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  • Portfolio risk is traditionally quantified by volatility.  The benefits of diversification are measured in how portfolio volatility is changed with the addition or subtraction of different investments.
  • Another measure of portfolio risk is the dispersion in terminal wealth: a measure that attempts to capture the potential difference in realized returns. For example, two equity managers that each hold 30 stock portfolios may exhibit similar volatility levels but will likely have very different realized results.
  • In this commentary we explore existing literature covering the potential diversification benefits that can arise from combining multiple managers together.
  • Empirical evidence suggests that in heterogeneous categories (e.g. many hedge fund styles), combining managers can reduce portfolio volatility. Yet even in homogenous categories (e.g. equity style boxes), combining managers can have a pronounced effect on reducing the dispersion in terminal wealth.
  • Finally, we address the question as to whether manager diversification leads to dilution, arguing that a combination of managers will reduce idiosyncratic process risks but maintain overall style exposure.


In their 2014 paper The Free Lunch Effect: The Value of Decoupling Diversification and Risk, Croce, Guinn, and Robinson draw a distinction between the risk reduction effects that occur due to de-risking and those that occur due to diversification benefits.

To illustrate the distinction, the authors compare the volatility of an all equity portfolio versus a balanced stock/bond mix.  In the 1984-2014 sample period, they find that the all equity portfolio has an annualized volatility of 15.25% while the balanced portfolio has an annualized volatility of just 9.56%.

Over 75% of this reduction in volatility, however, is due simply to the fact that bonds were much less volatile than stocks over the period.  In fact, of the 568-basis-point reduction, only 124 basis points was due to actual diversification benefits.

Why does this matter?

Because de-risking carries none of the benefits of diversification.  If there is a commensurate trade-off between expected return and risk, then all we have done is reduced the expected return of our portfolio.1

It is only by combining assets of like volatility – and, it is assumed, like expected return – that should allow us to enjoy the free lunch of diversification.

Unfortunately, unless you are willing to apply leverage (e.g. risky parity), the reality of finding such free lunch opportunities across assets is limited. The classic example of inter-asset diversification, though, is taught in Finance 101: as we add more stocks to a portfolio, we drive the contribution of idiosyncratic volatility towards zero.

Yet volatility is only one way to measure risk.  If we build a portfolio of 30 stocks and you build a portfolio of 30 stocks, the portfolios may have nearly identical levels of volatility, but we almost assuredly will end up with different realized results.  This difference between the expected and the realized is captured by a measure known as terminal wealth dispersion, first introduced by Robert Radcliffe in his book Investment: Concepts, Analysis, Strategy.

This form of risk naturally arises when we select between investment managers.  Two managers may both select securities from the same universe using the same investment thesis, but the realized results of their portfolios can be starkly different.  In rare cases, the specific choice of one manager over another can even lead to catastrophic results.

The selection of a manager reflects not only an allocation to an asset class, but also reflects an allocation to a process.  In this commentary, we ask: how much diversification benefit exists in process diversification?

The Theory Behind Manager Diversification

In Factors from Scratch, the research team at O’Shaughnessy Asset Management (OSAM), in partnership with anonymous blogger Jesse Livermore, digs into the driving elements behind value and momentum equity strategies.

They find that value stocks do tend to exhibit negative EPS growth, but this decay in fundamentals is offset by multiple expansion.  In other words, markets do appear to correctly identify companies with contracting fundamentals, but they also exaggerate and over-extrapolate that weakness.  The historical edge for the strategy has been that the re-rating – measured via multiple expansion – tends to overcompensate for the contraction in fundamentals.

For momentum, OSAM finds a somewhat opposite effect.  The strategy correctly identifies companies with strengthening fundamentals, but during the holding period a valuation contraction occurs as the market recognizes that its outlook might have been too optimistic. Historically, however, the growth outweighed the contraction to create a net positive effect.

These are the true, underlying economic and behavioral effects that managers are trying to capture when they implement value and momentum strategies.

