Question

Consider a 20-year maturity, 9% annual coupon bond trading at a price of 134.41. When rates...

  1. Consider a 20-year maturity, 9% annual coupon bond trading at a price of 134.41. When rates rise 0.001, price reduces to 132.99, and when rates decrease by 0.001, price goes up to 135.85. What is the modified duration of the bond?
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Answer #1
Nper 20
Annual coupon rate 9%
Par value 100
PV 134.41
YTM 6.00%
Years T NCF PV @ 6% PV x T
1 9 8.49056604 8.49056604
2 9 8.00996796 16.0199359
3 9 7.55657355 22.6697206
4 9 7.12884297 28.5153719
5 9 6.72532356 33.6266178
6 9 6.34464486 38.0678692
7 9 5.98551402 41.8985982
8 9 5.64671134 45.1736907
9 9 5.32708617 47.9437755
10 9 5.02555299 50.2555299
11 9 4.74108773 52.151965
12 9 4.47272427 53.6726913
13 9 4.2195512 54.8541656
14 9 3.98070868 55.7299215
15 9 3.75538555 56.3307832
16 9 3.54281655 56.6850648
17 9 3.34227977 56.818756
18 9 3.15309412 56.7556942
19 9 2.97461709 56.5177248
20 9+100 =109 33.9867152 679.734305
134.409764 1511.91275
Macaulay Duration = $1511.91/134.41 11.25
Modified Macaulay Duration  = 11.25/(1+6%) 10.61
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