Bond Price Change Calculator (Duration & Convexity for a Yield Shock)

How it works

ΔP ÷ P ≈ −D_mod × Δy + ½ × C × Δy² · D_mod = D_Macaulay ÷ (1 + y/f) · numerically: D_mod = (P(y−h) − P(y+h)) ÷ (2hP), C = (P(y+h) + P(y−h) − 2P) ÷ (h²P) · DV01 = value × D_mod × 0.0001 · break-even yield rise ≈ yield ÷ duration

A bond's price and its yield move in opposite directions along a curve, and duration is the slope of that curve — the percentage price change for a small change in yield — while convexity is its curvature, the correction that makes the estimate right for bigger moves and that always works in the holder's favour. Together they turn a rate scenario into a dollar figure for a bond or a fund, show how many basis points of rising yields a year of income can absorb, and explain why long-maturity, low-coupon bonds are the most rate-sensitive. Because an individual bond held to maturity returns its face regardless, these are measures of interim price risk and of what a fund, which never matures, will actually show on the statement.

Worked example

A 10-year 4% semi-annual bond yielding 4.6% prices at 95.23 with a modified duration of 8.10 years and convexity of about 78. A 100 bp rise in yields cuts it by about 7.7% (duration −8.10% plus convexity +0.39%; exact −7.73%) — about $7,350 on a $95,230 position, with a DV01 of $77 — and it would take a rise of roughly 57 bp within a year to erase a year of coupon income. A 200 bp fall would add about 17.8%, where the duration-only estimate of 16.2% is off by 1.6 points.

Frequently asked questions