These are not, however, effects we can observe directly in the market; they are effects that we have to forecast.  To do so, we have to utilize semi-noisy signals that we believe are correlated. Therefore, every manager’s strategy will be somewhat inefficient at capturing these effects.

For example, there are a number of quantitative measures we may apply in our attempt to identify value opportunities; e.g. price-to-book, price-to-earnings, and EBITDA-to-enterprise-value to name a few. Two different noisy signals might end up with different performance just due to randomness.

This noise between signals is further compounded when we consider all the other decisions that must be made in the portfolio construction process.  Two managers may use the same signals and still end up with very different portfolios based upon how the signals are translated into allocations.

Consider this: Morningstar currently2 lists 1,217 large-cap value funds in its mutual fund universe and trailing 1-year returns ranged from 1.91% to -22.90%. This is not just a case of extreme outliers, either: the spread between the 10th and 90thpercentile returning funds was 871 basis points.

It bears repeating that these are funds that, in theory, are all trying to achieve the same goal: large-cap value exposure.

Yet this result is not wholly surprising to us.  In Separating Ingredients and Recipe in Factor Investing we demonstrated that the performance dispersion between different momentum strategy definitions (e.g. momentum measure, look-back length, rebalance frequency, weighting scheme, et cetera) was larger than the performance dispersion between the traditional Fama-French factors themselves in 90% of rolling 1-year periods.  As it turns out, intra-factor differences can cause greater dispersion than inter-factor differences.

Without an ex-ante view as to the superiority of one signal, one process, or one fund versus another, it seems prudent for a portfolio to have diversified exposure to a broad range of signals that seem plausibly related to the underlying phenomenon.

Literature Review

While foundational literature on modern portfolio diversification extends back to the 1950s, little has been written in the field of manager diversification. While it is a well-established teaching that a portfolio of 25-40 stocks is typically sufficient to reduce idiosyncratic risk, there is no matching rule for how many managers to combine together.

One of the earliest articles on the topic was written by Edward O’Neal in 1997, titled How Many Mutual Funds Constitute a Diversified Mutual Fund Portfolio?

Published in the Financial Analysts Journal, this article explores risk across two different dimensions: the volatility of returns over time and the dispersion in terminal period wealth.  Again, the idea behind the latter measure is that two investors with identical horizons and different investments will achieve different terminal wealth levels, even if those investments have the same volatility.

Exploring equity mutual fund returns from 1986 to 1997, the study adopts a simulation-based approach to constructing portfolios and tracking returns.  Multi-manager portfolios of varying sizes are randomly constructed and compared against other multi-manager portfolios of the same size.

O’Neal finds that while combining managers has little-to-no effect on volatility (manager returns were too homogenous), it had a significant effect upon the dispersion of terminal wealth.  To quote the article,

Holding more than a single mutual fund in a portfolio appears to have substantial diversification benefits. The traditional measure of volatility, the time-series standard deviation, is not greatly influenced by holding multiple funds. Measures of the dispersion in terminal-wealth levels, however, which are arguably more important to long-term investors than time-series risk measures, can be reduced significantly. The greatest portion of the reduction occurs with the addition of small numbers of funds. This reduction in terminal-period wealth dispersion is evident for all holding periods studied. Two out of three downside risk measures are also substantially reduced by including multiple funds in a portfolio. These findings are especially important for investors who use mutual funds to fund fixed-horizon investment goals, such as retirement and college savings.

Allocating to three managers instead of just one could reduce the dispersion in terminal wealth by nearly 50%, an effect found to be quite consistent across the different time horizons measured.

In 1999, O’Neal teamed up with L. Franklin Fant to publish Do You Need More than One Manager for a Given Equity Style? Adopting a similar simulation-based approach, Fant and O’Neal explored multi-manager equity portfolios in the context of the style-box framework.

And, as before, they find that taking a multi-manager approach has little effect upon portfolio volatility.

It does, however, again prove to have a significant effect on the deviation in terminal wealth.

