Viewing Trades in Terms of Martingale Strategies and the Gambler's Fallacy

[RichardCox 10]

There are trading tutorials that approach the topic the same way a gambler would approach a casino, using the argument that it is impossible to know what what is going to come next in forex markets, so attempting to forecast future prices is no different than guessing the outcome of a coin toss. While it is true that short-term price fluctuations in the forex markets can be difficult to forecast, statements like these should be viewed with some skepticism, as looking to solve these uncertainties with a gambling approach can, in many cases, turn a bad strategy into a terrible one.

 

The reason for this is that this logic assumes that the outcome of each change in prices for a given time period (ie. 15 minutes, 30 minutes, 1 hour) has no relationship to the outcome of the previous period. That is to say, if you are looking at 4 hourly bars and one of them (let's say the second bar) has a bullish outcome, this result will have no influence on whether or not the other bars in the sequence finish in the same way. But this would change completely if the opposite assumption is true, that there is memory in trading activity and that the outcome of one price bar will influence those around it.

 

If this latter assertion is accurate, it suggests that price activity can be tamed and that mathematical tools can be applied to reduce losses and maximize gains. So, let's take a look at some potential strategies as a way of assessing their validity.

 

The Martingale Strategy

 

Developed in France in the 1700s, the martingale strategy was based on the prevailing math and science ideas of the time. The strategy calls for larger betting sizes each time a losing bet is seen. If you enter into a bullish trade for your first price bar, you would double your trading size and bet on the same direction in bar 2. If this trade is also unsuccessful, the trade size would be increased to 4 times the initial size, and the next bullish trade for bar 3 would be initiated. This process continues until either a winning trade is placed or until the trader goes bankrupt.

 

The logic of this method is simple to understand. Any initial losses can be erased (and eventually improved on) once a winning trade is seen. In this case, the trader is operating under the assumption that each trade has some influence on the next, and that a losing streak can only continue for so long. But if trading results are independent, it would not be uncommon to see a long string of up or down periods, which makes long losing streaks very possible.

 

The Anti-Martingale Strategy

 

In the anti-martingale trading strategy, the opposite actions are taken but a similar outcome is reached. This is because each outcome is independent of the others and an infinite losing streak would be impossible. In this case, the trader will double only on winning trades, so if a successful trade is followed by a losing trade, the same trading size would be taken during the next opportunity. This would continue until a winning trade is seen, and this is when the trading size would double.

 

Of course, the problem with this strategy is that there is no reason to double the trading size the following price bar in not influenced by the previous bar.

The Gambler's Fallacy

 

The Gambler’s Fallacy suggests that a rare series of events (such as a long streak of “heads” coin tosses) will lead to a regression to the mean later. So, a martingale strategy would rely on an increased probability of a win after a long streak of losing trades, as this would constitute a reversion to the mean. But the fact remains, the coin toss probabilities will be 50/50 on each occasion with an infinite number of coin flips. Limiting the number of events, however, will also reduce the odds of a successful trade each time an unsuccessful trade is seen.

 

It should remember that the reverse is also incorrect. So, suggesting that random events (such as coin tosses) that occur in succession will influence the next event in order to conform to the event series as a whole is an equally incorrect assertion. So, the Gambler's Fallacy can be valid only in cases where events are random (based on z-scores), and where there is no causal relationship between each event in the series.