Hello, colleagues Forex traders!

The average book about trading is pretty useless, with a focus mainly on the choice of the point and time of entry, and, as a result, its readers are losing money when applying it. Of course, there are books that on par with the usual nonsense get to much more important topics of mathematical expectation. However, most of these books present this aspect incorrectly again. Either they underestimate its importance, which makes them similar to the already mentioned books. But most often they will even teach you to look incorrectly at the expectation of profit of the system, forcing you to make another step in the wrong direction, giving confidence to its readers and at the same time forcing them to lose money because of financial myopia. In this article we will try to fix this problem once and for all.

One proverb reads as follows: “Losers focus on their profitable positions, and winners focus on winning”. One and the same position can be considered in different ways: if we change the point and time of entry, they are important, but if you use a constant approach with adding to profitable positions, the point and time of entrance is almost irrelevant in the long term.

## Concept of Expectations in trading

Although every trader should be familiar with the concept of mathematical expectation, we will briefly discuss this aspect again.

Look at the picture below. In the end, total net profit (or loss) comes both from the frequency of profitable and unprofitable positions (however many there are) and from their average size. The goal of any analysis of the market, any strategy is to try to have more profitable positions (and therefore less losing positions). And although the analysis of the entry point can have its advantages, in the end, we can’t predict the future.

The average size of profitable and unprofitable positions, on the other hand, gives us much more information and, in fact, a very high degree of control. For if we risk in our position, say, by three percent, our average loss will not exceed three percent with minus. And the only thing we have to do for this is to close the positions when the risk comes to three percent or less.

We don’t need any forecasts or analysis. Similarly, we can also increase the average amount of profitable positions, simply by holding them (i.e. not closing them) and adding to them (i.e. to open more positions in that direction), because they will bring us major profit. Thus, in the end, it all implies the **reducing losses to a minimum and profits to the maximum**. Referring back to the picture, it means that we must focus on the mass of the weights.

To be profitable in trading in the long term is to minimize losses and let profits run. It’s not that you act correctly or not – it’s how you manage your profits and losses.

## Problems with expectations in trading

It is not difficult to understand mathematical expectation. And to help understand it, very simple analogies are used often, for example, gambling: craps, roulette and even lottery. Due to the expectation it is easy to prove that all such games, in the end, are losing games, if you play for quite a long time (if you are interested in this topic, look into Google, for example, “mathematical expectation of roulette).

So there is no sense in gambling, except for the sake of entertainment.

It might be difficult to convince someone who just won a few million in the lottery. Just ask him to spend all his income on lottery tickets next week and he’ll understand everything.

And so we come to the crux of the problem. The concept, or, one might say, the myth of “expectations from your system”. More popular for traders is the term “advantage”. The legend says that you must have positive expectations from your trading system. But it is a futile exercise because, unlike gambling, the system may not have, and probably has not constant percentage of profitable trades. After all, markets do not move randomly. Thus, in the financial markets, we know only our historical frequency of profitable and losing trades, unlike dice game, where we also know the imminent expectation.

The myth about the need to have positive expectations from your system, before you trust it with our money, has severe consequences. This myth nurture your belief that you need to have the advantage (from the point of view of mathematical expectation) to be profitable in the long term. In addition, it energizes the useless need to back testing. Any system with negative expectations and, of course, reinforced by back testing, is discarded. Good systems are criticized because they may be some time not in sync with the markets, i.e. do not make profit for a while. And it comes down to adjustment of the yield curve on historical data, i.e. re-optimization.

What do the traders in search of a system with positive expectations? They do the same thing: do not take into account the distribution of probabilities in the measurement area. And if “The Black Swan” of Nassim Nicholas Taleb has taught us anything, it’s that we just can’t do it.

**We cannot apply the measurement outside the interval in which the measurements were made**. And we certainly need to understand that we need to look at expectations in general. This is not the probabilities that kill us, but just the results. And again, even the probabilities (and perhaps such distribution) are not stable in the financial markets. Markets have chaotic, fractal character, with changing at an exponential behavior (not always though).

## What should we do to improve mathematical expectation?

The good news is that when a trader starts to think with his head but do not rely on waiting, he doesn’t need to do anything with his “system”. Trading expectations (in contrast to expectations from your system) are simple use of knowledge that we have much more control over the size of our profits/losses (an average size of profitable and losing positions) than we have over probability (frequency of winning and losing positions). And because we do not focus on the historical expectations, trading expectations can work for us. *Keeping losses small and increasing your profits (and adding to profitable positions), we get the true benefits*.

The following experiment was conducted: the simulator was opening the random positions; the mathematical expectation and net income were calculated of it.

In this model, several millions sets of 30 long positions during the bear market were averaged. Average net loss was 12 percent, only around one-third of all positions were profitable. Now, just opening the same positions, reducing the losses to minus three percent (using Stop loss) and at the same time adding to profitable positions, we achieved average net result for the same positions in 1.8 percent of the profits (on average **in a** **falling market**). So, using expectations in our favor, we actually changed the values of expectations! Traders, who believed that the original negative expectations were useless, would never have been able to do so because they had refused from the outset from this system.

This does not mean that losses can be accurately converted into a profit, but *in the long term expectation works by closing losing positions and adding to profitable positions*. But when looking at possible trading history on the chart in the past, traders often delude themselves. Thus, any of the trading systems is neither profitable nor unprofitable, they seem so only in relation to the applied method of management of position size and money management.

## In conclusion

In conclusion we should say the following: one thing is to look as Forex strategy behaved on history, but another thing is to expect that it will behave the same in the future.

Traders should focus on testing on history less and focus on the current situation more: to reduce losses and maximize your profits to even greater extent and add to profitable positions. Follow this rule for quite a long time, and you will feel the true power of mathematical expectation in trading on Forex.

Another important point in choosing a strategy is its logical justification, but we’ll tell more about it some other time, stay posted on our website 😉

Take care, Michael