I keep a set of statistics on my trades, including the "hypothetical" results of the trades using different position-sizing techniques. By far, the best profit factor comes when using full Kelly position-sizing, about 15% higher than the profit factor using a fixed fraction. So my question is whether or not those traders who are trying to maximize profit factor (which is definitely a good thing) are also betting close to full Kelly position sizes and, if not, why? Is it simply the fact of the larger draw-down?
But that's exactly the point. Is the "apple" (fixed fraction) a better position-sizing algorithm than the "orange" (Kelly sizing) for objectively maximizing "eating satisfaction" (profit factor)? I don't know the details of other traders' statistics and perhaps there are strategies where increasing bet size decreases profit factor. My question was more if there is a generalizable linear relationship between bet size (up to a certain point, i.e. Kelly, because clearly if you were to increase bet size to 100% all it would take would be one loss for your profit factor to go to zero, so you'd need to keep your size below the threshold which would incur "ruin") and profit factor. Maybe there isn't, but if there is, I would find that interesting and would be curious to know why traders who want to maximize profit factor would not be Kelly bettors.
The increase comes from the higher compounding effect of the larger profits, assuming the system is profitable. The reasons to avoid Kelly are simple - firstly, a drawdown is not necessarily just a bad run in a winning system, it also has a non-negligible chance of signalling the system no longer works. If you know your system works (e.g. A casino using a roulette wheel) then you just keep using it and will recoup your losses. If there is a chance of system degradation, then by using Kelly you have the risk of betting way too large during a drawdown. This is why trader lore recommends reducing position size during losing streaks beyond a certain amount. The second reason is related, it's that your uncle point (or that of your investors) is likely to be a lower drawdown than the maximum that Kelly sizing will inevitably produce. For example if you would lose confidence and stop trading your system properly after a 50% drawdown, then your results will degrade below that amount. If your investors will flee after a 25% drawdown, then that is your effective total loss point. Also, many traders simply don't want the stress of large drawdowns - due to the diminishing marginal utility of money, profit maximising becomes irrational and takes a back seat to some degree of capital preservation. Fixed fraction only makes sense if your trades don't identifiably have different trade expectation. So, even if you have Spock-like emotional control, there are sound reasons for betting a lot less than Kelly size. My approach is to work out th Kelly size, then multiply it by my maximum preferred drawdown. So if I don't want more than a 20% drawdown, I'll bet 1/5 of Kelly size. In the real world, maintaining robustness and long-run survival is far more important than maximising profitability, let alone maximising profit factor. Being reasonably profitable is a 'problem' that can easily be solved - recovering from a massive drawdown is rather less tractable.
I think the author of this paper provides a reasonable answer to your question: "...Optimal position sizing based on the Kelly formula cannot be applied to newly developed trading systems because the actual values for the two parameters that are used by the formula are not available in advance. But even in the case of systems used in actual trading for an extended period of time, there is no guarantee that these parameters will remain constant or even within a certain range." http://www.priceactionlab.com/Literature/Kelly.pdf
Interestingly, I've seen this strategy recover from 90% drawdowns to go on to new highs, at least on paper. I wonder if that in and of itself is significant, as I would imagine that the vast majority of strategies which experience 90% drawdowns never recover to new highs, regardless of their position-sizing algorithm. At the very least, I doubt it's a 50-50 proposition of that occurring.
While over time the Kelly risk-percentage has declined (I recalculate it after every trade), it's not doing so at a very fast rate of decay and even at the rate it is declining, the strategy seems to have the potential for hundreds more trades before the optimal bet size is 0. Could it degrade at a faster rate unexpectedly? Sure. But given that there have been times when the Kelly percentage has risen or stayed flat for a couple hundred trades, the market could also enter a period in which the strategy is ideally-suited for price behavior and extend its life beyond my current estimate. Seems that the fluctuations in the parameters can run both ways. Also, it might happen that the strategy hits a bottom in terms of Kelly and never goes much below it, which I would expect if the strategy really does rely on some nearly permanent market feature. The future is, of course, uncertain and there are no advance guarantees.
It is possible to have high profits with big lots. As much we take risk there will be a chance of high return . We need to see both sides of picture. It may be a great loss or profit when we trade in forex. So remember your risk management plan while deciding about betting high.
============================ Good profit points; even though plenty of MS casinos got flooded stormed /shut out, so even when one region/one casino is in the ''know'' dosent mean its so. Plenty of money has been made with 30% drawdown; but it takes about 60% +/ to get to zero % gain from there.50% dd takes about 100% gain to get to zero % gain . And while plenty of money has been made with a low % hit rate; a HI 80% hit rate could be wrong easily 20 months in a row-not a prediction. Wisdom is profitable to direct
Since Kelly sizing was specifically designed to maximize profits, it makes sense that Kelly sizing would correspond to the highest profit factor. The main problem for most traders is that the publicly available Kelly formulas are all approximations once you're dealing with any betting or trading scenario more complicated than the coinflip varieties. Even as few as three different outcomes can yield some shockingly poor results from the public-domain Kelly formulas. And most traders lack the mathematical skills to get around this obstacle.