $1,050. The bonds sell at a price of $1,300, and the yield curve is flat. Assuming that interest rates in the economy are expected to remain at their current level, what is the best estimate of the nominal interest rate on new bonds? Do not round intermediate calculations. Round your answer to two decimal places.
Explanation / Answer
Answer 1.
Two year nominal rate w/out maturity risk premium:
(1 + real)^n(1 + inflation yr1)(1 + inflation yr 2) = (1 + nominal)^n, [where n = 2 here)
1.02^2(1.07)(1.05) = (1 + nominal)^2
1.168889 = (1 + nominal)^2
1.168889^1/2 = (1 + nominal)
1.081152 = 1+ nominal
2 yr nominal rate = 0.081152 or 8.1152%..since it "currently" yields 10% WITH the MRP, the maturity risk premium is: 0.10 - 0.081152 = 0.018848, or 1.8848%
Next calc the nominal of the 5 yr. note w/out MRP):
1.02^5(1.07)(1.05)(1.03^3) = (1+nominal)^5
1.277278 = (1+nominal)^5
1.277278^1/5 = (1+nominal)
1.050164 = 1 + nominal
nominal = 0.050164, or 5.0164%
maturity risk premium: 0.10 - 0.050164 = 0.049836, or 4.9836%
MRP5 - MRP2 = 0.030988, or about 3.10%
Answer 2.
Let YTC be i%
1,300 = 55*PVIFA(i/2%, 16) + 1,050*PVFA(i/2%, 16)
i/2% = 3.299%
i% = 6.60%