Effective Duration Calculator

Formula

To calculate the Effective Duration ($D$):

\[ D = \frac{V_d - V_i}{2 \times V_0 \times \Delta y} \]

Where:

$D$ is the Effective Duration
$V_d$ is the Value if Yield Decreases ($)
$V_i$ is the Value if Yield Increases ($)
$V_0$ is the Initial Value ($)
$\Delta y$ is the Change in Yield (%)

What is Effective Duration?

Effective duration is a measure of a bond’s sensitivity to changes in interest rates, taking into account the possibility of changes in the bond’s cash flows due to embedded options. It provides a more accurate measure of interest rate risk for bonds with features such as call or put options, which can alter the bond’s cash flows when interest rates change. Effective duration is particularly useful for assessing the risk of bonds with complex structures, as it reflects the bond’s price volatility in response to interest rate movements.

Example Calculation 1

Let's assume the following values:

Value if Yield Decreases ($V_d$) = $1050
Value if Yield Increases ($V_i$) = $950
Initial Value ($V_0$) = $1000
Change in Yield ($\Delta y$) = 1%

Using the formula:

\[ D = \frac{1050 - 950}{2 \times 1000 \times 0.01} = 5 \]

The Effective Duration is 5.

Example Calculation 2

Let's assume the following values:

Value if Yield Decreases ($V_d$) = $1100
Value if Yield Increases ($V_i$) = $900
Initial Value ($V_0$) = $1000
Change in Yield ($\Delta y$) = 2%

Using the formula:

\[ D = \frac{1100 - 900}{2 \times 1000 \times 0.02} = 5 \]

The Effective Duration is 5.