Question

What is the modified duration for a four year semi annual pay, $1000 par value, 8% coupon bond that is currently prices to yield 7%?

Answer 1

par value = $1000

Semiannual coupon =(8% of 1000)/2 = 40

YTM = 7% , Semiannual YTM = 3.5%

Time = 4years

The Macaulay duration calculation is shown below:

(The Weights are calculated as = CF*PV for the time period / total CF*PV )

Time(T)	Cash flow(CF)	Present value factor @3.5% (PV)	CF * PV	Weights(W)	W*T
0.5	40	0.966	38.647	0.037	0.019
1	40	0.934	37.340	0.036	0.036
1.5	40	0.902	36.078	0.035	0.052
2	40	0.871	34.858	0.034	0.067
2.5	40	0.842	33.679	0.033	0.081
3	40	0.814	32.540	0.031	0.094
3.5	40	0.786	31.440	0.030	0.106
4	1040	0.759	789.788	0.764	3.054
Total	1034.370	1.000	3.511

The macaulay duration = 3.511 years

Modified duration = Macaulay duration / (1 + YTM/2 )

= 3.511 / (1 + 0.035)

= 3.392 Years