How many positions is too much?

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Suppose I have a portfolio consisting of N amount of positions each with R% risk and risk/reward=k. Suppose that positions are independent from each other cov (pos1, pos2)=0. Find relationship between amount of positions N to profit, and overall risk to portfolio.

Motivation behind the question:
I could open 10 positions (different instruments) with 2% risk of each, so that in the worst case scenario it yields -20% to my account. I feel that those positions are loosely correlated* and thus it is very unlikely to being stopped out on all positions. Such practice increased my overall profit, however I do not quite understand “the math” behind it and the risk I take.

* also a new important question arises: on which time frames positions or under what circumstances positions will not be correlated. I feel that the shorter the timeframe the less correlation.

I think this question requires more precise formulation, please share your thoughts below. Your answers would be highly appreciated.
In crisis, all markets correlate. There are no absolutes, only you have to navigate without getting caught in a crisis. 6-sigma events happen from time to time, and far more often than equations would suggest. I'd suggest not worrying about the "math" when you have to pay attention to your P&L daily and watch the markets and "see" when your systems and methods are all acting the same. I think you can see that Van Tharp has been recommended. Since I learned from Tharp in person, I can recommend his work.
+1 Balas
It is a complex question. I'd rather not risk 2% per trade to begin with, unless I only take one trade at a time. That's a lot of risk.
xiiimik IvanLabrie
Could you recommend any book on this topic?
xiiimik IvanLabrie
If you know any good books, you can recommend "math intense" books.
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