Arcsinus law: distinguishing trend from persistency of chance

Quote from harrytrader:

At high school you could have learned statistics and probability but never heard about the Arc Sinus law because it was discovered by the statistician Levy only lately (even on search engine you would barely find a link). This law is different from more famous Laws from the same Levy which concerns no-mean and no-variance family of laws. Some statisticians have given to the Arc Sinus Law the metaphorical name of "Fundamental Injustice Law of Nature" - but leave the consequences to the Philosophes :) .

Why ? Because this law says for example that at a fair coin game between 2 players chance will have tendancy to ALWAYS favor CONSTANTLY the SAME PLAYER for a LONG TIME so that persistency of apparent trend of the fortune of this player is in fact totally due to chance since the two players here have no special advantage one above the other.

Some gurus have profited from that to show that some people could win at casino and stock market with only money management without specific knowledge of market (which is in this is case a soft word for martingale and pyramiding scheme). Yes some people could win but it doesn't change the fact that if they continue the game LONG TIME ENOUGH the chance will finally revert. That's why if you only count on chance and you make gain especially huge gains thanks to pyramiding the best decision is to STOP once you reach the fortune. If you make gain and have real knowledge of market's action you have more chance to escape ... this chance's law.

Some technical analysts even use this law to justify that trend exists in stock market whereas it cannot be used to justify the existence of trend from the statistical point of view and in a conference on Finance and Chaos Theory a Mathematician in the field has mocked precisely the abuse of that law to make a false justification by showing a chart from a technical analyst with a trendline and justifying - falsely - with arc sinus law.

P.S.: why is it called arc sinus law because the sinus is in the expression of the law but it is not important for the subject discussed here.
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Isn't this something like the probability law of very large numbers?
 
Quote from harrytrader:



I already said that :

http://www.elitetrader.com/vb/showthread.php?s=&threadid=25053&perpage=6&pagenumber=3

There is 2 things to distinguish:
Risk management and Money Management in the restricted sense of optimisation (position sizing,..) used by Ralph Vince for example - the author of the classical "New Money Management". Of course there is some overlap between the two.

The most important one is the Risk Management because it relates to the alpha risk type in term of probability theory which is the risk of being in error whereas optimisation relates to the beta risk type which is only the risk of missing some opportunity. Missing opportunity cannot conduct you to go broke (although it should be modulated in details but I simplify here) whereas not knowing the alpha risk can get you broke.

People focus too much on Money Management thinking that it is the "secret" of wealth - perhaps because of sellers of books/systems which have interest to put the accent on Money management rather than on risk management. Yes you will see people who become rich suddenly because they applied martingale rule (BTW so called anti-martingale rule is also a martingale rule mathematically it is amusing how marketing tried to disguise to people things through fake name !) but what you see is the "survival bias" of chance that's why the same person when ruined later is incapable to reproduce the same exploit. Money Management is only useful when Risk Management is already under state control. Then it becomes easy to optimise that is to say use Money Management (using probability with or without Monte-carlo, Linear Programming).

In conclusion: "PREMATURE optimisation is the root of all evil"
It is in fact Knuth's famous maxim in software programming but as you can see it can apply to other field since Money management is about optimisation. Doing Money Management before doing the essential part of Risk management is also the root of all evil (it will conduct to overfitting and constant tweaking for example).
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Okay harry, you sucked me in.

Does not money management = risk management?
 
All this academic stuff is based on one basic assumption which is not true - "that all market participants are equal"
In a simple game of dice this assumption is true but not for most
things in life.

SAT scores also have normal probability distribution but you
cannot say the person who got 1600 got it purely due to chance or you cannot differentiate him/her from the person scoring 400.
Chance definitley had a part but chance was only part of the reason.

You cannot say michael Jordan plays basketball the way he does because of the arcsinus law.

Chance plays the biggest part in assigning us our natural abilities, after that it is mostly hard work and some chance.

A model is good only if its basic assumptions are good. Most models need to have very simple assumptions, otherwise they become unmanageable.
 
Quote from TexTrader:

All this academic stuff is based on one basic assumption which is not true - "that all market participants are equal"
In a simple game of dice this assumption is true but not for most
things in life.

SAT scores also have normal probability distribution but you
cannot say the person who got 1600 got it purely due to chance or you cannot differentiate him/her from the person scoring 400.
Chance definitely had a part but chance was only part of the reason.

