Question

An insurance company is analyzing the following three bonds, each with five years to maturity, annual interest payments, and is using duration as the measure of interest rate risk. What is the duration of each of the three bonds? a) $10,000 par value, coupon rate = 10%, rb = 0.2 b) $10,000 par value, coupon rate = 12%, rb = 0.2 c) $10,000 par value, coupon rate = 12%, rb = 0.2

Answer 1

A
period	cash flow	present value of cash inflow = cash inflows/(1+r)^n r= 20%	present value*period
1	1000	833.3333	833.3333333
2	1000	694.4444	1388.888889
3	1000	578.7037	1736.111111
4	1000	482.2531	1929.012346
5	11000	4420.653	22103.26646
value of bond	sum of present value of cash inflow	7009.388
sum of present value* period			27990.61214
Duration = sum of (present value* period)/ value of bond	27990.61/7009.38		3.99
B
period	cash flow	present value of cash inflow = cash inflows/(1+r)^n r= 20%	present value*period
1	1200	1000	1000
2	1200	833.3333	1666.666667
3	1200	694.4444	2083.333333
4	1200	578.7037	2314.814815
5	11200	4501.029	22505.14403
value of bond		7607.51
sum of present value* period			29569.95885
Duration = sum of (present value* period)/ value of bond	29569.96//7607.51		3.89
C
period	cash flow	present value of cash inflow = cash inflows/(1+r)^n r= 20%	present value*period
1	1200	1000	1000
2	1200	833.3333	1666.666667
3	1200	694.4444	2083.333333
4	1200	578.7037	2314.814815
5	11200	4501.029	22505.14403
value of bond		7607.51
sum of present value* period			29569.95885
Duration = sum of (present value* period)/ value of bond	29569.96//7607.51		3.89