A 5-year Treasury bond has a 3% yield. A 10-year Treasury bond yields 6.9%, and

Question

A 5-year Treasury bond has a 3% yield. A 10-year Treasury bond yields 6.9%, and a 10-year corporate bond yields 9.85%. The market expects that inflation will average 3.3% over the next 10 years (IP10 = 3.3%). 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

Corporate bond yield = Treasury bond yield + Default Risk Premium + Liquidity Risk Premium + Maturity Risk Premium

Here Default Risk Premium and Liquidity Risk Premium are same for 5 year and 10 year bond

Maturity Risk Premium is 0

For 10 year corporate bond

Corporate bond yield = Treasury bond yield + Default Risk Premium + Liquidity Risk Premium + Maturity Risk Premium

9.85% = 6.9% + Default Risk Premium + Liquidity Risk Premium + 0

So Default Risk Premium + Liquidity Risk Premium = 9.85% - 6.9%

Default Risk Premium + Liquidity Risk Premium = 2.95%

For a 5 year corporate bond

Corporate bond yield = Treasury bond yield + Default Risk Premium + Liquidity Risk Premium + Maturity Risk Premium

Corporate bond yield = 3% + + Default Risk Premium + Liquidity Risk Premium + 0

Corporate bond yield = 3% + 2.95% = 5.95%

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