Equity factor modelling is all about a comparison of two populations. On the one hand is the set of stocks which your model suggests you own (think of this really as in the limit a set of weights $w_s$ over an agreed universe of stocks, $S$. In other words, you don't need to think of it as the selection of a subset of stocks out of a universe, you really are just working out what fraction of the universe to own. Secondly you don't really need to know what quantities to own, merely what percentage (long or short) of some reference investment amount (your capital).
This set of weights is then compared with a second set of seemingly uncontroversial weights - namely the stock weights in some well known index. Often you'll want this to be market capitalisation weighted and not price weighted (S&P 500, not Dow Jones). The wider this universe, the better, since you are looking in the maximum number of places for an edge. Or so they say.
Clearly, equity factor modelling is all about imagining the stocks of this universe as similar atoms, with more or less stable cross-reading semantically coherent 'properties'. With these atoms, we then apply in effect a form of statistical physics analysis to the atoms. We need to work hard to maintain the fiction of more-or-less-homogeneity since in reality there are all sorts of bespoke events which make you soon realise that the atoms are quite different in their own way.
Nonetheless, practitioners typically set a wide universe. The widest universe is the universe of stocks worldwide. But this approach is often carried out for at most the US and Europe. The ideal widest though, is all tradeable equities. But that decision, made many decades ago, to prefer capitalisation weighted proportions as the default must be seen for what it is - an assumption. It is a decision that has become performative in the industry - it is hard to go back. Since everyone assumes this, you must too. But it is important to point out that this is an assumption.
For example, for sophisticated investors, they may have access to private equity. Or they may prefer to ignore tiny stocks. Or illiquid ones.
Many equity factors and factor databases present fundamental factor data-sets which are in effect sector and accounting-regime-sensitive attributes, not globally applicable ones. This semantic variance need to be dealt with head on and can only be done by fully understanding the balance sheet of firm in all of the related accounting jurisdictions. And the common sector and region/country accounting practices.
If these anomalies are not fully understood and dealt with then you will be making comparisons between seemingly similar dimensions, leading to poor selection of portfolio weightings. I will cal this issue the factor polysemy issue.
So I think I will approach this from a more narrow point of view.
I'd like to make my market be a country-specific sector. This effectively eliminates a lot of this semantic cross fire. What do I lose in doing this.
Well, my universe is smaller. So the opportunity set is smaller. But there's no evidence to suggest that an equity factor edge is more appropriate in any one sector than another.
How will I deal with the fact that my sector, being only a sector, will not perform like the market as a whole? Option 1: I can just accept that as a given. In other words, I will be aiming to beat the sector ETF's performance.
Option 2: I can hedge the factor portfolio with short quantities of the ETF itself, becoming exposed only to the out-performance of the selection, and not to the ETF performance itself.
Option 3: I can hedge to the ETF as above but add back in the market. In this way I get exposure to the market, with just the sector beta knocked out, and with my factor exposure for those sector names (long and short) I can achieve a mostly beta performance with some sector alpha.
Option 3 opens up the possibility of the strategy being comparable in returns to the market. It opens up the possibility of an external 'sector switching' process which allows me to stop running on one sector and open on another. There are many cyclical phenomena which could drive this - the business cycle and observed sector rotation effects. There can be other pseudo-sectors too - the in-play m&a sector, the convertible new issue sector. In short, these represent a generalised way to think of 'sector' beyond e.g. GICS.
In general option 3 can be generalised to running some fractional allocation to all sectors in parallel to each other. So rather than turning on or off sectors binary fashion, you ease into them via a reallocation process.
This model could build well since it allows you to start small, it doesn't commit you to having a pan-sector factor set and it can be driven by economic considerations.
It also nicely partitions the universe of stock data so that they are held out for the appropriate models, minimising data mining and over fitting risks. It is grounded nicely in reality too. It parallelises the factor efforts and domain knowledge of the respective domain experts. This approach can also work at the geographic level too. It is also quite possible that there are multiple sector specific databases of information which make sense for stocks only in that sector.
The handy thing about basing my universe on an ETF is the company itself publishes its constituents and weights regularly so leverage off the back of their static data operation and their indexation algorithm.
It also suggests a first equity factor model to build - one where the only factor is the beta of the stock back to the target ETF. This would nicely operate as a quality check for the algorithm so far. The expected result of this will hopefully be fairly close to the performance of the ETF itself, adjusting for the ETF's own tracking error.
