Question

Calculate modi?ed Duration of a bond that pays annual coupon at a rate of 6% and matures in 2 years. This bond has face value of 1,000 and is currently selling at a yield of 8%. Show calculations. Using just modified duration, if yield changes by 0.5%, what is the expected change in the price of the bond? Show calculations. Solving this in a calculator or at some other website that allows you to solve this kind of questions and just putting the value is not going to be an acceptable answer.

Answer 1

if yield goes up by 0.5%, then yield = 8.5%

Price of the bond = (6 / 1.085 ) + (1006/(1.085)²) = 5.52995 + 854.55201 = 860.0819

if yield goes down by 0.5%, then yield = 7.5%

Price of the bond = (6 / 1.075 ) + (1006/(1.075)²) = 5.58139 + 870.52460 = 876.1059

Modified duration = (P_- - P₊  ) / (2 * P * y)

P_- = Price of the bond yield goes down

P₊ = Price of the bond yield goes up

P = Price of the bond at no yield change

y = Change in yield

= ( 876.1059 - 860.0819 ) / (2 * 1000 * .005)

= 16.024 / 10

Modified duration = 1.6024.

if yield changes by .5% the price of the bond will change by 1.6024.