My observation isn't scientific but its simple logic. If markets were random, then why do then go down faster than they go up? The reason is because they sell off on fear and rise on hope. Fear is a more powerful emotion than hope.

... this is a revelations or observations ..? ..of course are not random

If we knew the intensions of big institutions, all randomness would go away.

Interesting article summarizing important academic results. The obvious next step after rejection of the random walk hypothesis is the estimation of expected stock market returns. This is now a central issue in financial economics from both theoretical and applied standpoints (the classic random walk paradigm assumes expected market returns are constant implying nil return predictability, while the increasingly accepted time-varying expected return paradigm implies some predictability must exist).

Here are some references related to the question of return predictability (within the linear predictive regression framework using several economic predictors): see for instance Stambaugh, 1986; Pesaran and Timmermann, 1995; Stambaugh, 1999; Goyal and Welch, 2008; Lettau and van Nieuwerburgh, 2008; Rapach, Strauss, and Zhou, 2010.

@Jacques, thanks for bringing up this great article. Excellent coverage of the subject.

What struck me was: “In particular the variance ratio test they defined is not applicable to models of heteroskedasticity from the Pareto-Levy family ”. And I think stock prices are more Paretian than Gaussian.

What the author's tests show is that definitely stock prices do not follow a Gaussian distribution to a t, or should we say to a z (z*-score).

When you analyze a set of price series, it is easy to obtain all the statistics from the bunch. But whenever you use the same stats and same characteristics to rebuild time series you are in effect cloning a process and lose some information from the original data. Things like fat tails if you use a Gaussian distribution model. It will not see 10 or 20-sigma moves, as they are too highly improbable. Yet, you will see them in stocks a lot more frequently than what their stats suggests. Hence a Pareto like distribution.

@Maxime nailed it with: “...The obvious next step after rejection of the random walk hypothesis is the estimation of expected stock market returns. This is now a central issue...”. Yes.

However we try to classify and generalize on stock price movements, they come in so many varieties that they become hard to predict especially on the short term where there is so much “quasi-random” market noise. What is the probability of a risk/reward before undertaking a trade? What is the probability of a profit if the expected value of the price movement has for expected value zero? E[p(t+1)] = p(t).

Is: P(E[Δp > x]) really > 0.50 ? if E[Δp] → 0

You need a price movement, a Δp > 0, to make a profit. We need to identify when and how often it might happen, and then we need a trading strategy to extract these Δp > 0.

@Alex, when you say: “The fact that you don't understand the nature of things doesn't make them random.” Who are you referring to?

And when you say: “I am glad that eventually I've found someone else who thinks the same way as I've been trying to promote during the past decade.” Again, who would you be referring to?

Because if it was @Allan, I would not consider it the best of choices.

Guy, "you" in this context is an impersonal sentence. At least I thought it was possible to say this way in English. And my second remark was simply about the authors of the paper.

@Alex, an impersonal “you”, means all. Which would mean that as you expressed: “The fact that you don't understand the nature of things doesn't make them random.” would be the same as all do not understand ...the nature of things... I find it, how could I say: une exagération.

@Aurel, the EMH is just that: an hypothesis.

And markets become efficient if there is no arbitrage, if you can't extract a profit. And inefficient if you can.

In that sense, if: E[p(t+1)] – p(t) → 0 it would be a sufficient condition. But when you change the time frame, things change a little: E[p(t+d)] – p(t) might tend to zero, and not will tend to zero as d increases. The expression says that as you increase the time interval (t+d), zero might still be an attractor, but the variance is spreading the outcome away from it. Zero might be the most likely, but its occurrence level reduces to minimal levels as time increase, meaning as d increases.

If you look at stock prices, in general: E[p(t+d)] – p(t) ≠ 0, when d is large, it is most likely far away from p(t). Which makes |E[p(t+d)] – p(t)| > 0.

And therefore, in all probability, |E[Δp]| > 0, meaning that there is a profitable trade to be made, on average.

@Guy..same coment I made on other post . .the market is made up of Tier 1,2,3 banks, central banks, corporations (not necessarily trading but making multi million dollar deal, paying employees etc,) hedge funds, institution, brokers, government policy, . .however the behavior of price is predictable, the way it acts, i dont know what price will be tomorrow, but why is it that we trade? because there are certain patterns, and price does have direction according to investor sentiment. a bullish trend is made up of an environment where buy orders are more prevalent correct? that is why i attempt to follow the flow in the fix candle size and price not any time frame or Chart SL .. .. :) Thanks and have a nice weekend

In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (1962–1985) and for all subperiods for a variety of aggregate returns indexes and size-sorted portfolios. Although the rejections are due largely to the behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or time-varying volatilities. Moreover, the rejection of the random walk for weekly returns does not support a mean-reverting model of asset prices.

