Why fundamental indexation might-or might not-work

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.