To quote the paper,

Regardless of the style category considered, the variability in terminal wealth levels is significantly reduced by using more managers. The first few additional managers make the most difference, as terminal wealth standard deviation declines at a decreasing rate with the number of managers. Concentrating on the variability of periodic portfolio returns fails to document the advantage of using multiple managers within style categories.

Second, some categories benefit more from additional managers than others. Plan sponsors would do well to allocate relatively more managers to the styles that display the greatest diversification benefits. Growth styles and small-cap styles appear to offer the greatest potential for diversification.

In 2002, François-Serge Lhabitant and Michelle Learned pursued a similar vein of research in the realm of hedge funds in their article Hedge Fund Diversification: How Much is Enough?  They employ the same simulation-based approach but evaluate diversification effects within the different hedge fund styles.

They find that while diversification does little to affect the expected return for a given style, it does appear to help reduce portfolio volatility: sometimes quite significantly so. This somewhat contradictory result to the prior research is likely due to the fact that hedge funds within a given category exhibit far more heterogeneity in process and returns than do equity managers in the same style box.

(Note that while the graphs below only show the period 1990-1993, the paper explores three time periods: 1990-1993, 1994-1997, and 1998-2001 and finds a similar conclusion in all three).

Perhaps most importantly, however, they find a rather significant reduction in risk characteristics like a portfolio’s realized maximum drawdown.

To quote the article,

We find that naively adding more funds to a portfolio tends to leave returns stable, decrease the standard deviation, and reduce downside risk. Thus, diversification should be increased as long as the marginal benefits of adding a new asset to a portfolio exceeds the marginal cost.

If a sample of managers is relatively style pure, then a fewer number of managers will minimize the unsystematic risk of that style. On the contrary, if the sample is really heterogeneous, increasing the number of managers may still provide important diversification benefits.

Taken together, this literature paints an important picture:

  • Diversifying across managers in the same category will likely do little to reduce portfolio volatility, except in the cases where categories are broad enough to capture many heterogeneous managers.
  • Diversifying across managers appears to significantly reduce the potential dispersion in terminal wealth.

But why is minimizing “the dispersion of terminal wealth” important?  The answer is the same reason why we diversify in the first place: risk management.

The potential for high dispersion in terminal wealth means that we can have dramatically different outcomes based upon the choices we are making, placing significant emphasis on our skill in manager selection.  Choosing just one manager is more right style thinking rather than our preferred less wrong.

But What About Dilution?

The number one response we hear when we talk about manager diversification is: “when we combine managers, won’t we just dilute our exposure back to the market?”

The answer, as with all things, is: “it depends.”  For the sake of brevity, we’re just going to leave it with, “no.”



If we identify three managers as providing exposure to value, then it makes little logical sense that somehow a combination of them would suddenly remove that exposure.  Subtraction through addition only works if there is a negative involved; i.e. one of the managers would have to provide anti-value exposure to offset the others.

Remember that an active manager’s portfolio can always be decomposed into two pieces: the benchmark and a dollar-neutral long/short portfolio that isolates the active over/under-weights that manager has made.

To “dilute back to the benchmark,” we’d have to identify managers and then weight them such that all of their over/under-weights net out to equal zero.

Candidly, we’d be impressed if you managed to do that.  Especially if you combine managers within the same style who should all be, at least directionally, taking similar bets.  The dilution that occurs is only across those bets which they disagree on and therefore reflect the idiosyncrasies of their specific process.

What a multi-manager implementation allows us to diversify is our selection risk, leading to a return profile more “in-line” with a given style or category.  In fact, Lhabitant and Learned (2002) demonstrated this exact notion with a graph that plots the correlation of multi-manager portfolios with their broad category.  While somewhat tautological, an increase in manager diversification leads to a return profile closer to the given style than to the idiosyncrasies of those managers.

