B5
Price–Yield Visualizer
See convexity instead of reading about it: price–yield curves for up to four bonds, and how far a duration estimate misses as the yield move grows.
Learning focus: duration's error grows with the size of the move, and longer and lower-coupon bonds curve more.
Bonds
NameYearsCoupon %
Semiannual coupons, settling today.
Yields
%
bp
bp
Price–yield curves
The dashed line is the duration estimate: a straight tangent at the centre yield. The dotted line adds convexity. The real curve bows above both, so duration alone always underestimates the price.
Estimates for a 200bp move (price change, % of starting price)
| Bond | Mod. duration | Convexity | Move | Actual | Duration only | + Convexity | Duration error |
|---|---|---|---|---|---|---|---|
| 2-year 4% | 1.90 | 4.6 | −200bp | 3.90% | 3.81% | 3.90% | -0.09% |
| +200bp | -3.72% | -3.81% | -3.72% | -0.09% | |||
| 10-year 4% | 8.18 | 78.9 | −200bp | 18.05% | 16.35% | 17.93% | -1.69% |
| +200bp | -14.88% | -16.35% | -14.77% | -1.47% | |||
| 30-year 4% | 17.38 | 420.8 | −200bp | 44.96% | 34.76% | 43.18% | -10.19% |
| +200bp | -27.68% | -34.76% | -26.34% | -7.09% | |||
| 10-year zero | 9.80 | 100.9 | −200bp | 21.78% | 19.61% | 21.63% | -2.17% |
| +200bp | -17.73% | -19.61% | -17.59% | -1.88% |
Callable bonds, whose curve bends the other way (negative convexity), arrive with B6 in Phase 3.