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)