Question

Problem 6-17
Interest Rate Premiums

A 5-year Treasury bond has a 4.65% yield. A 10-year Treasury bond yields 6.1%, and a 10-year corporate bond yields 8.8%. 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.

Answer 1

Yield of T year Corporate Bond

= Risk free rate(T year TreasuryBond) + Market Risk Premium(MRP) + (Default Risk Premium(DRP) + Liquidity Risk   Premium(LRP))

Acc. to question; MRP = 0;

DRP + LRP (5 year Corporate Bond) =  DRP + LRP (10 year Corporate Bond)

So Yield of 10 year Corporate Bond = Risk free rate(10 year Treasury Bond) + Market Risk Premium (MRP) + (DRP + LRP (10 year Corporate Bond))

So DRP + LRP (10 year Corporate Bond) = 8.8% - 6.1% = 2.7% = DRP + LRP (5 year Corporate Bond)

So Yield of 5 year Corporate Bond,R = Risk free rate(5 year Treasury Bond) + Market Risk Premium (MRP) + (DRP + LRP (5 year Corporate Bond))

= 4.65% + 2.7% = 7.35%

Inflation Adjusted yield = {(1+R)/(1+Inflation Rate)} - 1

So Inflation Adjusted yield of 5 year corporate bond = 1.0735/1.0285 - 1

= 4.38%