For traders, there is no exact Kelly formula. For traders, there is a Kelly equation to be solved. The most well-known Kelly "formula" for traders is a grotesque overestimation of the true Kelly solution. It is this account-busting overestimation that is responsible for Kelly's negative reputation among traders. The true Kelly fraction doesn't destroy trading accounts. Ideally, short of continually resolving the Kelly equation with each newly completed trade, you want an adaptive Kelly approximation that consistently falls between 90% and 100% of the true Kelly fraction. Good luck.
Trading probabilities aren't the same as that used in the Kelly criteria. It postulates a known fixed-odds game (e.g. blackjack or similar) whereas trading odds are unknown and are variable. Monte Carlo analysis, along with conservative odds estimates, and maximum drawdown tolerance, are a better way for traders to decide position size. If you do wish to use the Kelly rule, bear in mind that it optimises long-run profit. This can be long-run as in 1000 runs after your first bet - by that time any real-world bettor would have quit. 1/2 Kelly is generally considered the better real world amount to wager. For traders, the way to use Kelly (IF you have a system which has roughly fixed odds) is to set your maximum drawdown as your hyopthetical net worth for the Kelly calculation, and then bet half what the kelly recommendation is. E.g. if you have 1 million and don't want to lose more than 20%, you work out the Kelly bet size for the trade setup, using a 200k notional account, then halve the answer.
if you trade it, you're guaranteed to blow up. the theory sort of obscures the common sense of it (as applied to trading) but it's a fun intellectual exercise during slow markets.
Wrong. Wrong. I've already addressed both these subjects. If you're too lazy to do a search to find the truth, that's your choice but this disinformation you're spreading is uncalled for.
Because error in estimating the trade odds is potentially gigantic, if you try to aim for 90-100% of the true Kelly fraction, then you will often be taking excessive risk, potentially by quite a large margin. Secondly, the limitation on career success is almost always excessive drawdown, rather than good but not great profitability. In the worst case, sizing a robust method based on drawdown avoidance will lead to 2 or 3 good years that could have been great years - in which case you can simply increase your size once the consistency and tiny drawdowns become obvious. The reverse outcome, oversizing a robust method by overestimating the trade odds, can and does lead to career death. So, it is a completely skewed situation - the rational response is therefore to focus on eliminating large drawdowns, not on maximising profits. I have never heard of any trader who failed because they were too consistent at grinding out solid returns with minimal risk. I heard of many who failed because they had a big drawdown. Ergo, Kelly is inferior and a simple estimate of drawdown risk based on conservative trade %-loss-rate estimates is all you need to know how much to risk. For example, if your maximum drawdown tolerance is 20%, then risking no more than 4% on 70% win rate trades, no more than 2% on 50% win rate trades, and no more than 1% on 30% win rate trades, will make it unlikely to hit your drawdown limit. It's that simple and spending hours reading up on the Kelly formula won't alter that reality.
Some good comments from Cutten, thank you. The attached research paper describes using a fraction of Kelly to produce a 'never look back trading goal' to reach a point where your chances of giving everything back to the market is very small. It is one of the better papers I have seen on the subject. However, using historical data to determine risk is not a low risk approach as your historical data probably does not include 'black swan' size adverse moves. (see Taleb's Black Swan for a full description.) I think you can combine a Kelly Fractional approach as long as size does not exceed a 'max loss limit' based on non-historical data (as Cutten suggests). Good trading,
I don't know what you mean by "trade odds" but fortunately I don't need them. My Kelly fractions are based entirely on trade returns, which are calculated with complete accuracy. This is obvious from the Kelly equation which I have repeatedly referenced in this thread and elsewhere.
For most traders the key to position sizing is not how to optimize but how to comfortize. Figure out where you are comfortable on the capital base you have at any given time even if that means you are leaving some money on the table. You are a better trader when you can afford to take losses at the appropriate moment and not let it bum you out; and when you can let the right trades run and not be greedy to take even a penny off the table begore its time. These trade management decisions are very difficult and making them even more difficult by being even slightly outside your comfort zone is really stupid. The key is to find trades that fit for your plan and manage accordingly not to optimize size. PS ... if you are an accomplished, profitable trader who is scaling up from really solid money to big and then hopefully huge money ignore what I have said. That applies to very few traders and I am not trying to advise them -- they do not need it!