A FEW OF MATHS

 

The order of gains and losses doesn't influence on the final result:

 

The order in which occurs gains and losses don't have any importance on the final result, even though he/it influences on the measured risk (for example) by the Drawdown.

To show it, we will name O1, O2,....... ,On, courses of opening of n consecutive days.

For example, 100, 101, 105, 103 and 108.

We will have: 101/100 * 105/101 * 103/105 * 108/103    = S 108/100  after simplification.

In a different order: 105/100 * 103/105 * 101/103 * 108/101  deal also 108/100

What doesn't mean that the order of gains and losses is neutral with regard to possibilities to make again if losses are situated in beginning of period.

 

Gains and losses don't have the same weight in the final result:

 

It can seem paradoxical, but if to lose 10  on a trade of 100, then to regain them to the following stroke represents a hopeless operation well, it is necessary to surrender very account that, after the loss of 10% the capital fell to 90 and that it needs to a gain of 11.11% to make again.

The picture gives account of this unbalance that accelerates more here under that proportionally with the loss:

 

DECREASE

RISE

OF THE

NECESSARY

COURSE

FOR

To RECOVER

5%

5,26%

10%

11,11%

15%

17,65%

20%

25,00%

25%

33,33%

30%

42,86%

35%

53,85%

40%

66,67%

45%

81,82%

50%

100,00%

55%

122,22%

60%

150,00%

 

One will notice that until 15% of decrease, the necessary growth to regain his/her/its capital seems tolerable, but that to the delà, the return to the balance becomes more and more uncertain.

It is for this reason that all works counsel to cut losses quickly. (cut losses shorts).

These considerations must very évidement to be integrated in your systems of trading.

Only Warren Buffett yours not account of these considerations, considering that he/it bought a value on his/her/its own quality, and that an any decrease would know how to be only temporary, and that the decrease of the value gives him the opportunity to acquire some more to good account.

 

The mathematical hope of gain:

 

It is the middle gain that one can wait for the system that you finalized.

His/her/its calculation is very important when one knows that one is not able to in any way to transform a system not arranging a hope of gain in system winning.

The validation of this result that can be gotten while testing the historic, or throughout other means, is not treated in this chapitre. 

This hope of gain is calculated as follows:

Number of gains * middle Gain - Number of losses * middle Loss.

 

                                                          Eg = Nbg * Gm - Nbp * Pm

 

 

The rule of the 1 to 2%:

 

It is the maximum percentage of sound to have exposed to the risk that the trader accepts to lose on a position.

For example, if he/it arranges 100.000 units, he/it will decide of ever to accept to lose more 2%, either 2.000 units on a trade.

He/it will act consequently, and will determine the number of actions to acquire according to this maximum risk.

If he/it wishes to buy an action to 100 for which he/it placed a stop losses to 90, he/it will determine his/her/its joint-stock loss (here 10) and will invest on 2.000 / 10 = 200 maximum actions.

It is a rule of security that seems to make the unanimity at runs them " term ".