A Bond has a Macaulay duration of 842 and is priced to yield

A Bond has a Macaulay duration of 8.42 and is priced to yield 7%. If interest rates go up so that the yield on this bond goes up 7.5%, what will be the percentage change in the price of the bond? Now, if the yield on this bond goes down to 6.5%, what will be the bond’s percentage change in price? Comment your finding.

Solution

Modified Duration = Macaulay Duration / (1 + YTM)

= 8.42/1.07 = 7.87

% change in bond price = -1 x Modified Duration x Change in Interest Rates

a) YTM = 7.5%

% change in bond price = -1 x 7.87 x 0.5% = -3.93%

% change in bond price = -1 x 7.87 x -0.5% = 3.93%