Lesson 3 of 5 · 12 min
Estimating price changes with effective duration and convexity
Plug effective duration and effective convexity into the familiar duration-plus-convexity formula, with ΔCurve in place of ΔYield, to estimate the percentage change in a bond's full price for a shift in the benchmark curve.
In short
- %ΔPV^Full ≈ (−EffDur × ΔCurve) + ½ × EffCon × (ΔCurve)².
- The duration term has the opposite sign to ΔCurve; the convexity term has the sign of EffCon whatever the direction of the shift.
- With negative effective convexity, losses from a rise are bigger than gains from an equal fall.
- Issuer's view of a callable: it can refinance at lower rates. Investor's view: price gains are capped. A put limits the investor's losses.
- Unlike yield duration, a smaller ΔCurve does not necessarily make effective measures more accurate, because pricing models embed assumptions about issuer and borrower behaviour.
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