The average income of an ordinary casino is comparable in size only with the profitability of transactions on Wall Street. Smart people have long understood that you can not always rely on your luck and began to use statistical methods to ensure the stability of their profits.
The casino gets huge sums because the "probability" or, in other words, the mathematical expectation of the game, is on the side of the gambling house. And regardless of which game to participate in, sooner or later the casino will win. Casino profits grow even faster if the assortment of games includes those that end in a relatively short time - roulette, craps or several cards.
I think that any trader needs to solve three most important tasks in order to succeed in his work:
1. To ensure that the number of successful transactions exceeds the inevitable mistakes and miscalculations.
2. Set up your trading system so that the opportunity to earn money is as often as possible.
3. To achieve a stable positive result of their operations.
And here we are,For working traders, mathematical expectation can be a good help. This term in the theory of probability is one of the key. With it, you can give an average estimate of some random value. The mathematical expectation of a random variable is similar to the center of gravity, if we imagine all possible probabilities as points with different masses.
With regard to a trading strategy, to evaluate its effectiveness, the mathematical expectation of profit (or loss) is most often used. This parameter is defined as the sum of the products of given levels of profit and loss and the probability of their occurrence. For example, the developed trading strategy assumes that 37% of all operations will bring profit, and the remaining part - 63% - will be unprofitable. At the same time, the average income from a successful transaction will be $7, and the average loss will be $1.4. Let's calculate the mathematical expectation of trading using the following system:
MO=0.37 x 7 + (0.63 x (-1, 4))=2.59 - 0.882=1.708
What does this number mean? It says that following the rules of this system, on average, we will receive 1.708 dollars from each closed transaction.
Since the resulting efficiency score is greater than zero, such a system can be used for real work. If, as a result of the calculation, the mathematical expectation turns out to be negative, then this already indicates an average loss and such trading will lead to ruin.
The amount of profit per trade canbe expressed also as a relative value in the form of%. For example:
- percentage of income per trade - 5%;
- Percentage of successful trading operations - 62%;
- loss percentage per trade - 3%;
- percentage of unsuccessful deals - 38%;
In this case, the expected value will be (5% x 62% - 3% x 38%)/100=(310% – 114%)/100=1.96%. That is, the average trade will bring 1.96%.
It is possible to develop a system that, despite the predominance of losing trades, will give a positive result, since its MO>0.
However, waiting alone is not enough. It is difficult to make money if the system gives very few trading signals. In this case, its profitability will be comparable to bank interest. Let each operation bring in only $ 0.5 on average, but what if the system assumes 1000 transactions per year? This will be a very serious amount in a relatively short time. It logically follows from this that another hallmark of a good trading system can be considered a short holding period.
If you want to delve deeper into the mathematics of randomness, to find out what the conditional mathematical expectation, confidence interval and other interesting tools are, we recommend that you read the book "Statistics for a Trader" (by S. Bulashev). Who knows, maybe the chaos of currency movements after reading the book will seem to you just the highest form of order…
