• James Damschroder

Despite the widespread acceptance of diversification as an investment benefit, the fact remains that there’s never existed a genuine way to actually quantify either its existence or its effect. While it’s easy enough to deduce that a collection of assets can have lower overall risk than any individual asset, investment professionals in and around the industry have become accustomed over the years to thinking of diversification in the abstract. As a result, the notion of ‘risk measurement’ has mistakenly replaced the pursuit of real ‘diversification measurement.’

I’m here to suggest, and I intend to show by way of some rigorous research that we’ve done on real-life portfolios, that there is now a way to truly measure and manage diversification, and it’s the best way to control risk.

Changing the Paradigm
To date, modern portfolio theory, or MPT, has represented the investment industry’s best attempt toward maximizing return and minimizing losses. MPT is a mathematical formulation of the concept of diversification in investing, with the aim of selecting a collection of investment assets that has collectively lower risk than any individual asset. More technically, MPT defines risk as the standard deviation of return. By combining different assets whose returns are not correlated, MPT seeks to reduce the total variance of the portfolio.

One of MPT’s favorite analytics, mean variance optimization, or MVO, is (at this hour at least) still accepted as the primary tool in asset allocation. Yet few people are really happy with MVO as an asset allocation tool for real-world portfolios, in no small part because variance is not the only measure of risk and mean is not the only measure of reward.

Measuring and Optimizing Diversification
Any statistical measurement of the relationship of assets is an indication of diversification. Co-variances and correlations, for example, measure a unique relationship between any two single assets in the portfolio. But because a portfolio represents an entire composition of relationships, the measure of any one single relationship fails to indicate the actual level of portfolio diversification. We must account for all component relationships in the portfolio in order to get a true measurement of diversification.

While Beta and R-squared are both, in a relative way, measurements of diversification, they have meaningful limitations, not least of which is the requirement of an external portfolio for purpose of analysis. Typically, this portfolio is the S&P 500 or another broad index that approximates the market. This constraint has several problems, one of the largest being that simply defining the market is inherently problematic. Another is that there is little efficacy in comparing any facsimile of the market to any portfolio.

It’s reasonable to think that a measurement of diversification not concerned with items external to the portfolio but only those assets comprising the portfolio would better help investors construct and manage portfolios for performance purposes. Said another way, a holistic measurement of diversification independent of any market benchmark or index should be desirable by investors seeking performance.

 

What’s Really Inside?
What I call the ‘net diversification benefit’ is a reasonable means to measure diversification. Typically applied to a risk measurement, the net diversification measure is obtained by calculating risk statistics for the portfolio, then recalculating the same risk statistics as if all the correlations were one. The difference between the statistics is the net diversification benefit. It’s a genuine stab at diversification measurement to be sure, but the net diversification approach still comes up short. Why? Because it can only see diversification through a risk-colored lens.

A true holistic measure will account for the internal dynamics of a portfolio and will help explain the whole as a sum of the parts. Such a robust analysis requires three diversification measurements: systematic, non-systematic, and total diversification. System diversification measurement is called the Intra Portfolio Correlation, or IPC. Simply put, it’s the only approach ever conceived to measure diversification for the sake of measuring diversification.

The IPC is a weighted average intra-portfolio correlation that translates the range of correlations to percentage values. The greater the percentage (higher the number), the more diversification inside the portfolio.

To illustrate the IPC measure, we built a number of fairly standard portfolios with ten years’ worth of monthly return observations, as shown below in the chart "It’s What’s Inside That Counts" on page 38. Each portfolio was equally weighted.

The results are not intended to be a comprehensive survey of diversification, but they do give us a pretty good baseline. IPC values for typical (long-only) portfolios are less than 50%.

 

Informed Decisions…
Measurement adds utility to the investment process whenever it results in a reduction in the uncertainty of the object of measurement. This is the essence of investment management. Measuring diversification is at least as important as measuring risk. Diversification provides the essential element of portfolio optimization and analysis. Parsing diversification from the rubric of risk will give investment managers and investors a new element of control.

Most investors utilize some kind of non-systematic diversification these days—the quantity of assets inside a portfolio, for example—as a ‘floor’ for a portfolio. This floor would likely be different for a broad asset allocation portfolio invested in funds than it would be for equity portfolios. (The internal diversification within any fund product reduces the impetus for non-systemic diversification since funds are less subject to binary risk events like Enron, WorldCom, etc.) In any case, we tend to see practically diversified asset allocation portfolios maintain concentration values in the 10-20 range and equity portfolios in the 15-30 range. Values higher than this are indeed palatable from one risk reduction perspective, but they also introduce additional costs of research, monitoring, and trading.

