Dispersion and Correlation: Which is “Better?”

We recently introduced the concept of dispersion, which measures the average difference between the return of an index and the return of each of the index’s components.  In times of high dispersion, the gap between the best performers and the worst performers is relatively wide; when dispersion is low, the performance gap narrows.  Today’s dispersion levels are quite low by historical standards, which implies that:

  • The degree to which the average skillful (or lucky) manager should be expected to exceed index returns is below average, and
  • The degree to which the average unskilled (or unlucky) manager should be expected to lag index returns is also below average.

One consequence of low dispersion, in other words, is that the gap between the best and the worst performers is smaller than it would be if dispersion were higher.  If that’s the case, then the current environment is not especially good for demonstrating stock selection skill.

On the other hand, it’s frequently been argued in recent weeks that since the correlation of stocks within the U.S. equity market is falling, 2014 is poised to be a “stock-picker’s market.”  Correlations have indeed been declining — which means that correlation and dispersion seem to be delivering inconsistent messages.  Is one “right” and the other “wrong?”

The reason for this apparent contradiction is that correlation and dispersion measure two different things.  Consider a simple example, examining the behavior of two stocks over a 20-day holding period:

A and BThe correlation between A and B is -1.00.  The two stocks are ideal diversifiers, since  moves in one completely offset moves in the other.  The return of both stocks, however, is the same 0%.  Regardless of which one the investor bought, his return would be the same.  (The only reward available for selection strategies is in fact a penalty, since holding either stock entails more volatility than holding both.)  That doesn’t sound like a good environment for stock picking.

Now consider stocks C and D:

C and DThe correlation between C and D is 1.00, which is to say that both stocks always move in the same direction.  Holding both has the same volatility as holding either stock individually.  Does that mean that stock selection is irrelevant?  Hardly, since C’s return (9.2% as shown) is more than double D’s return (4.5%).

Correlation is primarily a measure of timing.  High correlations mean that things go up and down at the same time; negative correlations mean that they offset.  C and D always move in the same direction (hence the 1.00 correlation), while A and B always move in opposite directions (hence their -1.00 correlation).   But low correlation does not necessarily mean that the environment is favorable for skillful stock pickers.

Dispersion is a measure of magnitude.  It tells us by how much the return of the average stock differed from the market average.  In our hypothetical exercise, there’s no dispersion at all between A and B, and a considerable dispersion between C and D.  High dispersion gives skillful stock pickers a better chance to showcase their abilities.

Correlation is an essential tool in understanding portfolio diversification.  But as a measure of the magnitude of opportunity available to selection strategies – dispersion is the better metric.


10 thoughts on “Dispersion and Correlation: Which is “Better?”

  1. StreetEYE (@StreetEYE)

    Suppose every stock is 100% correlated, but you have wide dispersion.

    In other words every stock is perfectly correlated with the index, with betas from say -10 to +10.

    There is 0 opportunity for active management in that environment. The only decision to be made is how much beta to put on.

    In other words, dispersion alone tells you nothing about how large the opportunity is for active managers.

    1. Craig LazzaraCraig Lazzara Post author

      Fair point — except that the choice of beta is also an active management decision. A performance analysis would attribute all the manager’s excess return to his beta decision, but that doesn’t make it less active. (Perhaps my last sentences should have read “…as a measure of the magnitude of opportunity available to active strategies” as opposed to “selection” strategies.)

      Our point was that low correlations don’t automatically make it a good environment for active managers (as many have asserted), nor do high correlations mean that there’s no room for active managers to add value.

      1. StreetEYE (@StreetEYE)

        Yes, active managers want both high dispersion and low correlation.

        As another example, suppose every stock in your universe moves +/- a random 0.1% in 2014. Correlation is 0, but there is little opportunity for active managers.

        Correlation is a good summary of how much of the total variation in individual stocks is due to the market as a whole.

        What active managers want is a lot of variation unrelated to the market that they can mine for inefficiencies, e.g. a lot of individual stock abnormal return/excess return/alpha.

        Which means they want high dispersion AND low correlation.

  2. Adam

    Your correlation exercise assumes that you have perfect negative correlation between two assets, AND the magnitude of their changes is equal in every case. You can have 2 assets with perfect negative correlation and different return levels, resulting in a portfolio that has 0% return, as per your example.

    I think you’re right, though, that neither metric does a perfect job of determining whether the opportunity set for active management is better.

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  6. Stephen Lihn

    Do you agree with the hypothesis that low correlation plus high dispersion is an ideal environment for stock pickers, e.g. fundamental driven hedge funds? What is your thought on this? Is this hypothesis testable with the data you have (or we have)?

    1. Craig LazzaraCraig Lazzara Post author

      Stephen, I think you’re correct, with the caveat that high dispersion is much more important to a stock picker than low correlation. (This might not be true for a macro-style manager who is more concerned with directional bets than with selections within an asset class.) We showed the relationship between dispersion and the spread of active mutual fund managers here: http://www.indexologyblog.com/2014/04/15/right-conclusion-maybe-wrong-reason-definitely/.


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