Quieting The Noise

August 09, 2007


It's easy to see why alternatively weighted indexes have captured the public's imagination.

First, there is the stinging memory of the Internet bubble. Index investors—not exactly the Evel Knievel's of the financial world—watched in horror as the S&P 500 and other major indexes lost more than half their value in the aftermath of that bubble. That convinced many of us that there was something wrong with cap-weighted indexes.

Second, there is simple logic. The most popular ideas are often those that are easiest to grasp, and the case for alternatively weighted indexes can be captured in a single sentence:

By definition, capitalization weighted indexes overweight overvalued companies and underweight undervalued companies.

The argument seems to be transparent and irrefutable. A stock that is overvalued will have a higher market capitalization than it deserves, while a stock that is undervalued will have a lower market cap than it deserves. As a result, a capweighted index will overweight the overvalued stock and underweight the undervalued stock. And who wants that?

To date, supporters of cap-weighted indexes have responded with their own irrefutable argument:

By definition, investors as a whole will earn the market return; after costs, they will trail the market. Therefore, investors who track the market at the lowest possible cost will outperform the majority of investors.

Again: How can you argue? Who wouldn't want to outperform most investors? It's the classic case of an irresistible force meeting an immovable object.

An Attack On The Noisy Markets Hypothesis
For many, the core philosophical underpinning of alternatively weighted indexes is Jeremy Siegel's "noisy markets hypothesis." This theory stands in contrast to the efficient markets hypothesis, which argues that financial markets are "informationally efficient" and that prices accurately reflect all known information about each stock, and that essentially, prices reflect the best available estimate of a stock's true value. In contrast, the noisy markets hypothesis says that speculators, momentum traders and large sales by insiders or institutions can create temporary shocks that force stocks to deviate from fair value.

"These temporary shocks may last for days or for years," Siegel explained in a Wall Street Journal op-ed, "and their unpredictability makes it difficult to design a trading strategy that consistently produces superior returns."

Siegel says that because cap-weighted indexes overweight overvalued companies and underweight undervalued companies, cap weighting imposes a systematic drag on performance. Although Siegel does not claim that dividends (his preferred weighting metric) or other measures are optimal, at least they break the self-reinforcing tie to market capitalization. In other words, they may mis-weight companies against their true, fundamental value, but at least the errors are random: They are as likely to overweight undervalued companies as they are to overweight overvalued companies. As a result, those mistakes will cancel and the indexes will perform better than cap-weighted benchmarks.

A Simple Idea
Recently, Andre Perold, the George Gund Professor of Finance and Banking at Harvard Business School and a director of Vanguard, has been circulating a draft paper indelicately titled "Fundamentally Flawed Indexing" that makes a direct attack on Jeremy Siegel's theory. Perold's paper has attracted attention because, like cap weighting and alternative weighting, it centers on a simple idea:

Just because a stock is large, that doesn't mean it's overvalued. It may be large and undervalued. Therefore, a cap-weighted index is just as likely to underweight large stocks as it is to overweight large stocks.

The argument proceeds from there. Perold uses an example of a two-stock portfolio, with one stock priced at $12/share and one priced at $8/share. Each has the same number of shares outstanding, so the market capitalization split is 60/40.

In Perold's example, we assume that each company is mis-valued by 20 percent, meaning the $12 stock could be worth either $10/share or $15/share, and the $8/stock either $6.40/share or $9.60/share. We don't know which is which. Either way, however, the underlying fair value of each stock will grow by 10 percent this year: If the $12 stock is really worth $10/share, for instance, next year it will be worth $11/share.

For the purpose of the exercise, we assume that the stock returns to fair value by the end of the year, at which point the $12 stock is worth either $11/share or $16.50/share. In other words, a shareholder will either end up with an 8.3 percent (- $1/share) loss or a 37.5 percent ($4.50/share) gain. The same percentages apply to the $8/stock.

Perold then considers two portfolios: one using capitalization weighting and one using equal weighting to invest in the two securities. As the calculation plays out, it becomes clear that, regardless of which weighting methodology is used, the expected return is the same.

"The analysis shows that capitalization weighting imposes no drag on expected return, because capitalization weighting does not cause you to invest more in overvalued stocks and less in undervalued stocks," writes Perold. "It invests the same proportions, here 60/40, without regard to undervaluation or overvaluation of the shares."

Taken to its extreme, Perold's argument says that even the largest, most highly valued stock is just as likely to be overvalued as undervalued; the same is true of the smallest, cheapest stock. Since market capitalization does not tell you whether a stock is overvalued or undervalued, the fact that some stocks are mis-priced does not systematically shift the portfolio towards overvalued stocks.

Perold's point is not that alternative weighting measures are a bad idea. Rather, it is that they will not necessarily outperform cap-weighted indexes, and that they should be judged for what Perold thinks they are: a quantitatively driven value strategy that should be measured against other active strategies.


Where does this all leave us? I'm not sure. It feels a bit like a magic show, where you know something funny is going on with all three points of view, but you can't tell what.

It is telling that Perold used an equal-weighting strategy while supporters of Siegel's noisy markets hypothesis use value-based metrics like dividends, sales, earnings, book value, etc. The conceit of the noisy markets hypothesis is that, essentially, it claims that any passive strategy except for market-cap weighting will outperform a cap-weighted portfolio, because it will randomize its pricing errors. And yet, the creators of the new, alternatively weighted strategies haven't just chosen any weighting system: They have overwhelming chosen value metrics. Indeed, Siegel points out in his defense of the noisy markets hypothesis that value indexes have outperformed growth over the years.

What the Perold paper achieves is linking alternatively weighted strategies with the presumption that the chosen value-based metrics are in fact better-performing metrics than market capitalization. If over- and under-pricing are truly random, the argument goes, then a low-cost, cap-weighted index portfolio will remain the optimal portfolio.

The debate rages on.

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