Actually that Kelly formula is correct for a two-outcome situation so, yes, you are maximizing your potential gain with a 70% bet. But, as was pointed out, the chances of you actually having and knowing with certainty that you have a 75% chance of winning with a 5:1 payout are very slim in the trading world. It's not possible to calculate trading probabilities with the same certainty that one can calculate gambling probabilities. There are no black swans in the gambling world.
Actually that Kelly formula is correct for a two-outcome situation so, yes, you are maximizing your potential gain with a 70% bet. But, as was pointed out, the chances of you actually having and knowing with certainty that you have a 75% chance of winning with a 5:1 payout are very slim in the trading world. It's not possible to calculate trading probabilities with the same certainty that one can calculate gambling probabilities. There are no black swans in the gambling world. [/QUOTE] There is also an "approximate" version of Kelly which deals with financial markets without fixed odds or payout ratios, which results not in a percentage bet-size, but in an optimal amount of leverage to apply to your portfolio. An introductory discussion of it is here: http://epchan.blogspot.com/2006/10/how-much-leverage-should-you-use.html And the Thorp paper which discusses it is here (section 7.1) http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/KellyCriterion2007.pdf Yes, this is not as definitive an answer on position-sizing as one would get in a two-outcome scenario.
Going to the maximum leverage your margining allows on your capital with your broker is the mentality of a lurking or actual loser in the great trading game. There is no 'very favourable set-up', only probability. But you can become very precise as to that probability. There are only price gyrations - and you have to read them. OK, lets assume daytrading. And lets assume a liquid, volatile market (eg CL). Lets further assume that you aim to take net gains from the sessions swings. OK, so now lets put aside signals which arise from an existing price direction. Lets look at price entry on change of direction. And lets get precise about your price entry. Your signal goes 'on' to trade. Lets assume the signal was from price intersecting the line of an on-chart indicator. Heres the crux: you can do the arithmetic of the preconditions of that signal to learn the validity of your signal. The most important number is the distance from the assumed top or bottom of your price entry. Without going into all the necessary detail, a faster lengthier distance before your indicated price entry point usually means that your signal will be false. By this elimination, you are left with your other more robust signals which you play.
I agree that pre-trade odds cannot be calculated, what further complicates the problem in trading is that the odds of winning is also dependent on stop size. This fact makes it not analogous to any card game.
1-Divide your original stake in 20 sub-portfolios. 2-Bet all-in till you win 5 in a row. 3-Re-allocate and start at 1 again. This outperforms kelly/F in reward/risk and has less psychopathical problems to stick to it. There is an optimal math calc to do this, but above approach is good enough for government work. Also if you get to really big bets, stops do not guarantee your exit at a preconceived loss.
What do you do if you lose a bet? What about drawdowns/losing streaks, how do you handle them? What if you win 4 then lose 1, repeat ad infinitum, you would end up wagering an absurdly high % of total capital eventually.
Luckily there is no need to calculate pre-trade odds, when we can simply estimate them Just use the conservative estimates, not the optimistic ones. The effect of the stop on the win % is (or should be) already incorporated into the trade expectation.