Oxford University Press

http://rfs.oxfordjournals.org/content/1/1/41.short

Jacques asked me to take a look at the comments, thanks for the feedback!

@Guy I would agree with most of the discussion here. My only correction would be that "What the author's tests show is that definitely stock prices do not follow a Gaussian distribution to a t, or should we say to a z (z*-score)." is not accurate. The test extends to all finite-variance models of stochastic volatility which contain outliers. As such, even if the return series had 20+ sigma events, if the increments in the return series are uncorrelated then the variance ratio should asymptotically approach zero because "This is because the variance of the sum of uncorrelated increments must still equal the sum of the variances.". This is no ordinary Gaussian test, hence the z* not z notation.

@Alex " The fact that you don't understand the nature of things doesn't make them random. Same with markets." This is so true. Couldn't agree more!

A robust trading strategy should not include any assumptions about the underlying return distribution of the security being traded.

Can I get: |Δp| > 0 from point t (going forward)? Can I get: |E[p(t+d)] – p(t)| > 0? Can I predict with high probability that the difference in price will be meaningful enough to trade on? How large should d be to make it into a trading strategy with a higher hit rate than 0.50?

I like the payoff matrix notation: Σ(H.*ΔP) to describe the output of any trading strategy. In vector form: Σ(n)(q*Δp), representing the sum of all profits and losses generated by a trading strategy over all its n trades.

Some would like to have a global understanding of the nature of price movements. Sure, if they want to trade short term, they should have some basis as to what could trigger a trade whatever it may be. Accepting quasi-randomness would be self-defeating. It would turn out into a debate having for core: my nickel is better than your nickel which in turn would transform their respective trading strategies into Gaussian plays.

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I go for the quasi-random stuff for the simple reason that I can not know, nor could I aggregate, the expectancy of the output of all the millions and millions of participants in the market with their respective trading strategies (machine or human driven) being applied in real time and on a daily basis. All I can observe is their global output continuously reflected in stock prices and at most react to price variations whatever their nature may be.

Notwithstanding, whatever the distribution, what is important is: Σ(H.*ΔP), the trading strategy that will be applied going forward, on whatever basis it may be. And it has to be not only positive: Σ(H.*ΔP) > 0, but also outpace its benchmark: Σ(H.*ΔP) > Σ(H(S&P500).*ΔP) over the long term. Otherwise, one should consider buying index funds.

It is hard avoid over fitting when modeling the markets, and false conclusions are hard to avoid. It is at the implementation stage that theory differs from practice.

When you are investing other people's money you are not free to do anything you would like with it. Traditional investors will not thank you if you engage in high frequency trading, whereas re-balancing on a slower time scale is subject to event risk, e.g. if war breaks out, or central bank intervene unexpected losses will occur.

At one level, as a finite state Turing machine, the markets may not be random, but when push comes to shove, given the actual constraints that real life circumstances bring to the situation, often changes the rules of the game.

Note I didn't say you cannot make money, just that in my own experience, certain models work for a while before a switch in regime forces one to re-think.

Read the article and read all of the comments up to this point. I believe in simplicity, others in this forum do not. I believe portions of the market are absolutely not random and other portions (collectively) are. I think it is important to recognize this, understand the differences and the uniqueness of the opportunities these points give each of us.

I also find humor in that some people will step in dog poop, remove their shoe and spend months (if not years) evaluating the content of the poop instead of just saying . . . yuck . . . clean it off and move forward. #mydryhumorfortheday

Stock market are definitely not random. I applied deep learning on data gathered in several months for the italian stock market (all the single transactions) and in a short frame - say 5-30min - you can make a little better than a coin toss. Say 52-54% of "correct" trades, that is with gains >= 0. Not enough to balance for transation costs and make a viable trading system but this proves that market is not completely random. This has been tested with many stocks, with different combinations of training/validation periods, with different methods and even timeframes and with big quantities of data, so the results seems pretty robust.

http://www.safetrade.in/Home/ArticleReader?ArticleID=IsStockMarketGamble

@Marco, as you say: Yes, not completely random.

But sufficiently random to show that the small edge you got was not even enough to cover frictional costs.

