Index Duration

The average duration of the index is calculated as the weighted average modified Duration of all the assets in the index.

$$//<![CDATA[ \begin{array}{l}\displaystyle \text{Average Duration}_{t} = \frac{\sum_{i} (MD_{i,t} \times V_{i,t})}{\sum_{i}V_{i,t}}\end{array} //]]>$$

where,

$//<![CDATA[ \begin{array}{l}MD_{i,t}\end{array} //]]>$ is the modified duration of asset i at time t.
$//<![CDATA[ \begin{array}{l}V_{i,t}\end{array} //]]>$ represents the index weight of asset i at time t.