Question

Derive the duration of a 3 year semiannual paying 8% bond, when market rates are 10% annually.

Explicate the concept of duration.

Answer 1

Here interest = Face value x coupon rate x 1/2

=1000 x 8% x 1/2

=40$

n = no of payments = 3 x 2 =6

market rate = 10%/2 = 5%

Statement showing duration of bond

n	Cash flow	PVIF @ 5%	PV	Weight of PV to total of PV	Duration
A	B	C	D = B x C	E	F = A x E
1	40	0.9524	38.10	0.0401	0.04
2	40	0.9070	36.28	0.0382	0.08
3	40	0.8638	34.55	0.0364	0.11
4	40	0.8227	32.91	0.0347	0.14
5	40	0.7835	31.34	0.0330	0.17
6	1040	0.7462	776.06	0.8176	4.91
			949.24		5.43

Thus duration of bond = 5.43/2

=2.72 years

Duration of bond measures in how much time bond will repay it's price to investor. Duration is often confused with term of maturity , but both are different. Term of maturity is nothing but the life of the bond . ie 3 years in our case where as duration shows the period in which investor will be paid his investment. Further Duration is sensitive to interest rate changes, it is measure of sensitivity of bond's price to change in interest rates.