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Probabilities in a Random Walk (Question about one CP's post)

  • Post #1
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  • First Post: Feb 28, 2020 7:04am Feb 28, 2020 7:04am
Hi all,

I've been following Crucialpoint's posts with great interest. A lot of wisdom and useful information can be found within his writings here (not only about trading).

Now I'm trying to find information about the mathematical statement he made in one of his posts.

First, Craig posted this:

Attached Image (click to enlarge)
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And then CP replied:

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I asked a few mathematicians how to calculate these probabilities, and their replies were like "Random walk is “memoryless”. No matter how far the walker gets from the starting point, the probability stays the same."

Here is my recent conversation with one of them:

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Does anybody know how to calculate properly the probability that Craig and CP mentioned?

P.S. For CrucialPoint: If you ever read it, I want to thank you for all your posts and contribution here. Wish you all the best, and may good luck be with you in all your researches and other endeavours.
Let's go with the flow
The post quoted by Craig is indeed wrong.
A process can be non-random (=deterministic) and predictable: The position of a train running constant speed on the rail road.
A process can be deterministic and unpredictable: The Lorenz system of equation (https://en.wikipedia.org/wiki/Lorenz_system) from which comes the name "butterfly effect" (the attractor looks like a butterfly, and NO, butterflies don't provoke hurricans!)
A process can be random and unpredictable: A coin flip or the desintegration time of a radioactive atom.
A process can be random and somewhat predictable: The sum of two dice is more likely 7. The sum of 50 dice will be very likely between 150 and 200. Despite the values can go from 50 to 300.

The post by Craig is per definition a non-sense. He says "consider a stationary Gaussian random walk". This simply doesn't exist! A random walk is the text-book example of a NON-stationary process. One of the main charateritic of a non-stationary process it that it possesses NO mean. Thus there is no mean to revert to, to start with!

A Gaussian random walk is just the sum of Gaussian noise. That is a zero mean symmetric distribution (the so-called bell curve). Wherever you are on the path the next step is a value equally probably positive than negative. Because of the symmetry, each of the possible positive value has the same probability as its opposite. There is therefore exactly 50% chance to go up or down. Per construction it is independent of the path: it is memory-less.
No greed. No fear. Just maths.
Attached Image
Why is a Raven like a Writing Desk?
Quoting PipMeUp
The post quoted by Craig is indeed wrong...
Hi Pip,

Thanks for your reply!

You're saying:
Quoting PipMeUp
The post by Craig is per definition a non-sense. He says "consider a stationary Gaussian random walk". This simply doesn't exist!
But:
Attached Image

Source: https://www.investopedia.com/article...stationary.asp

I'm not strong at math, so can't argue anything right now. But I've done several thorough researches in some other fields. And within CP's posts (that are not related to trading) I have found that he has deep knowledge in those same fields as well, and his conclusions correspond to mine.

Of course, that doesn't automatically mean that all the rest of his statements are correct. But it gives me a "reference point" with high probability that Craig and CP weren't wrong. So I will continue searching for the answer assuming that the statement is true.

Also, it seems that Craig was talking about some specific simulation process and its results. Not just about some theoretical thing. So I may admit that he could be mistaken in terminology, but not in the results themselves.

Thank you for your participation anyway

Will update this thread when I find the answer.
Let's go with the flow
Actually pip up is correct. You took CP response out of context. He only bolded in red what he agreed with. He doesn’t care for random walk. That stuff is just drivel for CP. You know CP is a very intelligent person. He writes like his background involved legal processing. You imagine something as it is. But he didn’t mean it that way... you made an assumption to an otherwise direct order from him. You have to be careful with how you interpret someone like him. He always response to seemingly less intelligent posts (no offense to the writers) involving humor while simultaneously giving out the little pieces of bones of what his approach to markets are. Of course, as he said many times. If you don’t see it, you don’t have the depth. There’s certain characters that take what he says and run with it to achieve interesting results in their own quiet endeavors. With CP, have some empathy to what he is. Think of him as an accomplished guy coming from a mountain. Don’t cut him and since you haven’t been through the mountain successfully, don't throw your imagination to what the mountain is, or whatever theories you want to mesh with his. Follow his direct order and make his theories fit into your overall model of the market as a guide. He’s very selective about his wording but his themes always remain consistent. He doesn’t profit in randomness. He profits in the certainly predictable nature there is. If you can’t exploit the certainly predictable aspects of it. You clearly haven’t solved your problems and your market model is fragile. Everyone knows you can’t profit off random walks. That’s not new. But who ever said anything about random walks. It’s like fairies, if you’re told something exists repeatedly all your life, it’s just information and you’ll believe it.
Quoting Swisse
Actually pip up is correct.
Thanks for your post, Swisse! I understand what you're saying, but disagree with some points:

