Quote from Ghost of Cutten:
I think this is demonstrably false. It would imply that two traders with $1 million each and identical risk preferences and methods should place radically different size bets on the same trade, just because one of them had a good run recently and the other had a bad run. But this is nonsense - if you have a 3:1 payoff with a 40% win rate, then two traders with identical capital and identical risk preference must bet identical amounts. To claim otherwise is to say that some other input matters over trade expectation, trader risk preference, and trader capital. The only situation I could accept that claim is if the guy on a losing streak is making poor decisions because of this (in which case they would not be in identical situations).
Betting based on past profit is mental accounting i.e. irrational deviation from sound bet-sizing. The only situation I can see it is justified is if you have investors who also use mental accounting e.g. they will not mind if you go from up 100% on December 1st to up 80% on December 31st, but will crucify you if you go from flat on Jan 1st next year, to down 10% on Jan 31st that next year. Identical loss but irrational people (which is most investors) will have different reactions based on coincidental and meaningless calendar/date issues.
It's not false or irrational at all. On the contrary, it is the only rational and sound way to operate in the real world, for reasons that diverge from the hypothetical / theoretical world.
The first mistake is in comparing two identical traders, which creates issues for deeper reasons, though you hint at why this is problematic yourself.
With the two trader comparison one can still understand the idea, though, from a risk awareness standpoint. It's not about mental accounting, it is about exploiting conviction-based opportunity while remaining deeply cognizant of tail risk.
If one is considering a big-bet trade, then by definition conviction levels are high. (If conviction levels were not high, there would be no consideration - and if one's methodology did not allow for position sizing based on conviction, the question would be moot in the first place.)
Within this framework, the central challenge for the discretionary trader is exploiting conviction-based opportunity as fully as possible, while simultaneously reducing mortality risk as much as possible.
Thus high conviction levels must be coupled with a profit cushion in order to safely bet larger.
Think of it like this: If one has a 55% win rate on average, then the outcome of any given trade (win or lose) can be seen as the flip of a slightly biased coin. Call it 55% heads (win), 45% tails (lose) over a long series of trades.
Given the above, there will come periods (weeks, months, quarters etc) when you have an ugly streak of tails. Simply through the vagaries of probability, you will occasionally have a streak of X tails running against you, or an overall outlier period in which the mix of tails (losses) to heads (wins) is exceptionally high.
Because this negative outlier potential exists - it is wildness embedded in your results curve - you must be cognizant of mortality risk and excessive drawdown risk in a way that pure theory might not directly address. This means paying attention to your equity curve.
To wit, a trader with a cushion of profit in his account has "earned the right to swing" at a conviction based trade because his mortality risk has been reduced. If, for whatever reason, his swing is a miss leading to a long string of misses - and such could merely be a negative outlier within normal distributions - then his profit levels will asymptote above zero, and he will be back to trading small well before any great damage has been done.
If, however, a trader swings large at a conviction-based trade too close to the zero line, or, worse yet, below it, then
his mortality risk becomes elevated through the possibility that an outlier losing streak kicks in at the wrong time, thus eating through his capital. (Note that psychology issues contributing to poor trading could be a factor here, but they do not necessarily have to be - you simply must guard against mortality risk at all times, whether your psychology is good or not.)
When a Roman General won a battle and was enjoying the equivalent of a ticker tape parade, a servant would whisper "memento mori" in his ear - remember you are mortal - as a means of keeping him humble.
In similar fashion, one can take conviction-based trades in bigger size with an accumulated cushion of profit because the profit cushion itself reduces mortality risk. It lets you pull in the reins / hit the brakes without permanent damage to your risk capital if an outlier negative streak kicks in when you did not expect it.
Trading big without a cushion is like operating a shipping business without cargo insurance and without profits in the firm's bank account to pay for unexpected losses. Without that cushion, one has greater exposure to Fortuna's mood swings, and greater risk of a bad luck streak dealing a crippling or killing blow.
So in a sense you are looking at the question backwards in assuming big convictions always warrant big bets. Hypothetically it would always make sense for high conviction situations to be bet large
if there was no risk of tapping out... but given the real world, cognizance of mortality risk, not to mention potential threats to mental capital, require that in less cushioned situations the same opportunities are bet smaller, perhaps much smaller.
Then, too, there are
positive outlier considerations - especially given that winning and losing streaks for a trading methodology are typically not entirely random, and may not actually be random at all. If you are on an exceptional hot streak in markets lately, it may be that conditions are aiding your methodology and that those conditions will persist. If you are on a rough losing streak in markets lately, it may be that conditions are creating headwinds and those headwinds will persist. This is even more reason to be pro-cyclical in one's sizing efforts. By reducing risk when your cushion of profits is not there, you reduce the odds of being taken out and reduce your total market exposure in general terms in periods when results are poor. On the flip side, intelligently increasing risk while all is going well increases the odds of potentially exploiting what poker players refer to as a "heater" or a "sick run," while generally maximizing exposure when conditions are favorable.
In sum, because of mortality risk and pro-cyclical factors relating to market conditions, a smart discretionary trader will size positions differently well above the zero line than he will at the ZRL or below it, and it is absolutely rational and logical to do so.
