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Random walk and Pascals triangle

  • #41
  • Aug 5, 2010 7:37pm Aug 5, 2010 7:37pm
Quoting medici
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.
I have expanded your spreadsheet to 2000 steps and correct a minor calculation error.

Anyway guys, there is one fact that we can concluded from the spreadsheet, which is the profit factor is always one no matter how you manipulate your TP/SL. Base on this conclusion, we can do a simple calculation for any TP/SL without using a pascal's triangle. Of course this is assuming a random walk.
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  • #42
  • Aug 5, 2010 9:45pm Aug 5, 2010 9:45pm
This sounds like a Quant thing. Is there anyone in this thread who is an actual Quant?
  • #43
  • Aug 5, 2010 9:54pm Aug 5, 2010 9:54pm
Yeah, a bit off topic from the main discussion.

ForexQuant, since Troikaone1 mentioned it, are you in the field of mathematical finance?
  • #44
  • Aug 5, 2010 9:58pm Aug 5, 2010 9:58pm
I am not a Quant....but I find their work to be interesting. My claim to fame is more along the lines of pattern recognition.
  • #45
  • Aug 6, 2010 1:31am Aug 6, 2010 1:31am
Quoting sqrt(-1)
Yeah, a bit off topic from the main discussion.

ForexQuant, since Troikaone1 mentioned it, are you in the field of mathematical finance?
No I am not.
  • #46
  • Edited 4:30am Aug 6, 2010 3:30am | Edited 4:30am
Quoting ForexQuant
I have expanded your spreadsheet to 2000 steps and correct a minor calculation error.

Anyway guys, there is one fact that we can concluded from the spreadsheet, which is the profit factor is always one no matter how you manipulate your TP/SL. Base on this conclusion, we can do a simple calculation for any TP/SL without using a pascal's triangle. Of course this is assuming a random walk.
With a TP of 8 and a SL of -4, if the probabilities are .5 for steps left/ right, P(TP) = 33.3% which makes sense as probs of step L/R are equal and TP is twice the distance.
But if the prob of step left is increased to just .53, P(TP)=50% ?

Thats just over 50% increase in P(TP) for just 6% increase in Prob of step to the left? Didnt expect that at all!! We have to cover twice the distance too. Is this correct and, if so, intuitive to anyone?

Im assuming the B3 cell (Prob.+1) is P(step left)
  • #47
  • Aug 6, 2010 4:37am Aug 6, 2010 4:37am
Quoting Scotty2Cues
With a TP of 8 and a SL of -4, if the probabilities are .5 for steps left/ right, P(TP) = 33.3% which makes sense as probs of step L/R are equal and TP is twice the distance.
But if the prob of step left is increased to just .53, P(TP)=50% ?

Thats just over 50% increase in P(TP) for just 6% increase in Prob of step to the left? Didnt expect that at all!! We have to cover twice the distance too. Is this correct and, if so, intuitive to anyone?

Im assuming the B3 cell (Prob.+1) is P(step left)
Yes the further your TP, the more edge you gain from a small bias. That is why High Reward Risk Ratio is always recommended.
  • #48
  • Aug 6, 2010 7:12am Aug 6, 2010 7:12am
Quoting Scotty2Cues
My main reason for all of this is to see how ev results change if SL is moved to breakeven after x number of steps. So lets assume TP at 8, SL of 2 so risk:reward = 1:4 and prob of step to left is 0.55

I was confused at first reading what you guys were talking about, but then I realized. Small biases do work in your favour, and yes, by moving the stops closer to the current price will increase SLs being hit, but ensure smaller profits when SLs is hit. How people manage this affects the yields greatly. For sheer maximization, it is better (on a per trade basis) to let the position run and not change the SL.