Quoting Swisse
He doesn’t care for random walk.
He perhaps really doesn't care about random walks, but not about randomness:

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Source: https://www.forexfactory.com/showthr...63#post6278663

Of course, you can say once again that "I have to be careful with how I interpret someone like him" But, honestly, I clearly understand what he bolded in red, and how/why it can be used in trading.
What I still don't know is what probability (in %) exactly Craig meant.

Quoting Swisse
Everyone knows you can’t profit off random walks
In reality, not everyone, of course. But I get you
Let's go with the flow
Where do you want to get with all of this??

the market IS NOT random at all !!!

there is no need for "overthinking" what is going with the price, there are clear behaviour pattern before something very specific happens

Overthink = you are NEVER eva eva gona make it in this game.. period
Hey Havo! Nice to see you here

Quoting havo
Where do you want to get with all of this?? there is no need for "overthinking" what is going with the price, there are clear behaviour pattern before something very specific happens Overthink = you are NEVER eva eva gona make it in this game.. period
Don't worry - I've already found my edge It's just my curiosity, not necessity, to find out more about the subject I'm interested in.

Quoting havo
the market IS NOT random at all !!!
I don't care about it. My system is designed as if the market was completely random. It's based on things that remain the same both in random and non-random environments.
Randomness still produces trends. I don't need anything else.

That's why I created this thread. I'm just interested to know more about the simulation mentioned by Craig. No need to look for any other hidden meanings - they are not here.
Let's go with the flow
Quoting artem_t
Hey Havo! Nice to see you here {quote} Don't worry - I've already found my edge It's just my curiosity, not necessity, to find out more about the subject I'm interested in. {quote} I don't care about it. My system is designed as if the market was completely random. It's based on things that remain the same both in random and non-random environments. Randomness still produces trends. I don't need anything else. That's why I created this thread. I'm just interested to know more about the simulation mentioned by Craig. No need to look for...
Hi artem, if you do find the probability calculation pls post here. If possible post the link to this math. TQ
Trade the value
Quoting BWilliam
{quote} Hi artem, if you do find the probability calculation pls post here. If possible post the link to this math. TQ
Hi BWilliam,

Sure, I will post when find it
Let's go with the flow
Quoting artem_t
Hey Havo! Nice to see you here {quote} Don't worry - I've already found my edge It's just my curiosity, not necessity, to find out more about the subject I'm interested in. {quote} I don't care about it. My system is designed as if the market was completely random. It's based on things that remain the same both in random and non-random environments. Randomness still produces trends. I don't need anything else. That's why I created this thread. I'm just interested to know more about the simulation mentioned by Craig. No need to look for...
In a random walk there are no trends. Point of correction. If the market is random, you can't make a penny from it.
When you see it, BET big.
Quoting Rennaissance
{quote} In a random walk there are no trends. Point of correction. If the market is random, you can't make a penny from it.
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Let's go with the flow
where is the trend?
When you see it, BET big.
Quoting Rennaissance
where is the trend?
Choose any point on the chart, everything above that point is uptrend, everything below that point is downtrend.
Look at the volatility, impressive right?

There are three players in this debt merry go round global economy.
How much global debt is there these days? Anyone know the answer?
Has anyone studied economics?

The three players are America, Europe and China.
When China is "closed for business" due to a new virus, it wreaks havoc on trade world wide.

When China opens again, where will this leave the "Peter ows Paul ows Mary" debt situation?

The only thing that is going to begin to unwind this debt spiral (and it will unwind at some stage), is if one of these 3 parties initiate the unwinding.

