Price Change from Duration

Bonds & Fixed Income

Updated Apr 2026 • Has calculator

Approximates the dollar price change of a bond from a given yield shift using modified duration.

What is Duration Price Approximation?

The duration price approximation estimates how much a bond's dollar price will change when yields shift by a given amount. It applies the linear relationship implied by modified duration: a bond with modified duration of 4 loses about 4% of its price for every 1% rise in yield. The formula is ΔPrice ≈ −ModDuration × ΔY × Price, where ΔY is in decimal. This is a first-order approximation; adding the convexity adjustment improves accuracy for larger yield moves. The sign is important: a positive yield change (rates rise) produces a negative price change, and vice versa.

Formula

ΔPrice ≈ −ModDuration × (ΔY / 100) × Price

Worked Example

5-year maturity — 100 bps yield rise scenario

Step 1 Bond price: $1,000 | Modified duration: 3.99 yrs | Yield rises 1%

Step 2 ΔPrice ≈ −3.99 × (1/100) × $1,000

Step 3 ΔPrice ≈ −$39.90

Step 4 New estimated price: $1,000 − $39.90 = $960.10

Step 5 → For large moves, add convexity: + 0.5 × 21.04 × 0.01² × $1,000 ≈ +$1.05

Source: CFA Institute — Fixed Income Analysis, 3rd ed., Ch. 5 (2023-01-01)

Calculate Duration Price Approximation

Modified Duration (yrs)

Modified duration of the bond in years

Yield Change ΔY (%)

Yield change in percent (positive = rates rise)

Current Bond Price ($)

Current clean price of the bond

Estimated Price Change

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Not investment advice.

How to Interpret Duration Price Approximation

< -50

< −$50: Large loss — high-duration bond in a rising-rate environment

-50 – -20

−$50 to −$20: Moderate loss — intermediate duration, +1% yield rise

-20 – 0

−$20 to $0: Small loss — short duration bond

> 0

> $0: Price gain — yields declined

📚 Bond Risk — Complete the path

Sources