There's still the risk of going broke, because the $$$ value you can trade cannot get infinitely small. If you could buy a billionth of a share Kelly would work perfectly.
I certainly agree with your advancing what is mathematically correct rather than what is comfortable. If the goal is to maximise profit, it is important to find the optimum rather than vague subjective comfort levels. The goal of others may not be to maximise profit, or they may be effectively guessing with discipline which is not the same as understanding the probabilities of a trade. I am going to spend some time this week trying to get to grips with the mathematics involved - I have no formal background in this area. From reading your other threads it appears that you can calculate the Kelly fraction simply from historical profit and loss data rather than guessing at expected probability on the next trade. After re-reading your threads, the linked paper, and giving myself a more thorough primer on the mathematics I would welcome the opportunity to discuss this further. GoC, regarding your points: #2...for independent traders who lack imposed risk profile and the handcuffs of OPM, the uncle point is in your head. If you are position sizing smaller than what would provide you optimum growth, because of a psychological block, I would suggest that working on your psychology will pay better dividends than focusing on your trading knowledge/strategy. In fact, if we analyse what you say about the drawbacks of exceeding the comfort level, we can deduce that it is the existence of the comfort level which is a mistake. #3...do we really need to know this number to calculate Kelly, or can our realised historical profit and loss give us return, standard deviation etc, to come up with sensible position sizing? #4....why are we concerned with this "draw down". What about for successful short term trading strategies which have no negative days or day over day drawdown? #5....circular argument - you've introduced the psychological artefact from #2 as a justification for sizing less than Kelly. #6....I've never seen this in liquid futures markets. I'm talking about day trading and being out by the close, not carrying through FOMC or NFP. Win rate alone tells you very little. What about slippage, costs, ratio of average profit to average loss....and it doesn't make sense for you to consider such things as bet more for 5:1 payoff ratio when you say in other places that its non trivial to work out the true odds or expectation of a trade. I don't think the solutions to any problems in trading / finance could be described as "trivially easy" - and judging from the quality of your other contributions I'd have expected better from you. Assuming the goal is to maximise the returns possible from a given strategy, the relevant inputs into position sizing are total risk capital and market liquidity.
well, I'll do my dead level best to be a gentleman in response to your miserable, anal, arrogant and insulting diatribe. To that end, I think subsequent posts disprove your adjudication. You surely have done your homework, so I won't point out where. The rest I edited.
Thanks, Blotto, for your thoughtful post. You've done a better job than I did of stating the case for Kelly.
Kelly is useful in telling you when you are not betting enough and need to expand your comfort zone a bit. If you get 1% when Kelly says 12%, clearly you are being a bitch and need to expand your comfort zone. Its useful for people who tend to be too conservative sometimes (as least the ones who can improve themselves and don't get stuck being the same way for 50 years straight)
Based on what I've been able to get from the net about blackjack players playing multiple hands at the same time, you can use the following formula. If S represents the number of simultaneous trades, then multiply each full Kelly fraction by (1+S)/(2*S). This works so long as the sum of all the modified Kelly fractions does not exceed 100%.
I think that the Kelly formula uses your average win/loss and win rate, no? It should keep up with changes in those numbers, albeit in a lagging fashion.
The Bad Kelly formula requires the winrate and the win/loss ratio. The LessBad Kelly formula requires the winrate, the average win return and the average loss return. The best Kelly formula (undisclosed) requires none of those, just the trade returns. Ergo it is adaptive aka instantly upgradable. No lag.
That assumes the positions are not correlated. In the real market, there is a lot more correlation between positions. Moreover, you never get to know you will be in S positions at the outset. You take each trade as it comes to you, so you may not know what the maximum number of concurrent positions will be at any time. If you set size based on a pre-determined maximum number, again what should that number be? If too large, means each position size will be too small (and you may waste capital on days you find only 1 trade!).