WHAT IS EXPECTATION IN TRADING
✴️ What is expectation in trading?
Every trader should be familiar with the concept of mathematical expectation, we will briefly discuss this aspect again. Take a look at the figure above. In the end, the total net profit (or loss) comes from both the frequency of profitable and losing positions (however many there are) and their average size. The goal of any market analysis, any strategy, is to try to have more profitable trades (and therefore fewer losing trades). And while entry point analysis can have its advantages, at the end of the day, we can't predict the future.
The average size of profitable and losing positions, on the other hand, gives us much more information and, in fact, a very large degree of control. For if we take a risk in our position of, say, three percent, our average loss will not exceed minus three percent. And the only thing we have to do for that is to close positions when the risk gets to three percent or less. No forecasting or analysis is needed at all. Similarly, we can also increase the average size of our profitable positions by simply holding them (i.e., not closing them) and adding to them (i.e., opening more positions in that direction) as they bring us large profits. So, in the end, it's all about minimizing losses and maximizing profits. Going back to the figure above, this means we should focus on the mass of weights.
Being profitable in trading over the long term, comes down to minimizing losses and allowing profits to grow. It's not about whether you act right or wrong - it's about how you manage your profits and losses.
✴️ Problems with mathematical expectation
Mathematical expectation isn't hard to understand. And to help understand it, very simple analogies are often used, such as gambling: dice, roulette, or even the lottery. Thanks to expectation, it is easy to prove that all such games are ultimately losers if played for quite a long time.
And here we come to the heart of the problem. The concept, or you could say the myth of "expectation of one's system". A more popular term for traders is "edge". Legend has it that you should have positive expectations of your trading system. But this is a futile endeavor because, unlike gambling, the system may not have, and probably does not have, a consistent percentage of profitable positions. After all, markets do not move randomly. Thus, in financial markets, we only know our historical frequency of profitable and losing positions, unlike in a dice game where we also know the upcoming expectation.
The myth that we need to have positive expectations of our system before trusting it with our money has dire consequences. It feeds the belief that you need to have an edge (in terms of math expectation) to be profitable in the long run. It also feeds the unhelpful need for backtesting. Any system that has negative expectations and is naturally backed up by backtesting is discarded. Good systems are criticized because they may be out of sync with the markets for a while, i.e. not profitable for a while. And it comes down to adjusting the yield curve on historical data, i.e. over-optimization.
What do traders do in search of a system with positive expectations? The same thing: they do not take into account the probability distribution in the measurement domain. And if Nassim Nicholas Taleb's Black Swan has taught us anything, it's that we simply can't do that.
We can't apply measurements beyond the interval in which those measurements were made. And we certainly have to realize that we have to look at expectations as a whole. It is precisely not the probabilities that are killing us, it is the outcomes. And once again, even probabilities (and perhaps similar distributions) are not stable in financial markets. Markets are chaotic, fractal in nature, with exponentially changing behavior (and not always).
✴️ What can we do to improve our mathematical expectation?
The good news is that when a trader starts thinking with his head instead of relying on expectations, he/she doesn't have to do anything to his "system". Trading expectations (as opposed to expectations of one's system) is simply using the knowledge that we have much more control over the size of our profit/loss (average size of profitable and losing positions) than we have over probability (frequency of profitable and losing positions). And, because we don't focus on historical expectations, trading expectations can work for us. By keeping losses small and increasing our profits (and adding to profitable positions), we gain true advantages.
The following experiment was conducted: the simulator opened random positions, from which the expectation and net profit were calculated. This model averaged several million sets of 30 long positions during a bear market. The average net loss was -12 percent; only about one-third of all positions were profitable. Now, by simply opening the same positions, cutting the losses to minus three percent (using a stop loss) and at the same time adding to the profitable positions, we achieved an average net result for the same positions of 1.8 percent profit (on average in a falling market). So, by using expectations in our favor, we actually changed the values of expectations! Traders who believed that initially negative expectations were useless would never have been able to do this because they had abandoned the system from the start.
This doesn't mean that losses can be turned into profits exactly, but in the long run expectation works by closing out losing positions and adding to profitable positions. But when looking at the possible history of trades on the chart in the past, traders are often fooling themselves. Thus, none of the trading systems are either profitable or unprofitable, they look that way only in relation to the method of position size management and money management applied.
✴️ Conclusion
To summarize, it is one thing to see how a forex strategy has behaved in history, but to expect it to behave the same way in the future is another. Traders should focus less on testing on history and more on the current situation: to cut losses and even more on maximizing their profits and adding to profitable positions. Follow this rule long enough and you will experience the true power of mathematical expectation in Forex trading.
