Concentrating on concentration – Concentrate…

By: Rob Bush | September 12, 2017

I’ll go out on a limb here and suggest that you will have read neither Max O. Lorenz’s 1906 doctorate on “The Economic Theory of Railroad Rates”, nor Orris C. Herfindahl’s 1950 Columbia university thesis on the steel industry. And, frankly, that’s ok - neither have I. But that doesn’t mean that these two – is it fair to call them “relatively more obscure” - works of economic academia don’t have some very relevant implications for investors today. How so?

Well, the former led to the creation of the Lorenz curve, and the latter to the Herfindahl index and, subsequently, “Effective N”, both incredibly useful measures of, amongst other things, index concentration. So what do each of these metrics show, and how can they be interpreted? Well, let’s consider three different types of weighting schemes for the Russell 1000 – market cap, multifactor, and equal weight – and see how they look through Lorenz and Herfindal’s eyes.

Source: Bloomberg as of August 24, 2017. Note that equal weight data is theoretical “pure” equally weighted numbers, not representative of any specific index.

The chart shows the relationship between the percentage number of stocks in the index (x-axis) against the amount of the index by market cap that those stocks account for (y-axis). The easiest case is the equal weight where it makes intuitive sense that, since every stock will be held in the same weight, half the stocks will account for exactly half the market cap.

Compared to the equal weight’s straight line, the most curved line is the market cap line. What this shows is that even relatively small numbers of stocks can account for quite large amounts of the market cap of an index. In the case of the standard, market cap, Russell 1000 you can infer from the chart that just 10% of the names account for nearly 60% of the total market cap of the index. Finally, when looked at through a multifactor lens (the Russell 1000 Comprehensive Factor Index), the line is less curved, lying between market cap and equal weight. For this weighting scheme, 10% of the names account for just over a third of market cap.

So much for Lorenz, how about Herfindahl? Well, his insight eventually led to a metric known as “Effective N” and what this shows is the equivalent number of equal weighted positions that an index roughly equates to. So for the Russell 1000 equal weight, Effective N is, of course, 1000. Weighting the index in this manner results in 1000 equally weighted positions, exactly as one would expect and, yes, stating the obvious.

How about the standard market cap weighting? How many equal weighted positions is that equivalent to? Well, the answer, it turns out, is about 170 (and the math that gets you there is to take all the weights of all the stocks, square them, add them up, and then divide one by that number). So there is a drop off in Effective N from an equal weighting to a market cap weighting that reflects the fact that a small number of stocks now account for a large weighting. The genius of Effective N is that it recognizes, and explicitly shows, that it’s not just the number of stocks that you hold that matters, it’s also, of course their relative weightings. It makes intuitive sense that a portfolio of 30 stocks, where the biggest holding accounts for 90% (and the other 29 all equal), is too concentrated compared to a portfolio of 20 stocks that is equally weighted. Yes, the latter has fewer holdings, but their influence is more disperse. Effective N is the number that crystallizes that intuition - for the former portfolio it would be 1.2 (indicating that you really only hold one position), for the latter 20.

How does the multifactor weighting look on Effective N? Now the number is around 435, so, amongst other things, one potential advantage of increasing factor exposures in your portfolio is that it can lead to a less concentrated portfolio compared to the market cap approach.

So hats off to Lorenz and Herfindahl - I’m off to the library to find those doctoral theses.

Diversification neither ensures a profit nor protects against a loss.

Rob Bush
ETF Strategist
For general inquiries:
(844) 851-4255


It’s not just the number of stocksthat you hold that matters,
it’s also, their relative weightings.

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