New First Step In Portfolio Construction

by: Newfound Research

Haecceity (pronounced:/hakˈsēətē/) is a philosophical term that translates to "thisness." It can be thought of as the discrete properties, characteristics, and qualities that make a thing so particular relative to its more general categorization. Haecceity contrasts quiddity (pronounced: /ˈkwidətē/) which describes the "whatness" of the more general category of the object. So for example, the "quiddity" of a chair could be that it provides the ability to sit at some elevation above the floor (a general categorization of "chair" that makes it a chair) whereas the "haecceity" of the chair you are sitting in specifically relates your chair-specific back support, elevation, design, and comfort (among others) -- those properties which make your chair unique among all chairs. A common sequence in static asset allocation construction is to begin with broad asset class assumptions and then move to more refined allocation decisions of sub-asset classes. By following this process, an implicit assumption is being made that the inherited properties of the specific sub-asset class, the sub-asset class' "haecceity," that which makes it unique relative to its parent asset class, are preserved and consistent with the more general asset class. Take for instance a static Moderate Aggressive allocation model. The broad asset allocation pie chart that is used as a "starting point" looks something like this:

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Then, specific sub-allocations will be chosen to determine how each "piece of the pie" is filled with sub asset classes. Take the Fixed Income sleeve for example: a likewise standard sub-asset class allocation of fixed income would be something along the lines of:

Sub Allocation Percentage
High Yield Debt 20%
Investment Grade Debt 20%
U.S. Government Debt 40%
Emerging Market Debt 10%
Inflation Protected Securities 10%
Click to enlarge

The sub-asset class allocation would then look like this: Click to enlarge

However, beginning with a broad asset class framework as a first step is failing to understand that the sub-asset class haecceity is not necessarily inherited from its parent asset class. In fact, sub-asset classes may behave most similarly to sub-asset classes within a different parent asset class, and in fact to blindly follow this hierarchy is failing to understand the more sophisticated and complex attributes that comprise a sub-asset class' "thisness."

Clustering, "Whatness" and "Thisness"

An highly valuable innovation of the computational evolution we live in is a concept known as "clustering." An easy way to understand the premise of clustering is as follows: assume you were presented the following 4 items:

  • A couch
  • A car
  • A semi-wheeler (also known as "an 18 wheeler")
  • A chair

You are then asked to place these four images into two distinct groups. Easy right? The groupings almost anyone would choose are:

Group Chosen Image
1 Couch, Chair
2 Car, Semi
Click to enlarge

How and why were those choices made? Without necessarily grasping the underlying process, you created "relationships around similarity and hierarchy by which to understand, group, and assimilate objects" -- you performed your own clustering algorithm. In numerical analysis, statistical data is grouped based on the way it "expresses itself" along certain dimensions (much innovation with regards to clustering has developed as a result of genetic analysis, where "gene expressions" are common nomenclature). Let's say for instance, we collected data about 6 people's height and weight, resulting in the following table:

Person Height Weight
Person 1 76" 210
Person 2 68" 150
Person 3 77" 257
Person 4 67" 157
Person 5 75" 249
Person 6 63" 112
Click to enlarge

Although grouping this sample may not seem straightforward, a scatterplot of the height (x-axis) against weight (y-axis) can provide insight as to how the data should be clustered, assuming two groups were needed:

Click to enlarge

The numerical explanation as to why you likely agree with the two clusters I've drawn circles around is something called Euclidean Distance. By visual inspection alone, the reader can determine that Persons 2, 4, and 6 are "closer together" along the dimensions of height and weight to Persons 1, 3, and 5. Similarly, a numerical clustering algorithm could have been used and arrived at the exact same grouping decision (buyer beware: clustering has many pitfalls and challenges not detailed in this post).

Haecceity & Quiddity of an Asset

Consider a portfolio construction process that includes 19 different holdings, with the following ETF vehicle (and ticker) to allocate towards its respective asset class and sub-asset class:

Name Ticker Sub Asset Class Asset Class
iShares Russell 1000 IWB US Equity Equity
iShares Russell Midcap IWR US Equity Equity
iShares Russell Small Cap IWM US Equity Equity
iShares Preferred Stock PFF US Equity Equity
iShares EAFE Small Cap SCZ Foreign Equity Equity
iShares EAFE EFA Foreign Equity Equity
iShares EAFE EM EEM Foreign Equity Equity
Dow Jones Real Estate IYR US Real Estate Alternative
SPDR Gold Trust GLD Commodity Alternative
iShares GSCI Commodity GSG Commodity Alternative
iShares TIPS TIP US Fixed Income Fixed Income
iShares 20+ Yr Treasury TLT US Fixed Income Fixed Income
iShares 7-10 Yr Treasury IEF US Fixed Income Fixed Income
iShares 1-3 Yr Treasury SHY US Fixed Income Fixed Income
iShares High Yield Bond HYG US Fixed Income Fixed Income
iShares Inv Grade Corp LQD US Fixed Income Fixed Income
PowerShares EM Sovereign Bond PCY Foreign EM FI Fixed Income
iShares JPM EM Bond EMB Foreign EM FI Fixed Income
iShares Barclays MBS Bond MBB US Fixed Income Fixed Income
Click to enlarge

