A 5-year Treasury bond has a 4.4% yield. A 10-year Treasury bond yields 7%, and

Question

A 5-year Treasury bond has a 4.4% yield. A 10-year Treasury bond yields 7%, and a 10-year corporate bond yields 8.35%. The market expects that inflation will average 3.75% over the next 10 years (IP10 = 3.75%). 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

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Interest Rate Premiums. A 5-year Treasury bond has a 5.2% yield. A 10-year Treasury bond yields 6.4%, and a 10-year corporate bond yields 8.4%. The market expects that inflation will average 2.5% over the next 10 years(IP10 = 2.5%) 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? K T-10 = 6.4%; kC-10 = 8.4%; LP =?; DRP = ?

solution:

k = k* + IP + DRP + LP + MRP.

K T-10 = 6.4% = k* + IP + MRP; DRP = LP = 0.

K C-10 = 8.4% = k* + IP + DRP + LP + MRP.


But we know from above that k* + IP + MRP = 6.4%; therefore,

K C-10 = 8.4% = 6.4% + LP + DRP
2% = LP + DRP.

K T-5 = 5.2% = k* + IP + MRP; DRP = LP = 0.

K C-5 = k* + IP + MRP + DRP + LP
= 5.2% + 2%
= 7.7%   

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