## What is Effective Duration?

Effective duration is a duration calculation for bonds that have embedded options. This measure of duration takes into account the fact that expected cash flows will fluctuate as interest rates change and is, therefore, a measure of risk.

Effective duration can be estimated using modified duration if a bond with embedded options behaves like an option-free bond.

Effective duration is a duration calculation for bonds that have embedded options.

Cash flows are uncertain in bonds with embedded options, making it difficult to know the rate of return.

The impact on cash flows as interest rates change is measured by effective duration.

## How to Calculate Effective Duration

**Effective duration = (P(1) – P(2)) / (2 x P(0) x Y)**

### where:

**P(0) =**the bond’s original price per $100 worth of par value.**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).

## 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. It is also found that by increasing the yield by 10 basis points, the bond’s price is expected to be $99.25. Given this information, the effective duration would be calculated as:

**Effective duration = ($101 – $99.25) / (2 x $100 x 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.