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January 01, 2010 at 02:00 AM
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.