All of this becomes a matter of tradeoffs, of course, but one could argue that all investment decisions are a matter of tradeoffs. As the stakes are raised—more assets under management, greater competition, more demanding clients—errors from intuitive decisions regarding tradeoffs become increasingly untenable. The ability to actually measure diversification provides further opportunity for informed decisions.

As an investor evaluates tradeoffs between diversification and other portfolio attributes, it might be best to look at total diversification. We created dimensionality to represent the total diversification of a portfolio. In a nutshell, more dimensions equal more diversification. Normally, we think of having three dimensions to our world, but in mathematics, there are no limitations to the dimensionality. (The branch of physics investigating string theory, for example, has discovered that it takes 13 dimensions to attain harmony among its calculations.)

A perfectly undiversified portfolio is one-dimensional, like a dot on a line. The dot can only move up the line or down the line. Now imagine a dot placed in a five-dimensional space. That dot now has freedom to move up or down along any of the five directions. More than that, the direction the dot moves along one axis (dimension) does not connote anything about how it moves along another axis. Every extra dimension of a portfolio allows it to perform in a simultaneous and independent direction.

For the purpose of pursuing total diversification, the use of dimensionality accounts for both the quantity of a portfolio’s assets and the commonality among them.

 

…Mean Better Performance
To help prudent investors better understand the relationships between diversification and other primary performance statistics, we worked with the University of Denver’s Reiman School of Finance to examine the relationship of IPC and return for 95 actual portfolios that RIAs had in place between the years 2002 and 2009. (These advisors volunteered the portfolio information to Gravity Investments as part of their due diligence of the Gravity Investment diversification platform—Gsphere.) Qualifying portfolios had assets limited to U.S. and Canadian equities, U.S. mutual funds, ETFs, and indexes. The portfolios were tested across the bull market from October 4, 2002, to October 12, 2007, and the bear market from October 12, 2007, to March 6, 2009.

Our research showed that risk had a significant negative correlation to returns in the bear market. The implications of this relationship reversal are utterly destructive to those who would connect a risk profile to select portfolios from an efficient frontier. Without a commensurate or larger increase in the relationship of return and risk in the bull market, investors are better off focusing optimization on diversification and not risk.

Essentially, the risk/return relationships in the bull and bear market cancel each other. On the other hand, the IPC in the bull market showed no significant relationship—in the bear market the correlation jumps from 0.06 to 0.77, indicating that diversification delivers capital preservation across market downturns.

Because there was no significant relationship between market diversification and returns in the bull market, the significant and large correlation in the bear market is the first quantitative evidence of a true ‘free lunch’ impact of diversification. A predictive regression test of the bear market IPC/return relationship further showed that an extra percent of diversification is responsible for protecting 98 basis points of capital, almost a one-to-one relationship.

Diversification, in other words, does a better job of preserving capital across a full bull/bear market cycle while providing a significant impact to bear market returns with no cost of the diversification in the bull market.

Not only does diversification better relate to returns than risk, it is a significantly more stable portfolio input and diversification shows greater internal consistency. What that means is portfolio models built on this more stable attribute will more closely conform to the actual future performance. This predictability is essential in setting and meeting client expectations.

We also looked at how four broad portfolios’ risk and diversification values changed during the last four market crises: the Mortgage Meltdown of 2008; 9/11; the tech bubble collapse of 2000; and the 1997 Asian Currency/LTCM crisis. We compared the two months after the start of each crisis to each of the portfolio’s 10-year average.

Results showed that risk jumped significantly from its 10-year average while systemic diversification levels (IPC) barely budged. The greater consistency of diversification would help well-diversified portfolios better deliver to expectations.

In total, diversification, not risk, is merited as the focus of portfolio optimization and asset allocation construction.

Building Better Portfolios
If the risk and return relation breaks down as the research shows, then optimizing for diversification instead of risk makes perfect sense. To optimize for diversification means that volatility measurements for any portfolio can be disregarded (or diminished) and the asset allocation can be a product of, and only of, diversification. Investment managers can independently adjust the significance and prominence to the asset allocation or risk, return, and diversification respectively. Diversification optimization, the central part of our Gsphere diversification platform, lets investors take any number of investment philosophies and strategies and combine them with a diversification-focused asset allocation model. Diversification is combined with some kind of utility function (returns, risk-adjusted returns, etc.) and the optimization is ensured to produce a well-diversified portfolio. This diversification maximization produces portfolios that look and act more like the highly-vaunted endowment model.

