| | | Convexity of a Bond |
| | N = | 10 | | | | | | | | | Duration of the bond |
| | Coupon = | 5% |
| | FV = | 100 |
| | YTM = | 5.50% | with continuous compounding | | | | | | | | Time | CF | PV | Weight | Time x Weight |
| | | 3 | | | | | | | | | 1 | 5 | $ 4.74 | 0.0492494859 | 0.0492494859 |
| | Time | CF | PV | nx(n+1) | PV x (n(N+1)) | | | | | | 2 | 5 | $ 4.49 | 0.0466819772 | 0.0933639543 |
| | 1 | 5 | $ 4.74 | 2 | $ 9.48 | | | | | | 3 | 5 | $ 4.26 | 0.0442483196 | 0.1327449588 |
| | 2 | 5 | $ 4.49 | 6 | $ 26.95 | | | | | | 4 | 5 | $ 4.04 | 0.0419415352 | 0.1677661406 |
| | 3 | 5 | $ 4.26 | 12 | $ 51.10 | | | | | | 5 | 5 | $ 3.83 | 0.0397550096 | 0.1987750481 |
| | 4 | 5 | $ 4.04 | 20 | $ 80.72 | | | | | | 6 | 5 | $ 3.63 | 0.0376824736 | 0.2260948415 |
| | 5 | 5 | $ 3.83 | 30 | $ 114.77 | | | | | | 7 | 5 | $ 3.44 | 0.0357179844 | 0.2500258911 |
| | 6 | 5 | $ 3.63 | 42 | $ 152.30 | | | | | | 8 | 5 | $ 3.26 | 0.0338559094 | 0.2708472754 |
| | 7 | 5 | $ 3.44 | 56 | $ 192.48 | | | | | | 9 | 5 | $ 3.09 | 0.0320909094 | 0.2888181846 |
| | 8 | 5 | $ 3.26 | 72 | $ 234.58 | | | | | | 10 | 105 | $ 61.47 | 0.6387763957 | 6.3877639569 |
| | 9 | 5 | $ 3.09 | 90 | $ 277.93 |
| | 10 | 105 | $ 61.47 | 110 | $ 6,761.72 | | | | | | | Price = | $ 96.23 | 1 | 8.07 | Macaulay Dutaion |
| | | Price = | $ 96.23 | Total | $ 7,902.04 | | | | | | How we apply duration and convexity to bond analysis |
| | | Find the value of (1+YTM)^2 x Price | | | | $ 107.11 | | | | | Assuming an increase of 100 basis points in yields, what is the total bond price change? |
| | | | | | | | | | | | | | ∆y = | 0.001 |
| | | The convexity of the bond estimate = | | | | 73.7765400882 | | | | | Total price change = | | | 6.5711090351 |
| | | | | | | | | | | | This means that if rates increase by 100 basis points, the price will decrease by 6.57% |
| | The convexity estimate of a bond measures the sensitivity of duration itself to changes in interest rates. |