##  [Modified Duration](/modified-duration-1) 

 Definition

A bond-price sensitivity measure equal to the negative percentage change in price per unit change in yield for small parallel shifts in the yield curve; numerically, modified duration is Macaulay duration divided by (1 + yield per period) and serves as a first-order (linear) approximation to price changes.

 

 

 

 

 

 





## Principle

Principle

Modified duration provides a linear approximation: for a small parallel change Δy in yield, the percentage change in bond price ≈ −(Modified Duration) × Δy, making it usable for first-order hedging and immunization under the parallel-shift assumption.

 

 

 

 

 





## Demonstration

Demonstration

Illustrative calculation: compute Macaulay duration from discounted cash flows and divide by (1 + yield per period) to obtain modified duration; if MD = 6.2 and yields rise by 0.01 (1 percentage point), the bond price is approximated to fall by about 6.2%.

 

 

 

 

## Misapplication

Misapplication

Applying modified duration to large yield moves, non-parallel curve shifts, callable or path-dependent cash flows, or treating its linear estimate as exact; the semantic error is ignoring curvature (convexity), option features or changing cash-flow timing that invalidate the linear approximation.

 

 

 

 

 





## Consequence

Consequence

Used for interest-rate risk management, duration-matching and immunization strategies; relying solely on modified duration can leave residual exposure (convexity gap) leading to hedge ineffectiveness or unexpected P&L for large moves or non-parallel shifts.

 

 

 

 

## Reversal

Reversal

When yield changes are large or when instruments have significant convexity, embedded options, or cash flows that change with rates, the linear approximation fails and second-order (convexity) or scenario-based analysis is required.

 

 

 

 

 





## Boundary

Boundary

Applies to fixed-income instruments with determinable discounted cash flows and when considering small, parallel yield changes expressed in the same compounding convention; it excludes credit spread risk decomposition, non-parallel curve dynamics and instruments with optionality unless adjusted.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Simplicity versus accuracy: modified duration offers a simple, comparable sensitivity metric but conflicts with the need for convexity and option-adjusted measures when precision across realistic yield scenarios is required.

 

 

 

 

 





## Synthesis

Synthesis

Modified duration is a practical first-order sensitivity for small, parallel yield moves and a foundational tool for hedging and immunization; practitioners must pair it with convexity analysis and instrument-specific adjustments when facing larger moves, optionality or non-parallel shifts.