Question

Calculate the modified duration of a 9% coupon $1,000 par value 2-year bond with coupon paid every 4 months and yield-to-maturity of 12%.

Answer 1

We first need to calculate the Macaulay’s duration, which is the average maturity of the bond cash flows weighted based on their relevant contribution to the present value of the bond.

Macaualy Duration = [ {$90 / (1+12%)1 } / [{$90 / (1+12%)1 } + ($90+$1,000)/(1+12%)2]] x 1 + [ {($90 + $1,000) / (1+12%)1 } / [{$90 / (1+12%)1 } + ($90+$1,000)/(1+12%)2] x 2 ]

= [($90 / 1.12) / {($90/1.12) + ($1,090/1.2544)}] x 1 + [($1,090 / 1.12544) / {($90/1.12) + ($1,090/1.2544)}] x 2]

= {$80.36 / ($80.36 + $868.94)} + {$868.94 / ($80.36 +$868.94)}

= ($80.36 / $949.30) x1 + ($868.94 / $949.30) x 2

= 0.0847 + 1.8307

= 1.9154 or say 1.92

Modified duration equals Macaulay’s duration divided by (1 + y/m)

Modified Duration = 1.92 / {1 + (12%/1)} = 1.92 / 1.12 = 1.71

Modified duration works out to 1.71 which means the bond prices increases (decreases) by 1.71% given a 1% decrease (increase) in bond price.