You cannot say michael Jordan plays basketball the way he does because of the arcsinus law.

Chance plays the biggest part in assigning us our natural abilities, after that it is mostly hard work and some chance.

A model is good only if its basic assumptions are good. Most models need to have very simple assumptions, otherwise they become unmanageable.
More...


Smartest words spoken in this thread. I agree 100% (and thats no statistical anomaly!). The eggheads throughout my finance classes back in the 80's with their efficient market hypothesis forgot one thing. All market participants are not equal in "size,shape and stature" such as dice. Thank you TexTrader you summed it up perfectly.
 
Quote from traderkay:

Harry's English improved significantly, props Harry. I understood completely what he said. And he shared something of value here.
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amen.

so does that make harry GG?? :D
 
There are several "Large Number Laws" in fact but I suppose that what you refer to is the "Central Limit Theorem" or "Laplace-Liapounov" theorem which says that n random independant variables that can follow ANY RANDOM LAW (I remind that a random law can have any functional form : rectangular, triangular,... see http://www.elitetrader.com/vb/showthread.php?threadid=25033) if they admit a mean and a standard deviation (because there are laws that have no mean and no standard deviation - in fact it is the same Levy the author of persistency law who also discovered probability distributions with no mean and no variance) then as n grows, their sum probability law will tend towards a normal law. This is rather INTUITIVE because it translates the COMMON SENSE that NUMEROUS "LITTLE causes" - numerous so that none is preponderant - won't affect much the "MAIN cause" so that the distribution of the sum (or the multiplication) of the little causes could be approximated by the normal law (or the log normal law if it is multiplication). So with this theorem that COMMON SENSE has been demonstrated. But COMMON SENSE is NOT ALWAYS true as we're going to see:

The theorem above is a STATIC point of view which is old of a few hundred years already - attributed to Laplace although it should be attributed to de Moivre :) - but it says nothing about the DYNAMIC point of view which is what Levy's discovery is about - and it is recent since Levy has made his discoveries after 1935 - this law, says that even in a VERY LONG GAME of two players which plays a coin toss game with SAME 1/2 PROBABILITY AT EACH BET - that is to say a FAIR game for each player - the periods of gain of each player will tend towards 0 or 1 whereas COMMON SENSE would expect 1/2 that is to say one player will appear as to be practically always the winner and the other always a loser whereas they have exactly the same chance at each bet. Most people will then think that this winner has more ability than the second one whereas in this case it is absolutlety only due to chance !

That's why this law is <font color=RED>NOT COMMON SENSE</font> and you can read that it is really not common sense in Hedge Fund Manager Peter Bertein's Book "The Improbable Origins of Modern Wall Street" where he detailed the case (sorry I'm too lazy to translate see p.144 in the french edition or the equivalent in american edition :) )

Quote from oddiduro:



Isn't this something like the probability law of very large numbers?
More...
 
Did I say the contrary since I have posted this in another thread:

http://www.elitetrader.com/vb/showthread.php?s=&threadid=25356&perpage=6&pagenumber=2

it is absolutly STATISTICALLY FALSE to ASSUME that such indicators follows NORMAL LAW for - translated from a french statistical book untitled "Statistical techniques : rational tools for making choices and decisions" written by a chief engineer of Military Air Force -

"Contrary to natural phenomenas, economical phenomenas must take into account the intervention of humans who don't always obey to random law"

BTW probability is not a question of being academics or not: they are MATHEMATICAL LAWS that contains PREMISCES and so it doesn't prevent from being unrigorous in scientific approach to apply them in PHYSICAL LAWS if one doesn't take these PREMISCES into account. It is not scientific for example to assume normal law when one knows that the multiple causes I mentionned in the answer above about "Large Number Law" are not equal.

So your remark is not really the subject of this thread ! The subject here is that EVEN if one assumes PERFECT RANDOM LAW it is not evident to judge a performance of a player. The DIFFICULTY is WORST in the case of NON PERFECT RANDOM LAW or UNKNOWN RANDOM LAW haha :) !

I didn't say that there is no mean to judge I only insist that the cumulative gain which is MOSTLY used is in fact the MOST MEANINGLESS CRITERIA. One must absolutly look at details - that I have began to talk about see "Stragedy break down" http://www.elitetrader.com/vb/showthread.php?s=&threadid=25063&perpage=6&pagenumber=4.

