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Wednesday, May 24, 2006

EXPECTANCY AND WINRATIO (3)

One of the results of my last posting on expectancy is the size of average win compared to the average loss:

"With these examples we see that increasing the average win is more favourable for the expectancy and therefore the profability than decreasing the average loss, but also that increasing the win ratio proportional increasing the expectancy."

There is a restriction to these statements: this is only true for a winratio p < 1/2. I stated it here due to my own bias towards trading in the sense that I never look at tradingsystems with a winratio smaller than 1/2.


Although completely possible for someone to trade, it is not my cup of tea. You may find and trade a sytem which produces 3 winners out of ten, the winners to be bigger than the losers. See the graph for the expectancy in this case in my posting before. I personally discard these systems because of the following reasons.

  • The problem of outliers.

  • Psychology involved

  • Consistency

  • Formal reasons



I. The outlier problem.
One of the problems of data sampling and data processing is the uneven influence outliers have on the results. A big trade outcome may be not representative but just a coincidence. You have to watch for this trap. How many data do you need to obtain reliable results? Though allways important for valuating a trade system, for a system with the need of bigger winns (a trend following system) this becomes very urgent. You may be waiting for another winner which may never show up.


There is another practical problem: you may not miss the bigger trades , this is allways possible for many reasons, your final outcome of your system being very sensitive to pick these winners.



II. The psychology involved
It can be very hard to trade a system in which many losers occur in a row. You have to be very patient and disclipined to trade a system like that. Your account has to be big enough to take this easily, the risk of a gambler's ruin is allways at stake here.


III. Consistency
Time consistenccy is an important facor in my trading and may be treated on a next occasion. For the moment it is enough to note that consistency in trade systems with lower win ratio's only may be expected in longer lasting time frames, a result badly bearable for me.


IV.Formal reasons
There exists a rigorous and formal model for a maximum betting size based on the work of Dubins and Savage (1976) in their book with the inspiring title How to Gamble if you Must. One of their results was that in an unfair game, eg. a game where your win chances are less than 1/2 (a play in which the odds are against you) your maximum chances are only achieved when staking the maximum. This is called 'bold play' in these models.


Later work confirms these results, see eg. an overview of Schweinsburg : Improving on bold play when the gambler is restricted. For a superfair game, eg when p>1/2, it has been shown that a more realistic timid strategy of staking being optimal.


Now these models cannot directly transformed to trading systems because they are restricted to so called red and black models in which outcomes are either black or red (plus 1 or minus 1 and so on, the casino games) but may give some clues to sub-optimal strategies when using winratios > 1/2.


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1 Comments:

Blogger Paolo Pezzutti said...

Carlo,
excellent series of posts.
I totally agree with you.
Paolo

5:13 PM  

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