If short term price movement were not so “quasi-random”, as I've said before, one could extract a worthwhile predictable edge with ease, at least enough to cover frictional costs and then some.

Here is a chart I've shown before. It depicts the origin of profits depending on the trading interval. Notice that on the short term, most of the price movement is due to randomness, but it is the long term trend that prevails in the end.

http://alphapowertrading.com/images/divers/SDE_long_term.png

People often misunderstand (and misuse) the term "random" when they mean chaotic or more commonly that they simply haven't captured a deterministic effect in their model of an outcome (market returns) that are often the result of irrational (and unknown) human decisions.

Dwayne is absolutely correct. Just because some domain of human experience is more complex than our current understanding can apprehend does not mean observed behavior within that domain is random.

Those who think that aggregated human behavior within a stock market is truly random face one of two correlatives that they need to establish with systematic evidence: (1) Many, if not all, areas of human behavior produce aggregated randomness. Or (2) human behavior within the stock market is uniquely different from other areas of human behavior AND has determinate characteristics that produce randomness.

Maybe. But I think these are extremely high barriers. My instinct is that people use randomness as a lazy substitute for the challenges attending highly complex multicausal environments.

These are not pedantic distinctions. Randomness has a precise mathematical meaning. So does multivariate causality under conditions of incomplete understanding. They are not the same.

I like dr. klink's point ( and dwayne's ) in the sense that, because one can't easily make money in the market, doesn't necessarily imply that aggregate movements are random. at the same time, it's also hard to prove that the aggregate market is not random. the only way to do that would be to consistently generate excess returns over a long period of time and anyone who does that probably isn't going to talk about it publicly in depth.

@Guy .. my friend ( and I rely appreciate your work ) .. how is the market random if I can predict 70% of the next swing ? https://www.linkedin.com/pulse/activities/0_2q70ICenpwFxwDufUF8Mn7?trk=hp-identity-wvmu

https://image-store.slidesharecdn.com/9dd278fe-dbf2-4b2e-8421-1a2439dc8633-original.png

Aurel, just out of curiosity — what does you statement on predicting 70% of the next swing mean?

@Alex .. I am using same particulars Algorithms (never use before) + NN /GA and in same ceases (in study we have just 6 currency / 6 Supercomputers /only ) .. we can predict the next swing / size > X> nn % from previews X/numbers of swings ) ..and the swing move directions (witch can be between 4 to 15 candle /Xhours/X/Days ) .. .. ... before 2 months we can do this on small TF .. no we can on HTF .. method is similar with the HFT / the only think we done was to scale up //.. need to be refine and make a full trading system .. i will be ready in 1-2 months

I have my own final conclusion and I will not make any more comments :) .. I want to quit every month for the last 5 years ... because I cannot find/have the solutions .. but in the end we succeed .... "market can be predicted and is not random" .. just because we don't understand / know the way is moving .. we cannot say that is random .. This is other example .. https://image-store.slidesharecdn.com/91296a37-5260-4e56-87d0-ce8de9999977-original.png (i don't know how they are doing.. but is ok )

Not random means you can predict with 100% certainty the direction of the price and the futur price itself. Obviously this is not possible. Because the future price is based on the action of the market's intervenants which you can't predict individually. You can try to figure out in average how they will act. But at the end of the day, you can predict the price of the stocks. But you can built algorithms or read the news or whatever to find a way to have more probabilities to win than to lose. The randomness of the stocks is not based on what we know today about the mathematics, it is based on how the prices are made.

Randomness is different from unpredictability. Market are definitely NOT random, still they are mostly unpredictable. But it's only a matter of time (and data).

If by randomness you mean "true randomness" as it's defined in the theory of probabilities, maybe. But I don't see how time and data can help you predict the close price of the Apple stock tomorow with certainty!

true/fals .... / big/small . . ...unpredictable / "true Randomness "/ "less randomnesses " / define what is "random "/ Time frame cannot be predicted and I will send you my predictions in the "Randomness "..or we are talking about Chaos ? .. Fractals ..what ? ..

I don't believe in any mathematical models for stock prices or derivates or other financial products. But here is a possible connection of chaos theory to stock price modelling, I'll simply throw some buzz words at you..If you have a dynamical system with a long time trend and short time "random noise influences", you can try to model this system with a stochastic differential equation. The famous Black-Scholes formula for option pricing is derived from a linear Ito stochastic differential equation. On a conceptual level, it combines the long time trend coming from fixed interest rates with the short time noise coming from day-to-day trading by many different agents, each having a small influence..The expectation values of certain stochastic differential equations solve certain partial differential equations. The expectation value of an Ito process, for example, solves the Kolmogorov forward equation. This is also true for the equations that describe the classical flow of a fluid...

