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Indexes
Fundamental Indexing: Breakthrough or Old Idea in New Marketing Garb?
Authors: Michael Edesess
Source: Advisor Perspectives
Date: August 2008

In this article, Edesess analyses the arguments of fundamental indexing promoters to see if they hold up. Fundamental indexation appears to be a strategy consisting of value-tilting stock portfolios. Its promoters have introduced this new form of index weighting as an alternative to capitalisation weighting, which was said to overweight overpriced stocks and underweight underpriced stocks. Several authors, including Arnott and Hsu (2008), Hsu (2006) and Treynor (2005), have attempted to mathematically prove this over-weighting/under-weighting argument. Other authors, including Kaplan (2008) and Perold (2007), have criticised these proofs, underlining that part of the demonstration assumed that the fair values of stocks were known by the asset allocator. In fact fair values are not known. They are not observable, not even a posteriori. Thus, it is necessary to estimate them using fundamental ratios. As a result, according to Edesess, it is not possible to test hypotheses related to fair values using observable data. So he proposes to test the assertion made by fundamental indexing promoters about the mathematical relation between fair values and market prices.

The advocates of fundamental indexing claim that a market-cap-weighted portfolio will be overpriced on average, though some of the stocks in it may be overpriced and some underpriced. Using mathematical arguments, the author of the present article proves that these claims are false. He also proposes an intuitive explanation of his formal proof. Using simple arguments, he explains that if a sample of data is measured with an unbiased error, and if we don’t know whether the average measurement error is negative or positive, the best estimate of the average measurement error of the sample will be zero. As a result, the market price of stocks can be considered an unbiased estimate of their fair value. This conclusion is extended to a market-cap-weighted index portfolio which is the average market cap of all stocks. So, the author concludes that the average mispricing in a market-cap-weighted portfolio is expected to be zero. The formal proof is provided in the appendix of the article.

Indeed, there is no theoretical argument to claim that fundamental indexing has a superior ability to outperform market-cap indexing. This is not a passive strategy based on the statistical properties of stock prices. Fundamental indexing is nothing but an active stock-picking strategy that takes advantage of superior returns produced on average by value-oriented stocks for some years. The author notes that the observation of historical records is not a sufficient argument to claim that the strategy will continue to perform in the future. He underlines that, if historical records have shown small-cap stocks and value stocks to be underpriced, a time could come when larger-cap and growth stocks would be underpriced, and smaller-cap and value stocks would be overpriced. This could happen, for example, if massive investment in small-cap and value stocks were to cause a value and small-cap stock bubble.

References

Arnott, Robert and Jason Hsu, “Noise, CAPM and the Size and Value Effects”, Journal of Investment Management, vol.6, n°1, 2008, pp. 1-11.

Hsu, Jason, “Cap Weighted Portfolios are Sub-optimal Portfolios”, Journal of Investment Management, vol. 4, n°3, Third Quarter 2006, p. 44-53.

Kaplan, Paul D., “Why Fundamental Indexation Might – or Might not – Work”, Financial Analysts Journal, vol. 64, n°1, January/February 2008, pp. 32-39.

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