Monday, February 14, 2011

An animated debate on geometric vs. arithmetic attribution

Here's a new way to communicate ideas, issues, and controversial topics. Hope you like it!


  1. He Who Joined the Dark SideFebruary 14, 2011 at 10:12 PM

    I say "Go Animate!" Who wouldn't rather watch a video than read? The English guy defending geometric attribution was hilarious! Who was he? I can't imagine anyone like that... Love the video!

    Perhaps you can create a sequel where the British guy talks about how the "residual" is really an error term caused by the ridiculous process of linking arithmetic effects that are not mathematically linkable. Then show the entourage of PhD-types who create insanely complex gyrations to eliminate the self inflicted wound of the residual error term and then fight with each other over whose method is best. Maybe have the English guy talk about how you can only reconcile beginning and ending quantities of money when you use geometric attribution - while the American keeps saying "But arithmetic is more intuitive." Then have a chorus of investment clients all look bored while holding up a sign that says "Who cares? Just tell me what happened!"

    More videos please! I want to put this on my iPod!

  2. While there are exact arithmetic models that do not have residuals, the ones mentioned in this animation do have residuals but do not “eliminate the residual.” The “residuals’ they confront arise due to mistaking an economic question about multi-period results as one that should formally privilege single-day calculations. Then, some of these “linking” methods you mention distribute the created residual across time, implying that the evaluation of past results need to be constantly revised in light of any future results. The other arithmetic models you mention (along with an old one of mine you do not) distribute the residual to the current period’s elements, like allocation, even when such period’s allocation decisions are exactly null. These are all untenable and, thus, mislead their users about the sources of the results of the investment processes.
    There are also “residuals” in standard geometric models. Instead of arising from the geometric process of temporal compounding over time, they arise from taking the weighted average. These geometric residuals show up in nesting situations such as when one considers the selection decision within a single sector. Then the standard geometric models encounter residuals when they multiply this sector’s allocation effect times the selection effect obtained within another sector. Such standard approaches to geometric attribution then also find it necessary to “smooth” the residual they create over their various attribution components. This again leads to the warping of the measures of allocation and/or selection effects.
    I believe that, when the economic question regarding attribution is properly formulated, the fact that multi-period fund returns are geometric products of arithmetically weighted sums of issue returns leads to the recognition that there are other economically, as opposed to mathematically, necessary contributors to attribution than the standard ones.
    When seeking the arithmetic contributions to the arithmetic active return, one finds that the clear and precise economically formulated question leads to cases where there are economically meaningful contributions due to the effects of temporally dependent decisions. When seeking the geometric contributions to the geometric active return, one finds that the clear and precise economically formulated question leads to cases where there are economically meaningful contributions due to the effects of the nesting of decisions.
    As is common in basic research, when a clear enough formulation of a question is finally achieved, the mathematical answer is fairly straightforward. It is only while the question is unclear that we have arguments such as that highlighted by this animation.

  3. Thanks for your enthusiastic and supportive comments. I was thrilled to learn that I could do these, as I think they can be a helpful way to communicate. More are in the works.

    I am thinking of making Mondays animation day.

    As for the identity of the British chap, I must remain silent on that one. Sorry.

  4. Andre, thanks for your input. I always appreciate and value your insights and contributions. Thanks!

  5. I love this video, and yes, geometric is indeed better, thanks...

  6. William, you made me laugh. Perhaps you can offer a clear explanation/justification for your clearly incorrect opinion. :-)


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