My approach .. Despite this different testing methodology, semi-strong efficiency

depends on the validity of the random walk model, which depends in turn on empirical conclusions concerning the absence of statistical dependence in security price data. ... The distinction between nonlinear and linear systems goes well beyond noise theory, however,because noise theory itself is constrained by the efficiency paradigm, whereas nonlinear dynamics and chaos theory break from that context and imply a fundamentally different understanding of public capital market behavior with a broader perspective on investor and market behavior. ... Although noise theory makes the important point that psychological emotional trading is likely to be a factor, noise theory models explain biased price changes on the grounds that risk-averse arbitrageurs will not correct the effects of such trading... that why the market is "random" or unpredictable .. just take the noise out and you will see ..new way

.. there are thinks ..and ways' ..witch obviously... I will not make public.. but definitely the market is not "random" .. is just noise ..,have a good day .. same time is to much :)

Predictability can be defined different ways. Some examples are:

- value of price (or interval of values) in the time ahead of current moment

- the trend persistence

- the trend break

- range break

- etc.

Still, may be the most important part is to identify the period of time where the price movement is monotonous enough, making simple trading techniques (like SR, trend lines etc.) profitable.

of course they don't

Stock Markets are Not Random , but to predict the future price , we use some random models based on stochastic calculus , In general , the future price is the discount expected value of all different scenarios ... the values that we get are very close to the market value,,, this is the strength of the Monte Carlo Simulation ,,,

Wow, this is a lot of heated discussion! There are a few misconceptions here which I would like to discuss or rather elaborate on. Firstly, the exact definition of randomness matters a great deal in this discussion.

Definition 1 - true randomness. If markets evolved according to a truly random walk then the long-run expected return of every agent would be zero. This is the strongest possible form of the random walk hypothesis and it isn't very compelling, because it isn't true. My first article was about this definition of randomness, if you are interested in it you can find it here: http://www.turingfinance.com/hacking-the-random-walk-hypothesis/

Definition 2 - a Markov process with drift. What is this process? A Markov process with drift essentially consists of two components, one deterministic (predictable) called drift and another stochastic (unpredictable) called noise. Drift goes by a few names. Drift can refer to the risk free rate of return, it could refer to the overall market, or it could refer to the average daily momentum of a security. The point is that if markets evolved according to such a process then the long-run expected return of every agent would be equal to drift not zero. In other words, we would be able to earn a return on our investments but we would not, at least in the long run or very consistently, be able to "beat the market". This is the correct interpretation of the random walk hypothesis.

The analysis done by Lo and MacKinlay in 1988 does not relate to the first definition, it relates to the second. They developed a statistical test to see whether or not stock market prices might evolve according to such a process and the results indicate that many stocks and broad-based stock market indices do not. What does this mean? Well it means that there exists some structure in market returns which is predictable beyond what is predicted by drift. This is termed auto-correlation. What it does not mean is that markets are 100% predictable, they are still affected by noise. There is quite a lot of complimentary analysis done in this space such as the study of three, four, and five factor models.

Secondly, this does not invalidate the use of stochastic processes for asset pricing. Our models are not exact representations of the world. The world is complex and chaotic and our models are simple and elegant. However, just because a model is wrong does not mean that it isn't useful. Derivatives pricing without the use of stochastic processes is intractable. Making some assumptions, which may prove to be wrong in the future, are what allow our markets to function. This has always been the case and it will always be the case.

And lastly, the statement that one "cannot beat the market, at least in the long run or very consistently" is in no way, shape, or form obvious to disprove. It is fun to look at the track records of successful managers and assume that their performance constitutes evidence against the hypothesis, but unfortunately it does not. The average investor does underperform the market in the long run especially when his or her performance is adjusted for risk. Personally, I do believe that very smart people can "beat the market" which is why I am writing these articles.

Thanks again for all the comments, it's great to see how everybody thinks.

Thanks to Stuart to help us remember what a random walk is, by the way clearly stated in the article we're discussing about (as RW1, RW2, RW3). Are these the "misconceptions" you mentioned?

Thanks also to acknowledge what I wrote before in my little comment, with respect to the expected returns in the random walk case - because of zero mean (just kidding).

About "beating the markets", many have done it, no doubt. Off topic.

But what about this article? What about the approach? The test procedure? The R code?

