In: Finance
Use the following information to determine duration and convexity, and then use those metrics to predict a percentage change in the price of the bond assuming a 130 basis-point increase in yield. Time-to-maturity = 7 years, Coupon rate = 4%, paid semi-annually, Current bond-equivalent yield-to-maturity = 6.0%.
We use excel to find the duration and convexity
We first chalk out the cash-flows
Bond pays (4%/2) 2% coupon every 6 months and has a face value of $1000
Duration = Time weighted PV / PV
Convexity = Time^2 weighted PV / (PV*(1+ytm/2)^2)
Term | Period | Cash-flow | Present value | Time weighted PV | Time^2 weighted PV |
0.5 | 1 | 20 | 19.41747573 | 9.708737864 | 9.708737864 |
1 | 2 | 20 | 18.85191818 | 18.85191818 | 28.27787727 |
1.5 | 3 | 20 | 18.30283319 | 27.45424978 | 54.90849956 |
2 | 4 | 20 | 17.76974096 | 35.53948192 | 88.84870479 |
2.5 | 5 | 20 | 17.25217569 | 43.13043922 | 129.3913177 |
3 | 6 | 20 | 16.74968513 | 50.2490554 | 175.8716939 |
3.5 | 7 | 20 | 16.26183023 | 56.91640579 | 227.6656232 |
4 | 8 | 20 | 15.78818469 | 63.15273875 | 284.1873244 |
4.5 | 9 | 20 | 15.32833465 | 68.97750591 | 344.8875296 |
5 | 10 | 20 | 14.8818783 | 74.40939149 | 409.2516532 |
5.5 | 11 | 20 | 14.44842553 | 79.46634043 | 476.7980426 |
6 | 12 | 20 | 14.0275976 | 84.16558562 | 547.0763066 |
6.5 | 13 | 20 | 13.6190268 | 88.5236742 | 619.6657194 |
7 | 14 | 1020 | 674.3401619 | 4720.381134 | 35402.8585 |
887.0392686 | 5420.926658 | 38799.39753 | |||
Duration | 6.111258937 | ||||
Convexity | 41.22946377 |
We get
Duration | 6.111258937 |
Convexity | 41.22946377 |
Percentage change in price of the bond = -Duration*Change in yield + 0.5*Convexity*(Change in yield)^2
For a 130 basis-point increase in yield
Percentage change in price of the bond = -6.111258937*0.013+0.5*41.22946377*(0.013*0.013)
Percentage change in price of the bond = -0.0759 = -7.59%