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How Well Do Forex Traders Understand Probabilities?

Are you a probability literate person? As a Forex trader, you should be. Understanding the probabilities is one of the most important conditions for success in Forex market and in any other financial trading field. Almost all the FX books we have available on our website mention mass misconceptions that roam the minds of beginning and even professional traders. Fooled by Randomness is a good example of a book that is dedicated entirely to the problem of "probability blindness".

The most interesting thing about probability literacy is that you do not have to be a math guru to judge probabilities correctly. Even some professors and Ph.D.'s may misinterpret random numbers. One just has to understand how probabilities work — what they are and what they are not. It is also important to understand how they relate to the real-world processes and events they describe.

Quite some time ago, we decided to measure the probability literacy among the visitors of this website, who, presumably, are Forex traders or at least are trying to become them. To that end we launched a survey consisting of three questions with two options for an answer each. Later, when we gathered enough responses, we conducted some analysis of the obtained answers to publish the study you can find below.

The results of the suggested polls are quite curious, in our opinion. But first, let us list those questions and the possible answers below.

1. What would you choose?

a. 99.9% chance to win \$1,000 (one thousand).

b. 5% chance to win \$1,000,000 (one million).

2. What would you choose?

a. 10% chance to lose \$3,000.

b. 99.9% chance to lose \$200.

What trading strategy would you choose?

a. A strategy that is right 30% of time and is yielding \$50 on winning trades and -\$10 on losing trades.

b. A strategy that is right 90% of time and is yielding \$10 on winning trades and -\$40 on losing trades.

Probability questions explained

The first question was "What would you choose?" And the possible answers were: either a 99.9% chance to win \$1,000 (one thousand) or a 5% chance to win \$1,000,000 (one million). In currency trading, as well as in any other risk-taking activity, a trader has to consider the probability of an outcome and the value of that outcome. Together they form an expected value — a very important yet rather simple to understand term from the probability theory and statistics. The expected value can be calculated as `P × V`, where P is the probability of the outcome and V is the value of the outcome. So, the expected value of the first answer is `0.999 × \$1,000 = \$999`. This value means that if you take this choice a huge lot of times, the average gain per outcome will be \$999. Not bad, at least you are not losing anything here. The expected value for the second answer is calculated as follows: `0.05 × \$1,000,000 = \$50,000`.

Obviously, the second answer is more favorable than the first one as it yields more than 50 times higher expected gain. The point of this test question was to determine how cautious or greedy are the FX traders when the odds are in their favor. Those who chose the first answer rarely follow the "let your profits run" rule and usually prefer to take whatever profit the market is offering them. Those who chose the second answer most probably prefer to keep their profitable positions open for as long as the market conditions remain in their favor.

The second question again was to choose from two possible answers were: either a 99.9% chance to lose \$200 or a 10% chance to lose \$3,000. Using the formula from the explanation to the first test question, we can calculate the expected values (EV) for both answers. The first `EV = 0.999 × \$200 = \$199.80`; the second `EV = 0.10 × \$3,000 = \$300`.

Obviously, the first answer is more favorable as it results in losing less in the long run, even though the probability of loss is rather high. The point here is that the traders who prefer to cut their losses short will choose the first answer as it implies an almost guaranteed but a small loss. At the same time, the market participants that stick to their losing trades in hopes of a reversal will probably choose the second option as it gives them a chance to avoid any loss at all even at the cost of losing a lot if the chances turn against them.

The third question was "What trading strategy would you choose?" and there were two variants to select from: either a strategy that is right 30% of time and is yielding \$50 on winning trades and -\$10 on losing ones or a strategy that is right 90% of time and is yielding \$10 on winning trades and -\$40 on losing ones. Let us calculate the expected value for each strategy. The calculations are a bit different here as they are composed of two parts — positive (winning trade) and negative (losing trade). The EV of the first strategy is: `0.3 × \$50 — 0.7 × \$10 = \$15 — \$7 = \$8`. Not much, but that is a profitable strategy. The EV of the second trading strategy: `0.9 × \$10 — 0.1 × \$40 = \$9 — \$4 = \$5`. As you see, it is also profitable, but performs almost twice worse than the first one.

Choosing the first option here would be the most rational choice. This question was meant to detect traders' bias towards strategies that win often but have poor risk-to-reward ratio. Traders choosing the first strategy prefer neglecting the psychological comfort of being right on the market often in favor of bigger long-term profits. Traders choosing the second option prefer emotional feedback over some part of their profits. Additionally, the first strategy is safer because of the lower average loss and would perform better with fixed fractional position sizing even with equal expected values.

Results analysis

Based on the answers of the website visitors, the results were the following:

1. More than two thirds of the survey participants chose the first option, which, if you remember, is an irrational choice. It shows that the vast majority of the respondents would prefer to cut their profit short even if the trading conditions favored their profitable position. It is a bad signal and if you were among those who have chosen the first option in this question, it is probably worth thinking about it and trying to correct this trading bias somehow.
2. Less than two thirds of the participants are cutting their losses short and thus chose the first option here. Unfortunately, about one third of the respondents seem to be sticking to their losing positions, even when it is obvious that a small loss now is better than a chance to avoid it at a potentially much higher price. If you are among those who would choose the second option in this survey question, switching to tighter stop-loss levels (you are using stop-loss, aren't you?) is recommended.
3. About two thirds of the blog readers chose the first strategy, which is a more rational choice but forfeits the psychological comfort of winning often. Traders who chose a less profitable strategy are not necessarily probability-blind. Perhaps they are less self-disciplined and prefer emotional stability, which in its turn helps against deviating from their strategy.

Let's hope that these explanations are clear enough and that they will help you become more self-aware and improve your understanding of both the role of probability and the psychological biases in trading.

If you want to share an opinion or ask some questions about the probability theory and its application in currency trading, feel free to do so on our Forex forum.