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Setup frequency and probability - Math problem

  • Post #1
  • Quote
  • First Post: Nov 15, 2010 8:39am Nov 15, 2010 8:39am
Dear all,

I have the following probability problem, wonder anyone who are good at maths can answer.

The problem:
Someone sold me a trading system and claimed that this system on average signals 1 setup for each 100 bar on a chart. I used the system to trade and 1000 bar on a chart have passed, but I only got 5 setups. Given only this result, what is the probability that I have been cheated?

Thanks in advance.

kk007
If the seller is correct and the probability for a trade setup to occur is p = 1/100, then the expected number of trade setups in a 1000-bar-sample would of course be E = 1000 * p = 10.
The number of trade setups follows the Poisson distribution. For a rough error estimation, you can calculate the standard deviation s = sqrt(E) ~= 3.16 (where sqrt() is the square root). The number of trade setups will be between (E-s) and (E+s) in 68.2% of the times, between (E-2*s) and (E+2*s) in 95.4% of the times and so on.

Now, to give you some probabilities, the probability of having exactly 5 trades in 1000 bars is 0.038. The probability of having 5 or less trades in 1000 bars is 0.067.
This means that, on average, you'll get 5 or less trades in 1000 bars every 15 times that you look at 1000 bars.

Thus, it is too early to say if you've been cheated on.
Quoting Carsten
If the seller is correct and the probability for a trade setup to occur is p = 1/100, then the expected number of trade setups in a 1000-bar-sample would of course be E = 1000 * p = 10.
The number of trade setups follows the Poisson distribution. For a rough error estimation, you can calculate the standard deviation s = sqrt(E) ~= 3.16 (where sqrt() is the square root). The number of trade setups will be between (E-s) and (E+s) in 68.2% of the times, between...
Thanks Carsten,

Let me spend some time to study your answer. I hope it is a perfect solution to my problem.

cheers,

kk007

P.S. Look like it is your first post on FF. Welcome to this paradise!
Quoting Carsten
Thus, it is too early to say
hey carsten...... well it's not too early to say that is beyond any doubt the best first post by any new member on their first day i've seen...... and i've seen a lot of new members.....

..... please keep it up.......h
to trade and code, keep both simple... no call to impress....h
Bingo!

Thank you very much, Carsten. I found the excel built-in formula and got the same value as you "=POISSON(5,10,TRUE)" = 0.067

cheer,

kk007

Quoting Carsten
If the seller is correct and the probability for a trade setup to occur is p = 1/100, then the expected number of trade setups in a 1000-bar-sample would of course be E = 1000 * p = 10.
The number of trade setups follows the Poisson distribution. For a rough error estimation, you can calculate the standard deviation s = sqrt(E) ~= 3.16 (where sqrt() is the square root). The number of trade setups will be between (E-s) and (E+s) in 68.2% of the times, between (E-2*s)...
Quoting kk007
Dear all,

I have the following probability problem, wonder anyone who are good at maths can answer.

The problem:
Someone sold me a trading system and claimed that this system on average signals 1 setup for each 100 bar on a chart. I used the system to trade and 1000 bar on a chart have passed, but I only got 5 setups. Given only this result, what is the probability that I have been cheated?

Thanks in advance.

kk007
I don't think the problem here is in the math! One of the great myths in this business is that it is possible to "buy a system" and make money - that, my friend, is the real problem being presented in your statement. But the perpetuation of that myth is of course important for some, for reasons I need not outline here..
Quoting Hedginghog
I don't think the problem here is in the math! One of the great myths in this business is that it is possible to "buy a system" and make money - that, my friend, is the real problem being presented in your statement. But the perpetuation of that myth is of course important for some, for reasons I need not outline here..
This is not a real story. I made up the story to ask for the maths solution for easier presentation. The real story is that I worked out the expected frequency of my system, but it turned out that the frequency is a lot lower than expected, and so I need the maths to help me to verify.
[quote=Carsten;4173331
The number of trade setups follows the Poisson distribution.[/quote]

I'd just like to note that this is an assumption, which may or may not hold. A strategy may kick in only during trending periods, or more often during high volatility, etc.
The Poisson model is very useful, but please keep in mind its limitations and assumptions, namely, that on average, you'd get the same number of trades during equal intervals.

Good luck!
  • Post #9
  • Quote
  • Last Post: Nov 16, 2010 7:14am Nov 16, 2010 7:14am
Quoting 6pack
I'd just like to note that this is an assumption, which may or may not hold. A strategy may kick in only during trending periods, or more often during high volatility, etc.
The Poisson model is very useful, but please keep in mind its limitations and assumptions, namely, that on average, you'd get the same number of trades during equal intervals.

Good luck!
You are right.. it seems that it is based on the assumption that each time period is independent and probabilistic similiar.

cheers
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