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Elisabeth Kashner Analyst Blogs

Kauffman's Fuzzy ETF Math


Bradley offered up his latest ideas to Senator Jack Reed (D-RI) of the U.S. Senate’s Committee on Banking, Housing, and Urban Affairs Subcommittee on Securities, Insurance, and Investment, about the effects of ETFs on the U.S. equity market and small businesses.

We’ve questioned Kauffman’s logic before. This time we’d like to tell the U.S. Senate that Kauffman’s math is faulty. Bradley made claims that turned out to be backed up by backward statistics. Worse, his key take-home message relied on assumptions that were the exact opposite of those he delivered in the body of his testimony.

Bradley’s thesis is simple: “ … ETFs have increasingly distorted the role of equities markets in capital formation … ” (Bradley’s written testimony, p.2)

Let’s look at the math behind the evidence that Bradley uses to support his thesis.

Bradley claims that ETF trading is driving single-security prices. He leans on statistical evidence about market correlations to back up this claim. Check it out: “We believe that these instruments may now be undermining the fundamental role of equities markets in pricing securities to ensure that capital is efficiently allocated to growing businesses. When individual common stocks increasingly behave as if they are derivatives of frequently traded and interlinked ETF baskets, then it is trading in the ETFs that is driving the prices of the underlying stocks rather than the other way around. This tendency is especially pronounced for ETFs that are comprised of small-cap stocks or stocks of newly listed companies, that generally are thinly traded.”

“High comovement of securities is not new, often occurring when markets reflect crowd panic or euphoria. What is new, however, is how ETFs decrease diversification benefits, with stocks and sectors worldwide moving together, even when there is no panic. Stocks move together today more than at any time in modern market history with recent data indicating that individual common stock prices that make up the S&P 500 index now move with the index 86% of the time.”

Really? Bradley backs up this claim with a graph.



Let’s forget for a minute that this chart tops out at 80 percent, and thus his “86” is nowhere to be seen.

What does this graph actually show? ­Correlations. Pay attention, because correlations do not reveal the percent of the time that variables move together, as Bradley claims. Correlation is an easy-to-toss-around derivative of the actual measure of comovement, also known as “goodness of fit.” Goodness of fit shows the statistical strength of a relationship—the frequency that two variables move in the same direction.

We can calculate actual recent high goodness of fit for the results shown in this graph. Let’s make a generous reading and peg the highest recent reading of quarterly correlations at 0.7. Correlation is the square root of goodness of fit, so correlation² = goodness of fit.

The goodness of fit calculation goes like this: 0.7² = 0.49, or 49 percent.

Now look a bit more carefully at the data that feed this graph. The title says it measures “Quarterly return correlation among all stocks.” The word “among” implies that this metric shows correlations of single securities to their index-mates, and not to the index as a whole.

So, let’s revisit Bradley’s assertion and rephrase it to fit the math: Individual common stock prices that make up the S&P 500 Index now move with their fellow S&P 500 member securities 49 percent of the time. Does it pack more punch that way? (The italics are mine to emphasize what’s different when the math is done correctly.)

Bradley continues his case by positing a crisis of correlation:




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