As mentioned earlier, static portfolio allocations tend to look at the right-most column as the starting point to determine broad allocations. From these broad allocations more granular sub-allocation decisions are made. I would argue that a much more effective starting point would be to group assets based on their volatility (in a prior blog post I showed that relative volatility persists, whereas returns do not) and co-movement structure. Once subclasses are grouped into specific clusters that more effectively represent "similar behavior," specific allocation decisions can be made to incorporate the investor's "view" over the short to medium term -- much like the secondary process of in static portfolio construction.

Asset Grouping Based on Behavior … the Real Quiddity

One highly useful technique that can be employed to reduce the dimensionality of the volatility structure of a high number of sub-asset classes is Principal Component Analysis ("PCA"). Simply, the returns of 19 assets can be reduced into the returns of 19 "Principal Components", each with a decreasing power of explained variation. In this analysis, I used rolling annual periods (252 trading days) and kept the first two principal components (the one with the most and second most explained variation of the data). The first two principal components explained variation of the of the volatility structure of the above 19 assets is depicted below:

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Next, the sensitivity of each asset's returns to the two market factors is estimated using regression -- what in CAPM is referred to as Beta -- providing a table of sensitivities for each rolling period:

Asset Beta_1 Beta _2
IWB x_1 y_1
IWR x_2 y_2
MBB x_19 y_19
Click to enlarge

Much like the illustration of Height & Weight used above to illustrate simple grouping of people, two orthogonal (i.e. non-correlated) bases have been created to plot asset-specific sensitivities to each of the risk factors derived from the Principal Component Analysis. The final step is to run a clustering algorithm over the two dimensional factor sensitivity table at each time step to determine which assets are "most similar." The clustering algorithm I wrote determines:

  1. 1. The optimal number of clusters to be used based on a Silhouette Coefficient Maximization Scheme)
  2. 2. Which assets belong to which clusters

By examining which ETFs belong to which clusters, we should be able to determine whether the first step in static asset allocation construction erroneously assumes that sub-asset classes will follow parent asset class behavior, i.e. whether sub-asset classes from one parent asset class will be "most similar" to sub-asset classes from a different parent class.

The Results & Next Steps

The results of the analysis show how much the fundamental behavior, or haecceity of a specific sub-asset class, can change based on the capital market environment. Take for instance the periods leading up to and just after QE2, where "N" is the "optimal number of assets" chosen by the Silhouette Coefficient. Click to enlarge

The change in similarity matches what we would most likely expect based on our intuitive understanding of the potential impacts of Quantitative Easing:

  1. 1. Medium term and long term treasuries break off into their own cluster. Recall that Fed purchases were targeted towards medium to long term treasuries, therefore IEF and TLT took on volatility and sensitivity attributes unto themselves and were unlike any other sub-class.
  2. 2. Gold breaks into a cluster of its own as many see it as the only hedge to inflation caused by the multiple developed countries simultaneously devaluing their currency
  3. 3. Inflation protected securities, short term treasuries, investment grade debt, and mortgage back securities are similarly treated as a safe haven

Next, consider the optimal clusters in April of 2013, versus this past Friday, August 23rd, 2013. Click to enlarge

Again, the changes in cluster constituents match our intuition around capital market developments. In April, sub-asset class clusters actually mirrored parent asset class assumptions fairly effectively, except that an Alternative (Real Estate, IYR) was grouped with Equity (IWB, IWR, IWM, EFA, SCZ, EEM). However, as of late, Emerging Markets have experienced isolated volatility and unique attributes of sensitivity towards underlying market factors as considerations of Fed tightening have grown more pronounced.

Conclusion & Next Steps

This methodology is still new, with further testing to be done before it can be implemented as a standalone construction methodology. In following posts, I plan on using the optimized clusters as "base case starting points" much in the same way that static allocation methodologies use broader asset classes. However, it should be clear that static methodologies of portfolio construction suffer from an implicit assumption that sub-asset classes necessarily inherit the behavior (quiddity) of their parent, when in fact their responses to the most prominent risk factors that drive market volatility can be, and quite often is different other members from the parent asset class.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

Business relationship disclosure: Newfound Research is a quantitative asset management firm. This article was written by Benjamin M. Gross, Managing Director of Quantitative Strategies and Product Development. We did not receive compensation for this article (other than from Seeking Alpha), and we have no business relationship with any company whose stock is mentioned in this article.