Hi Moh
Thank you for this excellent thread.
I definitely agree with you that a positive expectancy method (i.e. involving entries and exits) is a prerequisite for profitable trading; whereas many seem to believe that all that’s needed is MM + psychology. Position sizing will magnify wins and losses, but MM in itself can not turn a negative expectancy method into a winning one. As you point out, with games like Roulette, it does not matter what betting system is used, the odds are always 5.26% in favor of the house. I believe that the same logic applies with trading.
This of course assumes that events are independent, where each past event has no influence on a future one. i.e. a coin toss (binomial distribution), as opposed to the non-replacement of cards from a deck (hypergeometric distribution). Where there is no serial correlation, optimal bet size should be in some way proportional to the probability associated with the next event. For example, if one is playing Blackjack, one should increase bet size when the number of high count cards remaining in the deck exceeds the number of low count cards, since this shifts the balance of probability in favor of the player.
With regard to trading, I have overlooked the possibility of dependency and serial correlation. In the absence of of strong evidence that wins and losses cluster in a statistically significant way, I have assumed - rightly or wrongly - that each trade is an independent event.
I like the fixed fractional sizing method, in that bet size decreases (in absolute dollar terms) as account balance diminishes, prolonging survival, while conversely, allowing gains to be compounded exponentially. I realize that it creates asymmetric leverage, i.e. that following an X% drawdown it requires a 10,000/(100–X)–100 % increase, on the diminished remaining balance, to recover to breakeven.
I don’t understand the complex math behind the Kelly formula, but have always reasoned that it ‘oversized’ positions (in terms of what is workable in a trading context), because its aim is to maximize profit with respect to loss, while not giving special attention to the possibility of total ruin (account wipeout). Because I’m not very well versed in statistics, I’ve calculated optimal position sizes by plugging win rates and sizes into a Monte Carlo type analysis, and then allowed a ‘good’ margin for error. In terms of what amounts to ‘irretrievable’ drawdown, we need to think in both statistical and psychological terms, as one individual’s appetite for risk might not be the same as another’s.
Gmak’s post (#63 in this thread) makes the point that pips don’t necessarily equate to profit, and I totally agree. This also applies when people (salespeople, mainly) count the same pips multiple times because they are scaling in/out of the same pair using simultaneous positions. IMHO profit factor:
(# wins / #losses) x (avg net win size / avg net loss size)
gives something closer to a true measure of system performance.
In other words, average number of dollars won, for each dollar placed at risk, across a given time period.
I believe that the single most important function of MM is to preserve capital; we can only keep playing the game while we have a bankroll to play with.
Many thanks, and I look forward to reading more of your ideas, especially other MM systems, and diversification. I assume that you’ve read Ryan Jones’ book The Trading Game: Playing the Numbers to Make Millions (Wiley & Sons, 1999). I found it a very worthwhile and interesting read.
Best wishes
David
Thank you for this excellent thread.
I definitely agree with you that a positive expectancy method (i.e. involving entries and exits) is a prerequisite for profitable trading; whereas many seem to believe that all that’s needed is MM + psychology. Position sizing will magnify wins and losses, but MM in itself can not turn a negative expectancy method into a winning one. As you point out, with games like Roulette, it does not matter what betting system is used, the odds are always 5.26% in favor of the house. I believe that the same logic applies with trading.
This of course assumes that events are independent, where each past event has no influence on a future one. i.e. a coin toss (binomial distribution), as opposed to the non-replacement of cards from a deck (hypergeometric distribution). Where there is no serial correlation, optimal bet size should be in some way proportional to the probability associated with the next event. For example, if one is playing Blackjack, one should increase bet size when the number of high count cards remaining in the deck exceeds the number of low count cards, since this shifts the balance of probability in favor of the player.
With regard to trading, I have overlooked the possibility of dependency and serial correlation. In the absence of of strong evidence that wins and losses cluster in a statistically significant way, I have assumed - rightly or wrongly - that each trade is an independent event.
I like the fixed fractional sizing method, in that bet size decreases (in absolute dollar terms) as account balance diminishes, prolonging survival, while conversely, allowing gains to be compounded exponentially. I realize that it creates asymmetric leverage, i.e. that following an X% drawdown it requires a 10,000/(100–X)–100 % increase, on the diminished remaining balance, to recover to breakeven.
I don’t understand the complex math behind the Kelly formula, but have always reasoned that it ‘oversized’ positions (in terms of what is workable in a trading context), because its aim is to maximize profit with respect to loss, while not giving special attention to the possibility of total ruin (account wipeout). Because I’m not very well versed in statistics, I’ve calculated optimal position sizes by plugging win rates and sizes into a Monte Carlo type analysis, and then allowed a ‘good’ margin for error. In terms of what amounts to ‘irretrievable’ drawdown, we need to think in both statistical and psychological terms, as one individual’s appetite for risk might not be the same as another’s.
Gmak’s post (#63 in this thread) makes the point that pips don’t necessarily equate to profit, and I totally agree. This also applies when people (salespeople, mainly) count the same pips multiple times because they are scaling in/out of the same pair using simultaneous positions. IMHO profit factor:
(# wins / #losses) x (avg net win size / avg net loss size)
gives something closer to a true measure of system performance.
In other words, average number of dollars won, for each dollar placed at risk, across a given time period.
I believe that the single most important function of MM is to preserve capital; we can only keep playing the game while we have a bankroll to play with.
Many thanks, and I look forward to reading more of your ideas, especially other MM systems, and diversification. I assume that you’ve read Ryan Jones’ book The Trading Game: Playing the Numbers to Make Millions (Wiley & Sons, 1999). I found it a very worthwhile and interesting read.
Best wishes
David
1
. I use 0.5-1% risk for each and every trade. Return is more then enough if you know how to trade.