Combining time- and money-weighting

I am in Montana this week, conducting a session titled "Current Topics in Performance Measurement" for a conference of operations folks. One individual asked about combining time- and money-weighting into a single number. I think the idea lacks merit, as it takes away the best that both have to offer.

Time-weighting eliminates (or at least reduces) the effect of cash flows, so as to present the best representation as to how the manager performed.

Money-weighting takes cash flows into consideration, to present the return from the client's perspective, taking into consideration their decisions (as to when to add or remove money) as well as the manager's investment decisions.

There is absolutely nothing wrong having two different returns;  they serve two very different purposes. Perhaps someone can offer a justification for doing so which isn't clear to me, but until that happens, I vote for having two measures.