Duration:
Duaration = Sum [ Weight * Year ]
Period | CF | PVF @5% | Disc CF | Weight | Wt * Period |
1 | $ 45.00 | 0.9524 | $ 42.86 | 0.0457 | 0.0457 |
2 | $ 45.00 | 0.9070 | $ 40.82 | 0.0435 | 0.0871 |
3 | $ 45.00 | 0.8638 | $ 38.87 | 0.0415 | 0.1244 |
4 | $ 45.00 | 0.8227 | $ 37.02 | 0.0395 | 0.1579 |
5 | $ 45.00 | 0.7835 | $ 35.26 | 0.0376 | 0.1880 |
6 | $ 45.00 | 0.7462 | $ 33.58 | 0.0358 | 0.2149 |
7 | $ 45.00 | 0.7107 | $ 31.98 | 0.0341 | 0.2387 |
8 | $ 45.00 | 0.6768 | $ 30.46 | 0.0325 | 0.2599 |
9 | $ 45.00 | 0.6446 | $ 29.01 | 0.0309 | 0.2784 |
10 | $ 45.00 | 0.6139 | $ 27.63 | 0.0295 | 0.2946 |
11 | $ 45.00 | 0.5847 | $ 26.31 | 0.0281 | 0.3086 |
12 | $ 45.00 | 0.5568 | $ 25.06 | 0.0267 | 0.3207 |
13 | $ 45.00 | 0.5303 | $ 23.86 | 0.0255 | 0.3309 |
14 | $ 45.00 | 0.5051 | $ 22.73 | 0.0242 | 0.3393 |
15 | $ 45.00 | 0.4810 | $ 21.65 | 0.0231 | 0.3463 |
16 | $ 45.00 | 0.4581 | $ 20.62 | 0.0220 | 0.3518 |
17 | $ 45.00 | 0.4363 | $ 19.63 | 0.0209 | 0.3559 |
18 | $ 45.00 | 0.4155 | $ 18.70 | 0.0199 | 0.3589 |
19 | $ 45.00 | 0.3957 | $ 17.81 | 0.0190 | 0.3608 |
20 | $ 45.00 | 0.3769 | $ 16.96 | 0.0181 | 0.3617 |
20 | $ 1,000.00 | 0.3769 | $ 376.89 | 0.4019 | 8.0387 |
Duration in Periods | 13.3632 | ||||
No. of periods per anum | 2.0000 | ||||
Duration in Years | 6.6816 |
Modified duaration :
Modified duration = Duration / [ 1 + YTM ]
It specifies% change in Price in opposite direction due to 1%
change in YTM.
= 6.6816 / 1.10
= 6.0742
i.e 1% change in YTM leads to 6.0742% chnage in price in opposite direction
2% change leads to 12.15% [ 6.0742* 2 ]
Price if Int dec by 2% :
= Old price * ( 1 + 0.1215 )
= 937.69 * 1.1215
= 1051.62
Price if Int inc by 2% :
= Old price * ( 1 - 0.1215 )
= 937.69 * 0.8785
= 855.39
Pls do rate, if the answer is correct and comment, if any further assistance is required.
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