2020 is going to be an interesting year.
Well sir, looks like you're playing checkers at a chess match.
Quoting John.Doe
{quote} Choose any point on the chart, everything above that point is uptrend, everything below that point is downtrend.
What follows any point on a random walk is just a random path which may equally be up or down. Spurious trend is to trend what fool's gold is to precious metals.
No greed. No fear. Just maths.
  • Post #17
  • Quote
  • Edited 10:14am Mar 2, 2020 9:43am | Edited 10:14am
Quoting artem_t
Hi all, I've been following Crucialpoint's posts with great interest. A lot of wisdom and useful information can be found within his writings here (not only about trading). Now I'm trying to find information about the mathematical statement he made in one of his posts. First, Craig posted this: {image} And then CP replied: {image} I asked a few mathematicians how to calculate these probabilities,...
I cannot read the response by he mathematicians easily (font too small - could blow it up,I suppose). I can read Craig's quote from April 15 2010. I am unsure what he is asking - if it is a trick of sorts, it isn't working.

This bit - "when it gets more than two standard deviations from the mean".

What exactly is "it"? It could be ambiguous - there may be a temporal element involved with theoretically infinite possible paths in a Weiner process. This gets tricky and I'll pretend it is not relevant. This is also where Mr Bollinger takes his own interpretation on what is the mean - the mean of prices (non-stationary) rather than the change in prices (stationary - as you have shown).

Ignoring that, the chances of a (the next) point being within two standard deviations of "the mean/average" are well known to be about 95% with a normal distribution. There are about 20 or 30 other known probability distributions.. I was posting about this the other day on another gold thread.

Should that be the incorrect answer, the question needs clarification.

As to market randomness or otherwise, well that is just baiting. Edit - OK, I'll bite. Spend a few days trying to understand the Hurst exponent. Many wise words and research have and has been devoted to this.

https://en.wikipedia.org/wiki/Hurst_exponent

And that's old news. Many developments since then including stuff like chaos, and fractals credited to Dr Mendelbrot who once got into trouble with some stiffs for claiming something along the lines that variance is infinite (some folk may employ what is known as a "choppiness index" in their trading which is a VERY loose use of fractal theory - a rule of thumb kinda thing), but I digress. It all gets a bit religious and VERY mathmatical - I might try to read what the maths dudes wrote.
Quoting PipMeUp
{quote} What follows any point on a random walk is just a random path which may equally be up or down. Spurious trend is to trend what fool's gold is to precious metals.
For me a trend is a move from point A to point B, where there are more either upward or downward movement.

I remember the screenshot posted by some member here where he showed randomly generated chart. You won't tell the difference between real chart and that one.
Let's go with the flow
Quoting artem_t
{quote} For me a trend is a move from point A to point B, where there are more either upward or downward movement. I remember the screenshot posted by some member here where he showed randomly generated chart. You won't tell the difference between real chart and that one.
Yes, quite so.

However, any random generator is defined by its specified parameters. These may closely resemble financial markets. To my knowledge they haven't come up with a model that sufficiently describes financial markets.

For practical purposes, they are OK, but nevertheless cannot ever quite get there. There is evidence of weak persistence/non randomness in markets, for example.

Things get skewed (is that what Craig was alluding to? Plain vanilla overbought/oversold?) beyond what any model producing a random process defined primarily by average and standard deviation may demonstrate. Robert Plant named an album The Principle of Moments, and it was OK. That's academic. Or maybe not.
Quoting PipMeUp
Wherever you are on the path the next step is a value equally probably positive than negative. Because of the symmetry, each of the possible positive value has the same probability as its opposite. There is therefore exactly 50% chance to go up or down. Per construction it is independent of the path: it is memory-less.
That's right, innit. Here I was thinking of weird possibilities to justify the "hint" that it isn't 50% (and having now read the maths comments - the last one mirrored my confusion, seeking more information).

It matters not where you are in the scheme of things for the purposes of this exercise. Could be at the 100th standard deviation. The chances of the next step are 50/50. Those odds are perfectly predictable in the "law" of large numbers. Casinos have twigged onto this law.
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