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.

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