The most common risk fallacy

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There is a very common mistake that people and traders make when they are considering the likelihood of something happening: they think risk carries over each time they take a risk.

Let’s use coins as an example, but you’ll see how this applies to markets too: a coin has a 50:50 chance of landing on heads. Let’s say we flip the coin and it lands on tails. What are the chances that it will land on heads next time?

A lot of people will say that it’s now more likely to land on heads than it was before, because it has to maintain that 50:50 heads v tails ratio. This is akin to someone seeing the market go down and thinking, “well, the market went down, so it’s gotta start going up now.” But that’s not how it works.

risk fallacy

Each risk is independent

Each time you flip a coin, it has a 50:50 chance of landing on heads, and 50:50 chance of landing on tails. It doesn’t matter what the previous results were. Likewise, the market can go up, and then just keep going up.

If your last three trades went against you, that is no indication whatsoever that your next trade will be positive. The next trade is going to fall within the exact same risk profile as all the previous trades, so you need to keep trading with the same risk management strategy (now, if you get a string of bad trades, it might mean your strategy isn’t as good as you thought, and might need some work).

Try flipping a coin 10 times; you’ll see that it won’t always be exactly 5 heads and 5 tails. In fact, getting exactly 5 heads and 5 tails is statistically relatively unlikely. If you extend that to 100 flips, the likelihood of getting exactly 50 heads and 50 tails is quite small; you’ll probably get something like 53:47 or 48:52. However, the more often you do it, the closer it will come to 50:50.

Wait a minute, didn’t you say….

In previous articles we talked about how you shouldn’t consider just one trade, but a series of them in evaluating the risk profile and establishing your money management system. Doesn’t the fact that the risk of each trade is independent from the other trades contradict that?

Well, no; a previous risk can’t inform you about the next risk, but it doesn’t change the overall pattern.

Back to coins. A coin toss has a 50:50 chance of landing heads. If you do it twice in a row, you have a 25% chance that both will be heads, 25% both will be tails and a 50% chance there will be one heads and one tails.

So, if your strategy was to bet heads, then on one coin toss, there is a 50% risk that you will lose. On two coin tosses, there is a 25% chance you will lose twice, 25% you will win twice, and 50:50 chance you will break even – in other words, there is a 50:50 chance you will win compared to losing (just that the times it happens double).

Even though each toss doesn’t carry over the relative risk to the next, the total risk of the pattern stays the same. The same happens when you are trading, except more complicated.

Bankroll the variance

This is why people can go through periods where their strategy “isn’t working”; you can get several trades in a row that don’t work. This does not mean that your next trade is more likely to to work – conversely, it doesn’t mean your trade is less likely to work, either.

The key is trading consistency, and having enough reserve in your trading account to absorb the periods when your trades aren’t going your way. Consequently, not only is it important to know how often your strategy works v how often it doesn’t; but how long a winning or losing streak can likely be.

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