The Statistical Mystique

Jul 30 2010 | 9:00am ET

By Thomas Kuntz, Polymetis LLC -- Since the publication of Harry Markowitz’s seminal “Portfolio Selection” in the Journal of Finance in 1952, the genesis of modern portfolio theory (“MPT”), the application of statistical and quantitative methods to asset management, has increased dramatically.  That growth has been enhanced in the past few decades by the exponential growth of computing power, the convenience of user-friendly software, the accessibility of vast amounts of data, and the proliferation of innovative and functional research.

This has been a positive net development, but it has not come without certain costs, particularly for the existing or potential hedge fund investor.  The explosion in the availability of facts and figures, however, has not necessarily led to a commensurate increase in useful information.  If anything, there may be too much data to process efficiently, and too many ways to slice and dice them.  Statistics are neither informative nor useful just because they can be calculated.  Furthermore, chasing after every possible measure consumes investors’ most valuable resources, time and attention, and can lead to paralysis from analysis.

One useful tactic to combat this potential data and analytical overload is to, every now and again, refocus on the core quantitative elements embedded in the manager evaluation and portfolio construction process.  It is useful, therefore, to focus on the “big three” of asset management statistics:  mean, standard deviation, and correlation coefficient.  Why these three?  Not only are they the most widely-used and accepted investment statistics, but according to MPT, one can design efficient portfolios of assets using only these inputs.

Let us re-examine these three key measures with a fresh perspective, and with a minimum of mathematical theory, to see what they can tell us.

Statistics are like power tools, very helpful and effective when used properly, and potentially dangerous and destructive when used improperly.  It makes sense to handle them with care since we have learned the following:

  • Statistics can be calculated from data that may be inappropriate, misleading, or inaccurate.
  • Statistics may not be useful predictors as future results may not come from the same sample as the historical track record.
  • Statistics are easy to misinterpret or misconstrue.
  • Statistics or analyses derived from other statistics will suffer both from the flaws of the source as well as from their own limitations.
  • Statistics are sensitive to a number of underlying assumptions regarding their use, especially with regard to the shape of the distribution.

So, other than being aware of these limitations and taking care not to rely too heavily on these statistics, what should the intrepid hedge fund investor do?  There are a variety of other measures to consider, though there are no easy or complete solutions.

  • One can employ more complex statistics that incorporate higher statistical moments like skew and kurtosis.  Some examples include Kappa, Modified VaR, and Omega.  These can be powerful analytical tools, but they have their own limitations which can offset their utility.
  • One can employ a mosaic of statistics to overcome the limitations or biases embedded in any individual statistic.  The danger is that different statistics may not be independent of one another, but effectively may tell the same story in a different way.
  • One can employ common sense or qualitative overlays to adjust for known or perceived limitations in the data or statistical method.  This, however, can add a layer of subjectivity that offsets the rigor of statistical analysis.  The overlay also may make matters worse, not better.
  • One can apply other quantitative or statistical methods to adjust for non-normality issue limitations.  For example, one can transform data or inputs, or even attempt to normalize distributions.  These efforts can range from the relatively simple to the relatively complex.  Proceed with caution.

There is no one size fits all solution.  In the end, the use of statistical analyses in hedge fund evaluation and portfolio construction is a process that must be managed carefully.  Ultimately, the best defense is a well-constructed, comprehensive program implemented by experienced and knowledgeable practitioners.

The full white paper can be found here: The Statistical Mystique

Thomas Kuntz is chief executive officer of Polymetis LLC, an investment boutique founded in 2009 to provide premier due diligence, research, and investment advisory services in the alternative marketplace.

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