Question

Bond has following charaateristics: par value €1000, 5,5%coupon rate, paid annually and 15 years to maturity. YTM is 6.5%

A) Find Macaulay duration of that bond (Dmac)

B) Find modified duration of that bond (Dmod)

Answer 1

Years	Cash flow	Present value formula	Present value	Duration D = (PV*T)
1	55	55/(1+6.5%)^1	51.64	51.64
2	55	55/(1+6.5%)^2	48.49	96.98
3	55	55/(1+6.5%)^3	45.53	136.60
4	55	55/(1+6.5%)^4	42.75	171.01
5	55	55/(1+6.5%)^5	40.14	200.72
6	55	55/(1+6.5%)^6	37.69	226.16
7	55	55/(1+6.5%)^7	35.39	247.75
8	55	55/(1+6.5%)^8	33.23	265.86
9	55	55/(1+6.5%)^9	31.20	280.84
10	55	55/(1+6.5%)^10	29.30	293.00
11	55	55/(1+6.5%)^11	27.51	302.63
12	55	55/(1+6.5%)^12	25.83	309.99
13	55	55/(1+6.5%)^13	24.26	315.33
14	55	55/(1+6.5%)^14	22.78	318.86
15	1055	1055/(1+6.5%)^15	410.21	6153.18
Total			905.97	9370.54
Macaulay Duration = Duration D / Present value of cash flows			Macaulay Duration = 9370.54 / 905.97=10.34
Modified Macaulay Duration = Macaulay Duration / (1+ (YTM/number of periods)			Modified Macaulay Duration = 10.34 / 1.065=9.71