The issue with biases is this, how can you ensure 0.55 for a step to the left or right? It's hard to do, but that's where indicators, fundamentals, technical analysis, and trends come into play so well. My trades are mostly done by picking tops/bottoms -and yes, it can be dangerous, but RSI correlates so well with the movement of a pair that I wouldn't be surprised if historical probabilities garner 0.60-0.90 under given conditions of average price runs on certain timeframes.
  • #49
  • Aug 6, 2010 7:21am Aug 6, 2010 7:21am
Also, too often do humans mistake probabilities to be true when in fact conditional probabilities must be considered. With this notion, we can utilize forex system's apparent success rates (like swing trading, fibonacci, elliot wave) and determine different forex system pairings, triplets (or quadruplets) to increase our success rate of a new system. As we include more systems to consider, the chances that system A, B, and C exist decrease, but the success rate should in theory increase given the sets are not disjoint (which is true).
  • #50
  • Aug 6, 2010 7:51am Aug 6, 2010 7:51am
Seems like moving SL to BE seems to reduce profits over time. Also if we always risk x% of account, for a given TP, profits will increase, the closer SL is to starting point as the increase in money per step seems to more than compensate the increased chance of getting stopped out?

This is assuming a slight, constant bias in the TP direction.
  • #51
  • Edited 8:40am Aug 6, 2010 8:22am | Edited 8:40am
Quoting sqrt(-1)
Also, too often do humans mistake probabilities to be true when in fact conditional probabilities must be considered. With this notion, we can utilize forex system's apparent success rates (like swing trading, fibonacci, elliot wave) and determine different forex system pairings, triplets (or quadruplets) to increase our success rate of a new system. As we include more systems to consider, the chances that system A, B, and C exist decrease, but the success rate should in theory increase given the sets are not disjoint (which is true).
When i tried to extract a probability of a certain events from a chart, I do not consider the impact on other condition. Who care about the other condition when you have P(win) of 60% with RRR = 1.

Further more, the more condition you put into consideration, the more likely you are going to curve fit your result. It is same like how people put dozen of parameter into their trading plan, you risk over optimization.

Even if you just have another one condition, it will complicated the calculation because they are not a mutually exclusive (Mostly). So P(Condition A win OR Condition B Win) = P(Condition A win) + P(Condition B win) - P(Condition A Win AND Condition B Win).

Imagine you have more conditions to be considered, the above equation will be much more complicated. Futher more P(Condition A Win AND Condition B Win AND so on...) could be very small therefore you will need a huge sample size to confirm its validity.
  • #52
  • Edited 9:26am Aug 6, 2010 9:10am | Edited 9:26am
As my trading is highly discretionary and not based on any quantitative system, my risk management approach is a bit more practical, and I evaluate things based on my own trading record. Here's a few observations.

While a high RRR is desirable, setups for such trades are less frequent, so there's a point to not being too ambitious with the RRR. A bit more than one should be enough, and I tend to be happy with 1.5+.

Risking less than 5% per trade seems like a waste of opportunities. The risk level is, more than anything, a psychological matter as long as your equity volatility isn't too high.

RRR, risk level and win rate come together in the Kelly ratio, which is a good measure of the stability of your strategy/method. Many quant traders trade at half Kelly, but for discretionary trading that is a bit too much - for my nerves at least.

A win rate of 2/3, 5% risk per trade, and RRR at 1.5 with two trades a day gives an account growth rate of 6.4% per day. The Kelly ratio would be 44% but 22% per trade is out of the question for me. Instead I take more than two trades a day and catch the occasional runner.

Also, I do take longer term trades when the setup is right.

