How Well Forex Traders Understand Probabilities — Analysis

Last week I have tried to measure the probability literacy among the readers of this blog, who presumably are Forex traders or at least are trying to be them. Now, with more than 50 answers to each question of the test poll, it looks like a good time for my follow-up post with some explanation and analysis of the obtained answers.
The results of the suggested polls are quite curious, in my opinion. But first, let me explain more about the offered questions and the possible answers.
About Questions and Answers
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
As of May 30, 2012, the results were following:

I hope that my 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 reply using the form below.