The average income of a regular casino in its size is comparable only with the profitability of transactions on Wall Street. Smart people have long realized that you can’t constantly rely on your luck and began to use statistical methods for the stability of their profits.
The casino receives huge amounts, 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, the casino will win sooner or later. Casino profits grow even faster if the range of games includes those that end in a relatively quick time - roulette, craps or several cards.
I think that for any trader to succeed in their work, it is necessary to solve the three most important tasks:
1. To ensure that the number of successful transactions exceeds the inevitable errors and miscalculations.
2. Set up your trading system so that the earning opportunity is as frequent as possible.
3. To achieve stability of a positive result of their operations.
And here, working traders, mathematical expectation can provide good help. This term in probability theory is one of the key. With its help, one can give an average estimate to some random value. The mathematical expectation of a random variable is similar to the center of gravity, if you imagine all the possible probabilities with points with different masses.
In relation to a
trading strategy , the mathematical expectation of profit (or loss) is most often used to assess its effectiveness. This parameter is defined as the sum of the products of the given profit and loss levels and the probability of their occurrence. For example, the developed trading strategy assumes that 37% of all operations will bring profit, and the rest - 63% - will be unprofitable. At the same time, the average income from a successful transaction will be $ 7, and the average loss will be equal to $ 1.4.
We calculate the mathematical expectation of trading according to this 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 from each closed transaction.
Since the resulting
efficiency estimate is greater than zero, then such a system can be used for real work. If, as a result of the calculation, the mathematical expectation is negative, then this already speaks of an average loss and such trading will lead to ruin.
Profit per trade can also be expressed as a relative value in the form of%. For instance:
- the percentage of income per 1 transaction - 5%;
- the percentage of successful trading operations - 62%;
- loss percentage per 1 transaction - 3%;
- the percentage of failed transactions is 38%;
In this case, the mathematical expectation is (5% x 62% - 3% x 38%) / 100 = (310% - 114%) / 100 = 1.96%. That is, the average transaction will bring 1.96%.
It is possible to develop a system that, despite the prevalence of losing trades, will give a positive result, since its MO> 0.
However, one expectation 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. Suppose that each operation gives an average of only $ 0.5, but what if the system involves 1,000 operations per year? This will be a very serious amount in a relatively short time. It logically follows from this that one more distinctive feature of a good trading system is the short retention period.
If you want to delve deeper into the mathematics of randomness, find out what conditional expectation, confidence interval and other interesting tools are, we recommend that you read the book “Statistics for the Trader” (author S. Bulashev). Who knows, maybe the chaos of currency movement after reading a book will seem to you simply the highest form of order ...