Do you seriously believe a single player at a blackjack table playing 2 or more hands has uncorrelated hands?? Uncorrelated trades would require no modification to their Kelly fractions. Moreover, if you can't figure out how many trades you have going at any one time, you have no business trying to have multiple trades.
The conventional Kelly formula advocates betting exactly the same % of capital even if you have lose 100 trades in a row. An adaptive Kelly formula that cuts % of capital risked during drawdowns is more in line with the conservative approach I'm advocating. However, using this implicitly admits that drawdown management is more important than theoretical profit-maximisation i.e. what I've been arguing all along. It thus admits that optimising theoretical long-run profit is NOT the goal. Rather, path dependence is important (1 million down to 10k then up to 1 billion is not viable for most traders), robustness is important (1 million to 10k, then your edge disappears, is not good news), not aggressively estimating your trade odds is important (Niederhoffer-style 5 good years then blowup in 5 hours). In this case, since managing the drawdown becomes critical, the payout ratio is almost irrelevant - instead of trading to maximise profits, you trade to optimise the chances of avoiding blowup (i.e. set blowup risk approximately the same chance as risk of dying, becoming a cripple, and other unhedgeable critical risks), and then let the profits take care of themselves. Of course in the real world almost everyone overbets and we hear from the lucky gamblers who didn't hit their personal grey swan, until lack of experience with risk, and general arrogance of recent success, takes them out of the game during the next 'unanticipated' market blowup. Also, if you aren't using win rates or win/loss ratios(the same thing) then you aren't using the Kelly formula - win % is one of the only two inputs into it: Kelly fraction = [(win rate * payout ratio) - (1- win rate)]/payoff ratio
More straw man nonsense - stop putting words into people's mouths. You are wrong anyway, bceause BJ pro teams generally don't multiple bet at the same table except for deceptive purposes, almost all their main wagers are big bets by a second player, so they are indeed uncorrelated. Even the correlation between 2 hands at the same table is far lower than the correlation between most trades in a portfolio - it is actually quite tricky to find 2 totally uncorrelated trades, let alone a whole portfolio of them. Uncorrelated trades of course require modification to their Kelly fractions - if you have 10 separate and uncorrelated stock trades, and the Kelly fraction is 70% for each trade, you need 1000% of capital to be able to trade them. Generally that will be above your margin limits, so you'll have to reduce the Kelly fraction. Finally, you are again talking bollocks by putting words into people's mouths - he said you can't KNOW how many trades you will have on in future. Obviously any competent trade knows how many current trades they have on - but they have no idea how many they might have on in the next week, month, year, decade etc.
The problem, as I tried to explain, is that discomfort affects the mathematics. There are both rational reasons to limit maximum drawdown (never being sure your edge will last, or that you assessed the current trade correctly; black/grey swans etc), and psychological ones (most people are incapable of remaining indifferent after losing a big chunk of their net worth, and loss aversion becomes dominant over profit-seeking - so they will exit +EV trades in order to cut open position risk down to the desired lower levels). Therefore, the +EV of an individual trade is not the only input - if it was, we could just bet full Kelly on every trade, which no career-successful trader has ever done (and survived). You can't calculate the Kelly formula without knowing the win % rate, and the payoff ratio (odds e.g. 5:1). If you can only estimate the odds, then you can only have an *estimated* Kelly fraction - your estimate could be totally wrong. But Kelly's theorem is not based on estimates, it is a mathematical proof based on known odds, such as for an unbiased coin, or unbiased roulette wheel, or perfectly shuffled unmarked blackjack shoe full of cards. Since in trading we virtually never have known odds, the Kelly formula cannot strictly be used at all for trading. It's use is only as a rule of thumb (and even then it has many limitations, that I've tried to point out). Even Blackjack pro teams do not use full Kelly, so for traders (with much less knowable odds) it would be insanity to. 2. firstly, you don't know what position size gives optimal growth, so you can't position there. You can only guess. And, since the costs of over-guessing are far worse than the costs of under-guessing, the approach that maximises the likelihood of a desirable outcome (e.g. reaching financial independence or a given level of wealth, or even just to stay in business and earn a reliable living) is to err on the side of caution. Secondly, because of the risk of your edge degrading or disappearing (or even becoming an anti-edge), or simply because of a bad run, there is always the chance that a given loss is the start of a losing streak that will run your account down to zero. The only way to avoid this is to have an uncle point at which you will cut your size significantly (or even stop trading altogether). This applies to individual trades as well - every small loser that seems to still be +EV could be the start of a next 9/11 or 1987 crash. So your choice is to risk becoming a blown up trader, or to have an uncle point based on a comfort level. Personally I view it as irrational to risk blowup to any significant degree, therefore I have an uncle point. Since my emotions are aware of the risk of blowup, they start to kick in once a market moves far enough against my position to make its probability rise above trivial levels. Any trader without similar instincts is a blowup waiting to happen. I agree that discomfort is an irrational input (but one present in most traders - until they 'cure' themselves, that is a very real constraint on their risk-taking ability) into trades with moderate losses, but discomfort for total portfolio risk and potentially large drawdowns is very rational indeed. 3. The precision of your Kelly fraction is going to be related to how accurate your estimates are, since those estimates (win rate; payout ratio/betting odds) are the only 2 inputs into the Kelly formula. Garbage in, garbage out. 4. If you never have drawdowns then just keep trading until you do, then revisit this thread. 5. The drawdown referred to here is not about psychology, it is based on the 'real money' uncle point e.g. a fund hitting the point at which investors quit in droves; or a sole trader such as yourself being unable to survive a 99% drawdown then recover to a 300% gain on original capital - at some point before losing 99% of your capital, living costs and the need to earn an income would bust you out, and also your confidence would be shot anyway, even if (unlikely, given the drawdown) your method was still long-run profitable. 