Question

A bond portfolio named VEX comprises four bonds (face value=$1000):

1) 100 semi-annual bond, 5-year maturity, a coupon rate of 4%

2) 200 annual bonds, 30-year maturity, 8% coupon bond.

3) 300 zero-coupon bonds, 10-year maturity.

4) 400 zero-coupon bonds, 20-year maturity.

According to the price-duration formula with Macaulay’s duration D, if the yield increases from 6% to 7%, the VEX’s market value should fall by how much ($)?

Answer 1

Scenario 1
Face Value	Period	Annualy Compunded interest 7%	Discount Rate	Discounted rate of Interest
1000	1	35	0.9709	33.98058252
	2	35	0.9426	65.98171364
	3	35	0.9151	96.08987423
	4	35	0.8885	124.3881867
	5	35	0.8626	150.9565373
	6	35	0.8375	175.8716939
	7	35	0.8131	199.2074203
	8	35	0.7894	221.0345856
	9	35	0.7664	241.4212707	1308.931865
	10	1035	0.7441	7701.372019	9010.303884	9.010303884
					901	Per Bond discounted Value
					99	Per Bond price
					9900	Total Value for 100 bonds
Scenario:2
Face Value	Period	Annualy Compunded interest 7%	Discount Rate	Discounted rate of Interest
1000	1	70	0.9709	67.96116505
	2	70	0.9426	131.9634273
	3	70	0.9151	192.1797485
	4	70	0.8885	248.7763734
	5	70	0.8626	301.9130745
	6	70	0.8375	351.7433878
	7	70	0.8131	398.4148406
	8	70	0.7894	442.0691712
	9	70	0.7664	482.8425414
	10	70	0.7441	520.8657404
	11	70	0.7224	556.264383
	12	70	0.7014	589.1590994
	13	70	0.6810	619.6657194
	14	70	0.6611	647.8954497
	15	70	0.6419	673.9550448
	16	70	0.6232	697.9469719
	17	70	0.6050	719.9695706
	18	70	0.5874	740.1172056
	19	70	0.5703	758.4804157
	20	70	0.5537	775.1460559
	21	70	0.5375	790.1974356
	22	70	0.5219	803.7144514
	23	70	0.5067	815.773715
	24	70	0.4919	826.4486771
	25	70	0.4776	835.8097462
	26	70	0.4637	843.9244039
	27	70	0.4502	850.8573154
	28	70	0.4371	856.6704362
	29	70	0.4243	861.4231155	17402.14868
	30	1070	0.4120	13224.77498	30626.92366
					30.62692366
					306	price drop
					694	Discounted price
					138800	Value
Scenario:3
Face Value	Period	Annualy Compunded interest 7%	Discount Rate	Discounted rate of Interest
1000	1		0.9709	0
	2		0.9426	0
	3		0.9151	0
	4		0.8885	0
	5		0.8626	0
	6		0.8375	0
	7		0.8131	0
	8		0.7894	0
	9		0.7664	0
	10		0.7441	0
	11		0.7224	0
	12		0.7014	0
	13		0.6810	0
	14		0.6611	0
	15		0.6419	0
	16		0.6232	0
	17		0.6050	0
	18		0.5874	0
	19		0.5703	0
	20	1000	0.5537	11073.51508	11.07351508
				110.7	Price Drop
				889.3	Per bond discounted rate
				266790	Total Value
Scenario;4
Face Value	Period	Annualy Compunded interest 7%	Discount Rate	Discounted rate of Interest
1000	1		0.9709	0
	2		0.9426	0
	3		0.9151	0
	4		0.8885	0
	5		0.8626	0
	6		0.8375	0
	7		0.8131	0
	8		0.7894	0
	9		0.7664	0
	10	1000	0.7441	7440.939149	7.440939149
				74.4	Price Drop
				925.6	Per bond discounted rate
				370240	Total Value