(A prerequisite, of course, to producing endowment-like portfolios is loading the portfolio with assets capable of truly adding diversification. The Gsphere software has been designed to separate the ‘wheat from the chaff’ on the front end.)

In other research we conducted pitting diversification optimization against equal weighted and market-cap weighted portfolios, diversification-weighted indexes outperformed the alternatives in 79 of 80 head-to-head tests. In the average of all the tests, diversification optimization outperformed market capitalization by an average of 462 basis points of annual performance and equal weighting by 192 basis points. In aggregate, maximized diversification outperformed the alternatives by 327 basis points. These tests were made using a "walk forward" backtest, so that the optimization could not benefit from hindsight.

Any optimization tends to be more accurate if the assets being optimized are the actual implementable investments. Remodeling the investment process from one of optimization first and selection next, to one of selection first and optimization next will benefit many portfolio managers. While investors can choose to optimize at a strategic asset class level, they might be surprised at how the assets actually selected for optimization may differ from the designated asset class. Such differences, thought by some to be a negative, can have positive performance implications, especially if the selection process precedes the optimization. Breaking out of the box, in this case, is what delivers diversification.

Determining whether a portfolio is diversified enough, if you will, can be assisted through what we call "portfolio visualization," a process that displays the portfolio holistically and presents diversification as a three-dimensional balance, or symmetry.

 

Finding Diversification Now
So where does diversification come from in today’s market? The stock/bond relationship can still be mined for diversification, but blindly assuming the presence of diversification can sacrifice a good amount of potential performance. While diversification has been apparent to me from several sources—gold, managed futures, alpha-generating active strategies (hedge funds), hard assets, real estate—I think investors have to get a little more creative these days to acquire true diversification. For example, hiring a ‘go anywhere’ unconstrained manager will likely produce a greater diversification effect than hiring a manager to fulfill some type of mandate like large-cap value. (An interesting question is how insurance and annuity products impact client diversification measures. While the results will vary from product to product, the engineering underlying these products can be very attractive from a diversification perspective.)

We can see from the table of IPC values above that the "style" constructed portfolio had the least diversification of any portfolio tested. Interesting this is the most prevalent means of market segmentation. Coincidence? Doubtful.

Commonality is the enemy of diversification. Large-cap companies share more in common with other large-cap companies than with small-cap companies whose performance is more likely driven by endogenous factors like execution and business strategy.

In my mind, portfolio construction is all about combining your best ideas with diversification. You can also subject this to certain constraints like income requirements and liquidity needs. Other criteria such as investment horizons and preferences for safety or absolute returns can manifest in the econometrics and relative importance of the input criteria.

 

What’s Next?
If the last 30 years of risk management are any kind of indication, I think in the coming years we’ll be able to slice and dice diversification in a myriad of ways to get superior results.

From an adoption perspective, diversification measurement is still in the domain of the early mover. But as more advisors hear of the success of their peers in the new science of diversification, I’m sure the curve will push into the mass adoption. Indeed, investment professionals of all sorts will eventually need to measure diversification just to stay competitive. Advisors are already inspecting the Gsphere diversification platform and progressive broker/dealers are embedding parts of Gsphere into their platforms.

Meanwhile, what we call ‘diversification search’ is set to join diversification visualization, measurement, and optimization. Diversification search provides the answer to the question, "Okay, I’ve optimized diversification, but now what?" This process will continue to mature for years to come, including integrating with client profiles, fundamentals, manager preferences, glide paths, and other temporal factors.

Actually, I think the educational opportunity for advisors has implications that may even exceed that of performance alone. While I can’t pretend to be unbiased, I do believe that the ‘Gsphere Certification’ will form the basis for a network full of advisors who have demonstrated high levels of diversification intelligence and practice management, and use MyDiversification.com, a diagnostic tool aimed at pairing retail investors with the right diversification-oriented advisor.

With such strong demands to differentiate an advisory practice by delivering real performance, diversification, beyond the hyperbole and intuition, may become an advisor’s new best friend. I welcome your feedback and invite you to explore our research.

 

 

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James Damschroder is founder of Gravity Investments and creator of the patented Gsphere diversification platform, software that explicitly measures, visualizes, and optimizes portfolio diversification. He can be reached atdamschroder@gravityinvestments.com.