a. What is the duration of a 5-year 8% annual coupon bond with a par value of $100 if the prevailing continuously compounded interest rate is 10%?

b. What is the duration of a 5-year 12% annual coupon bond with a par value of $100 if the prevailing continuously compounded interest rate is 10%? What does this tell you about the relationship between coupon rates and duration? Comment.

c. What is the duration of a 5-year 8% annual coupon bond with a par value of $100 if the prevailing continuously compounded interest rate is 12%? What does this tell you about the relationship between interest rates and duration? Comment.

Expert Solution

2a.

Year	CF	PVF@10%	Disc CF	Weights	Weights * Year
1	$ 8.00	0.9048	$ 7.24	0.0799	0.0799
2	$ 8.00	0.8187	$ 6.55	0.0723	0.1446
3	$ 8.00	0.7408	$ 5.93	0.0654	0.1963
4	$ 8.00	0.6703	$ 5.36	0.0592	0.2368
5	$ 8.00	0.6065	$ 4.85	0.0536	0.2678
5	$ 100.00	0.6065	$ 60.65	0.6696	3.3479
Duration	4.2734

2b

Year	CF	PVF@10%	Disc CF	Weights	Weights * Year
1	$ 12.00	0.9048	$ 10.86	0.1029	0.1029
2	$ 12.00	0.8187	$ 9.82	0.0931	0.1862
3	$ 12.00	0.7408	$ 8.89	0.0842	0.2527
4	$ 12.00	0.6703	$ 8.04	0.0762	0.3048
5	$ 12.00	0.6065	$ 7.28	0.0690	0.3448
5	$ 100.00	0.6065	$ 60.65	0.5746	2.8732
Duration	4.0646

If the coupon rates increases the duration of the bond decreases

Year	CF	PVF@12%	Disc CF	Weights	Weights * Year
1	$ 8.00	0.8869	$ 7.10	0.0853	0.0853
2	$ 8.00	0.7866	$ 6.29	0.0756	0.1513
3	$ 8.00	0.6977	$ 5.58	0.0671	0.2013
4	$ 8.00	0.6188	$ 4.95	0.0595	0.2380
5	$ 8.00	0.5488	$ 4.39	0.0528	0.2639
5	$ 100.00	0.5488	$ 54.88	0.6597	3.2985
Duration	4.2382

If the Interest rate increases the duration of the bond decreases

jeff jeffy answered 2 years ago

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