January 13, 2009
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For a related discussion of fundamental indexing, see Michael Edesess’ article in this issue, Fundamental Indexing: Breakthrough or Old Idea in New Marketing Garb?, and our article, Fundamental Indexing Debunked, which appeared on August 5, 2008
The bedrock argument for fundamental indexing relies on a verbal optical illusion
The “fundamental indexing” debate continues in the January/February 2009 Journal of Indexing.
Fundamental indexing can be viewed merely as a low-cost, automated way to tilt a diversified portfolio toward value stocks—a strategy that has a foundation in empirical historical results. That is where fundamental indexing advocates should leave it. But its advocates make a further claim for the practice, one that relies on the argument that the market-cap-weighted portfolio is necessarily overvalued.
This argument depends on frequent repetition of the following statement or statements like it: “Capitalization-weighted indexes overweight overpriced stocks and underweight underpriced stocks.”
This statement and its variations have an illusory effect. The effect is like showing that line A is shorter than line B by drawing arrowheads at the ends of line A and arrow-tails at the ends of line B.
But this statement and its variations are wrong at their core.
The claim is wrong, as shown by using fundamental indexers’ own assumptions. They assume that the stock-pricing error is unbiased, so that on average it will be zero. Therefore, the pricing error averaged over the whole stock market is zero. But if the average pricing error of the whole stock market is zero then so is the average pricing error of a market portfolio.1
1 Mathematically: If Pi is the market price of the i'th company, Vi is its fair value and Ui = Pi – Vi is the error term, then the expected value of Ui is zero, since it is unbiased. Therefore, the expected value of the difference between the sum of the Pi and the sum of the Vi, which is the sum of the Ui, is also zero. But the sum of the Pi is the market value of the market-cap-weighted portfolio, and the sum of the Vi is its fair value. Therefore, the expected difference between the market-cap-weighted portfolio’s market value and its fair value is zero. Hence, the expected overvaluation of a market-cap-weighted portfolio is zero.
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