A 5-year Treasury bond has a 5% yield. A 10-year Treasury bond yields 6.05%, and

Question

A 5-year Treasury bond has a 5% yield. A 10-year Treasury bond yields 6.05%, and a 10-year corporate bond yields 9.6%. The market expects that inflation will average 3.6% over the next 10 years (IP10 = 3.6%). 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. What is the yield on this 5-year corporate bond? Round your answer to two decimal places.

Explanation / Answer

r = r* + IP + DRP + LP + MRP

For a 10 year treasury bond

r= r* + IP10

6.05%= r*+ 3.6%

r*= 6.05%-3.6% = 2.45%

For a 5 year treasury bond

5%= 2.45%+ IP5

Hence IP5 = 2.55%

For a 10 year corporate bond

9.6%= 2.45%+3.6%+ DRP+ LP + 0

DRP+LP= 9.6%-2.45%-3.6% = 3.55%

5 year corporate yield=

r = r* + IP5 + DRP + LP + MRP

= 2.45%+ 2.55%+ 3.55%+ 0

=8.55%

ANSWER= 8.55%

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