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In this Post I introduce the concepts of Cluster Analysis to Portfolio Construction.
Hierarchical Clustering is a mathematical/statistical method of analysis supported by widely accepted scientific methods. Don’t worry, I’m not going into all that technical detail – anyone who is so inclined can Google the subject on the Internet. Rather, I describe the practical use of functions/spreadsheets available within the Hoadley Finance Add-in for Excel, and the complementary apps, to perform this analysis. Many Platinum subscribers who are familiar with this site will be familiar with the Hoadley Add-in and apps since some of these tools are used by Lowell to perform his Modern Portfolio Theory (MVO) optimizations and generate Efficient Frontier graphs. I have also described the use of these tools in earlier parts of the Feynman Study. This Post introduces the Correlation Analyzer app.
I begin with an introduction to correlation matrices. Again, for the non-mathematically inclined, these can be confusing at best and daunting to the extent of total rejection at worst. However, to totally discard or ignore correlation is a mistake since this is the key link to developing a truly diversified portfolio.
Most readers will accept that (generally) Equities are highly/strongly correlated to each other, as are Bonds, but that there is (generally) low correlation between the two groups/asset classes or “clusters”. This is the basic concept behind Cluster Analysis – it gets a little more complicated as we add other asset classes such as REITs, commodities etc., and expand into the global universe of investment vehicles.
In a recent Post, Lowell has introduced the subject of “Diversification Through Correlation Analysis” and this post expands on that theme. Quoting from Richard Bernstein, “It’s not the number of asset classes that determines diversification; it’s the correlation among those asset classes that determins diversification”.
Cluster Analysis is compatible with many strategies that Platinum subscribers may follow, such as Gary Antonnacci’s work on Momentum, including derivatives such as “Dual Momentum” and “Pairs Switching” (the “pair” may now become a “cluster”) and the work on Structural Diversification as described by the good folks at GestaltU.
Even if you decide not to apply this method of analysis to your portfolios I think it is worth your time to read this article as it will at least make you more aware of what we mean by diversification and may help you construct more “robust” portfolios.
The Introduction to Cluster Analysis is available as a downloadable Word File here.
In a future Post I will be applying these ideas to construct a portfolio from the Feynman Asset List to analyze performance and compare with portfolios/strategies presented in earlier parts of the Study.
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Thank you David. Testing my understanding (or lack thereof), if I were using fig. 58 to “cook-up” a 5-asset portfolio, I would add 1 ingredient from each of the 5 colored-asset groupings (i.e., looking at the “standard” column I would pick 1 each from Blue, Salmon, Green, Gold, and Grey).
Is that a correct interpretation?
Dick
Dick,
You got it! Of course, you might also add the SHY filter.
David
To all;
Lowell has pointed out that I missed a question as to the definition of RSQD on the Ranking Spreadsheet. I still can’t find the question/comment so I’ll answer the question here since the reader is obviously following the Feynman Posts.
RSQD is the statistical value r-squared and is related to Beta.
Beta tells us how much the asset/ETF is expected to move relative to the market (for the Feynman Asset List this is VTSMX) – Beta can vary from +1 to -1. If Beta is greater than 1, the asset price should move (up or down) more than the market, if Beta is less than 1, the asset should move (up or down) less than the market. However, this is only valid if the asset is highly/strongly correlated with the “market” index being used to calculate the Beta. As we have seen in Part 9-1, this is not necessarily the case for all assets.
r-squared is a measure of the validity of the Beta value and varies between 0 and 1, with 1 being totally valid (perfect correlation) and 0 being totally meaningless (no correlation). A value greater than 0.8 is generally considered to be an acceptable level of correlation for the validity of the Beta value.
Thus, the value of Beta calculated for Bonds, using an equity (VTSMX) index, will have a low r-squared value since the correlation between Equities and Bonds tends to be inverse. Ideally we would like to use a more diverse “market” index for calculating portfolio Beta’s – but it is not easy to find one.
Hope this helps and answers the question.
David
David,
Is it possible to come up with the correlation of the portfolio against the index? For example, what is the correlation of the Feynman portfolio vs VTSMX? I think it would be great if one can measure the correlation of the entire portfolio and come up with a single number, for example a portfolio correlation of 0.50 against the VTSMX?
Nelson
Nelson,
In principle this is possible, but in practice it’s not so easy. To do this we obviously need to know the value of the portfolio on every day. If the composition of the portfolio didn’t change this would be relatively straightforward to calculate. However, since we are continuously changing the allocations it becomes more complex. On a forward looking basis one could record the portfolio everyday but this needs dedication – for a backtest the amount of work would be overwhelming.
In the end, I’m not sure how helpful the number is – other than it’s interesting to see.
The QPP program calculates the portfolio beta, but that is for a static/passive portfolio with no adjustments.. As mentioned at the beginning, that is relatively easy to do.
David
David, Lowell,
Thanks for all the great work and contributions. Since as you show so many of the broad general equity markets are, now with the “global economy”, very closely correlated, might it be an interesting study to look at broad sector ETFs (health care, housing, energy, finance, recreation, food etc.) as opportunities to set up a non-correlated portfolio (sure throw in a pure non-US equity ETF and the TIP, and BNDX)? The companies in these big sector ETFs are sure plenty of U.S. based but global companies (JNJ, XOM etc.) but that are individually non-correlated in the past and may give a hint of opportunities for a future ETF diversified but non-correlated portfolio.
Thanks again for stimulating work
Robert
Robert,
Certainly, it’s a great idea to break the markets into Sectors and look at momentum to find sector rotation within the asset classes. The Cluster analysis will also help separate the sectors as “mean” correlations break down.
One thing to keep in mind is the frequency and amplitude of the sector cycles and the momentum (ROC1 and ROC2 values) that may be needed to effectively detect shorter period swings. This may not be appropriate for all “Investors”.
I may look for examples similar to this in the future but, at present, I will stick to the original Feynman Asset list for simplicity and clarity – but I would encourage you to use the SSs to test your thoughts and ideas. Let us know how it works for you.
David
David:
Selfishly, I hope you do this first:
“In a future Post I will be applying these ideas to construct a portfolio from the Feynman Asset List to analyze performance and compare with portfolios/strategies presented in earlier parts of the Study.”
Dick
Dick,
I’ve finished the analysis – I just need to write it up – should be out by tomorrow. 🙂
David