I rushed straight to the conclusion (section "Remarks and Conclusions"); a great probability is not a proof, and Stuart Reid states here that "we can confidently conclude...". Okay, these are stats, but can anybody explain to me what this means (incidentally, the backbone of the work):

- "Between 4 and 5 stocks passing for sampling intervals of 2 and 4, ...

Instead, etc...

- Between 88 and 116 stocks passed for sampling intervals of 2 and 4..."

Hence the result. Is it satisfying to a scientific standpoint?

No need for math to devise that stocks and so do not behave just randomly. But thanks to that kind of work we know we have a good chance to make money by trading (just joking).

I'll make my own checking, maybe on the European markets, after homeworks, and having gone further in "Critique of pure reason". Probably ask for help.

Kindly.

Sorry for being thick about this enormous amount of work you people have been doing, but I think it is not necessary. The Random Market idea comes as an offshoot of the Efficient Market Theory, so far so good. An efficient market is efficient because millions of traders find all possible facts available and reach a consensus which is reflected in the price of the security. I hope this is still so far so good. The issue here is what effect these prices have upon investing. I know this is an oversimplification of a problem or a theory that can be made incredibly complex, as is quite efficiently proved in the articles quoted.

The issue here is that although everyone can access more or less the same information about a security, the consensus opinion (which is what is reflected in the pricing) is dependent upon factors that have little or nothing to do with factual information about that particular security. To put it in another way the consensus may be off, sometimes way off. Continued

Part 2. This gap between the consensus opinion and reality may be small or quite large but it is there. I causes mispricing which can be small or insignificant, or very pronounced. Psychology and crowd beliefs have a lot to do with the formation of consensus. You know the idea, get 10 professional ___ (fill the blank) to discuss a problem and they may come with 10 different solutions, or sometimes less, maybe even a single solution. However, there is no way to ascertain that any one of the solutions reached is firmly correct. This is not possible with things like price of securities.

Finding deviations, random or not, from expected price action may show among other things that the expected price action was incorrect. Furthermore, if you feel it is necessary to prove mathematically that at least some securities may not follow the random market dictum, then I would strongly suggest testing securities that can be expected to be subject to mispricing more often. Continued

Part 3. Such securities exist when they meet certain fundamental criteria. For example, information about these securities is not widely available or is hard to find; of the business these securities are in is exceedingly difficult to understand properly. I would suggest concentrating such research in small securities, or newly formed companies, privately owned companies which do not have to follow stringent reporting requirements, or companies which are so complex that developing a good idea of how they function becomes exceedingly difficult. Such companies should provide a fertile substrata in which non random pricing is found.

.. Muhammad A... yes is not random ... but you can win with random trading .. my friend Guy R. Fleury already made the system .. witch is working good :)

I guess it's possible

@Stuart, great article. Well done. And it does show that you can't put stock price variations in square bins. Under randomness tests, stock prices will show they do not comply to a Gaussian distribution. But this does not remove all the notion of randomness.

One has to contend with a long term positive drift component for the average stock. Any kind of diversified trading strategy that would be biased to the upside would have a tendency to positively perform over the long run.

Your test results do not identify the real underlying price distribution. Even a stochastic process has randomness in the drift and random components which are or might themselves be subject to other random-like functions or distributions.

This non-Gaussian randomness makes it difficult to make short term predictions. Except that someone will still be able to catch the long term trend simply by participating in the market.

...more

The job is not to identify what kind of price distribution do we face on a daily basis, but to extract a profit even within all the overwhelming surrounding quasi-random-like noise. You might not need to make short term predictions if your method of play is to be biased to the upside over many stocks over the long term.

I have programs trading randomly, meaning random-like entries and random-like exits, and still they outperform over the long term, catching the long term drift and more.

With an upward bias stance, you would be practically assured of winning the game and perform at about the same level as market averages. Buying index funds for the duration will almost assure you of achieving close to the overall market index return minus expenses and frictional costs.

.

http://alphapowertrading.com/images/divers/DJIA_1789-2014_w_drift.png

I do think that the above chart reinforces the notion that there is a long term drift.

...more

One could say: that line is not random, there is memory, auto-correlation, long term predictability, on average.

One line to describe the economic history of a nation. It says the US has progressed over time and prospered. Which is what I think it will also do going forward.

