Question

An investor buys a bond with the following characteristics: Maturity - 10 years Coupon - 4.5%, paid once per year Nominal Value - £100 The yield to maturity at the time of purchase is 8.50%. The investor sells the bond immediately after the sixth coupon payment, when the yield to maturity rises to 9.50%. a.What is the Macaulay duration of the above bond, at the original time of purchase

Answer 1

Time	Cashflow	[email protected]%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	4.5	0.922	4.15	0.0562	0.06
2	4.5	0.849	3.82	0.0518	0.10
3	4.5	0.783	3.52	0.0478	0.14
4	4.5	0.722	3.25	0.0440	0.18
5	4.5	0.665	2.99	0.0406	0.20
6	4.5	0.613	2.76	0.0374	0.22
7	4.5	0.565	2.54	0.0345	0.24
8	4.5	0.521	2.34	0.0318	0.25
9	4.5	0.480	2.16	0.0293	0.26
10	104.5	0.442	46.22	0.6267	6.27

  Macaulay duration = Time*Weight

= 7.93 years

You can use the equation 1/(1+i)^n to find PVF using calculator