Old Idea in New Marketing Garb?
August 26, 2008
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For a related discussion of fundamental indexing, see Michael Edesess’ article in this issue, Fundamental Indexing: A Verbal Optical Illusion, and our article, Fundamental Indexing Debunked, which appeared on August 5, 2008.
Advocates of “fundamental indexing” claim that capitalization-weighted indexes overweight overpriced stocks and underweight underpriced stocks. Therefore, they argue, a portfolio created using weightings that are independent of market prices will have less overpricing bias than one created using market weightings. This paper examines their claims and finds them to be provably false, given the advocates’ own assumptions. Therefore, their argument cannot provide support for any particular portfolio strategy.
Several respected names in the investment field have lined up behind a concept they call “fundamental indexing”. In its typical implementation (though not necessarily the only implementation), fundamental indexing takes the form of a discipline for value-tilting a stock portfolio. Its proponents make larger claims for its superiority however, beyond the well-known fact that value and small-cap stocks have historically outperformed the broad stock market (Fama and French 1992, Arnott et al 2005).
Efforts to gain wide acceptance for fundamental indexing have resembled a well-designed marketing campaign, combining two words, both having a certain heft—“fundamental” and “index”—with an intuitively plausible postulate: “the cap-weighted market portfolio overweights overpriced stocks and underweights underpriced stocks.”
Is there substance behind the arguments for fundamental indexing, or is there only marketing buzz? In this paper I attempt to pin down the claims made for the fundamental indexing concept, and investigate whether the claims can be substantiated.
The search for alpha and the Schwert rule
The historical record showing that value and small-cap stocks have outperformed market averages has prompted money managers who specialize in these areas—or wish to—and who seek to promise “alpha” to suggest that this record will continue. But historical records are notoriously poor predictors in the investment field. Historical patterns of anomalous risk-adjusted market-beating performance tend to obey the Schwert rule: “After they are documented and analyzed in the academic literature, anomalies often seem to disappear, reverse, or attenuate.” (Schwert 2003.) Hence, justifications not based on the historical record are needed to present a strong argument that some particular style of investing will produce alpha in the future.
The search for a justification has led several advocates of value and small-cap philosophies to advance the argument that it is in the nature of market-cap-weighted indexes to “overweight overpriced stocks and underweight underpriced stocks.” Several advocates have attempted mathematical proofs of this conjecture (Arnott and Hsu 2008, Hsu 2006, Treynor 2005). Both Kaplan (2008) and Perold (2007) have pointed out, however, that some of the proofs implicitly assume that the person allocating investment weights has knowledge of the “fair” values of the investments—in direct contradiction to the advocates’ assumption that fair values are unknown.
The fundamental indexing approach
The approach of the fundamental indexing advocates (“FI advocates”) involves first making estimates of the fair values of stocks based on a fundamentalist methodology (which for the FI advocates is a value-tilted methodology, based on factors such as low price-to-dividend ratio). They then weight a portfolio in the same way it would have been weighted in a market index if the market prices had been equal to the fundamental price estimates. This could be characterized as a “fair-value-weighted portfolio,” where fair values are estimated according to a fundamental estimation methodology, as contrasted with the market-cap-weighted portfolio in which fair values are estimated by the market prices.
Pinning down the claims
Many claims have been made for the fair-value-weighted portfolio, and against the market-cap-weighted portfolio (Arnott and Hsu 2008, Hsu 2006, Arnott et al 2007, Treynor 2005), though they are not easy to pin down. Among the various statements, the most complete set of claims against the market-cap-weighted portfolio and in favor of alternatively-weighted portfolios is the following (RAFI 2008 p. 4):
“The return drag from capitalization weighting—overweighting overpriced securities and underweighting underpriced securities—is a structural long-term return inhibitor. … [T]he goal of price indifferent indexing is to randomize portfolio weights to approximately allocate half of our money to overvalued shares and half to the undervalued.
“We know that capitalization weighting will structurally place more in securities whose stocks are priced above fair value and less in those that are priced below fair value. Why? Because the weights relative to fair value are not random; they are linked to price and the errors embedded within that price!”
An effort to obtain specific and testable claims from this passage yields the following:
- A market-cap-weighted portfolio will be overpriced on average—that is, its weighted average price will be greater than the weighted average of the stocks’ fair values—though some of the stocks in it may be overpriced and some underpriced.
- For a portfolio to have zero expected pricing error it must use weightings that are not based on market prices, even if the weightings have to be chosen by a random process.
It should be noted that the FI advocates assume a quantity called “fair value” is meaningful, though it is unknown and ill-defined. “Fair values” are unobservable even after the fact. Fair values are stocks’ “(unknowable) discounted future cash flows” (Arnott et al 2005). The fair value of a stock is the best estimate at any point in time of its future cash flows, discounted by the best estimate at that point in time of the future discount rate. It is not the present value of future realized (and therefore observable)—i.e. ex post—earnings discounted by the future realized discount rate, because the future realized values are not the same as, and may bear little relation to, the best estimates of these values ex ante. Hence, it is difficult if not impossible to test hypotheses about fair values using observable data.
Nevertheless, it is possible to evaluate the claims of the FI advocates, because they base their claims on an assumed mathematical relationship between fair values and market prices.
Assumptions made by FI advocates
FI advocates base their claims on the following assumptions:
- Each stock has, at any point in time, an unknown fair value.
- Each stock has a known market price which is an estimate of the stock’s fair value, and is therefore equal to the fair value plus an unknown estimation error (often called “noise”).1 The estimation error is the overpricing (underpricing) of the stock relative to fair value.
- The estimation error is uncorrelated with fair value, and its expected value is zero.
1 The assumption is often stated in a slightly different multiplicative form in which the known market price P is equal to V times a factor (1 + ε).
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