VB or VE, which to use?

I had a call on Friday from a longstanding friend and colleague who wanted to know whether she should use the beginning (VB) or ending (VE) values to asset weight portfolio returns. Let's put this into context.

This manager has a client whose history includes returns from a variety of managers, and they want to provide the client with a consolidated return. Of course, you won't be surprised to learn that I suggested that they use money-weighting, not time-weighting, since that would have greater value. But, putting that aside for now, if we are treating the collection as a "composite," do we use VE or VB?

Well, if you're already familiar with GIPS(R) (Global Investment Performance Standards), you probably know that they require the use of beginning values, and even though this client isn't creating performance that needs to comply with GIPS, the rationale behind this rule makes sense. I stumbled upon this scenario, which I think demonstrates why quite well:

If we use VE, we're using the values after the returns have been applied, which is arguably double-counting. In addition, what will we find? Well, let's see:

In spite of the overall market value not changing, by using the ending values we get a nonsensical 25% return.

However, if we use the beginning value:

Doesn't this result make a lot more sense? There was no change in the overall market value, and the 0.0% return reflects this. Using the VE method "double counts" the underlying returns, and this is the reason it's not what we do. Bottom line: VE means an erroneous result. VB is the rule in GIPS and should be the rule in any situation where you're looking to consolidate returns to provide a "big picture." Now, if I can just convince them to use money-weighting!