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Trading price or mathematic expectation of profit

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ach beginning trader considers trading at financial markets as a unique opportunity to make a good amount of money. He put on rose-coloured glasses and anticipates his profit which will enable him to drop his current job, give him an opportunity to travel all over the world and work only when he feels like doing it, and not when his stupid and always angry boss wants him to. Being immersed in such rainbow thoughts, a trader opens a real account, begins trading and suddenly finds himself in the cruel reality. Money evaporates out of his account, then enormous losses cause forced closing of the bargains by a broker. The beginner realizes at least that the market allows not only making money, but also losing it. Why does it happen? Why do thousands and thousands of clients leave the business with losses? There are many reasons for it, and, to my mind, one of the main reasons is that the accent is made on potential profit, while a beginning trader tries not to think about the risks, the trading price which may be paid by a trader, which is not correct in principle. At the same time, understanding and taming of risks is one of the main elements of work at FOREX and other financial markets.
Paradox consists in the fact that mathematicians have developed the formula of mathematical expectation of profit long ago. Even if you are not on good terms with mathematics, do not worry—this formula is understandable for everyone and looks like this:
possibility of profit to be obtained, multiplied by the amount of the profit itself
without
possibility of loss to be obtained, multiplied by the amount of the loss itself
Your trading price will be the result!
Now let us write down the formula as follows:
Trading price = T/P Possibility*T/P – S/L Possibility*S/L
In order to understand the nature of the formula, let us remember the commonly known game with coin tossing. Let us assume that if heads falls, you gain 10USD. If tails falls, you lose 10USD. What is the possibility of heads or tails falling? If you toss a coin ten times, heads may fall six times, tails may fall four times; the possible ratio will be 4:6 or 5:5. In hundred cases, the ratio may be 49:51, 50:50 or something like this. Finally, if we toss a coin 10,000 or 1,000,000 times, it is possible to say virtually for sure, that in 50 percent of cases heads will fall, while in 50 percent of cases tails will fall. This is the law of large figures: the larger values of a phenomenon are, the closer the accidental value to the average value is.


I think at least that most of readers will agree with the chances of 50:50. And then, by data substitution into the formula, it is quite easy to calculate the trading price:
0.50*10 - 0.50*10 = 0. And now let us imagine that your friend agrees to give you the profit in the amount of 20 dollars. What will change now?
0.50*20 - 0.50*10 = 5. It means that at every coin tossing you will get averagely five dollars. It is not a bad outlook, but where is it possible to find such a friend? -  You will say this and will be right. However, now we will consider some other things. A shrewd reader has surely grasped that the most difficult thing in the formula is to determine the possibility of profit and loss. How to do it?!
Let us imagine that two traders, John and Harry, trade at the market, with application of the same tactics – crossing of moving averages in hour scale of the price graph. Sizes of T/P and S/L by both of the traders are also similar, for instance, 50 points. The difference consists in the fact that John trades with the trend direction in the day scale, while Harry tries to find the reversing point of the day trend and opens positions against it. For this example, the trend is the coincidence of inclination of the week and the day MACD histograms. EUR/USD pair is taken as an example.

Figure 2. The week histogram is moving downwards


Figure 3. The day histogram at this time section is moving downwards.

Consequently, by trading with the trend direction, John opens positions for sale. Meanwhile, by attempting the trend reversing point, Harry makes buying bargains.

In the third figure the arrows mark entrance points for buying and selling at crossing moving averages in EUR/USD day graph. The signals to bring some profit are marked with green. The signals to bring some loss are marked with red. Now let us count the number of profitable and false bargains. In spite of the fact that in the flat both of the tactics bore losses, in general seven (70 percent) selling signals out of ten ones appeared to be true, while three (30 percent) happened to be false. With buys in the descending trend seven (70 percent) bargains became loss-making, and three (30 percent) turned out to be profitable ones. I would like to remind you that both profit and loss equal to 50 points. And now, with substitution of the values obtained into the formula of mathematic profit expectation, we can see the trading price for each participant.
For John: 0.7*50 – 0.3*50 = 20
For Harry: 0.3*50 – 0.7*50 = -20
It means that by trading with the trend direction, at every following position opening John would make 20 points averagely, and, by trying to determine the trend reversing and opening positions against the trend, Harry would continue losing the same 20 points. It is not difficult to guess who of them will have vacation in the Hawaii earlier.
Regarding the capital management, it is very important to understand that with gambling with negative profit expectation there is no plan of money management, which can make you a winner. If you continue gambling, you will lose all your account independently of a money management method, no matter how big it was initially.
This axiom is correct not only for gambling with negative expectation, it is valid also for gambling with equal chances. Therefore the only case when you have some chance to win in long-term outlook, - is trading with positive mathematic expectation.
Now let us divide the trading price formula into two parts:
Take-profit possibility / T/P Value
Stop-loss possibility / S/L Value
In the aforesaid example I have attempted to show the way of explaining the famous phrase “Trend is your friend” mathematically. Trading with the trend, you have more chances to gain profit than to bear loss. It means that you should determine for yourself exactly, what implies the trend for you and the parameters of the trend determination, and trade only when it is present and only according to its direction. Then you should try to achieve bigger take-profit than stop-loss in every bargain. And then you will reach positive mathematic expectation of profit, at east in theory, but it will become a big step forwards on the way to your and your relatives` thriving. After that persistence and consistence in your actions and your labour will allow setting a bridge between the theory and its implementation in practice.
It is required to achieve the following results:
High possibility of take-profit / Big T/P value
Lower possibility of Stop-loss / Smaller S/L value
Thus, the order of your activities in work can be written down as follows:
Determine the trend
Wait for a signal with its direction
Count the ratio of possible profit / possible loss
To define approximately the time of being in the market.
In the core, these are the four filters which will help you improve your result. If there is no trend, you just remain out of the market. Maybe, you have waited for a clear trend, but there is no signal in its direction. Finally, there are both a trend and a signal in its direction, but the potential risk exceeds the potential profit. In all these cases, the best way is not to conclude any bargains and wait for the situation further development. If you have opened a position and defined it as a short-term one, but the day is coming to its end and the price has not reached your target, the possible way may be to close the bargain by hand with the current price. You may remain in the market, but only if you have thoroughly analyzed the situation and got the confirmation that the trend will continue moving in your direction.
By the way, the example of the trade according to the trend suggests one more important conclusion. Take the fact that any trading system will bring you some loss sooner or later as an axiom. Therefore losses should be perceived calmly as production expenditures. And the following conclusion suggests itself. Develop a trading tactics which would bring you, first of all, minimum losses instead of a tactics which would bring enormous profits but make you take an enhanced risk for your deposit.

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