But a “trader” needs to go beyond this to generate some alpha in order to reduce his/her doubling time and outperform the averages. The quest is for finding as many positive Δps as one can, whatever trading method used. The Buy & Holder has for each of his portfolio stocks: 1*q*(p(T)-p(0)). A trader needs to execute the following: Ʃ(over n) q*(p(t)-p(t-d)) > 1*q*(p(T)-p(0)) to generate alpha. Meaning that the sum of Δps over the entire trading interval needs to be greater than the Buy & Hold ΔP for all the stocks in the portfolio. Note that most short term “traders” can not show they could achieve this, meaning outperform the averages over the long term.

Nice to be around all those masterminds. Mister C, "private investor", stock prices have nothing to do with a consensus, that's very funny. The consensus is the order book, nothing more. "Traders find all possible facts available and reach a consensus which is reflected in the price..." Are you serious?

Aurel, maybe you're friend Guy Fleury made money with random trading, but I'd rather go to the casino: at least, you can meet girls there - every math man knows that the gambler is the loser on the long run...

Yes! Guy R. F. is right: it's a great article from Stuart. Could you tell us why, Guy? (no joke here). Personally, as a beginner, I didn't finish a preparatory work (like reading the article by Lo & MacKinlay...). But, at this time, could you explain us what did you mean by: "under randomness tests (we don't use precisely this terminology in stats, by the way), stock prices will show they do not comply to a Gaussian distribution". What tests are you talking about? What are you talking about? Man! We are discussing about random Walks (To put it simply), and you're talking about gaussian distribution for stock prices? The works from Bachelier to Fama - rings a bell somewhere? And please, save us the cheap talk about trading - we are not talking about trading here.

@Alain I don't want to go back in to this debate witch is "around " this group for the last 3 years .. I advice you to read my last article and "watch" an interview in case you want to go more deep read the papers from Guy made back in 2007 .If you rely have an interest in "randomness 'entry/exit" .. i am building a team witch will prove the true about and make public the software and results .... this year ...

https://www.linkedin.com/pulse/random-entry-proves-strength-money-management-aurel-ispas

https://www.youtube.com/watch?v=ZmRz1NxAqww http://alphapowertrading.com/AlphaPower.pdf

Alain Bouhier.. is not necessary to be sarcastic ..when you don't agree with same one or same body .. just say and/or come with your argument .. we are not looking to promote or self . . or finding any job or be more reach than we are .. we just do it for passion and ..personalty .. not every day i agree with Guy .. but i respect his life work and results . :) thanks

Sorry Aurel I hurted your feelings. I just don't see any common thread here. Everybody goes by his comments and "this is it and that and blablabla", just self-satisfaction, massive assertions which often relates, by the way, to trading, algorithmic jokes (so to speak), that are... off topic. Your dear friend said, just like that: "great article". Good boy! Did he check that work? I undertook to do so: hence I asked (below) a question concerning the conclusion of the paper (searching help and willing to check what's been really done by mister so-and-so, - must admit): no answer. I worked more than ten years making programs, actually studying math & finance to be a quant (to put it simply: cos' like more math than money). I thought it'd be a good thing to thoroughly check that "great article", which need to be done with the academic others writen by specialists of great renown, on a "hot topic". Makes sense? Those are falling straight in the middle of what I'm studying at the moment. Absolutly no word about the paper itself. You're right, no need to be "sarcastic".

Mr. Bouhier, wow, if you can't see that the output of thousands and thousands of random walk trails have for result a Gaussian distribution. Then sorry, I can't help you much on that. I'm not in the education business. There are lots of statistical books out there that will explain it all in detail. Maybe, your stats have not encountered the phenomenon before.

You ask the question: “What tests are you talking about”? Read Stuart's article and conclusion again. All he could say was, with all the randomness tests performed, that stock prices were not random. And that is somewhat imprecise. He should have written: stock prices are not random walk. They don't have a pure Gaussian distribution. It is not a 50/50 game. And I certainly agree on that. But that does not mean that there is no randomness in market prices, only that this randomness is not Gaussian. It's the same conclusion as reached way back in the 60's

....more

If one accepted market price variations as random walk, then the expected long term profit from trading would tend to zero. No alpha generation. They should simply stop trading altogether. Or, continue playing just for the fun of it, since no skill, no educated guess, no forecast would help them win the game, except by pure luck. A random walk has the same expected value as a 50/50 game: zero.

A casino wins because they put the odds in their favor, they bias their coin, on average, to 52/48 or 54/46 or worst depending on the game you play. Mr. Buffett wins the investment game because he too puts the odds in his favor. He expects an upward long term drift for the average stock in his portfolio, he uses an upward biased coin. He knew from the start that his “coin” was biased in his favor, he can put 50 years of results on the table and say: I told you so. Read Mr. Buffett's argumentation, Stuart provided a link at the end of his article.

