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. Some proponents of fundamental indexation claim that their strategy is based on a revolutionary new paradigm, the “noisy-market hypothesis,” in which market prices of stocks deviate from their fair values. Skeptics are quick to argue that fundamental indexation is nothing more than value investing in a different guise. Proponents claim that their approach is different from value investing because it takes advantage of the noise in stock prices rather than value premiums. Researchers have already shown, however, that noise in stock prices can serve as the rationale for value investing. Proponents of fundamental indexation assert that fundamental weights can be unbiased estimators of the unobservable fair value weights, with “errors” that are statistically independent of market values. Referring to this assertion as the “independence assumption,” I demonstrate that it is internally inconsistent. The so-called errors are actually restatements of the fair value multiples of the stocks in question. (The fair value multiple is the ratio of the unobservable fair value of a stock to some observed measure of the stock’s fundamental value.) For example, if the fundamental weights are based on earnings, the “errors” in the fundamental weights are restatements of the fair P/Es of the stocks. A stock’s fair value multiple, by definition, reflects investors’ assessments of the stock’s risk and future growth prospects. Ideally, such factors should be fully taken into account in portfolio construction. Because they are unobservable, however, they must be either taken into account through proxies or ignored. Market-cap weighting takes risk and expected growth into account by using the market values of stocks as proxies for their unobservable fair values. If market prices contain noise, market-cap weights contain errors. Fundamental-weighting schemes introduce weighting errors of a different type by ignoring risk and expected growth. The superior weighting scheme is the one with the less egregious type of error. In this article, I demonstrate that, except in trivial cases, fundamental weights cannot be unbiased estimators of fair value weights with errors that are statistically independent of market values because the sources of those errors, risk and expected growth, are also determinants of market values. I carry out this demonstration formally by showing that the errors are restatements of fair value multiples and that fair value multiples are correlated with market values unless all stocks have the same fair value multiple. I also show under what conditions fundamental weights are better than market value weights as estimators of fair value weights and under what conditions they are worse. Specifically, in order for fundamental weighting to be superior to market value weighting, the valuation errors that the market makes must be more variable across stocks than the variability of fair value multiples. Conversely, if the market’s value errors across stocks are less variable than fair value multiples, weighting by market value will be superior to weighting by fundamental value. Thus, the case for fundamental indexation is a conjecture about unobservable variables rather than a theory. I next show in a precise fashion that fundamental weighting is inherently value biased by developing a formula for the bias. According to this formula, the yield on a fundamentally weighted index exceeds the yield on a market-value-weighted index of the same stocks by the ratio of the variance of yield across the stocks in the index to the yield on the market-weighted index. Finally, I discuss two approaches to combining fundamental data and market value data to form weights that yield better portfolios than could be obtained by using only one or the other. Note: Morningstar develops and licenses equity indices; it may use commercially some of the methods discussed in this article.