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

\text{Average Duration}_{t} = \frac{\sum_{i} (MD_{i,t} \times V_{i,t})}{\sum_{i}V_{i,t}} |

where,

MD_{i,t} is the modified duration of asset *i* at time *t*.

V_{i,t} represents the index weight of asset *i* at time *t.*