# Understanding Effective Duration: Definition, Formula & Examples

![Effective Duration: A calculation for bonds with embedded options that takes into account that expected cash flows fluctuate as interest rates change.](https://www.investopedia.com/thmb/97dE2kTqcuouyGraSzejic_S0ZU=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/final111-8868f6c3ce884d28b2a2aea534a65f44.jpg)

*— Jake Shi / Investopedia*

> **Definition**
>
> Effective duration is a measure that tells you how sensitive bonds with embedded options are to changes in interest rates.

## What Is Effective Duration?

Effective duration is a [duration](https://www.investopedia.com/terms/d/duration.asp) calculation for bonds that have embedded options. It is used to measure the risk that expected cash flows will fluctuate as interest rates change.

Effective duration can be estimated using [modified duration](https://www.investopedia.com/terms/m/modifiedduration.asp) if a bond with embedded options behaves like an option-free bond.

### Key Takeaways

*   Effective duration shows how sensitive bonds with embedded options are to changes in interest rates.
*   It accounts for fluctuating expected cash flows due to changing interest rates, providing a risk measure.  
    
*   Effective duration estimates a bond's price decline when interest rates increase by 1%.  
    
*   A bond behaves like an option-free bond if exercising its embedded option offers no benefit.  
    
*   Effective duration is lower than the bond's maturity, indicating how price sensitivity decreases over time.

## How Effective Duration Impacts Bond Pricing

A bond that has an embedded feature increases the uncertainty of cash flows, thus making it hard for an investor to determine the [rate of return](https://www.investopedia.com/terms/r/rateofreturn.asp) of a bond. The effective duration helps calculate the [volatility](https://www.investopedia.com/terms/v/volatility.asp) of interest rates in relation to the yield curve and, therefore, the expected cash flows from the bond. Effective duration calculates the expected price decline of a bond when [interest rates](https://www.investopedia.com/terms/i/interestrate.asp) rise by 1%. The value of the effective duration will always be lower than the maturity of the [bond](https://www.investopedia.com/terms/b/bond.asp).

A bond with embedded options acts like an option-free bond if exercising the [option](https://www.investopedia.com/terms/e/embeddedoption.asp) doesn't benefit the investor. As such, the security’s cash flows can’t be expected to change given a change in [yield](https://www.investopedia.com/terms/y/yield.asp). For instance, if interest rates are 10% and a [callable bond](https://www.investopedia.com/terms/c/callablebond.asp) pays a 6% coupon, the bond behaves like an option-free bond. The company wouldn't benefit from calling and reissuing it at a higher rate.

> **Important**
>
> The longer a bond's maturity, the greater its effective duration.

## Calculating Effective Duration: A Step-by-Step Guide

The formula for effective duration contains four variables. They are:

*   P(0) = the bond’s original price per $100 worth of [par value](https://www.investopedia.com/terms/p/parvalue.asp)
*   P(1) = the price of the bond if the yield were to decrease by Y percent
*   P(2) = the price of the bond if the yield were to increase by Y percent
*   Y = the estimated change in yield used to calculate P(1) and P(2)

The full formula for effective duration is:

Effective duration = (P(1) - P(2)) / (2 × P(0) × Y)

## Example of Effective Duration

As an example, assume that an investor purchases a bond for 100% par and that the bond is currently yielding 6%. Using a 10 basis-point change in yield (0.1%), it is calculated that with a yield decrease of that amount, the bond is priced at $101. Increasing the yield by 10 [basis points](https://www.investopedia.com/terms/b/basispoint.asp) is expected to lower the bond's price to $99.25. Given this information, the effective duration would be calculated as:

Effective duration = ($101 - $99.25) / (2 × $100 × 0.001) = $1.75 / $0.20 = 8.75

The effective duration of 8.75 means that if there were to be a change in yield of 100 basis points, or 1%, then the bond’s price would be expected to change by 8.75%. This is an approximation. The estimate can be made more accurate by factoring in the bond’s effective [convexity](https://www.investopedia.com/terms/c/convexity.asp).