 
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 endofperiod 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 crossproduct 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 20130508.(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), 4859.
