Fundamental Indexing
Partner and Chief Investment Officer
Fair Advisors
February 10, 2009
This really is a deceptive example, if it is meant to prove that most of the money is in companies that are above fair value. Let’s suppose that instead of one company with a fair value of $10 billion and a market value of $9 billion, Company A is split into four companies, A1, A2, A3 and A4, each with a fair value of $2.5 billion and a market value of $2.25 billion. Then Companies A1, A2 and A3 have fair values totaling $7.5 billion, while A4 and B together have fair values also totaling $7.5 billion—hence, the additional condition that Arnott wants to impose, that the universe can be divided in two equal halves by fair value, is satisfied. But Companies A1, A2, A3 and A4, comprising most of the portfolio at a total of $9 billion, are all undervalued, while only Company B, comprising $6 billion of the portfolio, is overvalued.
Thus, it’s still the case that more than half ($90,000) of the $150,000 market-cap-weighted portfolio is in undervalued companies and less than half ($60,000) in overvalued companies—there’s no deception. Mr. Arnott’s claim is simply false. An infinite number of other counterexamples can also be constructed.
Is a cap-weighted index portfolio mispriced on average?
A second major claim Arnott has repeated frequently is that “capitalization-weighted indexes overweight overpriced stocks and underweight underpriced stocks.”
If capitalization-weighting overweights overpriced stocks and underweights underpriced stocks, then the capitalization-weighted market portfolio must be overpriced on average.
But Advisor Perspectives posed this question to Mr. Arnott:
In your papers, in which you approach fundamental indexing mathematically, you assume that the market price of a security is an unbiased estimator of its fair value—which of course means that the average of all mispricings in the market is zero. But doesn’t that obviously also mean that the average mispricing in a market-cap-weighted portfolio is zero—and doesn’t that contradict your basic premise?
Arnott answers, “This is a mathematical truism.” In saying that it is a mathematical truism Arnott concedes that the average mispricing in a market-cap-weighted portfolio is zero. He can therefore no longer claim that a market-cap-weighted portfolio has a built-in “structural performance drag”—as he has claimed many times—because it is not on average mispriced. And it cannot be true that capitalization-weighting overweights overpriced stocks and underweights underpriced stocks, because if it were true, then the market would be overpriced on average.
In short, the intimations of mathematical certainties that advocates attribute to fundamental indexing are completely groundless. All that can be claimed for it is that it is an algorithmic methodology for the tilting of a portfolio toward a stock selection philosophy that is attractive because it has exhibited superior returns in the past. This places it securely in the crowded field of active management.
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