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July 21, 2005

How Not to Diversify

Welcome Hugh Hewitt listeners. Scroll down if you're looking for the posting of the mosque pictures. Start here if you want to learn something about investing.

What follows is the blogger's digest version of this Word working paper.

For generations now, investors have been told to diversify on the basis of size and value-growth. There's no question that 1) value tends to outperform growth, 2) small tends to outperform large, and 3) it's good to diversify.

But size and value-growth do not denote asset classes. Instead, US Equities should be seen as a single asset class. Diversification is still a good idea, but the differences in returns among cap sizes, and between value and growth stocks, are not great enough for them to define asset classes.

Who says otherwise? Lots of people. Fund managers, advisors, journalists, researchers.

I'd like to propose three requirements for asset classes:

  1. Orthogonality in Performance. Different asset classes should have low correlations in their returns. Individual stocks may be exposed to interest rates or commodities, but in general will not rise or fall solely in response to those factors. This quality is necessary to make sure that different asset classes actually contribute to return while lowering risk and volatility.
  2. Mutually-Exclusive Definition. An asset should not be able to live in more than one asset class. A corollary to this is that an assetís class should be clear and generally agreed-upon. Different analysts should not be able to classify the same asset differently.
  3. Stability. Assets should not be changing class frequently, if at all. While this follows from No. 2, it isnít the same thing. An asset could change characteristics in such as a way that analysts agree it should be re-classified, but this should be rare. Still, for definitions to have integrity, assets shouldnít be popping in and out of them, or drifting across class lines easily.

There are a number of large indexing firms that break US stocks down into these categories. They don't fit any of these requirements.

Orthogonality in Performance

There is very high correlation among these various indices. Here, for instance, is a scatterplot of the daily returns of the Morgan-Stanley Large-Cap Value vs. Small-Cap Growth for the last 13 years.

If I use the following list of asset classes as a baseline,

  • Cash Equivalents
  • Foreign Cash
  • Government Bonds
  • Tax-Exempt Bonds
  • Corporate Bonds
  • Large Stocks
  • Small Stocks
  • Foreign Stocks
  • Investment Real Estate Unlevgd
  • Residential Real Estate Unlevgd
  • Farm Real Estate
  • Energy
  • Precious Metals

The average correlation in annual returns is 0.068. Here's what that looks like:

These high correlations hold across countries, indexing services, decades, value-growth, and size. Once in a while, you'll get something as low as 0.444, such as the Morgan-Stanley Value and Growth indices for Ireland. But those are anomalies, serious outliers, which probably show that whatever metric their overlaying on the stocks doesn't work all the time.

If you believe in modern portfolio theory, CAPM, and the Efficient Frontier, this is a problem. Because if you add in any sub-class by itself, you end up moving the frontier to the right, not to the left. The risk contribution, as measured by standard deviation, adds up faster than the return contribution, because the correlations are higher within US equities than between US equities and anything else in the list.

If you don't believe in modern portfolio theory, because returns aren't normally distributed, you should still come up short, because correlations still matter in normal times, and correlations within US equity "asset classes" dwarf anything else in the list.

Mutually-Exclusive Definition

If you're going to draw lines, draw lines. It's no good having the same stock rated as Value by Mr. Morgan and Growth by Mr. Stanley. It's no good having the same stock rated as Large by Morning and Small by star. It's also no good having your mid-cap range cover the same ground as your small-cap.

Guess what.

Here's how five different indexing services define Small, Medium, and Large:

Now we know where shirt-makers have been taking their cue from. Note that one of them doesn't even believe that "mid" exists, slicing it off as the smaller part of "large."

Comparing the latest S&P and Morningstar index components, and looking only at the components they have in common, we also see a fair amount of disagreement:


What's really problematic is that the indexers aren't even internally consistent:

This may overstate the amount of overlap, since the distributions aren't flat. But still. Now part of this is a result of drift. Indexing services are reluctant to reclassify stocks just because they happen to float over the line between "Large" and "Mid." Maybe they just swam into the lane markers, and are really still behaving like a Large stock. Which brings us to


Every six months, S&P reconstitutes their 1500 index, comprised of the Large 500, the Mid 400, and the Small 600. Each of those is broken into Value and Growth. Over the course of six months, they'll have more than 1500 stocks in the list. Here's how many of the total 1500 change categories every six months:

Again, these are only the stocks that stay in the 1500, but change index. It averages more than 1 stock in 9.

Now, indexers will argue that it's not fair to expect mutual-exclusivity and stability. I would argue that that's an excellent reason why you can't break US equities down into separate asset classes, at least not by size and value-growth.

This means that while you still want to diversify your portfolio, maybe by industry, maybe by Barra risk factors, you don't gain anything by diversifying across size and value-growth.

Posted by joshuasharf at July 21, 2005 07:01 PM | TrackBack

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