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Random walk and Pascals triangle

  • #21
  • Aug 4, 2010 5:04pm Aug 4, 2010 5:04pm
Quoting sqrt(-1)
How will you be able to obtain P(stopped out) or P(take profit) without using historical data of walks for pinbars at a swing high? Mere deviation from a central price based on probabilities of random walks? I like the idea, but forex isn't random, it isn't like flipping a coin. GBP/USD has run up ~1500 pips from the low a few months ago. We can examine the random probability of it doing this, and the odds are very small by random (given p,q=50%), but as you know, historically the pair has moved this much and more in the past. This is how we know...
In practice the probabilities are, more than anything, dependent on your entry rules/technique. So the only way to get statistics useful for risk assessment/management is from you own trading record.
  • #22
  • Aug 4, 2010 5:33pm Aug 4, 2010 5:33pm
Quoting Scotty2Cues
can you give some theory plz?
Theory for which part? I thought that is just an application of pascal triangle, nothing new.
  • #23
  • Aug 4, 2010 6:08pm Aug 4, 2010 6:08pm
Quoting medici
In practice the probabilities are, more than anything, dependent on your entry rules/technique. So the only way to get statistics useful for risk assessment/management is from you own trading record.
I agree, we can also apply back-tests to theoretical entries as well. For example, when an indicator reaches a certain level.
  • #24
  • Aug 5, 2010 3:01am Aug 5, 2010 3:01am
Quoting ForexQuant
Theory for which part? I thought that is just an application of pascal triangle, nothing new.
How did you come up with the figures; did you count paths or something else? I couldnt come up with a formula and as Medici stated, Pascals triangle may not be the best route
  • #25
  • Aug 5, 2010 3:11am Aug 5, 2010 3:11am
Quoting sqrt(-1)
How will you be able to obtain P(stopped out) or P(take profit) without using historical data of walks for pinbars at a swing high? Mere deviation from a central price based on probabilities of random walks? I like the idea, but forex isn't random, it isn't like flipping a coin. GBP/USD has run up ~1500 pips from the low a few months ago. We can examine the random probability of it doing this, and the odds are very small by random (given p,q=50%), but as you know, historically the pair has moved this much and more in the past. This is how we know...
I was going to get P(stopped out) or P(take profit) once I inputted the probabilities for a step to the left/right P(step right) = 1 - P(step left).

So if I got the direction of the trend correct P(step right) would not equal P(step left) and I was looking at how different values of SL/TP affects ev calculations. I was then going to include a move to breakeven after x amount of steps:

EV = -risk*P(Stopped out before moving SL to BE) + P(SL to BE after x steps)*P(TP)*reward

compared to not moving SL to BE:

EV = -risk*P(Stopped out) + reward*P(take profit)
  • #26
  • Aug 5, 2010 3:47am Aug 5, 2010 3:47am
Quoting Scotty2Cues
How did you come up with the figures; did you count paths or something else? I couldnt come up with a formula and as Medici stated, Pascals triangle may not be the best route
You can see the formula used by simply clicking on a cell or hit F2 to see the formula displayed in the cell.

I had a look at the spreadsheet and it simply calculates the proportion of all paths that end up at a certain level. It doesn't take the TP/SL into account, i.e. that some paths are not permissible, so the calculations don't seem related to your original question.
  • #27
  • Aug 5, 2010 8:09am Aug 5, 2010 8:09am
Quoting medici
You can see the formula used by simply clicking on a cell or hit F2 to see the formula displayed in the cell.
DOH!

Quoting medici
I had a look at the spreadsheet and it simply calculates the proportion of all paths that end up at a certain level. It doesn't take the TP/SL into account, i.e. that some paths are not permissible, so the calculations don't seem related to your original question.
Agreed. FQ has just used thae standard random walk model. So the method allows the SL to be hit more than once in n steps which is what I tried to avoid
  • #28
  • Aug 5, 2010 8:50am Aug 5, 2010 8:50am
Quoting medici
You can see the formula used by simply clicking on a cell or hit F2 to see the formula displayed in the cell.

I had a look at the spreadsheet and it simply calculates the proportion of all paths that end up at a certain level. It doesn't take the TP/SL into account, i.e. that some paths are not permissible, so the calculations don't seem related to your original question.
Which paths are not permissible? if you dont mind pls let me know.
  • #29
  • Aug 5, 2010 8:54am Aug 5, 2010 8:54am
Quoting ForexQuant
Which paths are not permissible? if you dont mind pls let me know.
For example, in a triangle of size 20, if the SL is -6, then the path that first goes -12 and then +8 ends up at -4 but has actually hit the -6 level before arriving at -4.
  • #30
  • Aug 5, 2010 9:07am Aug 5, 2010 9:07am
Quoting Scotty2Cues
DOH!



Agreed. FQ has just used thae standard random walk model. So the method allows the SL to be hit more than once in n steps which is what I tried to avoid
I sum it up does not mean my method allow SL to be hit more than once. In fact the SL can be only hit once.

