A Mathematical Approach to Eliminating Emotions

Additional resource that further elaborate importance of Positive Expectancy and Opportunities: A Mathematical Approach to Eliminating Emotions.

Most traders spend countless hours looking for that magical combination of indicators that will reveal the “holy grail” of trading strategies. Obviously, the goal is to find a winning strategy, but more oftentimes than not “winning” is misconstrued into trying to find a strategy that wins a high percentage of trades. After all, winning a trade means making money, and losing a trade means losing money, right? Don’t be so sure about that.

Like many of the seemingly obvious components that go into creating a great trading plan and becoming a great trader, what we think seems logical in reality is what is holding us back.

For those of you whom have been following us here on FX360 this may not be the first time you’ve read something similar to this, and it won’t be the last. Along with other ways to think in terms of probabilities, the following is an example of something I deeply believe needs to be not just simply understood, but ingrained into the subconscious of our trading psyche (if through nothing more than repetition) in order to ultimately eliminate emotions for every single trade we place. This may perhaps be the most difficult aspect of becoming a true professional trader, but a trait that one simply must have to stand any chance of survival—both financially, and psychologically.

Being a profitable trader is not just about winning percentages. In other words, you can earn positive returns without winning most, or even a majority, of your trades! It’s all about risk vs. reward. If your strategy allows you to identify trading opportunities that offer more reward than risk, then even a 50% winning ratio could yield a significantly positive return over time.

For example, let’s assume a $10,000 trading account where 10 trades are placed, and $100 (1%) is put at risk for each trade…

If risk-to-reward is 1-to-1, then a 50% win ratio will result in a “break-even” return…

[10 trades placed] x [50% losers] = [5 losses] x [$100] = [$500 loss]

[10 trades placed] x [50% winners] = [5 wins] x [$100] = [$500 profit]

[$500 profit] – [$500 loss] = [$0]

If risk-to-reward is 1-to-1.5, then the same 50% win ratio will result in a positive return…

[10 trades placed] x [50% losers] = [5 losses] x [$100] = [$500 loss]

[10 trades placed] x [50% winners] = [5 wins] x [$150] = [$750 profit]

[$750 profit) – [$500 loss] = [$250 profit]

In terms of percentage return, this second (profitable) example would result in a 2.5% return based on the starting account balance (total equity) of $10,000 after just 10 trades. This, of course, is the case when just 1% of total equity is put at risk. If 3% ($300) is put at risk (a rather high amount to most veteran traders), then this same example (same track record) would yield a 7.5% return. . In other words, greater profits are achieved based on the exact same performance…

[10 trades placed] x [50% losers] = [5 losses x $300] = [$1,500 loss]

[10 trades placed] x [50% winners] = [5 wins x $450] = [$2,250 profit]

[$2,250 profit] – [$1,500 loss] = [$750 profit]

Conversely, a high winning percentage (which typically necessitates a bigger margin for error, or greater risk) may actually result in smaller, less profitable returns over time. This occurs when the average risk is higher than the average reward. For example, using the same hypothetical $10,000 account that’s risking 3% ($300) let’s assume an 80% win ratio with an average risk-to-reward ratio of 2-to-1…

[10 trades placed] x [20% losers] = [2 losses x $300] = [$600 loss]

[10 trades placed] x [80% winners] = [8 wins x $150] = [$1,200 profit]

[$1,200 profit) – [$600 loss] = [$600 profit]

So the trader that boasts an 80% win ratio may actually be less profitable than the trader with a seemingly unimpressive 50% win ratio. So the question is…do you want to be right, or do you want to make money? Believe it or not, even negative returns are possible with a higher winning percentage when risk far outweighs reward, so make sure to factor this in when performing due diligence in assessing a strategy and/or track records results.

“10 Dimes Make a Dollar”

Hopefully, this demonstrates the importance of assessing risk/reward in addition to winning percentage when trying to determine the actual success, or profitability, of a trading strategy/track record. Remember, trading success not just about winning and losing individual trades—it’s about sustaining profitability over time (making money and holding onto those profits in the long run). The most common mistake newer traders make is in determining the success of a trading strategy (i.e. track record) based on winning percentage alone, which can be quite misleading when risk/reward is not taken into account. Most newer traders (unknowingly in most cases) are willing to risk far more than they are looking to gain (reward) just to be “right,” or win, each trade.

Another good piece of advice is to always keep in mind that trading is all about making profits over time , not about trading ego (which is usually the result of focusing just on winning percentages). In other words, significant returns can be achieved when you allow yourself to look at the big picture. As the saying goes, “10 dimes make a dollar.” The key is to be able to determine both entries and exits in advance so that risk vs. reward can be determined. This will significantly help to keep the decision making process as consistent and mechanical as possible, which is essential regardless of the technical/fundamental strategy that is used as it helps to eliminate emotions when making trading decisions. Only then can a truly objective decision be made as to whether or not to take the trade since this decision will be based on established/actual results, and not a “gut” feeling or reaction. Understanding the mathematical “law of averages” and “law of large numbers” reinforce this mechanical approach to trading which, again, is crucial to trading success because mixing emotions with money-based decisions is usually a recipe for disaster!


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