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stupid probability questions
 Updated: January 14th, 2012 (02:21 PM) Views / Replies: 7,476 / 56 Created: October 30th, 2010 (11:56 AM) by stephenszpak Attachments: 12

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# stupid probability questions

Elite Member
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stephenszpak
 I get it. I don't get it. I can see you've thought about this more than I. There have been a number of mathematicians before the mid 20th century that actually flipped a fair coin 10000 times or more. (I tried to find their actual recorded data of the flips but just can't.) Many years ago I think I saw it briefly. Anyway each coin flip in the XX,XXX total is independent of all the others, yet there were runs of >10 heads in a row and >10 tails in a row. There was no feedback, yet there were trends. - Stephen

Yes, if you build a chart with a random series, there will be trends as well. These trends are just meaningless, but they exist.

The only way to detect whether a trend is random or not, is to analyze the frequency of the individual moves and their correlation. If you do this for ES, you will get something totally different than a normal distribution. One of the first guys to do this was Mandelbrot. The fact that there are more larger moves (call it bubble or panic) thatexpected from a random series is a proof that the moves are not entirely random.

So you might build an indicator that identifies random price action versus negative or positive autocorrelation.

The fact that you can observe trends on coin flipping is contradiction with the fact that the outcome is random.

Elite Member
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Posts: 778 since Jun 2009

Fat Tails
 Yes, if you build a chart with a random series, there will be trends as well. These trends are just meaningless, but they exist. The only way to detect whether a trend is random or not, is to analyze the frequency of the individual moves and their correlation. If you do this for ES, you will get something totally different than a normal distribution. One of the first guys to do this was Mandelbrot. The fact that there are more larger moves (call it bubble or panic) thatexpected from a random series is a proof that the moves are not entirely random. So you might build an indicator that identifies random price action versus negative or positive autocorrelation. The fact that you can observe trends on coin flipping is contradiction with the fact that the outcome is random.

(Sorry I can't fully join in with you on the math stuff. I'm poor at math.)

See attachment.

Ok, assuming one bought GE stock at the peak at the far left and then sold it at the close at the far right?
Isn't a sideways stock (daily) equivalent to a lot of coin flips, with a result of about the same percentage
of heads/winners as tails/losers? (This isn't really a perfect analogy since there is variation in the closing prices,
which makes things more complicated. Like, two higher closes could be taken out by just one lower close.)

But if one traded GE during this time using a shorter term horizon, like 5 or so trading days, then one sees
trends or runs. Some groups of days are bullish, that is more heads than tails. Some groups of days are bearish,
that is more tails than heads.

To me it seems that even a sideways market, much like XXXX coin flips, has a final result of no loss or gain.
Yet there are runs of ups and downs within this zero sum area that began in mid year and went towards the end

- Stephen

Attached Thumbnails

Elite Member
Berlin, Europe

Broker/Data: Interactive Brokers
Favorite Futures: Keyboard

Posts: 9,680 since Mar 2010

stephenszpak
 (Sorry I can't fully join in with you on the math stuff. I'm poor at math.) See attachment. Ok, assuming one bought GE stock at the peak at the far left and then sold it at the close at the far right? Isn't a sideways stock (daily) equivalent to a lot of coin flips, with a result of about the same percentage of heads/winners as tails/losers? (This isn't really a perfect analogy since there is variation in the closing prices, which makes things more complicated. Like, two higher closes could be taken out by just one lower close.) But if one traded GE during this time using a shorter term horizon, like 5 or so trading days, then one sees trends or runs. Some groups of days are bullish, that is more heads than tails. Some groups of days are bearish, that is more tails than heads. To me it seems that even a sideways market, much like XXXX coin flips, has a final result of no loss or gain. Yet there are runs of ups and downs within this zero sum area that began in mid year and went towards the end of the year that a trader could have taken advantage of. - Stephen

For the coin flip, there is absolutely no connection between the 57th and the 58th coin flip. The 58th coin flip is stochastically independent from all prior coin flips. This is the main point to understand.

For a stock price, you do not have this independance. The trader/investor who enters a trade watches out what others are doing. His decision depends on the price traded as well. The whole pseudo-science of technical analysis relies on feedback. If you watch a trendline, you voluntarily rely on prior price action, so you are a feedback trader.

By design markets require that somebody purchases and somebody sells. Imbalances between buyers and sellers drive price. This game can be very similar to the random behaviour of coin flips. So this gave birth to a nice picture:

Most of the time noise traders populate the market. Their actions are compesated by the action of value traders that conmpensate for the action of noise traders. This produces a similar result to the coin flipping experiment.
However, from time to time feedback drives markets away from the trading range. During these sudden shifts, the shape of the probability distribution changes. The last candle on your chart shows such an event.

So this is the difference: The coin flips are not affected by feedback, the markets are.

Elite Member
Massachusetts (USA)

Futures Experience: None
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Posts: 778 since Jun 2009

Feedback in the markets does not necessarily mean prices move.
It is just feedback. We agree on this, correct?

Attached Thumbnails

Elite Member
Berlin, Europe

Broker/Data: Interactive Brokers
Favorite Futures: Keyboard

Posts: 9,680 since Mar 2010

stephenszpak
 Feedback in the markets does not necessarily mean prices move. It is just feedback. We agree on this, correct?

