Thanks for the explanation. Ok, if I understand it right the "alpha" does not come from entry/exit rules, but from keeping memory of lost trades and using it for recovering losses by entering further trades with some hedging algorithm - is that correct?
If so, why does this method produce an edge? Suppose the win chance of any trade is 50%, then I would assume that this is also valid for the hedging trades. How does using memory of lost trades increase that chance? Do you have a math formula for that?
> is that correct?
That's right, in the sense that it provides a
necessary condition to play trading games which are not uniformly dominated (clearly, it does not "guarantee" an "edge").
> Suppose the win chance of any trade is 50%
In very rough and simplistic terms, assume you were trading with ("memory-less") stops with 50/50 chances and no trading fees. If you keep your trades relatively small to the available capital, you would be fluctuating around a PNL = 0 with positive and negative periods (which, in some cases, may even be longer than your lifetime, clearly.)
If you add the trading fees, you add a long term negative drift.
Now assume somehow you could "get back" a fraction of the 50% losers. That would provide some positive drift.
Clearly, this is an oversimplification, as the matter here, if meant to be applied in the real world, can get so articulated that investigations must be carried necessarily through simulations, intuitive insight, and actual trading. And efficient games are necessary to take into account all the structural characteristics and the problems with "real" instruments (decay, contango, execution issues, drifts working against you, etc.)
> Do you have a math formula for that?
Following the idea sketched, I believe it is possible to prove a "
theorem of strategic dominance", under specific assumptions. However, I preferred to leave the matter at an intuitive (and somehow more powerful) level, and if there are researchers interested, they can certainly propose some actual "incarnations" of the above (which could be based on all sort of formalizations: probabilistic models, fuzzy, chaotic, etc.).
Note that the theorem could not say that you are going to be "profitable", it would "merely" say, that for any strategy S, which does not use the
past trading information (eg., "stop-and-forget" orders), you can build a new strategy S*, which improves it (dominance) by efficiently
using that information.
For the moment, I am more interested in the actual $$$ creation process. I think I can leave the task to develop theoretical "proofs" to other academics.
I prefer to work out a "practical demonstration", with real money and real world difficulties, which can be hardly captured by abstract theoretical models, (often containing a lot of unrealistic assumptions). Math is just a more precise language for ideas: here we are just discussing the ideas.