Question

A bond currently selling for $1,050 which gives it a yield of 8%. Suppose that if the yield increases by 25 basis point, the price of the bond falls to $1,020. What is the duration of the bond?   

Answer 1

Given,

Bond price = $1050

Yield = 8% or 0.08

Change in yield = 25 basis point or 0.25%

New price = $1020

Solution :-

Change in price = $1020 - $1050 = -$30

Modified duration = (-change in price/bond price) change in yield

= (-(-$30)/$1050) 0.25%

= 0.02857142857 0.25% = 11.42857 years

Macaulay duration = modified duration x (1 + yield/2)

= 11.42857 years x (1 + 0.08/2)

= 11.42857 years x (1 + 0.04)

= 11.42857 years x (1.04) = 11.8857 years