We can also see this with a practical example.  Below we take several available ETFs that implement quantitative value strategies and plot their rolling 52-week return relative to the S&P 500. We also construct a multi-manager index (“MM_IDX”) that is a naïve, equal-weight portfolio.  The only wrinkle to this portfolio is that ETFs are not introduced immediately, but rather slowly over a 12-month period.3

Source: CSI Analytics.  Calculations by Newfound Research.  It is not possible to invest in an index.  Returns are total returns (i.e. assume the reinvestment of all distributions) and are gross of all fees except for underlying expense ratios of ETFs. Past performance does not guarantee future results. 


We can see that while the multi-manager blend is never the best performing strategy, it is also never the worst.  Never the hero; never a zero.

It should be noted that while manager diversification may be able to reduce the idiosyncratic returns that result from process differences, it will not prevent losses (or relative underperformance) of the underlying style itself.  In other words, we might avoid the full brunt of losses specific to the Sequoia Fund, but no amount of diversification would prevent the relative drag seen by the quantitative value style in general over the last decade.

We can see this in the graph above by the fact that all the lines generally tend to move together.  2015 was bad for value managers.  2016 was much better.  But we can also see that every once in a while, a specific implementation will hit a rough patch that is idiosyncratic to that approach; e.g. IWD in 2017 and most of 2018.

Multi-manager diversification is the tool that allows us to avoid the full brunt of this risk.


Taken together, the research behind manager diversification suggests:

  • In heterogeneous categories (e.g. many hedge fund styles), manager diversification may reduce portfolio volatility.
  • In more homogenous categories (e.g. equity style boxes), manager diversification may reduce the dispersion in terminal wealth.
  • Multi-manager implementations appear to reduce realized portfolio risk metrics such as maximum drawdown. This is likely partially due to the reduction in portfolio volatility, but also due to a reduction in exposure to funds that exhibit catastrophic losses.
  • Multi-manager implementations do not necessarily “dilute” the portfolio back to market exposure, but rather “dilute” the portfolio back to the style exposure, reducing exposure idiosyncratic process risk.

For advisors and investors, this evidence may cause a sigh of relief.  Instead of having to spend time trying to identify the best manager or the best process, there may be significant advantages to simply “avoiding the brain damage”4 and allocating equally among a few.  In other words, if you don’t know which low-volatility ETF to pick, just buy a couple and move on with your life.

But what are the cons?

  • A multi-manager approach may be tax inefficient, as we will need to rebalance allocations back to parity between the exposures.
  • A multi-manager approach may lead to fund bloat within a portfolio, doubling or tripling the number of holdings we have. While this is merely optical, except possibly in small portfolios, we recognize there exists an aversion to it.
  • By definition, performance will be middling: the cost of avoiding the full brunt of losers is that we also give up the full benefit of winners. We’re reluctant to label this as a con, as it is arguably the whole point of diversification, but it is worth pointing out that the same behavioral biases that emerge in portfolio reviews of asset allocation will likely re-emerge in reviews of manager selection, especially over short time horizons.

For investment managers, a natural interpretation of this research is that approaches blending different signals and portfolio construction methods together should lead to more consistent outcomes.  It should be no surprise, then, that asset managers adopting machine learning are finding significant advantages with ensemble techniques. After all, they invoke the low-hanging fruit of manager diversification.

Perhaps most interesting is that this research suggests that fund-of-funds really are not such bad ideas so long as costs can be kept under control.  As the asset management business continues to be more competitive, perhaps there is an edge – and a better client result – found in cooperation.


  1. For the sake of brevity, we are just going to charge forward and completely ignore the empirical evidence of semi-flat security market lines and the question of, “how do you measure risk?”
  2. Data as of 1/3/2019
  3. This is done to make the graph’s interpretation clearer; otherwise you would have an ETF like QVAL influencing the return of MM_IDX before the line for QVAL is plotted, which can lead to strange-looking results. Blending does not perfectly fix this issue, but it helps.
  4. Language courtesy of friend-of-the-firm Wesley Gray.

Corey is co-founder and Chief Investment Officer of Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Corey is responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients. Prior to offering asset management services, Newfound licensed research from the quantitative investment models developed by Corey. At peak, this research helped steer the tactical allocation decisions for upwards of $10bn. 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.