Positive feedback reinforces a price move and creates additional momentum. Trend following creates additional momentum in the direction of the prevailing trend.

Negative feedback slows a price move down and causes mean reversion. Arbitrage and pairs trading typically create negative feedback.

Noise traders are supposed to create random price moves.

My understandíng is that positive feedback typically moves price, unless it is compensated by negative feedback or random trades by noise traders, which take the opposite side. Accordingly negative feedback will move price, unless it is compensated by positive feedback or noise traders.

This is something that should not exist according to the efficient market hypothesis, even in its weaker form. But it does, as bubbles have shown throughout the centuries.

Without feedback markets would show a random behaviour, and LTCM should still be well and alive.

Elite Member
Massachusetts (USA)

Futures Experience: None
Favorite Futures: YM

Posts: 778 since Jun 2009

We might be on the same page here. Maybe we are just thinking of the
same matter with different time frames.

If one has a stock that opens at 50 and goes sideways all day and closes
at 50, to me there was positive and negative feedback, yet no change in
price. The same could be seen in the multi-month graph of GE I posted.
Of course there are multi-year graphs of whatever, out there as well.
A sideways trend, by definition, is a horizontal line. No price change,
as the end result. Positive and negative feedback didn't move the
price, even though prices moved, so to speak.

Elite Member
Berlin, Europe

Broker/Data: Interactive Brokers
Favorite Futures: Keyboard

Posts: 9,680 since Mar 2010

stephenszpak
 We might be on the same page here. Maybe we are just thinking of the same matter with different time frames. If one has a stock that opens at 50 and goes sideways all day and closes at 50, to me there was positive and negative feedback, yet no change in price. The same could be seen in the multi-month graph of GE I posted. Of course there are multi-year graphs of whatever, out there as well. A sideways trend, by definition, is a horizontal line. No price change, as the end result. Positive and negative feedback didn't move the price, even though prices moved, so to speak.

I agree with this. In the absence of external causes, such as unexpected news, sideways action can be

- either the result of random movements (noise traders)
- or the result of positive feedback being balanced by negative feedback,

or both. The interesting point about this is that probability distributions for random movements are different from those created by feedback. Time series are non-stationary. I think it is possible to measure this and use it to detect whether noise traders or feedback traders dominate.

Elite Member
Massachusetts (USA)

Futures Experience: None
Favorite Futures: YM

Posts: 778 since Jun 2009

Fat Tails
 I agree with this. In the absence of external causes, such as unexpected news, sideways action can be - either the result of random movements (noise traders) - or the result of positive feedback being balanced by negative feedback, or both. The interesting point about this is that probability distributions for random movements are different from those created by feedback. Time series are non-stationary. I think it is possible to measure this and use it to detect whether noise traders or feedback traders dominate.

Basically I have no real idea.

This might not even be possible with a highly traded stock like GE. With
GE, or any number of stocks, there are large investors involved buying and selling,
yet never trading (as far as I understand this).

If one looks at the CL, that is oil, not Colgate-Palmolive, maybe it's different.

Perhaps one could look at the amount of time it took for the price to move one tick
and also the time it stayed at the new level.

Regardless, how could one ever know what percentage of noise trades (ie. number of contracts)
or feedback trades (ie. number of contracts) resulted in a profit?

How many feedback traders looked at the CL at 11:30:00 let say, and decided to
go long as opposed to the feedback traders that at the same time decided to go short? They
all looked at the same chart, (or their trading software made an analysis with a
corresponding trade) but made the exact opposite decision, based on the exact
same feedback.

- Stephen

Attached Thumbnails

Elite Member
Berlin, Europe

Broker/Data: Interactive Brokers
Favorite Futures: Keyboard

Posts: 9,680 since Mar 2010

stephenszpak
 Regardless, how could one ever know what percentage of noise trades (ie. number of contracts) or feedback trades (ie. number of contracts) resulted in a profit?

Futures are a zero sum game, so the aggregate profit of noise, fundamentally oriented and feedback traders is zero before commissions. It is a sucker's game.

stephenszpak
 How many feedback traders looked at the CL at 11:30:00 let say, and decided to go long as opposed to the feedback traders that at the same time decided to go short? They all looked at the same chart, (or their trading software made an analysis with a corresponding trade) but made the exact opposite decision, based on the exact same feedback.

The game is designed that way that for every trade their need be a buyer and a seller. As traders can base their decisions either on new information (fundamentals), feedback (technical analysis) or irrelevant facts (nosie traders), there are exactly six possible constellations. Enjoyed your cartoon.

Elite Member
Massachusetts (USA)

Futures Experience: None
Favorite Futures: YM

Posts: 778 since Jun 2009

Probability (part 2) | Khan Academy

This is the video that proceeds it, if one wishes to start from the beginning:

Probability (part 1) | Khan Academy

Also more on coins here:

Probability using Combinations | Khan Academy

And here:

Conditional Probability and Combinations | Khan Academy

If one wants a complete study one can go here:

...and scroll down to Probability to check out the 25 or so videos available for free.

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