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  • This week’s commentary is a short addendum to last week’s piece, attempting to serve as a (very) brief and simplified summary of process diversification.
  • Volatility is only one way of measuring risk; dispersion in terminal wealth is another.
  • Using simulations of dart-throwing monkeys, we plot the dispersion in terminal wealth for different levels of portfolio and manager diversification.
  • We find that increased diversification within a portfolio as well as increased diversification across managers can lead to more consistent portfolio outcomes.


In last week’s commentary (What do portfolios and teacups have in common?), we explored at great length the potential benefits of diversification in the domains of what, how, and when.

The crux of our argument is that for investors, return dispersions across time (i.e. “volatility”) can be a potentially misleading risk characteristic and that it is important to consider the potential dispersion in terminal wealth as well.

These are by no means original or unique thoughts.  Often the advisors and institutions we work with intuitively understand them: they just have not been presented with the math to justify them.

Therefore, in contrast to last week’s rather expansive note, we aim to keep this week’s note short, simple, and punchy in an effort to drive how manager / process diversification can help deliver more consistent outcomes.

Dart-Throwing Monkeys

Consider the following experiment.

We begin with thousands and thousands of dart-throwing monkeys.  Every month, the monkeys throw their darts at a board that determines how they will be invested for the next month.  In this hypothetical scenario, we will assume that the monkeys are investing in different industry groups.1

Some monkeys are “concentrated managers,” throwing just a single dart and holding that pick for the next month.  Other monkeys are more diversified, throwing up to 30 darts each month and equally allocating their portfolio across their investments.  Portfolio sizes can be either 1, 5, 10, 15, 20, 25, or 30 equally-allocated investments.

It is our job, as an allocator, to choose different monkeys to invest with.  Do we invest with just 1 concentrated monkey manager? Five different diversified managers? How much difference does it really make at the end of the day?

We learn in Finance 101 that once we diversify our portfolio sufficiently, we have eliminated nonsystematic risk.  But does that mean we expect the portfolios to necessarily end up in the same place?

As an example, if we pick 10 dart-throwing monkeys who each pick 10 investments per month, how different would we expect our final wealth level to be from another allocator who picks 10 different dart-throwing monkeys who each pick 10 investments per month?

Process Diversification and Terminal Wealth Dispersion

Below we plot the dispersion in terminal wealth2 as a function of (1) the number of securities picked by each monkey manager and (2) the number of monkey managers we allocate to.

As an example of how to read this graph, the orange line tells us about portfolios comprised of monkey managers who pick five investments each.  As we move from left to right, we learn about the dispersion in terminal wealth based upon the number of managers we allocate to.

We can think of this two ways.  First, we can think of it as potential dispersion in results among our peers who make the same type of decision (e.g. picking 5 managers who pick 5 investments each) but different specific choices (e.g. might pick different managers). Second, we can think of this as the dispersion in possible results if we were able to live across infinite universes simultaneously.

Source: Kenneth French Data Library. Calculations by Newfound Research.


Unfortunately, we cannot live across infinite universes and this graph tells us that choosing a single, highly concentrated manager can lead to wildly different outcomes depending upon the manager we select.

As the managers further diversify and we further diversify among managers, this dispersion in potential outcomes decreases.3


The intuition behind these results is simple:

  • More diversified managers are more likely to overlap in portfolio holdings with one another, and therefore are likely to have more similar returns.
  • Similarly, as the number of managers we choose goes up, so does the likelihood of overlap in holdings with a peer who also selects the same number of managers.

It is equally valid to interpret this analysis as saying there is greater opportunity for out-performance in taking concentrated bets in highly concentrated managers.  We would argue this is more right thinking: the win condition requires both that we pick the right managers and the managers pick the right stocks.  While a little bit of diversification can go a long way here in clipping outlier events, the dispersion can still far exceed a more diversified approach.

At Newfound, we prefer the less wrong approach.  Allocations to a few diversified managers each taking a different approach can lead to significantly less dispersion in outcomes and, therefore, allow for better financial planning.



  1. Specifically, the 49 industry group portfolios as provided by the Kenneth French database.
  2. Specifically, we measure this dispersion as the standard deviation of log differences in terminal wealth and the median terminal wealth achieved.
  3. As a geeky aside, if we plot only the dollar standard deviation in terminal wealth, the graphs closely follow a 1/sqrt(n) rule.

Corey is co-founder and Chief Investment Officer of Newfound Research. Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University. You can connect with Corey on LinkedIn or Twitter.