Does it make sense to aggregate different modified durations into one overall duration measure?
In the context of insurance liabilities:
Total Value Discounted Outstanding Claims: $1500 Duration of Discounted Outstanding Claims: 0.73 Total Value Discounted Recoveries: -$650 Duration of Discounted Recoveries: 0.43 Total Value of Discounted Net Outstanding Claims: $850 Duration of Discounted Net Outstanding Claims: ????
So I know that this is a simple example, and we could have a number of other components for which we have calculated the duration.
If I take a sum product / weighted average, I get a "Total" duration of 0.959 which I'm finding hard to make sense of since, both the duration components are less than 0.959.
Should the underlying cashflows be brought together upon which a duration calculation can be made, rather than some sort of weighted average portfolio approach?