The answer is "infinity" in both cases. If your loss = 0 (which is not entirely improbable in a finite number of trade sequence) you are dividing your profits by zero which produces infinity as your PF. So your Max PF = INFINITY
And the Min PF = 0 I'm not sure I understand the criteria that Jerry has used for applying to both situations, and whether it is equally applied, but I am curious as to the window of time used to make the comparison. To be fair, the entire available window of market data should be used. Second, a monte carlo sim of GBM could be run with the trading criterion defined, and divided into quantiles to get a min-max range of the possible PL scenarios. It is likely that the out-performance results from the earlier real trading data would fall into this range. I would also suspect that a very long term run of the real data, would not show much better PL than the mean of the GBM dataset.
What would be the probable Profit Factor from any strategy or method if the markets are random? What would be the Minimum Profit Factor that is needed from any strategy or method to prove that the markets are NOT random? In both case we assume a statistical representative number of observations.
There is only way by which one can prove "non-randomness" of the markets: It is by showing that the outcome of any given trade can be known ahead of time with 100% accuracy. Any other outcome will prove that the markets are random.
In theory true, but that has no practical relevance to the real world trading. Based on Quantum Theory there is the possibility of a person being able to walk through a solid wall, if you have exactly the right conditions at the quantum level. If I recall the math predicts such an occurrence every 100,000,000,000,000,000,000,000,000,000,000,000,000,000 years. I was asking a simple serious question related to real world trading. If you can't answer it just so.
I am not trying to mock you or anything. As the matter of fact I am glad that you asked the question. It shows the interest and it is good enough for me. I welcome any interest. But sometime it is difficult to seriously answer the question that has a faulty logic in it. I probably will be much more helpful if I understood what is it that you would like to know. I also could be more helpful if I understood your hypothesis. If I sounded facetious please forgive me. It wasn't intentional. So, please explain what is the meaning of your question.
Criteria: Random Number = Excel RAND() assigned to each bar and recalculated for each run Random selection for trade: Rand() > .30 AND < .3205 which gives about 200 trades, of which about 50 will have a fill based on the Stop Limit order cited in the Rules For Predictive: value of NN model predicts higher prices tomorrow, using same Stop Limit order Time Window 11,000 bars, all available data