The weekend pause is perhaps a good time to reflect and remind us our "trading principles", and the nature of the
statistical edge we exploit.
I would also like to slightly improve some piece of terminology, as I think I used the expression conservation of trading information (pag.29). I am now thinking that "preservation of past trading information" can be a more appropriate wording. The point is that we are
preserving "past trading information", that we ourselves generate through the trading process. Clearly, it is by no means information "intrinsically" contained in the past tickprice/volume realization. It's merely the information
embedded in the "order cloud" that we ourselves generate in response to the tickdata received, and according to the scalping hedging game rules.
As to possible information in the tickdata past realization, we do not use that at algorithmic level. Clearly, this is a reflection of the conceptual stand that past tickdata does not carry information useful to be extracted to the purpose of a statistical edge. (That is why we need to avoid in our vocabulary, words such as data based "prediction" and so on.) [Clearly, such information (or "illusion of information") or other personal beliefs can still enter the system through the manager intervention, who has full control on every aspect of it.]
We do, instead, fully consider
"structural characteristics" of the instruments, which are public knowledge, and that might, for instance, impose "drifts" (of purely
mathematical nature), or change the
volatility or the
leverage level, which is very useful to consider in the
settings of the scalping/hedging games.
So our weekend (updated from pag.29) "flash card" might be:
Some notes
- Mere "preservation" without "
use" would be the same as the ordinary and common "
Stop & forget" approach (which is always largely dominated by the above approach).
- Scalping hedging games and architecture must ensure that past trading information is used. This is obtained by the
player superposition (architectural feature) and the game settings so that order sizing and entry styles are affected by the whole (past) order cloud. This property (that is the capacity to exploit the past trading information for some form of asymptotic convergence) might be called
"self-consistency" of an order cloud (let's skip any attempt of formalization at this point and keep all fluid, conceptual, and thus more powerful).
- Architecturally, the most powerful math device for past information preservation and hedging is the "
player superposition" concept, which allows to decompose the entire PNL into even the most minuscule contributions of each and every order, and also make visually apparent such contributions.
- For any strategy S, a new strategy S* can be created which "dominates" (in the sense of >= performances) it by using the above
"preservation principle". (We might call this,
"Theorem of strategic dominance", which could take different incarnations, depending of the formalization one introduces, but let's keep it purely conceptual for the time being, so that we leave open a wide range of possible approaches such as, probabilistic, fuzzy, chaotic, etc., suitable to researchers coming from diverse perspectives and backgrounds). As to a "formal proof" of this statement, it is clearly dependent on the formalization one introduces; anyway, the conceptual idea is the one I have sketched in the previous posts. That is, we transform a reduced increase of
entropy of the system, into an actual
imbalance of the Gain/Loss components, which in the long term generated a "positive drift", which is hopefully able to stand against all the various growing trading expenses (commissions, spread, interests, etc.).
This understandably may work in any practical meaningful settings, and especially well in purely theoretical settings (and unfortunately unrealistic) such as the "random walk hypothesis". In fact all we need for it to work is that we are in the zone of 50%/50% to close with a profit/loss any position we open, and clearly, no overwhelming trading expenses or other structural "drifts" strongly working against us. The
loss recycling feature (player superposition) will add, in the relatively long term, the desired
statistical edge to it, in the apparent form of a
statistical drift.
