Diversification, Spurious Correlation and Why You Shouldn’t Always Trust What You See or Hear

Posted on April 11, 2016

Author Name By Troy Brown, CFA

While difficult to find someone to disagree that one of the core tenants of designing an effective investment portfolio is sound diversification, the underlying impact of this diversification on return potential often defies common understanding. Contrary to a mantra I read and hear all too often, “We’re going to diversify this portfolio to maximize returns,” mathematically, and absent of leverage, quite the opposite is true in many instances.

If you were not fortunate enough to have been born into a royal bloodline, the fastest way to amass a sizable fortune, and in turn maximize your return, is to put “all of your eggs in one basket” and concentrate your wealth. While this may sound attractive to the average craps player, this excessive risk taking and low probability outcome is not a very sound strategy for the average person or institutional portfolio. In fact, a quick internet search supports my claim quite nicely by revealing the average millionaire goes bankrupt 3.5 times during their lifetime. Don’t you just love unattributed internet statistics? Look forward to more fun with statistics later on…

Now that we have established that diversification does not necessarily maximize returns, just what DOES it do? Simply put, diversification, in its various forms, is one of the strongest portfolio tools available to balance the expected return potential of a portfolio against the inherent risk and volatility of the financial markets. The most basic and accepted example of diversification is holding a combination of stocks and bonds in a portfolio. Taken to the next logical step by adding additional asset classes to the mix, along with sound and creative diversification, one can construct an investment portfolio having reasonable probability of achieving its return objectives over time (just not all at once). In practice, by combining several investments and strategies characterized by, and impacted by, different underlying economic, geopolitical, and other factors, we can use knowledge and experience to build an effective “all weather” portfolio.

Enough theory, let’s describe the math. The real foundation of diversification is how different assets “correlate” with each other, which is defined by their degree of co- movement, or their covariance divided by the product of each asset’s standard deviation. The correlation coefficient between two variables (asset classes) ranges from +1.0 for perfect positive correlation to -1.0 for perfect negative correlation. In an investment sense, while the expected return of each investment remains an important factor, the lower the correlation between two assets, the greater the diversification benefit from combining those assets in a portfolio. Rather than going through a series of formulas and theories, let me summarize by saying that, underneath the basic logic of why diversification makes sense in portfolios, there is some pretty hefty math involved in deriving the appropriate balance of return relative to risk. Unfortunately, as eager practitioners and clients, and as the formulas get bigger and more complex, we often tend to assign greater value to the output they produce.

While the combination of different asset classes or strategies with low correlations to one another is a solid foundation for building a diversified investment portfolio,

Remaining skeptical of the math is always a good idea. Patterns and generally accepted correlations between various assets tend to gain stature over time, but these coefficients are far from constant. The same underlying economic and geopolitical factors pushing and pulling on an asset’s ability to generate stable returns in isolation also impact long-held and expected patterns of correlation between assets. 2008 is the most recent example of this breakdown in action, as the majority of asset classes and strategies moved in tandem during the second half of the year as correlations between all assets moved loosely toward +1.0, largely, albeit temporarily, eliminating the benefit of diversification.

To further emphasize why investors should maintain a healthy skepticism of correlation as the sole basis of investment, consider the following example from outside the financial markets.


Courtesy of http://www.tylervigen.com/

The two data series depicted above are highly correlated over an extended period of time with a correlation coefficient of 0.9357 or 93.57%. Before dismissing these two series as spurious correlations outright, as dark as it is, one could argue that, if there is a greater number of cars on the road as represented by the first series, statistically, there is a higher instance of various forms of vehicle-related deaths as represented by the second series. This loose logic seems plausible in your mind until you consider the graph below.

Courtesy of http://www.tylervigen.com/

I did not choose this example for another death-related comparison, rather, as a Wisconsin native cheese consumption is near and dear to my heart and continues to be a large part of my diet. Although one cannot make the same logical leap relating these next two data series as easily as the first graph, they exhibit an even higher correlation over an extended period of time with a coefficient of 0.9471 or 94.71%.

So what is the ‘take-home’ message from all this? Simply put, if the primary merit and thesis of a new or complex investment structure you are pitched is its low correlation to other assets in your portfolio which you already know and understand, be cautious and tread lightly. Like investments, some correlations work for your portfolio until they don’t.