Question

An insurance company is analyzing the following three bonds, each with five years to maturity, annual coupon payments, and duration as the measure of interest rate risk.

What is the duration of each of the three bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

		Duration of the Bond
a.	$10,000 par value, coupon rate = 8.6%, rb = 0.16	years
b.	$10,000 par value, coupon rate = 10.6%, rb = 0.16
c.	$10,000 par value, coupon rate = 12.6%, rb = 0.16

Answer 1

For Bond 1:

Coupon No.	Years till the coupon payment	Coupon amount	Maturity value	Total cash flow	Present value @ 16%	Proportion (i.e PV/Price)	Duration (year till coupon payment * proportion)
1	1	$8.60	$-	$8.60	$7.41	9.78%	0.097845729
2	2	$8.60	$-	$8.60	$6.39	8.43%	0.168699533
3	3	$8.60	$-	$8.60	$5.51	7.27%	0.218145948
4	4	$           8.60		$8.60	$4.75	6.27%	0.250742469
5	5	$           8.60	$       100.00	$108.60	$51.71	68.24%	3.412017856
Total					$75.77		4.147451535

Duration = 4.15 years

For Bond 2

Coupon No.	Years till the coupon payment	Coupon amount	Maturity value	Total cash flow	Present value @ 16%	Proportion (i.e PV/Price)	Duration (year till coupon payment * proportion)
1	1	$10.60	$-	$10.60	$9.14	11.10%	0.111006592
2	2	$10.60	$-	$10.60	$7.88	9.57%	0.191390676
3	3	$10.60	$-	$10.60	$6.79	8.25%	0.247487943
4	4	$10.60		$10.60	$5.85	7.11%	0.2844689
5	5	$10.60	$       100.00	$110.60	$52.66	63.97%	3.19842432
Total					$82.32		4.032778431

Duration = 4.03 Years

Bond 3

Coupon No.	Years till the coupon payment	Coupon amount	Maturity value	Total cash flow	Present value @ 16%	Proportion (i.e PV/Price)	Duration (year till coupon payment * proportion)
1	1	$12.60	$-	$12.60	$10.86	12.22%	0.122227822
2	2	$12.60	$-	$12.60	$9.36	10.54%	0.210737625
3	3	$12.60	$-	$12.60	$8.07	9.08%	0.272505549
4	4	$12.60		$12.60	$6.96	7.83%	0.313224769
5	5	$12.60	$       100.00	$112.60	$53.61	60.33%	3.016309951
Total					$88.87		3.935005716

Duration = 3.94 years