Misunderstanding probability can seriously affect your trading capital

One of the main things I look for when entering trades is to have a high probability of having a profitable trade. In other words, because all of my conditions have been met, I enter the trade with confidence knowing there is a fair chance of the trade resulting in a profit. As we know, there are never any certainties.

Probability has its place in money management too, specifically position sizing.

Let’s set the scene. Perhaps we have a trading method that results in half of our trades being profits and the other half being losses or close to breakeven. We start with $10000 and after a few losses, our trading capital has lessened to $9400. (3 x $200 losses in successive trades).

Now, we begin to think that we are behind and need to make up the deficit so we can move forward and begin to make money. As each losing trade passes however, the money we need to make to get back to breakeven (back to the initial $10000) increases and we have less and less capital to do it with, which places pressure on us to perform.

The trap we can fall into is to increase our trade size on the back of successive losses. In the back of our mind are desperation, and the thought that we need to have a massive winner trade soon to get back on track.

Here is where probability enters the scene. As each losing trade passes, we can easily think that the chance of the next trade being a profit increases significantly. It is too easy to think this and with this in the back of our mind, we can be tempted to increase our trade size to get back to break even quickly because the chance of the next trade being another loss is not great.

Let’s explain this scenario with some numbers. The probability of an event is generally represented as a real number between 0 and 1, inclusive. An impossible event has a probability of exactly 0, and a certain event has a probability of 1.

As we have a proven method that is profitable in half of the trades, the probability of having a profitable trade is 0.5. The most common analogy used with a probability of 0.5 is that of tossing a coin. When we toss a coin, the probability that it will land heads up on any given coin toss is 0.5 or 50%, and the same of landing tails. So if we toss the coin 10 times, we would expect that the result will be 5 heads and 5 tails. There is however, no guarantee that this will occur. It is possible for example, to result in 10 heads in a row. The key here however, is that each coin toss is independent. In other words, the outcome of the next toss is unaffected by previous coin tosses, as the coin has no memory retention.

Let's assume I am now tossing a coin. We toss the coin once and it result in heads. For the second coin toss, the probability that heads will come up again remains at 0.5. The second toss now results in another head – that’s two heads in a row. For the third toss, the probability that heads will come up again still remains at 0.5. Guess what? The third toss was also a head – that’s three in a row. Do you know what the probability of the fourth coin toss being a head is? It remains the same probability as a tail coming up.

This scenario is applicable in trading.

If you have had 3 losses in a row, the probability that you are going to have a profitable trade doesn’t automatically shift in your favour. Nor does it continue to shift as each losing trade passes. We like to think it does, but it doesn’t. Perhaps we think, “The next trade HAS to be a winner!” Like the coin, the market has no memory retention and doesn’t keep track of your previous trades, in order to influence the outcome of future trades.

The key message here is that don’t increase your trade size according to these unfounded thoughts. This is a sure recipe for disaster. After a few losses, your trade size should be decreased slightly to reflect your diminished trading capital, even though you don't want to.

Article by Stuart McPhee