Problem 6-17. Interest rate premiums A 5-year Treasury bond has a 4.15% yield. A
ID: 2674520 • Letter: P
Question
Problem 6-17. Interest rate premiumsA 5-year Treasury bond has a 4.15% yield. A 10-year Treasury bond yields 6.7%, and a 10-year corporate bond yields 9.8%. The market expects that inflation will average 2.7% over the next 10 years (IP10 = 2.7%). Assume that there is no maturity risk premium (MRP = 0), and that the annual real risk-free rate, r*, will remain constant over the next 10 years. (Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP = LP = 0). A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond described above. What is the yield on this 5-year corporate bond? Round your answer to two decimal places.
%
Explanation / Answer
Yield = real risk-free rate+ maturity risk premium + DRP + LP + IP For 10-year Treasury: 6.7% = r* + 0 +0+0 + 2.7% r* = 4% For 5-year Treasury bond 4.15% = 4% + 0+0+0+ IP5 IP5 = .15% For 10-year corporate bond - 9.8% = 4% + 0 + (DRP + LP) + 2.7% (DRP + LP) = 3.1% A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond 5-year corporate bond, IP5 = .15% Yield = 4% + 0 + 3.1% + 0.15% =7.25% Answer = 7.25%