Quantitative Criteria for Defining Asset Classes

# What are the quantitative requirements to distinguish between asset classes?


# What are the quantitative requirements to distinguish between asset classes?












What are the quantitative criteria to distinguish between asset classes? I ask this as many institutional investors are undergoing strategic and tactical asset class decisions at the moment. How does one define an asset class? Does the fact that an equity trades publicly on an exchange vs privately a meaningful distinction to make it a separate asset class? What is the quantitative measure that is used to make this distinction? If there is a liquidity metric, would this metric be applied to a subset of the publicly traded equities to move a publicly traded equity into the same asset class as privately traded equity?

Although the return, volatility and correlation are used to determined an asset allocation, there seems to be quite a range within the asset classes of the underlying assets along these parameters. When would you exclude an asset from an asset class? Are there any other defining characteristics that are not used in the optimization that would define an asset class?

## Answer by lehalle (score 8, accepted)

https://quant.stackexchange.com/a/68786

Defining asset classes from a quantitative perspective is an interesting question that is not really addressed "officially" as far as I know.

Let's try to write some requirements

- you want strategic decisions to make sense: each asset class should have at least one or two different "economic drivers" than the others

- you want tactical decisions to make sense: each asset class should potentially be impacted differently by "short term events" (think about the Brexit or the covid announcements)

This is stated qualitatively, nevertheless if you have data focused on "economic contexts" and "economic events", you can try to make the difference. As you underlined, liquidity can be considered as an important criterion since it can split two assets in the context of an event: the less liquid may be subject to "fire sales" while the other will not, and the result may be a different behaviour.

Alternative data (supply chain, credit cards, texts, etc) can make the difference there since they can be used do describe "economic contexts and events" a quantitative way.

In any case you can also try to deduce this kind of requirement:

- You want the correlations inside an asset class to be "on average" higher than the correlation between two asset classes

You can replace "correlations" by "dependencies" if you want to state this a more non-linear way (and be pushed towards Machine Learning inspired techniques; you can have a look at A review of two decades of correlations, hierarchies, networks and clustering in financial markets by Marti, Nielsen, Binkowski, and Donnat).

Such a definition (intra-class vs. inter-class homogeneity) is somehow the definition of unsupervised clustering. Probably it would be good to have a multi-scale classification of assets, and may be ultimately some assets could belong to several classes (with different weights or probabilities).

As a conclusion I would recommend a mix of quantitative and qualitative layers if you want to build your own hierarchy of asset classes. If you want to use an off-the-shelf also, you can have a look at self-organising maps in two steps (the second one being a quantisation step, have a look at A Semi-Supervised Self-Organizing Map for Clustering and Classification by Braga and Bassani for inspiration)

## Answer by nbbo2 (score 2)

https://quant.stackexchange.com/a/68800

A quant technique that could be used to (partially) address this problem is the Mean Variance Spanning Test of Huberman and Kandel (1987). Abstract

This is a statistical test of whether adding K new assets to an existing set of N assets improves the Efficient Frontier or not. Roughly speaking the test involves checking whether the new assets "add something new" to the investment universe by checking whether the new assets could be simulated by linear combinations of the previously known assets. If not it can be concluded that the new assets offer some benefit in risk reduction (diversification) or return enhancement.

For example this test has been used to show that REITs (Real Estate Investment Trust stocks) do not improve a portfolio consisting of other major groups of US stocks, so REITs do not deserve to be considered a separate asset class.