What is the duration (in years) of a 4-year coupon bond selling of 89.84 of par, with semi-annual payments and a yield of 9.6% if we use a rate shock of 5bps?
|
Year (1) |
Value recieved (2) |
Present value @ 4.55% semi annual (3) |
Present value (4) |
Present value/ purchase price (5) |
Duration (1*5) |
| .5 | 4.8 | .9565 | 4.5911 | .05110 | .0256 |
| 1 | 4.8 | .9149 | 4.3913 | .04888 | .0489 |
| 1.5 | 4.8 | .8750 | 4.2002 | .0468 | .0701 |
| 2 | 4.8 | .8369 | 4.0174 | .0447 | .0894 |
| 2.5 | 4.8 | .8005 | 3.8426 | .0428 | .1096 |
| 3 | 4.8 | .7657 | 3.6753 | .0391 | .1227 |
| 3.5 | 4.8 | .7323 | 3.5154 | .0409 | .1370 |
| 4 | 4.8 | .7005 | 3.3624 | .0391 | .1497 |
| 4 | 100 | .7005 | 70.450 | .7797 | 3.1189 |
| 3.8692 |
Refer duration table above duration is 3.8692 year
Rate we use to discounting is 5 point lower than 9.6 i.e. 9.1% that become 4.55% semi annual
Interest we received 4.8,$ semi annual and redumption value of 100$ at end of 4 th year
These sum pull back at zero year devide by purchase prices than miltupiled by respective years
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