Last but not least, moving the stop to BE tends to cut more winners than losers if your win rate is higher than 0.5, so not recommended for other than longer term trades. This depends on your entry technique, however. For example, if you do momentum entries, moving stop to BE makes sense, whereas if you trade reversals it doesn't.
  • #53
  • Edited 9:42am Aug 6, 2010 9:25am | Edited 9:42am
Quoting sqrt(-1)
Originally Posted by Scotty2Cues
My main reason for all of this is to see how ev results change if SL is moved to breakeven after x number of steps. So lets assume TP at 8, SL of 2 so risk:reward = 1:4 and prob of step to left is 0.55
It seems like you deleted your post. Could you please post again how you calculate because I have just gone thru a calculation with your method but too bad I cant remember the detail. I think my spreadsheet cannot be used for trailing stop with based on your idea because some paths are not permissible in trailing stop situation. I need you to post it again so that I can double confirm.
  • #54
  • Edited 9:54am Aug 6, 2010 9:42am | Edited 9:54am
Quoting medici
As my trading is highly discretionary and not based on any quantitative system, my risk management approach is a bit more practical, and I evaluate things based on my own trading record. Here's a few observations.

While a high RRR is desirable, setups for such trades are less frequent, so there's a point to not being too ambitious with the RRR. A bit more than one should be enough, and I tend to be happy with 1.5+.

Risking less than 5% per trade seems like a waste of opportunities. The risk level is, more than anything, a psychological matter...
I am not sure about other but half kelly is too risky for me because market may change and no trading system has a static outcome, even it is a quantitative model.

For example, a profitable system with P(win) = 50% and RRR = 2 will have an optimum kelly bet size of 25%. What if the system begins to fail or perform poorly, say P(win) = 40% and RRR maintain at 2? The optimum kelly bet size will drop instantly to 10%. If P(win) drop further to 35% then the optimum kelly bet size will be only 2.5%!

Personally I only bet 5% of fully kelly for my quant model but that is just me.
  • #55
  • Aug 7, 2010 4:23am Aug 7, 2010 4:23am
Quoting ForexQuant
It seems like you deleted your post. Could you please post again how you calculate because I have just gone thru a calculation with your method but too bad I cant remember the detail. I think my spreadsheet cannot be used for trailing stop with based on your idea because some paths are not permissible in trailing stop situation. I need you to post it again so that I can double confirm.

Its not for TS just for moving SL to BE. Say we have an initial SL of 4 and a TP of 8 and decide to move SL to BE if we move 4 steps to left. I then use your chart with SL of 4 (BE) and TP of 4 although the reward is still the same. Without move to BE, if we assume step to left has prob 0.55 with initial Risk:Reward of 1:2 then

EV = -0.394 + 0.606*2 = 0.818

with move to BE:

EV = -0.309 + 0.691*(0.691*2-0.309*0) = 0.646

so we lose money in the long run by moving to BE
  • #56
  • Aug 7, 2010 4:44am Aug 7, 2010 4:44am
Quoting medici
As my trading is highly discretionary and not based on any quantitative system, my risk management approach is a bit more practical, and I evaluate things based on my own trading record. Here's a few observations.

While a high RRR is desirable, setups for such trades are less frequent, so there's a point to not being too ambitious with the RRR. A bit more than one should be enough, and I tend to be happy with 1.5+.
I'm happy with 1:1 to 1:2.


Quoting medici
Risking less than 5% per trade seems like a waste of opportunities. The risk level is, more than anything, a psychological matter as long as your equity volatility isn't too high.
I guess lots of experience and a very high success rate would be needed before risking more than 5%?


Quoting medici
RRR, risk level and win rate come together in the Kelly ratio, which is a good measure of the stability of your strategy/method. Many quant traders trade at half Kelly, but for discretionary trading that is a bit too much - for my nerves at least.

A win rate of 2/3, 5% risk per trade, and RRR at 1.5 with two trades a day gives an account growth rate of 6.4% per day. The Kelly ratio would be 44% but 22% per trade is out of the question for me. Instead I take more than two trades a day and catch the occasional runner.

Also, I do take longer term...
6.4% per day

Quoting medici
Last but not least, moving the stop to BE tends to cut more winners than losers if your win rate is higher than 0.5, so not recommended for other than longer term trades. This depends on your entry technique, however. For example, if you do momentum entries, moving stop to BE makes sense, whereas if you trade reversals it doesn't.
For momentum entries, do you mean using buy/sell stop orders instead of limit orders. I always use stop orders as I thought it gave me a greater chance to get my stop to BE, but now playing around with figures makes me question the BE move.

