Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 10% annual coupon. Bond L matures in 15 years while Bond S matures in 1 year.

A. What will the vaule of each bond be if the going interest rate is 5%, 8% and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L.

B. Why does the longer term bond's price vary more than the price of the shorter term bond when interest rates change?

*Please show work for part A.

Answer 1

Rate is 5%:

Bond L=(1000*10%)/(5%)*(1-1/1.05^1)+1000/1.05^1=1047.6905

Bond S=(1000*10%)/(5%)*(1-1/1.05^15)+1000/1.05^15=1518.983

Rate is 8%:

Bond L=(1000*10%)/(8%)*(1-1/1.08^1)+1000/1.08^1=1018.5819

Bond S=(1000*10%)/(8%)*(1-1/1.08^15)+1000/1.08^15=1171.19

Rate is 12%:

Bond L=(1000*10%)/(12%)*(1-1/1.12^1)+1000/1.12^1=982.1429

Bond S=(1000*10%)/(12%)*(1-1/1.12^15)+1000/1.12^15=863.7827

Because long term bond has higher duration and higher duration means higher interest rate sensitivity