Question

Which bond’s price would be the most sensitive to an unexpected change in the interest rate? Please provide the formula you used, and show your work.

Answer 1

A bond that has the longest duration is most sensitive to change in the interest rate.This is due to fixed income nature of bond.There is inverse relationship between bond's price and interest rate.

Bond's price thepresent value of fixed income(Interest) and its maturity value,discounted using market interest rate.Thus formula for calculating bond price is;

=Annual Interest*Present value annuity factor @market interest rate for the years to maturity+Maturity value/(1+market interest rate)^no. of year of maturity.

Market interest rate is commonly known as Yield.

For example:Lets take the 2 bonds with face value of $1000 and coupon rate of 10% each.However bond A has the maturity period of 10 years and bond B has maturity period of 20 years

Lets find the price of each bond at YTM of 10%

Bond A=$100*6.1446+$1000/(1+0.10)^10

=$1000

Bond B=$100*8.5136+$1000/(1+0.1)^20

=$1000

Now,lets find the price of bond at YTM of 12%

Bond A=$100*5.6502+$1000/(1+0.12)^10

=886.99

Bond B=$100*7.4694+$1000/(1+0.12)^20

=$850.61

In case of bond A,price change by 11.30% and in case of bond B price change by 15%(approx), due to change in yield by 2%.Since the bond B has longer maturity period,hence it is more sensitive to change in yield rate.