Please rank the duration of the following bonds and explain the reason: (4 points) Bond A:...

Please rank the duration of the following bonds and explain the reason: (4 points)
Bond A: 5-year bond, coupon rate of 3% selling at par
Bond B: 5-year bond, coupon rate of 3% selling at discount
Bond C: 10-year bond, coupon rate of 2% selling at par
Bond D: 10-year bond, coupon rate of 2% selling at premium

Expert Solution

	Term	coupon	yield	duration	ranking
1	5	3	3	4.71	2
2	5	3	4	4.736842	1
3	10	2	2	8.78	3
4	10	2	1.5	9.230769	4

Workings for duration is given below

Years T	NCF	PV@3%	Duration D	Convexity

NCF(1+0.03)TNCF(1+0.03)T	(PVT)(PVT)	D∗(T+1)(100)(1+0.03)2D∗(T+1)(100)(1+0.03)2

1	3	2.9126	2.9126	0.0549
2	3	2.8278	5.6556	0.1599
3	3	2.7454	8.2363	0.3105
4	3	2.6655	10.662	0.5025
5	3+100 =103	88.849	444.24	25.125
		100	471.7	26.15


Years T	NCF	PV@4%	Duration D	Convexity

NCF(1+0.04)TNCF(1+0.04)T	(PVT)(PVT)	D∗(T+1)(95.548177669)(1+0.04)2D∗(T+1)(95.548177669)(1+0.04)2

1	3	2.8846	2.8846	0.0558
2	3	2.7737	5.5473	0.161
3	3	2.667	8.001	0.3097
4	3	2.5644	10.258	0.4963
5	3+100 =103	84.658	423.29	24.576
		95.55	450	25.6


Years T	NCF	PV@2%	Duration D	Convexity

NCF(1+0.02)TNCF(1+0.02)T	(PVT)(PVT)	D∗(T+1)(100)(1+0.02)2D∗(T+1)(100)(1+0.02)2

1	3	2.9126	2.9126	0.0549
2	3	2.8278	5.6556	0.1599
3	3	2.7454	8.2363	0.3105
4	3	2.6655	10.662	0.5025
5	3	2.5878	12.939	0.7318
6	3	2.5125	15.075	0.9947
7	3	2.4393	17.075	1.2876
8	3	2.3682	18.946	1.6072
9	3	2.2993	20.693	1.9505
10	3+100 =103	76.642	766.42	79.466
		100	878.6	87.07

Years T	NCF	[email protected]%	Duration D	Convexity

NCF(1+0.015)TNCF(1+0.015)T	(PVT)(PVT)	D∗(T+1)(104.611092276)(1+0.015)2D∗(T+1)(104.611092276)(1+0.015)2

1	2	1.9704	1.9704	0.0366
2	2	1.9413	3.8826	0.1081
3	2	1.9126	5.7379	0.213
4	2	1.8844	7.5375	0.3497
5	2	1.8565	9.2826	0.5168
6	2	1.8291	10.975	0.7128
7	2	1.8021	12.614	0.9364
8	2	1.7754	14.203	1.1861
9	2	1.7492	15.743	1.4607
10	2+100 =102	87.89	878.9	89.706

jeff jeffy answered 2 years ago

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