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Everything he mentioned holds true today as it did when he first wrote it. And I do agree with every point Mr. Buffett made.

Does the market have randomness? Yes. Is it Gaussian? No. And Stuart's article says exactly that with sufficient tests to validate his point of view which is a lot more that the clichés you are throwing around without anything to support them.

I favor a Paretian distribution for stock prices since it takes into account fat tails (outliers and gaps). Does it make short term stock prices more predictable? Not at all. It is only that the randomness part is distributed differently.

This forum deals with anything related to automated trading, that it be machines, software, nature of markets, trading programs or trading methods. And what I expect from the forum is an exchange of ideas, methods and different points of view. I you think that what I might say is wrong, then challenge it, but please, not just with clichés, put some substance into it.

Brownian Motion (as in small lightweight particles responding to gentle physical forces) in the context of trading markets is an approximation as a model, biased by the believer's wanting it to be true so that the math simplifies. As a quick broad-brush-strokes tool, it has some value for guiding more rigorous thinking and modelling. Stepping back, one would expect that no trader puts on a trade randomly; traders work on ideas, simulate them, back-test them, and then decide whether and when to pull the trigger. At the atomistic trading level, the process is not random.

Hi there! (sorry for the fuss). Hope Guy is feeling better. Shortly - because too "personal" - in response to the great Guy (sorry, I can't help), no, I don't "see" that the output of thousands and thousands of random walk trails have for result a Gaussian distribution. I figured out that you are refering to the Central Limit Theorem, which is, by the way, a ground for the Maximum Likelihood Method, used in the paper. I don't see why you mentioned that either.

I don't have your knowledge, I thought Buffet was rather an investor than a gambler, putting money on companies with good fundamentals. If that is true, having at the beginning, by principle, a probability of 50% of being wrong, I estimate you have now a probability of 25% of being right.

Incidentally, I just hoped for more substance and that's why, as a beginner and student in the field, I asked before a question concerning the conclusion of the paper, and complained that there was not much of a common thread in the comments coming.

... I would not have refered to education as a business, but... you betcha! For those who would not have heard about it, watch that documentary about the subprime crisis: "Inside Job", by Charles Ferguson. Edifying.

Agree, the markets are not random as such but , but the markets change behaviour - at and increasing speed - this makes the market "random". Besides - the trading strategies used by traders may be and are often based on randomness.

Thanks for the article. As some have suggested the thesis may not be news and perhaps the conclusions could be expanded but the math never goes out of style :)

Price/return stats are great for projecting a probability field into the future to help decide whether to play the mean or the (fat) tails but as an algorithmic trader interested in automation I've found the same math (Markov processes) can be extended to Markov decision processes via Q-learning to manage expectancy for a given strategy.

No - random walk is not a zero game, as to there is a spread and perhaps also cost of execution. The spread has a significant influence in the lower timeframes - but not in the longer where other factors are more important, such as, can you at all trade the high, the close of a daily bar ? Try flip your strategy and see what happens.

@Søren, by definition, and I do mean by definition, a random walk is a zero sum game. That is what the math says. A random walk is 50:50, and as such, has for expected outcome zero.

The question should have been: how much randomness is there? Reid's article concluded with: “stock prices are not random” when in fact he should have stated: “stock prices are not random walk”. He should not have generalized outside his Gaussian premises.

A single word missing from Reid's conclusion. And I must say a major distinction as it will have an impact on trading methods we might use. Stock prices are not random walk, they do have, on average, a long term upward drift, they do have memory. It is as if a stock price series was generated to a large degree using a positively and randomly biased coin having random-like variations in µ and σ including low probability outliers as price shocks.

Every stock I have tested is a unit root process. Stationarity is created in first differences, and whilst we might specify an ARMA vs AR process, the trends in returns are stochastic stochastic - as opposed to deterministic function of time (taking of course a monotonic time series) . In the frequency domain - not much better. But of course this does mean that markets cant be traded - they are responding to a host of factors, and shocks. Whilst on average an AR(1) process is a zero sum game it does mean the trader (having some skill) is not able to trade for profit, or earn portfolio returns from equity investments.

