A step beyond MPT to address correlation and diversification.

    Unlike the go-go days of the late '90s, where everyone was happy with robust returns in an absolute setting, the subsequent markets haven't been nearly as friendly and investors are starting to get more selective. Not that they weren't selective before, but clearly the emphasis on comparisons to broad indexes has once again proved significant and necessary in the retail world. Additionally, asset allocation, supposedly dead in the late '90s, is without a doubt very much alive again and crucially imperative for long-term investors (it was only dead in perception, not in practice).
    Modern Portfolio Theory (MPT) and Dr. Harry Markowitz have taught us that diversification is the key to building a good portfolio. The main tool in determining the most appropriate vehicles to utilize in order to achieve proper diversification and reduce overall risk is correlation. The closer the correlation statistic is to -1 for two investments, the more attractive the pairing. This is indeed true if the goal is an ultimate reduction in standard deviation via the cutting of diversifiable risk. Ideally, when one investment "zigs" another component of the portfolio should "zag." These are the basic tenets of what correlation provides, and many optimization software tools are built exactly off of these very same tenets.
    However, what if the portfolio is designed to be measured against a passive benchmark? While a proper portfolio is built to help achieve financial goals within the context of an investor's risk-tolerance profile, there must be some hurdle or yardstick by which to measure success or failure along the way to those goals. The problem is that, as a stand-alone, the correlation statistic simply tells you whether or not two investments move in convergent or divergent paths versus each other only, and to what extreme.
    The statistic's caveat is that it fails to incorporate into the equation a measuring stick for the portfolio. While two investments may be perfectly negatively correlated (-1), they could simultaneously underperform or outperform their respective benchmarks or a shared benchmark; for that matter, in very similar fashions. In other words, while one component of the portfolio may lose value while another component gains value, they both could fall short of their benchmarks for the defined periods. Consequently, the portfolio could be well diversified by MPT standards, but certainly not in a relative sense versus a passive benchmark. When you examine the pattern of their excess returns, or lack thereof, theoretically two traditionally perfectly negatively correlated investments could be perfectly positively correlated based on their relative performance measures. By anyone's view, the pairing would not make for an attractive portfolio.
    Question: What statistic would be a better determinant in the selection of the more appropriate pairing of investment vehicles for relative performance and diversification purposes? Via the use of a more refined and further advanced version of correlation between two investment vehicles, modern portfolio theory is taken a step further to more appropriately diversify a portfolio of various components to achieve superior relative diversification.
    For lack of a better name, the answer is the Modern Correlation Statistic (MCS). By quantifying the correlation of excess or underperformance above or below the defined and respective benchmarks of two investment vehicles, one can construct a portfolio that may not only be just as diversified but even better allocated, and consequently more attractive versus the passive benchmark(s).
    The formula is as follows:
    Cov (Excess or Underperformance of Investment 1 and Excess or Underperformance of Investment 2) divided by [Std Dev (Excess or Underperfor-mance of Investment 1) * Std Dev (Excess or Underperformance of Investment 2)]
    The quantitative result from the above equation will produce a result resembling a traditional correlation statistic-between -1 and +1. The closer the statistic is to -1, the more attractive the pairing is from a relative diversification standpoint. A -1 result is indicative of two investment vehicles that historically have outpaced or trailed their respective benchmarks in opposite fashion from each other for any period defined in the population of data: said differently, when investment A surpasses its benchmark, investment B falls short of its benchmark. They are taking divergent paths of under- or outperformance, hence adding value from a relative diversification vantage point. Conversely, a +1 result is indicative of two investment vehicles that historically have always either outpaced or trailed their respective benchmarks in tandem for each defined period.
    Figure 1 is a very basic but powerful example demonstrating the use of the MCS.
Which investment is the better choice to be added to a portfolio already containing Investment A?

Portfolios    Correlation        MCS
A & B        -1.00                0.98
A & C        0.72                -0.85
    The correlation statistic tells us that Investment B is the better choice for the portfolio containing Investment A because the two are perfectly negatively correlated. In the example, during each period that Investment A is positive, Investment B is negative, and vice versa. According to MPT, Investment B would be the more attractive option. However, this analysis fails to take into account the relative performance against the indexes.

    After all, it's the benchmarks that tell us whether or not the active nature of the investment is indeed worth the actual investment itself. It is also what is tattooed to every quarterly performance report to gauge added value or lack thereof. According to the MCS, Investment C is the more attractive option. Although Investment A and Investment B are practically perfectly positively correlated, their relative performances versus their respective benchmarks take almost perfectly divergent paths. Investment C is clearly the better choice for the portfolio.
    This same theory holds true when utilizing one benchmark for comparison purposes (See Figure 2), regardless of the underlying investments under consideration, as demonstrated below:

Portfolios        Correlation        MCS

A & B        -1.00        0.93
A & C        0.84        -0.73
    While the construction of portfolios comprised of complementary components that move in divergent paths is desirable, it is not complete when the results of the portfolio are measured against a defined benchmark, as is the case in most circumstances. The actual desire for better relative diversification should be the construction of portfolios of complementary components that move in divergent paths relative to the benchmark rather than versus each other. This is what the MCS attempts to quantify.

  Utilizing MCS to build an allocation comprised of complementary investment vehicles should result in an enhanced portfolio where there always exists some winners and some losers. This does not mean that asset classes should be ignored to achieve the optimal mix of investments according to the MCS. In fact the absolute correlation of asset classes is what should help determine the mix within the portfolio itself. However, when it comes to filling those asset class buckets with actual active investments, absolute correlation just doesn't cut it in the world of benchmarking. 

Joshua M. Kaplan is chief investment strategist for Smart Financial Advisors LLC in Devon, Pa.