Existing attribution models have interaction terms that are difficult to understand and inconsistent with symmetry conditions that should ideally
exist. The author introduces a new attribution model without interaction terms that meets the symmetry conditions. In addition, he uses a ratio test
to illustrate how this new arithmetic model is consistent with a recently developed geometric model under certain conditions.
. . . Practitioners can benefit from the author’s demonstration of the difference between an arithmetic attribution model and a geometric attribution
model. The primary difference is in how security weightings are determined - that is, by either the initial holdings of securities (arithmetic)
or the end-of-period holdings of securities (geometric). The two models are connected through the two symmetry conditions and the newly introduced ratio condition.
     Furthermore, the author also makes the very logical point that attribution models should not contain cross-product or interaction terms that cannot be easily explained. Practitioners can certainly benefit from such logic and consequently benefit from the arithmetic model that is introduced, which does not have such terms because of its canonical form.

CFA Digest, Thomas M. Arnold, CFA
Posted online on 2013-05-08.(doi: 10.2469/dig.v43.n2.44)
Digest Summary of Y. K. Shestopaloff’s article “Conceptual framework for
developing and verification of attribution models. Arithmetic attribution models”.
Journal of Performance Measurement, 2012, 17(1), 48-59.

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