Question

1. A 25-year, 5% coupon bond, pays interest semi-annually, and is priced to yield 5%.

a. What is its approximate modified duration for 100bps change in yield?

b. What is its approximate convexity for 100bps change in yield?

c. Using its approximate modified duration alone, how much (in % terms) do you expect the price of this bond to change if interest rates increase by 200bps?

d. Using its modified duration and convexity, how much (in % terms) do you expect the price of this bond to change if interest rates increase by 200bps?

e. Compare the actual expected change in the value of the bond if yields across the yield curve increased by 200bps for this issuer vs. the answer obtained in part d above.

Answer 1

Macaulay Duration is a measure of the elasticity of the price of the cash flow versus the periodic yield to maturity, i. That is it relates the percent change in the price of a cash flow to the percent change in the yield to maturity. A bond would be trading at Par if the coupon rate is equal to the yield to maturity of the bond. The macaulay duration of the bond shall be calculated as under;

Years	Cashflow	PV Factor	Discounted cashflow	Weights
1	2.5	0.9756	2	2.44
2	2.5	0.9518	2	4.76
3	2.5	0.9286	2	6.96
4	2.5	0.9060	2	9.06
5	2.5	0.8839	2	11.05
6	2.5	0.8623	2	12.93
7	2.5	0.8413	2	14.72
8	2.5	0.8207	2	16.41
9	2.5	0.8007	2	18.02
10	2.5	0.7812	2	19.53
11	2.5	0.7621	2	20.96
12	2.5	0.7436	2	22.31
13	2.5	0.7254	2	23.58
14	2.5	0.7077	2	24.77
15	2.5	0.6905	2	25.89
16	2.5	0.6736	2	26.94
17	2.5	0.6572	2	27.93
18	2.5	0.6412	2	28.85
19	2.5	0.6255	2	29.71
20	2.5	0.6103	2	30.51
21	2.5	0.5954	1	31.26
22	2.5	0.5809	1	31.95
23	2.5	0.5667	1	32.59
24	2.5	0.5529	1	33.17
25	2.5	0.5394	1	33.71
26	2.5	0.5262	1	34.21
27	2.5	0.5134	1	34.65
28	2.5	0.5009	1	35.06
29	2.5	0.4887	1	35.43
30	2.5	0.4767	1	35.76
31	2.5	0.4651	1	36.05
32	2.5	0.4538	1	36.30
33	2.5	0.4427	1	36.52
34	2.5	0.4319	1	36.71
35	2.5	0.4214	1	36.87
36	2.5	0.4111	1	37.00
37	2.5	0.4011	1	37.10
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