| | Duration Example |
| | N = | 3 |
| | Coupon = | 10% |
| | FV = | 100 |
| | YTM = | 12% | with continuous compounding |
| | Time | CF | PV | W | TimexW |
| | 0.5 | 5 | $4.709 | 0.050 | 0.0249902967 |
| | 1 | 5 | $4.435 | 0.047 | 0.0470699502 |
| | 1.5 | 5 | $4.176 | 0.044 | 0.0664932145 |
| | 2 | 5 | $3.933 | 0.042 | 0.0834946015 |
| | 2.5 | 5 | $3.704 | 0.039 | 0.0982903181 |
| | 3 | 105 | $73.256 | 0.778 | 2.3326716564 |
| | Total | 130 | $94.213 | 1 | 2.653 | Duration | This is Macaulay Duration |
| | | ΔB = | bond price x duration x Δy = | | | -$0.25 | Change represented by duration relationship |
| | | | where Δy = | | 0.10% |
| | Which means that if interest rates increase by 10 basis points, |
| | bond price decreases to | | | $93.963 |
| | Or | new rate = | | 12.100% |
| | New bond price = | | $93.963 | Verification |
| | Modified Duration |
| | D* = D/(1+y/m) where y is the yield expressed with semi-annual compounding |
| | and m = # of compounding periods. |
| | 12% with semi-annual compounding = | | | | 0.12360 |
| | Here Modified Duration = | | | 2.499 |
| | Hence when yields increase by 10 basis points, duration predicts a relatioship ΔB = | | | | | | | | -$0.235 |
| | or price change of | | $93.978 |
| | Modified duration gives good accuracy for small yield changes |
Nino_09
DurationExampleFin4910aSpring2017.xls
