Private equtity attribution

I'll be teaching a class for a client later this month who asked for some specific topics to be included, one of which is private equity attribution. The challenges with private equity are:

1. They typically don't have indexes, so we can't use relative attribution
2. They use IRR, not TWRR, since the manager controls the cash flows.

And so, what is a private equity manager to do if they want attribution? The answer is simple: absolute attribution (aka contribution)! We can utilize IRR at all levels and reconcile to the overall return. We calculate our sector returns, for example, using IRR; calculate their weights, taking cash flows into consideration; and simply multiply the weights by the individual returns. Their sum should tie out to the overall return. For example:

We can see how each sector contributed to the overall return. And just like hedge fund attribution, we can slice up our private equity portfolio in countless ways (e.g., by industry, subsector, country). Does this not make sense? Thoughts?