Definition
Duration measures how sensitive a bond's price is to changes in interest rates, expressed in years. Macaulay duration is the present-value-weighted average time to receive the bond's cash flows, and modified duration converts it into an approximate percentage price change for a one percentage point change in yield.
How it works
A zero-coupon bond's Macaulay duration equals its maturity, while coupon payments return cash earlier and make a coupon bond's duration shorter than its maturity. Longer maturity, lower coupon and lower yield all lengthen duration, meaning greater price sensitivity. Modified duration is Macaulay duration divided by one plus the yield per period.
For a small, parallel shift in yield, the price change is approximately negative modified duration times the yield change. Portfolio managers use it to compare interest-rate sensitivity across bonds and to match assets with liabilities.
Formula / convention
Macaulay duration = Σ (t × PV of cash flow at time t) ÷ Bond price; Modified duration = Macaulay duration ÷ (1 + y ÷ m); Price change % ≈ −Modified duration × Yield change (m = payments per year, y = annual yield)
Illustrative example
A fictional bond has a modified duration of 6.0 years. If its yield rises by 0.50 percentage points (50 basis points), the estimated price change is −6.0 × 0.50% = −3.0%, or about −HK$30,000 on a HK$1,000,000 holding. A 0.50-point fall would raise the estimate by about 3.0%, although convexity means actual changes differ slightly.
What to watch for
Duration is a linear estimate for small, parallel yield changes; large moves, changes in the shape of the yield curve, credit-spread shifts and call features can make actual price changes differ materially.