For example,

Event A: Hit TP at Step 1
Event B: Hit TP at Step 2
Event n: Hit TP at Step n

All those events are mutually exclusive. So P(A or B or n) = P(A) + P(B) + P(n)

I may not understand your question properly but the pascal triangle managed to solve a similar problem in one of the thread here. This solution is proven by 2 other members by using a monte carlo simulation and brute force simulation.
  • #31
  • Aug 5, 2010 9:14am Aug 5, 2010 9:14am
Quoting medici
For example, in a triangle of size 20, if the SL is -6, then the path that first goes -12 and then +8 ends up at -4 but has actually hit the -6 level before arriving at -4.
No, if the TP is +6 and SL is -2 then my excel sheet does not allow it to touch -12 or +8. Any path above TP and below SL are not taken into consideration.
  • #32
  • Aug 5, 2010 9:56am Aug 5, 2010 9:56am
Quoting ForexQuant
No, if the TP is +6 and SL is -2 then my excel sheet does not allow it to touch -12 or +8. Any path above TP and below SL are not taken into consideration.
you have to do a new one each time you change sl/tp
  • #33
  • Aug 5, 2010 10:09am Aug 5, 2010 10:09am
Quoting ForexQuant
No, if the TP is +6 and SL is -2 then my excel sheet does not allow it to touch -12 or +8. Any path above TP and below SL are not taken into consideration.
Just had a closer look at your spreadsheet after solving the problem on my own and discovered that we ended up with the same solution!

So my earlier glance at your file was a bit too quick. Your spreadsheet does the trick. Apologies...
  • #34
  • Aug 5, 2010 10:19am Aug 5, 2010 10:19am
Quoting Scotty2Cues
you have to do a new one each time you change sl/tp
just copy & paste. It is not a difficult job.
  • #35
  • Aug 5, 2010 10:20am Aug 5, 2010 10:20am
Quoting medici
Just had a closer look at your spreadsheet after solving the problem on my own and discovered that we ended up with the same solution!

So my earlier glance at your file was a bit too quick. Your spreadsheet does the trick. Apologies...
Apologies accepted.
  • #36
  • Aug 5, 2010 10:47am Aug 5, 2010 10:47am
Quoting Scotty2Cues
you have to do a new one each time you change sl/tp
Actually you don't. I modified the original spreadsheet to handle varying TPs and SLs as well as varying probabilities for an 'up' move.

The triangle is of size 8 only, for the sake of illustration. You get the probabilities of hitting SL/TP on the bottom line.

One could implement the same in VBA using objects and recursive functions, but I don't quite have the energy today.
Attached File(s)
File Type: xls Random walk and Pascals triangle R1 -modified.xls   24 KB | 374 downloads
  • #37
  • Aug 5, 2010 10:52am Aug 5, 2010 10:52am
Many thanks people!
  • #38
  • Aug 5, 2010 5:21pm Aug 5, 2010 5:21pm
medici, if the initial condition is that the position moves "up", shouldn't step one be 100% for +1R, instead of 50%? Maybe I'm not understanding exactly what you're doing, but your excel spreadsheet is valid only for a trade where step 1 is "up", SL= -2R, and TP=+6R. A new one must be made or modified if SL/TP changes -right now, changing your TP to +7 means it would never be hit...but as we know there is one path after 8 iterations to achieve +7 and it is if there is no "down step", this would occur at step 7 and the probability is 0.5^7=0.0078=0.78%.

Note... If there confusion, try and think of a path where +7R is hit in 8 iterations or <7 iterations. You can't reach +7 with less than 7 steps, and 8 iterations would require a retrace, but then that gives you n-1 "up" steps and you would only reach +6, or if there is no retrace, you would achieve +8R, but the position would have been closed at +7.

Quote
you have to do a new one each time you change sl/tp
  • #39
  • Aug 5, 2010 5:50pm Aug 5, 2010 5:50pm
Quoting sqrt(-1)
medici, if the initial condition is that the position moves "up", shouldn't step one be 100% for +1R, instead of 50%? Maybe I'm not understanding exactly what you're doing, but your excel spreadsheet is valid only for a trade where step 1 is "up", SL= -2R, and TP=+6R. A new one must be made or modified if SL/TP changes -right now, changing your TP to +7 means it would never be hit...but as we know there is one path after 8 iterations to achieve +7 and it is if there is no "down step", this would occur at step 7 and the probability is...
Not sure I understand what you are trying to say. What do you mean by "initial condition" for example. And that the spreadsheet should be valid for 6/-2 only doesn't seem right, as it gives identical numbers as FQ's for 6/-6. Could you please clarify?
  • #40
  • Aug 5, 2010 6:01pm Aug 5, 2010 6:01pm
Quoting medici
Not sure I understand what you are trying to say. What do you mean by "initial condition" for example. And that the spreadsheet should be valid for 6/-2 only doesn't seem right, as it gives identical numbers as FQ's for 6/-6. Could you please clarify?
What I mean by initial condition is that your first move must be "up". That is, you open a position and then the first step (1) is to the left. Is that what you meant by...

Quote
I modified the original spreadsheet to handle varying TPs and SLs as well as varying probabilities for an 'up' move.

...?

Otherwise, I'm unsure what your spreadsheet represents, could you please explain what you mean by that?

Probabilities should be the same for most, but think about this. If have a SL at -2R then there is less of a chance that the position may return to some arbitrary TP relative to a SL set at -5R. The position may run to -3R and back to your TP, that is one path that the condition where you're stopped out at SL=-2R doesn't have, and hence a greater probability should be accounted for.
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