Question

John Glenn thinks that the Federal Reserve policy is going to push the interest rates down.  He is considering keeping only one of the three bonds in his portfolio.  He knows that bond A has a duration  of  4.434, bond B has a duration of  4.677, and bond C has the following characteristics:

Par Value        1,000

Life                  5 years

Coupon Rate   5%

Discount rate   14 percent

Solve for bond c duration and show steps. Which one of the three bonds should he keep? Why? Explain.

Answer 1

Price of Bond C = 1000*5%*PVAF(14%, 5 years) + 1000*PVF(14%, 5th year)

= 50*3.4331 + 1000*0.5194

= 691.02

Duration = [50*1*PVF(14%,1)+50*2*PVF(14%,2)+50*3*PVF(14%,3)+50*4*PVF(14%,4)+1000*5*PVF(14%,5)] / Price of bond C   

= [2937.31] / 691.02

= 4.2507 years

In case an investor wants to avoid the volatility in interest rate, the investor should invest or hold the bonds that have a lower duration or short maturity and higher coupon payment.

In the given question, John Glenn thinks interest rates will go down, hence he should keep the bond that have a lower duration i.e. Bond C with a duration of 4.2507 years.