What is Modified Duration?
Modified Duration adjusts Macaulay Duration for the current yield level to give a direct measure of price sensitivity: the percentage change in bond price for a 1% (100 basis point) change in yield. A Modified Duration of 6 means the bond price falls approximately 6% for every 1% rise in yield. This linearity is an approximation; convexity accounts for the second-order curvature. Modified Duration is the most practical tool for bond risk management, allowing portfolio managers to quickly quantify how much a rate move will affect their portfolio's value. Dollar Duration (DV01 × 10,000) expresses the dollar loss per basis point of yield increase.
Formula
Modified Duration = Macaulay Duration / (1 + y/n)
Price Change ≈ −Modified Duration × ΔYield × Bond Price
DV01 = Modified Duration × Bond Price / 10,000
y = yield to maturity
n = coupon payments per year
DV01 = Dollar Value of 1 basis point (0.01%)
Calculator
How to Use
- 1Calculate Macaulay Duration: Use the Macaulay Duration calculator or enter it directly.
- 2Divide by (1 + y/n): y = YTM, n = number of coupon periods per year (2 for semi-annual).
- 3Estimate price change: % Price Change ≈ −Modified Duration × Δ Yield. A 0.50% rate rise on a 6.0 Mod.Dur bond → −3% price change.
- 4Compute DV01: Modified Duration × Price / 10,000 gives the dollar loss per basis point, essential for hedging.
Worked Example
Example: 10-year corporate bond
Mac. Duration
7.80 years
YTM
5%
Price
$950
Mod. Duration = 7.80 / (1 + 0.05/2) = 7.61. If rates rise 1%, price falls ≈ 7.61%. On a $950 bond, that is −$72.30. DV01 = 7.61 × 950 / 10,000 = $0.72 per basis point per bond. A $10M bond portfolio at this duration has DV01 of $7,200, meaning every basis point of yield increase costs $7,200.