Do you see patterns in Random Walks?

I am sorry, you probably meant prices are random and they are normally (bell shape curve) distributed? Because the way you wrote it there is no possible answer to it. However, if you accept my rephrasing of your question the answer is:

Q: Is the price-time series a very efficient stochastic (random) process?

A: Absolutely YES!

Q: Is this "random" (stochastic) process normally distributed in price-time space?

A: Absolutely NOT!

I hope I answered your question.

Cheers;
MAESTRO

 

Yeah. I meant the distribution of price changes being normal, like a random distribution of coin flip outcomes.

Interested in your current opinion of RTM strategies.

 

Please explain exactly what you are interested in. I will try my best to share the knowledge. However, I apologize ahead of time; I will only be able to share non-sensitive info that my company allows me to share.

Cheers,
MAESTRO

 

It is my current opinion that all RTM strategies either do not work, are too risky, are too sensitive to design and/or execution mistakes, produce very low returns on capital or all of the above.

Of course then I'm biased towards away-from-the-mean trading strategies.

I want to read what you think about this.

 

The concept of regression comes from genetics and was popularized by Sir Francis Galton in the late 19th century with the publication of “Regression Towards Mediocrity in Hereditary Stature”. Galton observed that extreme characteristics (e.g., height) in parents were not fully passed on to their offspring. Rather, the characteristic in the offspring regressed towards a mediocre point (a point which has since been mathematically shown to be the mean). By measuring the heights of hundreds of people, he was able to quantify regression to the mean, and estimate the size of the effect. Galton wrote that, "The average regression of the offspring is a constant fraction of their respective mid-parental deviations." This means that the difference between a child and her parents on some characteristic was proportional to her parents’ deviation from typical people in the population. So if her parents were each two inches taller than the averages for men and women, on average she would be shorter than her parents by some factor (which today we would call one minus the regression coefficient) times two inches. For height, Galton estimated this correlation coefficient to be around 2/3: the height of an individual will center around 2/3rds of the parents deviation.
Although Galton popularized the concept of regression, he fundamentally misunderstood the phenomenon; thus, his understanding of regression differs from that of modern statisticians. Galton's was correct in his observation that the characteristics of an individual are not fully determined by their parents; there must be another source. However, he explains this by arguing that, "A child inherits partly from his parents, partly from his ancestors. Speaking generally, the further his genealogy goes back, the more numerous and varied will his ancestry become, until they cease to differ from any equally numerous sample taken at haphazard from the race at large. In other words, Galton believed that regression to the mean was simply an inheritance of characteristics from ancestors that are not expressed in the parents; he did not understand regression to the mean as a statistical phenomenon. In contrast to this view, it is now known that regression to the mean is a mathematical inevitability: if there is any random variance between the height of an individual and parents (providing the correlation is not exactly equal to 1) then the predictions must regress to the mean regardless of the underlying mechanisms of inheritance, race or culture.

It is very interesting that Galton missed the true meaning of the mean reversion and yet he came up with a device that demonstrates this principle with an amazing clarity. Galton’s “Bean Machine” that is also known as “Galton Box” consists of a vertical board with interleaved rows of pins. Balls are dropped from the top, and bounce left and right as they hit the pins. Eventually, they are collected into one-ball-wide bins at the bottom. A small demonstration of a Galton’s Box could be viewed by clicking on this link Galton’s Box .

Aside of vividly demonstrating the principle of regression to the mean the Galton’s Box provides an analogue proof that a normal mixture of normal distributions was itself normal! It, of course, was a stroke of genius. It was perhaps the most important breakthrough in statistics in the last half of the nineteenth century.

Mean reversion theory has been used to create market trading strategy for many years. Typically, the trading algorithms that are based on mean reversion suggest that prices and returns eventually move back towards their mean or average. This mean or average can be the historical average of the price or return or another relevant average such as the growth in the economy or the average return of an industry. This theory has led to many investing strategies involving the purchase or sale of stocks or other securities whose recent performance has greatly differed from their historical averages. However, a change in returns could be a sign that the company no longer has the same prospects it once did, in which case it is less likely that mean reversion will occur. More so, in the event of drastic market price moves caused by discussed above “flocking behavior” or “spontaneous synchronization” mean reversion might lead to significant losses as that reversion might not occur for a long period of time.

 

Although reversion to the mean is probably one of the most fundamental and stable observations of the stock market behaviour no known reliable trading algorithms exploiting this phenomenon were developed to date. Our breakthrough in this respect, we believe, is the first successful practical trading algorithm that utilizes reversion to the mean phenomenon with consistent positive expectations. Of course, as everything that is practical and efficient our invention is surprisingly simple and intuitively acceptable. Below is the summary of principles that we have used:

• Most of significant market moves caused by the phenomenon of “Spontaneous Synchronization” where the prices move irrationally too far and too fast creating stable “panic feedbacks” that ensure that the price volatility sustains. Those moves increase “price inertia” and make position of the price center of gravity fairly stable

• Price movements involve collectives of traders that behave like large synchronized flocks. In these flocks the average distance between the flock members and the flock’s center of gravity remains fairly stable.

• Flock’s center of gravity normally moves in a pattern that vividly exhibits inertia properties of a flock.

• Subconsciously observing the movements of the price center of gravity market participants synchronously anticipate its next position and place their bets with this observation in mind thus forcing the price to move towards the projected position of the flock’s center of gravity.

• Natural cubic splines calculated on a sequence of consecutive center of gravity positions create a very reliable expectation of the next center of gravity location in terms of price/time space.

 

So basically what you are saying is that your method trades away from the "old mean" to the predicted "new mean", in a way following the herd/flock as they move the price in time?. Like trend following, but better.

 

In a very simplistic way - YES. In practice, you need to convert your space (normalize it) to be able to do the efficient RTM.

 

So for the exit, do you get out at the predicted mean, or try to guess the meander, or a little of both?.

 

Apart from philosophy, keep in mind that

"the market can refrain from reverting to the mean for longer than you can remain solvent".