I never intend to use the random walk when placing trades. It was to give me a feel for the BE move and to explore different SL with the same TP using the same account risk. Do you think it is an accurate assumption that if the market sentiment is in one direction then we can assign a constant probability to a step left/right over the short term?
  • #57
  • Aug 7, 2010 4:56am Aug 7, 2010 4:56am
An idea I had with the BE move was to get another bite of the cherry.

Before looking into the random walk, I liked to use the BE move because I thought it enabled me to use a smaller SL than what seemed to be recommend as I get a bigger position size.

If I got stopped out at BE, depending on the dynamics, another order was going to be placed, giving me another shot. Havent tried it yet though...
  • #58
  • Aug 7, 2010 5:30am Aug 7, 2010 5:30am
Quoting Scotty2Cues
I'm happy with 1:1 to 1:2.



I guess lots of experience and a very high success rate would be needed before risking more than 5%?
Indeed.

Quote


For momentum entries, do you mean using buy/sell stop orders instead of limit orders. I always use stop orders as I thought it gave me a greater chance to get my stop to BE, but now playing around with figures makes me question the BE move.

It could mean entry by limit order, but that's not what I had in mind. A manual entry enables you to fine-tune the timing better.

As an example, take a look at a 1 minute or tick chart for sterling at 2.45 London time yesterday. Clear evidence of persistent buying over the past half hour, and the R1 level at 1.5936 had turned into support where buying continued. A thrust upwards could be expected, so if you bought at 2.45 with 5% for 7 pips you stood to make more than 35% on margin at 5% risk over the next 20 minutes or so.

Quote


I never intend to use the random walk when placing trades. It was to give me a feel for the BE move and to explore different SL with the same TP using the same account risk. Do you think it is an accurate assumption that if the market sentiment is in one direction then we can assign a constant probability to a step left/right over the short term?

I wouldn't use a random walk model to guide me in my trading. Or, quoting one of my old maths professors, "probability theory is a lot of non-sense. The probability of something happening is either 0 or 1, but you may not know which!" Differently put, probability theory provides models that may be useful, but be careful in concluding that the underlying reality is random. For more about that see my recent post here: http://www.forexfactory.com/showpost...9&postcount=10
  • #59
  • Aug 7, 2010 5:45am Aug 7, 2010 5:45am
Quoting Scotty2Cues
An idea I had with the BE move was to get another bite of the cherry.

Before looking into the random walk, I liked to use the BE move because I thought it enabled me to use a smaller SL than what seemed to be recommend as I get a bigger position size.

If I got stopped out at BE, depending on the dynamics, another order was going to be placed, giving me another shot. Havent tried it yet though...
In my experience not a workable strategy. By moving stop to BE too early you stop out many winners, which won't give you "another shot", whereas the "second shots" provided will be mostly losers.
  • #60
  • Aug 7, 2010 3:25pm Aug 7, 2010 3:25pm
Quoting Scotty2Cues
Its not for TS just for moving SL to BE. Say we have an initial SL of 4 and a TP of 8 and decide to move SL to BE if we move 4 steps to left. I then use your chart with SL of 4 (BE) and TP of 4 although the reward is still the same. Without move to BE, if we assume step to left has prob 0.55 with initial Risk:Reward of 1:2 then

EV = -0.394 + 0.606*2 = 0.818

with move to BE:

EV = -0.309 + 0.691*(0.691*2-0.309*0) = 0.646

so we lose money in the long run by moving to BE
P(Hit TP) = 47.7%
P(Hit BE) = 21.4%
P(Hit SL) = 30.9%
P(Hit TP or BE or SL) = 47.7 + 21.4 + 30.9 = 100%

So I think your logic works and the calculation is correct.
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