Bingo! Somebody gets it. I've tried repeatedly to direct the OP to the "Bad Kelly" thread which explains all of this but apparently he simply refuses to go there. You can lead a horse to water etcetera. One last word: just because a formula has been copied and pasted to a lot of books and websites, that doesn't automatically make it correct. Only actually being correct makes it correct.
Exactly. In trading, the true value of p is basically unknowable. It's not like tossing dice. All you can do is make an educated guess at p, knowing that at some point, that guess is going to be wildly wrong and could bite your account in the ass. Other risk management techniques, like a fixed percent of assets (1% for example) are probably just as appropriate.
Of course if a trader figures out how to calculate the Kelly fraction independent of p, that will alleviate this concern. Certainly solving the Kelly equation head-on, however odious that may seem, doesn't involve any side calculations of p or other summary statistics. And the Kelly estimation which I now refer to as the gummy fraction (k1) doesn't require p. There are other ways of estimating the Kelly fraction (k) that don't require p. But they do require thinking outside the box. k1 = sum[ Ri ]_i=1toN / sum[ (Ri)^2 ]_i=1toN
Ri is the return (%/100) of the i'th trade. For example, if the 37th trade concludes in a loss that is 52% of the 37th trade size, then R37 = -0.52
So for instance, say the 37th trade had an initial risk of £1000, but the actual loss of £520, would that mean R37 = -0.52?
The problem is that you do not know any of the variables in that equation for any of your trades or strategies.