Martingales vs Anti-Martingales

One has to learn from his/her own mistakes, but in trading, learn from others' mistakes is much cheaper! Last Friday, a fellow day-trader of mine took a big hit trading the EURUSD, more than 20% of his equity gone in a couple of hours. The post-mortem of the deal reveals at least 3 mistakes. Firstly as he was overconfident that day further to a long winning streak, his stake was the double or the triple of what the money management system he has spent years to develop indicated. Follow your system religiously! Secondly, during the action (Friday was US GDP and Jackson Hole's speech) he made a (silly) computation mistake in the last order he input, that order if correct would have resulted to a profit. While my trading is not as frantic and requires less reflexes as day trading, I always have handy a simple Excel spreadsheet with all the computations of orders, stop-losses, stake, risk... set up. The last mistake, but not the least : he went out the night before and got drunk which definitely didn't help. I know it may sound weird, but my experience shows the correlation between your trading results and your fitness and state of mind at the moment of the trade is pretty high. Maybe the old advice not to trade on Fridays is not only based on a particularly strong volatility that day of the week, but also because the day before on Thursdays, we go to the pub :)))

More seriously, we've been discussing for a while with this chap an endless debate regarding trading systems: Martingale vs Anti-martingale. If we consider the toss of a coin, Heads or Tails, the classical Martingale system consists in doubling the stake after every loss until a win finally recovers all the losses and gives a profit equals to the original stake. The anti-martingale at the opposite consists in increasing the stake after a win and decreasing it after a loss. You may have guessed, my friend's system is a Martingale (while I've to confess one of the most efficient I've seen, provided you don’t do mistakes and follow it…) while I'm a fervent defender of Anti-martingales. This said, like the gamblers in the 18th century in France, we spend our time experimenting new variants of martingales (and anti-martingales) systems. The main arguments I have against the martingale systems is you may need to put at stake a lot of money in order to earn a small amount : 2, 4, 8, 16, 32, 64, 128,... to win 1 and mostly that you bear a strong risk of ruin (or losing consequent amounts). Our intuition tends to underestimate the probability of ruin, and believe that a long streak of Heads (say 6-7) is very unlikely, but here's the magic formula (I think I found it on Wikipedia but I can't find it again there, the article may have changed) to compute the probability to have a sequence of n "Heads" during a sequence of N spins :

1-(1-p^n) x (1-q.p^n)^(N-n)

Where p is the probability to get "Heads" and q=1-p. Assuming a Head and Tails game with a 50% odd for each, the formula tells us the probability to get 6 Heads in a row during 150 spins is of more than 68% (56% for a 7-streak). Higher than what you thought, right?

Applied to the world of trading, putting more on losing deals and "averaging down" is a commonly used martingale strategy (I call it "when you're in trouble, double"), while “pyramiding” and put on winning deals is an anti-martingale. The trader using the former will have a high proportion of winning deals and makes quite often (small) profits, but the odds are that ultimately he or she will suffer a consequent loss that will wipe him or her out. The trader using the latter may see numerous and frequent small losses before a big winner will drive him/her ultimately to profits. That's where the anti-martingale meets the old good "cut your losses short and let your profits run" principle. This said, the two main enemies of a trader using an anti-martingale is on the one hand the faith he/she has in his/her own trading skills that can be strongly stress tested by frequent losses and on the other hand the "breakeven effect" as after a long losing streak, it's very tempting to take the profits at breakeven closing precisely the deal that's supposed to lead to consequent profits... Sometimes, we tend to forget that the goal of trading is to make money and not to recover from the previous losses...

I’ve to let you here, Fellow Trader, the US August ISM Manufacturing just surprisingly rose from 55.5 to 56.3 (vs an expected decrease to 55.3). That could trigger some action in the markets and I’ve to recover from some of my previous losses…

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FYI As this post is published: SPX 1077 // SX5E 2701 // NKY 8927 // DAX : 6066 // EURUSD 1.2826 // USDJPY 84.50 // XAUUSD : 1245