Fundamental Indexing
Partner and Chief Investment Officer
Fair Advisors
February 10, 2009
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In much of his interview in the February 3 issue of Advisor Perspectives, titled “Rob Arnott Defends Fundamental Indexing,” Arnott tries to defend his claims for fundamental indexing against criticisms that have been leveled by me. Arnott attempts a defense on one point, while on another major point he mounts no real defense but simply nullifies claims he has made repeatedly in the past.
Fundamental indexing is a weighting algorithm for tilting a broadly diversified portfolio in favor of a particular stock valuation philosophy. In practice it usually favors a value stock tilt.
My criticism of fundamental indexing is not of the algorithm used to do the tilting (that is, the algorithm that assigns weights to the stocks in a portfolio, given that there is a preference for one stock over another). My criticism is of the excessive claims made by promoters of the fundamental indexing methodology.
The promoters are not content to rest their case on the empirical evidence that an index weighted more heavily in value stocks would have significantly outperformed a market-weighted index historically. They go much further by intimating that it is mathematically provable that a fundamentally-weighted index must outperform a capitalization-weighted index. These intimations of mathematical certainties have mostly been made verbally (though erroneous proofs using mathematical notation have been attempted). When the verbal claims are analyzed, they do not stand up to scrutiny.
Does a cap-weighted index portfolio hold more in overpriced stocks?
One of the claims made by Arnott is that “If we have a cap-weighted portfolio, we know most of our money is in companies that are above fair value.”1
In the January 17, 2009, issue of Advisor Perspectives, I showed that we know no such thing, by presenting a simple counterexample:
Consider a two-company world. Company A has a fair value of $10 billion with a market value of $9 billion, and Company B has a fair value of $5 billion with a market value of $6 billion. If we have a $150,000 market-cap-weighted portfolio, it will have $90,000 in Company A, the undervalued company, and $60,000 in Company B, the overvalued company. It will not have most of its money in companies that are above fair value—it will have most of its money in the company that is below fair value.
Arnott calls this “a deceptive example.” Then he adds the condition that we must be able to “divide the universe in two equal halves by fair value.”
But his added condition doesn’t invalidate the example. All that is necessary is to divide each company in the two-company world into a number of smaller but identical companies. Then that world will divide into two halves by fair value; yet the portfolio still has most of its money in companies that are below fair value.
Let us walk further with Arnott. He makes much of the fact that you have to be able to divide the universe in two equal halves by fair value. Then he says, referring to my example:
1 Journal of Indexes, January/February 2009, page 33.
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