Why Fundamental Indexation Might – or Might Not – Work
Authors: Paul D. Kaplan
Source: Financial Analysts Journal, vol. 64, n°1
Date: January/February 2008
In this article, Kaplan makes his contribution to the debate between the supporters of fundamental-weighted indices and those of capitalisation-weighted indices. For Kaplan, fundamental indexers have based their theories on questionable assumptions. In this article, he examines the underlying theory of fundamental indexation from the point of view of fair value multiples, unobservable numbers that make it possible to equate the fair value of a stock, also unobserved, to some observed measure of the stock’s fundamental value. Like Hsu (2006), he assumes that a stock’s market value differs from its fair value by an independent multiplicative error term. But Hsu also assumes that the stock’s market value is independent of the fair value multiple, which is not true, because the sources of errors also influence market values. He also notes that Hsu’s conclusion that fundamental-weighted indices lead to higher expected returns than capitalisation-weighted indices has no theoretical underpinning despite Hsu’s arguments to the contrary.
According to Kaplan, it is impossible to make an absolute decision as to whether fundamental- or capitalisation-weighted indices are superior; this superiority will depend on market context, as capitalisation weighting will lead to weighting error if market prices contain noise, while fundamental weighting will lead to error by failing to consider risk and expected growth. Assuming that investors know only the probability distributions of the errors, not the pricing errors of individual stocks, the author comes up with a boundary condition, in the form of an inequality, that fundamental-weighting schemes must satisfy to add positive value. His argument is based on the fact that a fundamental-weighted index will outperform a capitalisation-weighted index of the same universe only if fundamental variables contain more information about stocks’ fair values than do market values, i.e., if they are highly correlated with these fair values. He also notes that as there is no theoretical foundation for deciding whether the inequality he derives holds or not, there is no theoretical foundation for fundamental indexation. In addition, he points out that fundamental indices are value-biased indices.
Finally, Kaplan suggests using a combination of both weighting systems to capture the information contained in both these systems. He puts forward two approaches, one theoretical, the other pragmatic. The second approach draws on Ara and Kaplan (2006, 2007) and makes it possible to combine the best elements of the two systems, i.e., low turnover but a rather diversified index. The purpose is to avoid concentration in a few large stocks, a drawback of capitalisation weighting, while limiting the more frequent rebalancing and thus higher transaction costs typical of fundamental indexation. He concludes by encouraging the development of other approaches mixing these two forms of indexation.
Arya, Sanjay, and Paul Kaplan, “Collared Weighting: A Hybrid Approach”, Morningstar Indexes Yearbook, vol.3, 2007, p. 22-25.
Hsu, Jason, “Cap Weighted Portfolios Are Sub-Optimal Portfolios”, Journal of Investment Management, vol. 4, n°3, 2006, p. 44-53.