Some proponents of fundamental indexation claim that the strategy is based on a
new theory in which market prices of stocks deviate from fair values. A key
assumption in this approach is that fundamental weights are unbiased estimators
of fair value weights that are statistically independent of market values. This
article demonstrates that, except in trivial cases, this assumption is
internally inconsistent because the sources of the “errors” are
also determinants of market values. The article shows under what conditions
fundamental weights are better—or worse—estimators of fair value
weights than are market value weights, thereby demonstrating that the new theory
is merely a conjecture. A formula is developed for the value bias inherent in
fundamental weighting, and two approaches to combining fundamental and market
values are discussed.