Diversification Potential, or What the Cap Doesn’t Tap

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Published on June 18, 2020

| 6 min read

Richard Yasenchak, CFA, Head of Client Portfolio Management


Indexes that attempt to replicate the performance of equity markets via the time-honored tradition of capitalization may seem diversified, but they barely scratch the surface of their potential. Weighting stocks more efficiently through exploiting their volatilities and correlations offers plenty more to be gained.

We advocate for a closer look at the frequently overlooked alpha that exists within nearly any collection of stocks. This is alpha that can be captured without forecasting, but via the systematic application of diversification and rebalancing. And we’ll introduce a new statistical measure we’ve developed – diversification potential – to do so.

In an earlier paper, we explored how a portfolio’s compound return is greater than the weighted compound returns of the underlying stocks. There’s an additional diversification effect – the ‘excess growth rate’ – that also contributes to the portfolio compound return. This component is due to the diversification benefit a portfolio experiences based on the volatilities and correlations of the stocks within the portfolio.


Stochastic Portfolio Theory


Because we can decompose a portfolio’s return in this way, there are two ways to increase that return: 1) selecting stocks that have higher compound return without focusing on their diversification, and 2) combining stocks into a more favorable mix based on their variances and covariances without attempting to pick winners.1 While the former requires forecasting stocks’ returns, the latter only requires reliable estimates of their volatilities and correlations.

Toward this end, we present a new concept:

Diversification Potential-2


For those interested in the underlying math, please refer to our technical paper on this topic.

In practical terms, this statistic is useful because it:

  1. reveals differences in potential alpha from diversification effects, e.g., between a cap-weighted index and what’s achievable via optimal reweighting and rebalancing;
  2. highlights variations in market efficiency over time; and
  3. quantifies the additional diversification that’s possible as the investment universe expands.

For our test cases, we’ll focus on two popular presumably diversified indexes: the MSCI EAFE and MSCI Europe. The MSCI Europe Index represents a narrower constituents list than the MSCI EAFE Index, and follows a similar construction methodology from the same index provider (see the table below for more details). As a result, it’s particularly useful in illustrating diversification differences due to the number of stocks available.


Comparing Non-U.S. Equities

Cap-Weighted Indexes vs Diversification


In the figure above on the left, we show the excess growth rate respectively for cap-weighted indexes and for portfolios approximating the diversification potential that use their constituents as an investable universe. Here are a few observations that confirm the consistency of this measure with the uses stated above:

  1. The maximum achievable excess growth rate via optimal diversification is significantly higher than the excess growth rate achieved by the cap-weighted index.
  2. There is substantial variability in the index’s diversification potential as the market conditions change.
  3. Indexes with expanded constituents (e.g., MSCI EAFE vs. MSCI Europe) have a higher potential excess growth rate because of the larger opportunity set of stocks’ correlations and volatilities.2

The most important takeaway here is that there’s quite a bit of diversification opportunity left on the table when investing in cap-weighted indexes, because they do not explicitly take into account volatilities and correlations in their construction methodology. To distill the relative level of difference between the indexes’ actual level of diversification and their potential, we also use diversification potential as the denominator of a ratio, with the actual excess growth rate of the index in the numerator (see the figure above on the right). This ratio, which we call the index diversification, reflects how diverse the index is based on current constituents and weightings relative to those constituents’ potential in a portfolio maximizing the excess growth.

As a result, such a portfolio uses the same constituents as the index. Yet, it will hold most of the names at zero weight to achieve the highest possible diversification potential. The outcomes illustrate the level of market efficiency at a given time – and in fact, levels of index diversification near historical extremes in either direction tend to coincide with times of greater market stress. Index diversification also varies over time, but adding stocks to an investment universe doesn’t equate to added efficiency, even though it increases the potential excess growth rate.

Active management has an opportunity to improve upon the level of diversification in traditional cap-weighted indexes. That said, accessing it meaningfully with an investor’s risk-return goals in mind comes with practical obstacles. We’re happy to discuss these challenges, as well as the ways a sophisticated manager can mitigate them. Contact us to have a conversation today.


1 As you might expect, in practice, these are not independent. Attempting either may affect the other.
2 The diversification potential increases not when you have more stocks, but when you add stocks. For example, if index A has 100 stocks and index B has 150 stocks, you can’t tell which one will have a higher diversification potential based purely on the number of names. However, if you know that B is A plus another 50 names, then you can prove mathematically that B will have a higher diversification potential than A.
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