A 5-year Treasury bond has a 3.65% yield. A 10-year Treasury bond yields 6.25%,

Question

A 5-year Treasury bond has a 3.65% yield. A 10-year Treasury bond yields 6.25%, and a 10-year corporate bond yields 8.85%. The market expects that inflation will average 2.85% over the next 10 years (IP10 = 2.85%). 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

For 5-year Treasury bond

Yield of bond=Risk-free rate+inflation premium

3.65=Risk-free rate+2.85

Risk-free rate=3.65-2.85 =0.8%

For 10-year Treasury bond

6.25=Risk-free rate+2.85

Risk-free rate=6.25-2.85 =3.40%

For 10-year corporate bond

Yield on Bond = Risk Free Rate + Inflation Premium + Maturity Risk Premium + Default Risk Premium + Liquidity Premium

8.85 =3.4+2.85+ Maturity Risk Premium + Default Risk Premium + Liquidity Premium

Maturity Risk Premium + Default Risk Premium + Liquidity Premium=2.6%

Since there is no Market Risk Premium, then:

Default Risk Premium + Liquidity Premium=2.6%

For the 5-year Corporate Bond:

Yield of Bond =0.8+2.85+2.6=6.25%

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