Question

A 5-year Treasury bond has a 4.4% yield. A 10-year Treasury bond yields 6.85%, and a 10-year corporate bond yields 8.4%. The market expects that inflation will average 1.5% over the next 10 years (IP₁₀ = 1.5%). 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? Round your answer to two decimal places.

Answer 1

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

For 5-Year treasury bond,

Default Risk Premium = 0; Liquidity Premium = 0; Maturity Risk Premium = 0

Inflation Premium = 1.5%

4.4 = Risk Free Rate + Inflation Premium

Risk-Free Rate = 4.4 - 1.5 = 2.9%

Similarly, for 10- year Treasury bond:

6.85 = Risk Free Rate + Inflation Premium

Risk Free Rate = 6.85 – 1.5 = 5.35%

Similarly, for the 10-Year Corporate Bond

8.4 = 2.9 + 5.35 + Maturity Risk Premium + Default Risk Premium + Liquidity Premium

8.4 = 2.9 + 5.35 + 0.00 + Default Risk Premium + Liquidity Premium

Default Risk Premium + Liquidity Premium = 8.4 – 8.25 = 0.15%

Now, for the 5-year Corporate Bond:

Yield = 1.0 + 1.5 + 0.15 = 2.65%