How this calculator works
Effective duration estimates how much a bond's price changes for a small change in yield. The bond is priced at the current yield, at the yield plus a shift and at the yield minus the shift. The difference between the up and down prices, divided by twice the base price and by the shift, gives the duration. Unlike Macaulay duration, the calculation does not read the bond's cash-flow schedule directly, so the same method can be applied to instruments with embedded options once their prices are known. The result here is in coupon periods; dividing by the coupon frequency expresses it in years, which is the form used for the familiar rule that price change is about minus duration times the yield change.
Formula
Effective duration = (P- - P+) / (2 x P0 x change in yield), with the yield change measured per coupon period. Modified duration in years = effective duration / frequency. Percentage price change is approximately -duration x change in yield.
Worked example
A $1,000 bond with a 5% semi-annual coupon and 10 years left is priced at a 5% yield. Pricing it at 4% and 6% gives $1,081.76 and $925.61 against a $1,000 base price. The effective duration is (1,081.76 - 925.61) / (2 x 1,000 x 0.005) = 15.61 periods. Dividing by two gives a modified duration of 7.81 years, so a one percentage point rise in yield lowers the price by roughly 7.81%.
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Frequently asked questions
Is effective duration the same as Macaulay duration?
No. Macaulay duration is a present-value weighted average time to the cash flows. Effective duration is a price sensitivity measured from shifted prices. For option-free bonds the two are closely related through modified duration.
Why divide by the coupon frequency?
The finite-difference duration is measured per coupon period. Dividing by the number of periods in a year converts it to a per-year sensitivity, which is how duration is usually quoted.
How large should the yield shift be?
Small shifts give a more local estimate but can lose precision in the price difference. A shift of 1 basis point to 1 percentage point is common. Use the same shift when comparing bonds.
Does duration replace convexity?
They answer different parts of the same question. Duration gives the linear price change and convexity corrects for curvature, so larger yield moves need both.