Effective Duration¶
One-line definition¶
Duration measured by bumping yield up and down and repricing, rather than from a closed-form price/yield formula.
Formula¶
EffectiveDuration = (Price_down - Price_up) / (2 * Price_base * bump)
Why PMs care¶
Modified duration assumes price is a smooth, closed-form function of yield. That breaks down for instruments whose cash flows themselves change with rates — an MBS whose prepayment speed responds to rates is the classic example. Effective duration works regardless, because it never assumes a formula — it just reprices.
Worked example¶
Price_base = 100, Price_up = 98 (yields +25bp), Price_down = 102.5
(yields -25bp):
EffectiveDuration = (102.5 - 98) / (2 * 100 * 0.0025) = 9.0
Common mistakes¶
- using too large a bump (introduces convexity error) or too small a bump (numerical noise dominates)
- holding cash flows fixed when repricing an instrument whose cash flows should change with rates (e.g. forgetting to update the prepayment assumption when bumping an MBS's yield)