Speaking of randomness, one could, theoretically argue that the entire bull cycle was "random" since the 90s. Whoever made or lost money during that time was random. Our entire human existence is random in the face of the universe. Yes, the random conversation does get interesting and digs deeper and deeper in theory and understanding. On the flip side, we humans go to work every single day, and work hard for our companies. The value of those companies is not random, aka fundamental analysis will lead us to believe company A is undervalued vs company B. Imagine if we only had a population of 40 people in a town, and it only had 4 companies, one of those companies will surely be making more money than the rest, not because it's random, but because the people running that company are stronger and are able to take everyone's money! Stock market is NOT a coin flip. So yes, we can have this randomness conversation from the academic perspective or come back to reality and realize that the entire bull market since the 90s was not random.

I think Umair we are talking more of knock-on effects from various policies - bubble inflation due to QE, QE caused via an adoption of monetarism and associated policies etc., as a response to GFC, which was a consequence of a number of fraudulent like activities, non acceptance of correlation risks, housing bubble inflation, de-linking between credit grade and risk premium etc., etc, which was a knock on effect of. on and on..

Will a game with 51:49 odds still show some randomness? YES, definitely, and a lot. Even if it has a positive expected value. The same goes for a 52:48 game, there would still remain a lot of randomness. It might not matter much how the data might be distributed, it would still be mostly random-like.

Does the classification of a quasi-random game require a Gaussian distribution? NO, not at all.

A 52:48 game has for expected value: 0.52*1.0 – 0.48*1.0 = 0.04 per dollar played. Such a game is won simply by betting all the time on the built in positive edge. And in such a scenario, what comes to matter most is not the distribution, but the bet size and the number of plays: n*(0.52*10000 – 0.48*10000) = n*400.

On average, US stocks have had a long term 8-10% CAGR, dividends included. This translates to 0.00038462 (0.038%) per trading day, on average. On a $100 stock, that is an expected move of $0.0385 for the day, and $10.00 for the year.

...more

If only 4¢ of a $100 stock can be explained by its average expected secular trend, then where does all the rest of the price movement come from?

How much randomness is there? Technically, as much as you can't predict.

And since you can not predict with much accuracy, then ensues plenty of randomness. Much more noise than most would want to admit.

Is a bet that your next flip of a fair coin is head a prediction? Or is it simply just a guess, a bet based on assumptions gathered from the probabilities of having observed millions of tosses of the same coin. But what if you throw in outliers, gaps and black swans events which will distort your distribution. Doesn't the picture change? And what if the bias is really 52:48 in your favor to start with? What should be your trading strategy then? The easy answer is: one should continuously attempt to trade on the positive bias side. You can win by default, just by playing often.

This entire discussion of whether markets are random or not is futile, markets are not random in a random manner, by laws of statistics (results derived by linear math) or by manipulation, I am sure who created this market for you is fair :) however I digress to my point, it does not matter for both are also ruled by higher laws of the macrocosm, so expect everything as all is true, everywhere but no where, so for example LTCM type scam is such an example that has been well thought of by this same idea that we can know all, so to protect your self and your investors, just know that you are never meant to know it all unless you have access to insider trading without the repercussions and you will do super within this industry, otherwise stick to a good risk management system that doesn't pay so big yet pays enough to venture into other parts of life, to sit here complaining that you are just a trader is ludicrous, for there are much better industries to diversify into after trading.

I like Christian Baha's Superfund, they accept as small as 10k investments, which attracts the masses for expanding their trading equity in order to generate more for both, now think of attracting monthly payments to cover exposure and forecast losses from stable business, letting trading become a means to an end instead of being just an end. This is what I meant, an ouroboros.

Just finished what became more than a post that could fit in this now limited space.

I noted that there was some confusion, for some, in the terms I used. So I tried to clarify my point of view.

Follow the link below where there is still sufficient writing space.

.

https://www.linkedin.com/pulse/randomness-stock-prices-ii-guy-r-fleury

Hope it helps.

The proof of the automated non-stopp CVT Robot randomness performance related to the following discussion is available. Price motion, its volatility definitely depends on the news and expectations. It demand solving not fully observable for the pricing solution in many variables problem and even more complicate its analytic to the prediction the future in form of variables contributing stochastic chances in the low informative price-volatility (P-L) space. Math governesses in this methodology. Who are its top activist? They are applied mathematicians far from Economics and Finance in their "creativity". Randomness involved by them is the convenient assumption to the desirable canonical solution. All of the activists overall are losers practically except the real and small group of intuitive FM genius Gurus' talents. May be they possess sort of latent determinietic analytic prevailing in their decisions making. The Elliot Waves (where are we on the waves?) is weak to their randomness

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