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(French) Mostafa Belkhayate’s Alembex method (martingale)
Hi,
This method has been presented by Mostafa Belkhayate in March 2013. The presentation is divided in three videos:
(video 1) Mostafa Belkhayate: Espérance mathématique de gain et séquence de mise  Présentation d'Alembex 1  YouTube
(video 2) Mostafa Belkhayate: Espérance mathématique de gain et séquence de mise  Présentation d'Alembex 2  YouTube
(video 3) Mostafa Belkhayate: Espérance mathématique de gain et séquence de mise  Présentation d'Alembex 3  YouTube
A fourth video gives a better view on the slides: Séquence BelkhayatePartie 1  YouTube
Normally, I do not lose time on this kind of things, but I will make an exception here, because what is proposed is not entry/exit rules, but a position sizing system (martingale). I wanted to drop some notes here in case some one would be looking for information. The proposed system is dangerous for your capital.
Let’s suppose that we have a (profitable) trading system with the following parameters :
 %win: percentage of winning trades
 Win/Loss: ratio between the gain in case of winning trade and the loss case of losing trade
Let’s consider a sequence of 12 trades. The question is: which position size to choose for each trade?
We can choose to risk the usual 1% of the capital per trade.
We can choose to double the position at each losing trade. A sure way to ruin.
Mostafa Belkhayate proposes a position sizing rule and pretends that this rule will lead to marvellous gains.
This system works a follows:
 if last trade was a loser, position size for this trade is the same as for the previous trade (no doubling)
 if last trade was a winner (and the one before was a loser), position size for this trade is the same as the cumulated loss until now, plus one unit
 if two last trades were both winners, we have obtained a cumulated gain of +1, and we stop.
Mostafa Belkhayate takes the exemple of a coin toss (%win = 50% ; Win/Loss = 1). The expectancy of this system is 0. But Mostafa Belkhayate pretends that his position sizing system will turn it into a (very) profitable system.
He asserts that the probability of not having 2 consecutive winners in a sequence of 12 trades is negligible, so the trader is “guaranteed” to finish the sequence with a gain of +1.
This is false.
First, the probability of not having 2 consecutive winners in a sequence of 12 trades is far from negligible. The probabilities shown in the videos are simply wrong (by the way, some are > 100%!). Actually, according to my calculation, the probability of having 2 consecutive winners in a sequence of 12 trades is 94% (in coin toss situation).
So, there are 94% of chances to gain +1. And 6% of chances to lose… much more!
The following graph (produced with R) shows the 4096 possible equity curves (on 12 trades).
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3863 sequences (94%) lead to a gain of +1.
But 233 sequences (6%) lead to a loss which could be as bad as 47.
It means that, if you have chosen to trade 1% of your capital for the first trade, you capital could be divided by 2 after 12 trades!
Of course, the expectancy remains 0.
In other words, in this coin toss hypothesis, the expectancy is not improved compared to a fixed risk of 1% of the capital for each trade, but the risk has increased a lot. A way to ruin.
Nicolas
Last edited by Nicolas11; February 19th, 2014 at 05:16 AM.
Reason: typo
