Regression Analysis and The Schwert Effect

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Regression Analysis is the investment communities effort to apply the scientific method to portfolio analysis.  Let’s take a little time to explain what is meant by Regression Analysis.  As you might remember from your math and science classes, data is plotted on an Y – X axis.  For example, in physics it is common to plot time on the X-axis and distance, velocity, or acceleration on the Y-axis.  Then a curve is drawn through the points in a manner so that we have a similar number of data points above and below the line.  Modern labs now have software to do this and it is called Regression Analysis or Least-Squares Fit.  If we were to plot the distance vs. time graph for a falling ball, we would see a set of data points that generate a very nice increasing curve as the ball falls a greater distance in a second than it did in the prior second.  A velocity vs. time of this same event will generate a straight line that increases constantly for each unit of time.  The acceleration vs. time is a flat line parallel to the X-axis and the value where the line intersects the Y-axis is 9.8 m/s/s or negative 9.8 m/s/s if the direction of motion is included.

In the financial world, the variable plotted on the X-axis is the return of the whole stock market.  We might use VTI or VTSMX if we define the whole stock market as the U.S. Equities market.  If we are less provincial, we might use VT which covers the entire world equity market.  On the Y-axis we plot the rate of return of a particular stock portfolio if we are examining stocks.  The slope of the line is called “beta,” and the place where the line intersects the Y-axis is called “alpha.”  The goal is to find a portfolio where the line intersecting the Y-axis is as high as possible.  This is called, adding alpha to the portfolio.  Most portfolios end up intersecting the Y-axis below the origin for a negative alpha.  Expenses are a significant factor in subtracting alpha from the performance of a portfolio.

Eugene Fama and Kenneth French are well known in the financial community for their regression analysis research.  Three factors or variables Fama and French examined over their years of research are value, size, and momentum.  There are other factors, but these are the primary ones we can control within the ITA portfolios.  A value stock is a stock with a low P/B ratio, where P is the market price and B is the book value.  F&F found portfolios made up of value stocks tend to outperform the broad market so such a value oriented portfolio will add alpha.  This is why we skew our portfolios toward value by assigning a higher percentage of the Strategic Asset Allocation (SAA) to VTV, VOE, vs. VBR instead of VUG, VOT, and VBK respectively.

A second factor is size.  Stocks with lower capitalization tend to outperform larger-cap stocks.  To gain this advantage, we invest a higher percentage in VBR than VTV as an example.  A third factor is momentum and this is what we do when we rank ETFs in the SAS 7.1.x spreadsheets.  Momentum states that stocks that performed well over the past few months have a tendency to continue to perform well and stocks that have declined in price over the past few months will continue to decline in price.  The Momentum Theory runs counter to the Reversion-To-The-Mean Theory.  You will recall HedgeHunter reminding readers that we do not know why momentum works.  Fama and French do not have explanations why value and size work.  To the best of our knowledge, there does not seem to be a fundamental reason for these factors to add alpha to a portfolio.  Therefore, future results are suspect.  Let’s be clear about that.

In all their research, Fama and French do not provide a good explanation for why these “alpha adding” results occur.  Just because a value or small-cap stock performed well in the past does not mean it will continue to do so in the future and this is where the Schwert Effect or Schwert Rule comes into play.  G. William Schwert, University of Rochester professor studied these “alpha producing” factors and termed them “anomalies.”  In other words, when these factors became known and used by large numbers of investors, the “anomalies seemed to disappear, reverse, or attenuate.”  Robert Novy-Marx (a former student of mine.) recently discovered something called profitability and it adds alpha to stock portfolios.  Is this just another “anomaly?”  If there is not a fundamental reason behind the “anomaly,” then it will eventually languish and cease to add alpha to the portfolio.

In science we begin with a hypothesis or what we might call a reasonable or good idea.  After capturing lots of data and analyzing the results we form a theory as to why this idea is true.  It is also essential that other scientists be able to take the data and reproduce the results.  More data is gathered, analyzed, refined, until the original idea becomes “settled” theory. It is not unusual for mathematics to lead the way in coming up with new ideas that eventually work themselves into theories.  While the financial community uses mathematics, so far they failed to provide any useful explanation why the well-known factors such as beta, value, size, and momentum benefit portfolios.  Most likely, they are nothing more than passing anomalies.

How do we plan to use the regression factors and the possibility they are suffering from the Schwert Effect?  The best we can do is to continue to test the most reliable factors while keeping our investments spread out across the globe.  Our risk reduction models will keep us out of major bear market declines and the Cluster Weighting Momentum or simply Momentum model does an adequate job of diversifying the portfolio.  For those who are still skeptical, then follow the Schrodinger Portfolio.  Yes, it has a size and value bent, but the portfolio is well-balanced across the world and should continue to closely track the U.S. Equities market as it has done for nearly 15 years.

An ITA Investor should do well by following these guidelines.

• Diversify by using ETFs of broad asset classes.  VTI, VEA, and VWO are examples.
• Track your portfolio using the TLH Spreadsheet.  If you don’t measure it you can’t manage it.
• Apply the risk reduction model of selling ETFs that are either under-performing SHY or are priced below their 195-Day EMA.

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