Question

Problem A,

A bond matures in 26 years, has an annual coupon rate of 8% on a face of $1000, yields an annual rate of 10%, and its first annual coupon will be paid a year from now. The following information applies to the above bond:

      YTM                                 $-Price

      10.2%                              801.5761

      10.0%   (presently)   P₀ = 816.7811

        9.8%                              832.4845

At the present price (P=816.7811), the annualized Modified Duration is

a. 19.02

b. 19.98

c. 9.46

d. 9.51

At the present price (P₀), the measure of Convexity is equal to

a. 261.31

b. 152.55

c. 184.18

d. 154.34

Assuming that the YTM changes by 200 Basis Points (i.e., 10% ± 2%), then the above Modified Duration suggests a price change of ($)

a. 154.535

b. 176.170

c. 155.170

d. 146.175

The combined effect of Duration and Convexity – when the YTM increases by 200 BPs – is to reduce the above bond price by ($)

a. 128.995

b. 180.355

c. 155.175

d. 129.615

Answer 1

	Years	cash flow	pvif	proportion	A	x+1	(x+1)*A
1	1	80	0.90	72	0.088	0.09	2	0.18
	2	80	0.83	66.08	0.081	0.16	3	0.49
	3	80	0.75	60.24	0.074	0.22	4	0.89
	4	80	0.68	54.64	0.067	0.27	5	1.34
	5	80	0.62	49.6	0.061	0.30	6	1.82
	6	80	0.56	45.12	0.055	0.33	7	2.32
	7	80	0.51	41.04	0.050	0.35	8	2.81
	8	80	0.47	37.28	0.046	0.37	9	3.29
	9	80	0.42	33.92	0.042	0.37	10	3.74
	10	80	0.39	30.8	0.038	0.38	11	4.15
	11	80	0.35	28	0.034	0.38	12	4.53
	12	80	0.32	25.44	0.031	0.37	13	4.86
	13	80	0.29	23.12	0.028	0.37	14	5.15
	14	80	0.26	21.04	0.026	0.36	15	5.41
	15	80	0.24	19.12	0.023	0.35	16	5.62
	16	80	0.22	17.36	0.021	0.34	17	5.78
	17	80	0.20	15.76	0.019	0.33	18	5.91
	18	80	0.18	14.32	0.018	0.32	19	6.00
	19	80	0.16	13.04	0.016	0.30	20	6.07
	20	80	0.15	11.92	0.015	0.29	21	6.13
	21	80	0.14	10.88	0.013	0.28	22	6.16
	22	80	0.12	9.6	0.012	0.26	23	5.95
	23	80	0.12	9.6	0.012	0.27	24	6.49
	24	80	0.10	8.08	0.010	0.24	25	5.94
	25	80	0.09	7.36	0.009	0.23	26	5.86
	26	1080	0.08	90.72	0.111	2.89	27	77.99
				816.56		10.41		184.86
		Duration is 10.41
		Modified duration is 10.89/1.1=9.46
	Answer is C
2	convexity	Sum (x+1)*A / (1+r)(1+r)
		184.86/1.1/1.1
		152.55
	Answer is B
3	Price change	MD * (change in basis point ) *price at present
		(9.46*816.56*2)/100
		154.54
	Answer is A
4	Answer is C