6. Black/grey swans can occur intraday as well, they don't just happen overnight. ---- The win rate tells you the probability of a given % drawdown, for a given bet size. It would take account of slippage and costs. Profit/loss ratio doesn't really matter for drawdowns, because the worst drawdowns (as i explained) are usually streaks of consecutive losers, or one very big loser. Just because it is hard to accurately calculate the odds of a trade does not mean you can't find high payoff trades e.g. if you buy deep OTM puts anticipating a market crash, you are almost certain to make >5 times your money if your prognostication is correct. What is hard is to know if it will be 5 times, 10 times, 50 times etc. The sizing thing is trivially easy in relative terms, because the win rate is the main factor, and to have a reasonable idea of trade profit expectation, you must have a reasonable idea of the win rate. Put another way, attaining profitability is far harder than estimating approximate win rate. If you are good/experienced enough to attain profitability, you are good enough to estimate win rate within 3-4 wide probability bands ranging from 10% to 70%+. And if you can make that estimate, then some simple maths lets you work out the correct range of % capital to bet, for a given drawdown tolerance. I don't think the goal is ever to maximise returns from a given strategy. There is always a constraint of limiting risk as well, which IMO is a fatal weakness of the Kelly formula. The goal of almost all traders is to maximise return relative to risk. There will be some variance based on risk tolerance, one trader might tolerate a 40% drawdown where another would be horrified at a 5% drawdown. Hence why I gave a formula that allowed for different risk tolerance. But all traders who are not degenerate gamblers (inevitable blowups in the long-run) will want to maximise return relative to risk, rather than increasing risk with no net gain in returns to compensate. I agree that liquidity is a consideration, but if your profit limit is dictated by liquidity constraints, rather than risk/drawdown concerns, then Kelly is irrelevant anyway - you won't be able to get anywhere near it.
If at any point your choice was to pass on a trade, or bet more than the Kelly amount, then obviously you would pass on the trade (since betting more than Kelly is always sub-optimal for long-run profitability; plus, you don't want to risk going broke). Rather, the risk would be having to stop trading once you hit your uncle point, and having to pass on good trades that your account was too small to handle. Yeah, being undercapitalised sucks!
It is foolish to talk about maximizing returns without relating it to risk. If I just want to max I can max out every play by utilizing all my capital. Once you take risk into account then it is certainly not irrational to take comfort into account. Only in an ideal world would there be an ideal trader with so much ice in his veins that drawdowns would never effect his play. I had a dear friend who was a world class poker player -- played with Brunsun, Sailor Roberts, Chip Reese, Stu Unger, Johnny Moss etc. during the 70's. He told me that all of them could and had been put on tilt over the course of their careers. I believe an extra hour's sleep and a better diet are probably worth more over the long haul than pushing for a theoretical ideal. Real world revolves around things beyond sterile numbers. I'm not knocking the numbers -- they are essential -- but I don't worship at that altar either.
It "admits" no such thing. What it reveals is that this "bright red line" you're trying to draw between risk management and profit optimization is delusional. The two are not mutually exclusive, they are connected. You maximize profits in part by minimizing risk. It's the old common-sense trading advice of Win Big, Lose Small. Why you think these two things don't go together is a question between you and your psychotherapist. Of course in the real world almost everybody overbets because they either guessing what bet size to use or they're using the Bad Kelly formula which I've written a whole thread about. And by now you should realize that "Kelly" has evolved beyond its 1950s origins to encompass optimal position sizing in general, not just simple gambling bets with fixed odds. This is especially true for trading where there are no fixed odds.
Maxing out is not most profitable, as the Kelly formula explains - overbetting creates excessively large drawdowns which reduce your long-run profit. If you exceed the Kelly fraction then you will be making less money than someone who bets the Kelly fraction. So, if you want to maximise returns then betting the Kelly formula (assuming you know the trade odds, and have no path dependency of results) will do this. Obviously in the real world none of us know the trade odds, and we are all path dependent, so Kelly is way too big.
You just admitted that drawdown management is more important than theoretical profit-maximisation by this statement - 'You maximize profits in part by minimizing risk.' Then there is the additional factor of risk-averse utility functions - the first million is worth more than the second; going from 1 billion to 500 million is less painful than going from 1 million to zero etc. Also, I am not trying to draw any red line between risk management and profit optimisation, and I am well aware they are connected, as should be obvious from my statements about how excessive drawdowns result in things like the end of trading careers, suboptimal trading decisions, investors withdrawing funds etc. Since my whole point was based on path dependency i.e. how drawdowns can stop traders from reaching their long run profitable end state, I'm not sure why you overlooked this. People who size based on drawdown tolerance are not using guesswork or the Kelly formula, they are using Monte Carlo analysis to simulate worst-case losing streaks for any given set of trade odds. Throughout this discussion I said that trade odds cannot be known, so your repetition of this is pointless.
The kelly number is arrived at using an historical number of trades made under past conditions of liquidity, etc. As the kelly number is highly dependent on the biggest loser in the historical set, it understimates risk for unknown events that will happen in the future. For example, if you had a wonderful system with a kelly of .45 and you actually bet that amount on a long trade, or short volatility trade, just before the Fukushima reactor meltdown, you probably lost all your capital. Your "biggest loser" is always in the future not in a set of historical past trades. You can use it as a guide to rate systems, or as a part of a bounded risk options systems, to size trades. Betting full kelly is overbetting, and will lead always to ruin, unless you are smart to quit early.