4.5. Empirical way to
In this article we intend to demonstrate the feasibility of a mathematical calculation to make the right decisions on the level of transaction. This is justified as follows.
At the moment of entering into a transaction a person must make two decisions. The first will deal with what the position (long or short) must be open. The second - about the amount that you enter into a transaction. The latest decision in all cases the activity (function) of the amount of capital that you have.
At the same time, the value of the account - not the only condition that has value for the number of positions that we intend to open. It is also important items such as our expectation of the maximum loss in a transaction and the rate of growth of our accounts, we would like to see. These aspects are not given us an exhaustive list of all the things that affect adoption of our subjective decision on the amount, which will enter into a transaction.
The adoption of subjective decisions often means a choice in favor of the wrong way, and pay for it over time will have all the big sums.
Assuming the deal, we mentally pretends worst-case scenario, in which events may unfold if we catch up with defeat. This scenario is defined and the maximum loss. Despite the fact that not all obviously aware of this scenario, it was he, together with the amount of capital affects the size of positions that will open. Most clearly this can be considered in this sample. For example, on your account - $ 50 thousand, with $ 5 thousand - is waiting for the maximum loss attributable to a contract. If you open up to five contracts, it is possible to derive a value of f (fraction, part), connects all three figures:
50.000 / (5.000 / f) = 5 f = 0.5
This value ranges from 1 to 0.
Traders when entering into a transaction in its calculations typically allow two errors. The first mistake is that they first of all assess the correctness of the direction of entering the market. A determination of the amount that must be included in the deal, it seems a matter of secondary importance to traders. The second error is that traders believe if the number of positions is in direct proportion with the size of profit or loss, which they suggest.
In fact, although the projected income and the amount of products they offer are definitely related, but their relationships are nonlinear. They are described by a curve in the top of which the right attitude we will have a maximum value.
For example, lose such a scenario. There are 50% of the game (ie a game in which the probability of winning or losing is 50%), and if you win on the first turn to the bill added $ 2, and at a loss - minus $ 1. In what remains the ratio of the size of bets to win and lose. For example, if the initial rate of $ 10, then win through to increase by 20%, and at a loss, respectively, decreased by 10%. After forty-rates, we have the following result (counting from the sum of the initial rate):
Look at the peak of this curve. It shows that the optimal f in this game is 0.25, after 40 consecutive rate at this value of f TWR will be 10.55. Indicator TWR (an acronym for Terminal Wealth Relative), we obtain the result of dividing the game on the initial bet. What does the TWR = 10,55 in practice? This means that up to forty-rate initial rate increased to 10.55 times, or 955% of income.
The peak of the curve represents the optimal f for this game. Shifting it by only 15%, we reduce the potential profit more than doubled, as at f 0,1 or 0,4 TWR will be only 4.66.
For clarity, we express these values in dollars. If f = 0,1, then the size of the first bet will be $ 10. At f = 0,4 to 2,5 $ rate. Optimal f, equal to 0.25, gives us the optimal size of the same rate - $ 4. If this game is 0.5 f (rate is $ 2), we obtain the TWR, equal to 1. In other words - the absence of any movement. Exceeding f, equal to 0.5, we will inevitably incur losses, despite the fact that the amount of potential gain is twice the loss.
Confirm this thesis the following example. Let the game will be 6 bets at an initial rate equal to $ 1.5. In this example, the first three betting we'll win, but all of the following - lose. I must say that the sequence of losses, gains does not affect the outcome of the game, as is easily seen, if this game to simulate a different sequence of the bets.
If the rate of one and a half dollar, the gain in the amount of $ 2 will be 2 / 1, 5 = 133% gain in a simulated configuration of the game. The loss in this case, we calculate as follows: 1 / 1, 5 = 67% of the initial rate. Let us follow the game moves on:
1 turn. 1.5 * 1.33 = $ 1.995
2 course. 1,995 * 1.33 = 2.65335 $
3 course. 2.65335 * 1.33 = 3.5289555 $
4 stroke. 3.5289555 * 0.67 = $ 2.3644
5 speed. 2.3644 * 0.67 = 1.584148 $
6 course. 1.584148 * 0.67 = $ 1.061379
We see that after six moves, we lose more than 29% of the initial rate (0.4386 $). With the passage of time - losing outright.
Thus, despite the presence of nonlinear relationships of potential profit and the amount of positions that are opening up, the optimal value of f determines the optimal value of the initial stake to risk-specific game. Deviations from the optimal rate reduces the amount of profit due to either too high (the maximum deviation to the right of f), or too low (deviation to the left) the relationship between risk and potential reward, when the potential rate is available until the end.
The decision about the amount of capital that may be compromised, is as important as that in which direction to open positions. And many traders are completely wrong direction associate entering the market with the accuracy of estimation of the volume, which must be opened. It should be noted that these two aspects are not connected, and if the trader is not able to determine a profitable or losing is going to be a deal, he, at least, is obliged to assess the correct amount of opened positions.
