Despite the increased adoption of indexing by investors and the strong theoretical and empirical support for indexing, pundits are keen to point to data whenever they might show (in advance) or do show (after the fact) that active management outperforms indexing.

Dispersion of stock returns is often put forth as a headwind or tailwind to active management. For the uninitiated, previous blogs have provided introductions and updates to the concept of dispersion and have addressed the role it does or does not play in determining what makes a “stock picker’s market.”

We thought it would be interesting to expand the discussion of dispersion and its effect on the ability of active management to outperform. After all, if greater dispersion really does make for a favorable environment for active managers, this should be reflected in the data. The chart immediately below shows how the dispersion of Russell 2000 Index constituent stocks affects the relative performance of active managers that are benchmarked to the Russell 2000 Index. (We picked the Russell 2000 Index because of the popular claim that it is easier to outperform in small-caps.)
 
2dispersion_042016
 
Well, on second thought, it seems to show that dispersion does not affect relative performance. Except for a few outliers, the dots suggest that, historically, dispersion falls in a tight range and forms a fairly vertical column.

Given that result, we created another chart (below). It is the same chart as the one above except that we color-coded the dots to indicate how well small-cap stocks performed relative to mid-cap stocks in order to test whether a manager’s style purity affects relative performance. The blue dots represent months in which small-cap stocks outperformed mid-cap stocks, the green dots represent months in which mid-cap stocks outperformed small-cap stocks, and the size of the dots reflects the magnitude of the difference (i.e., the larger the dot, the greater the outperformance).
 
1dispersion_042016
 

Now we see a clearer trend. Since the green dots cluster above the 50% mark, the trend indicates that when mid-cap stocks outperform small-cap stocks, small-cap managers tend to outperform their benchmarks (and when small-cap stocks outperform mid-cap stocks, small-cap managers tend to underperform their benchmarks). This relationship between style purity and relative performance is known as “Dunn’s Law.”1 In short, active managers in a poorly performing sub-asset class tend to outperform their benchmarks because they own securities from a better-performing sub-asset class.2 In our example, this is reasonable to imagine since it is likely that a small-cap manager owns some sliver of mid-cap stocks.

This is not to suggest that there is anything wrong with managers who pick securities outside of their benchmarks. It merely serves to provide insight into the performance of active management, and investors should give thought to how this affects their overall asset allocation. After all, if an investor’s portfolio holds a small-cap manager who holds mid-cap stocks, how much mid-cap exposure does the portfolio have overall?

That would be an important question. The next time you see statistics suggesting active management outperforms, perhaps another important question would be, “Is it dispersion or Dunn’s Law?”

I would like to thank my colleague Jonathan Kahler for his contributions to this blog.

1 To the best of our knowledge, Dunn’s Law first appeared in William Bernstein, 1999. When Indexing Fails. Efficient Frontier: An Online Journal of Practical Asset Allocation (April). Accessed April 8, 2016, at http://www.efficientfrontier.com/ef/499/indexing.htm.

2 For further discussion, see William Thatcher, 2012. When Indexing Works and When It Doesn’t in U.S. Equities: An Update of the Purity Hypothesis. Journal of Index Investing 3(3):18–26.

Notes:

  • All investing is subject to risk, including the possible loss of the money you invest.
  • Prices of mid- and small-cap stocks often fluctuate more than those of large-company stocks.