Every trader should be familiar with the concept of mathematical expectation, we will briefly discuss this aspect again. Take a look at the figure above. In the end, the total net profit (or loss) comes from both the frequency of profitable and losing positions (however many there are) and their average size. The goal of any market analysis, any strategy, is to try to have more profitable trades (and therefore fewer losing trades). And while entry point analysis can have its advantages, at the end of the day, we can't predict the future.
The average size of profitable and losing positions, on the other hand, gives us much more information and, in fact, a very large degree of control. For if we take a risk in our position of, say, three percent, our average loss will not exceed minus three percent. And the only thing we have to do for that is to close positions when the risk gets to three percent or less. No forecasting or analysis is needed at all. Similarly, we can also increase the average size of our profitable positions by simply holding them (i.e., not closing them) and adding to them (i.e., opening more positions in that direction) as they bring us large profits. So, in the end, it's all about minimizing losses and maximizing profits. Going back to the figure above, this means we should focus on the mass of weights.
Being profitable in trading over the long term, comes down to minimizing losses and allowing profits to grow. It's not about whether you act right or wrong - it's about how you manage your profits and losses.
✴️ Problems with mathematical expectation
Mathematical expectation isn't hard to understand. And to help understand it, very simple analogies are often used, such as gambling: dice, roulette, or even the lottery. Thanks to expectation, it is easy to prove that all such games are ultimately losers if played for quite a long time.
And here we come to the heart of the problem. The concept, or you could say the myth of "expectation of one's system". A more popular term for traders is "edge". Legend has it that you should have positive expectations of your trading system. But this is a futile endeavor because, unlike gambling, the system may not have, and probably does not have, a consistent percentage of profitable positions. After all, markets do not move randomly. Thus, in financial markets, we only know our historical frequency of profitable and losing positions, unlike in a dice game where we also know the upcoming expectation.
The myth that we need to have positive expectations of our system before trusting it with our money has dire consequences. It feeds the belief that you need to have an edge (in terms of math expectation) to be profitable in the long run. It also feeds the unhelpful need for backtesting. Any system that has negative expectations and is naturally backed up by backtesting is discarded. Good systems are criticized because they may be out of sync with the markets for a while, i.e. not profitable for a while. And it comes down to adjusting the yield curve on historical data, i.e. over-optimization.
What do traders do in search of a system with positive expectations? The same thing: they do not take into account the probability distribution in the measurement domain. And if Nassim Nicholas Taleb's Black Swan has taught us anything, it's that we simply can't do that.
We can't apply measurements beyond the interval in which those measurements were made. And we certainly have to realize that we have to look at expectations as a whole. It is precisely not the probabilities that are killing us, it is the outcomes. And once again, even probabilities (and perhaps similar distributions) are not stable in financial markets. Markets are chaotic, fractal in nature, with exponentially changing behavior (and not always).
✴️ What can we do to improve our mathematical expectation?
The good news is that when a trader starts thinking with his head instead of relying on expectations, he/she doesn't have to do anything to his "system". Trading expectations (as opposed to expectations of one's system) is simply using the knowledge that we have much more control over the size of our profit/loss (average size of profitable and losing positions) than we have over probability (frequency of profitable and losing positions). And, because we don't focus on historical expectations, trading expectations can work for us. By keeping losses small and increasing our profits (and adding to profitable positions), we gain true advantages.
The following experiment was conducted: the simulator opened random positions, from which the expectation and net profit were calculated. This model averaged several million sets of 30 long positions during a bear market. The average net loss was -12 percent; only about one-third of all positions were profitable. Now, by simply opening the same positions, cutting the losses to minus three percent (using a stop loss) and at the same time adding to the profitable positions, we achieved an average net result for the same positions of 1.8 percent profit (on average in a falling market). So, by using expectations in our favor, we actually changed the values of expectations! Traders who believed that initially negative expectations were useless would never have been able to do this because they had abandoned the system from the start.
This doesn't mean that losses can be turned into profits exactly, but in the long run expectation works by closing out losing positions and adding to profitable positions. But when looking at the possible history of trades on the chart in the past, traders are often fooling themselves. Thus, none of the trading systems are either profitable or unprofitable, they look that way only in relation to the method of position size management and money management applied.
✴️ Conclusion
To summarize, it is one thing to see how a forex strategy has behaved in history, but to expect it to behave the same way in the future is another. Traders should focus less on testing on history and more on the current situation: to cut losses and even more on maximizing their profits and adding to profitable positions. Follow this rule long enough and you will experience the true power of mathematical expectation in Forex trading.
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bit.ly/3spSQqC
🔻FREE Telegram channel🔻
t.me/DeGRAMChannel
🔻Contact for Paid SIGNALS🔻
t.me/DeGRAMForex
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