Modified duration
For annual compounding, modified duration equals Macaulay duration divided by (1 + yield). With m payment periods per year, the usual adjustment is by (1 + annual nominal yield/m), using consistent duration units. The approximation is ΔP/P ≈ −D_modified × Δy, where yield change is a decimal. It captures the first-order price effect, holding other factors constant. For larger yield movements, convexity improves the estimate. Changes in credit spreads, cash-flow expectations or embedded-option behaviour may require a more complete valuation.
Worked example
A bond has modified duration 4.5. A yield rise of 0.20 percentage point means Δy = 0.002, so estimated price change is −4.5 × 0.002 = −0.9%. For a $100 price, the first-order estimate is $99.10.
Common mistake
Using a 0.20 percentage point movement as 0.20 rather than 0.002, or forgetting the negative relationship between price and yield.
Where it appears in your exams
| Qualification | Exam | Relationship | Period |
|---|---|---|---|
| ACCA | AFM | Direct | September 2026–June 2027 |