Quote from TexTrader:

All this academic stuff is based on one basic assumption which is not true - "that all market participants are equal"
In a simple game of dice this assumption is true but not for most
things in life.

SAT scores also have normal probability distribution but you
cannot say the person who got 1600 got it purely due to chance or you cannot differentiate him/her from the person scoring 400.
Chance definitley had a part but chance was only part of the reason.

You cannot say michael Jordan plays basketball the way he does because of the arcsinus law.

Chance plays the biggest part in assigning us our natural abilities, after that it is mostly hard work and some chance.

A model is good only if its basic assumptions are good. Most models need to have very simple assumptions, otherwise they become unmanageable.
More...
 
I said "in the RESTRICTED SENSE of optimisation (position sizing,..) used by Ralph Vince for example - the author of the classical "New Money Management". " (http://www.amazon.com/gp/reader/0471043079/ref=sib_dp_pt/102-9050362-0445765#reader-link you lucky one there is a promotion on this book : it's now only 45$ instead of 65$ as I have paid a few years ago in a french bookshop which converst 1$ to 10 francs instead of 7 francs :) )

Since the book of Ralph is reference in the matter, I refer to his point of view. If you don't agree with this, you have the right to do so.

Quote from oddiduro:



Okay harry, you sucked me in.

Does not money management = risk management?

--------------------------------------------------------------------------------
Quote from harrytrader:



I already said that :

http://www.elitetrader.com/vb/showt...=6&pagenumber=3

There is 2 things to distinguish:
Risk management and Money Management in the restricted sense of optimisation (position sizing,..) used by Ralph Vince for example - the author of the classical "New Money Management". Of course there is some overlap between the two.

The most important one is the Risk Management because it relates to the alpha risk type in term of probability theory which is the risk of being in error whereas optimisation relates to the beta risk type which is only the risk of missing some opportunity. Missing opportunity cannot conduct you to go broke (although it should be modulated in details but I simplify here) whereas not knowing the alpha risk can get you broke.

People focus too much on Money Management thinking that it is the "secret" of wealth - perhaps because of sellers of books/systems which have interest to put the accent on Money management rather than on risk management. Yes you will see people who become rich suddenly because they applied martingale rule (BTW so called anti-martingale rule is also a martingale rule mathematically it is amusing how marketing tried to disguise to people things through fake name !) but what you see is the "survival bias" of chance that's why the same person when ruined later is incapable to reproduce the same exploit. Money Management is only useful when Risk Management is already under state control. Then it becomes easy to optimise that is to say use Money Management (using probability with or without Monte-carlo, Linear Programming).

In conclusion: "PREMATURE optimisation is the root of all evil"
It is in fact Knuth's famous maxim in software programming but as you can see it can apply to other field since Money management is about optimisation. Doing Money Management before doing the essential part of Risk management is also the root of all evil (it will conduct to overfitting and constant tweaking for example).
--------------------------------------------------------------------------------
More...
 
Next thread will be about so called "Anti-martingale" rule which is misnamed because MATHEMATICALLY it is ALSO a MARTINGALE that is to say it is also dangerous to believe in it :D. Now because of this Levy's law of persistency of chance there is some rationality behind it but it will be another thread - I will rather post in trading strategy than in TA then in fact this thread should have been also there but I mistakingly clicked on the wrong forum.

Quote from harrytrader:

There are several "Large Number Laws" in fact but I suppose that what you refer to is the "Central Limit Theorem" or "Laplace-Liapounov" theorem which says that n random independant variables that can follow ANY RANDOM LAW (I remind that a random law can have any functional form : rectangular, triangular,... see http://www.elitetrader.com/vb/showthread.php?threadid=25033) if they admit a mean and a standard deviation (because there are laws that have no mean and no standard deviation - in fact it is the same Levy the author of persistency law who also discovered probability distributions with no mean and no variance) then as n grows, their sum probability law will tend towards a normal law. This is rather INTUITIVE because it translates the COMMON SENSE that NUMEROUS "LITTLE causes" - numerous so that none is preponderant - won't affect much the "MAIN cause" so that the distribution of the sum (or the multiplication) of the little causes could be approximated by the normal law (or the log normal law if it is multiplication). So with this theorem that COMMON SENSE has been demonstrated. But COMMON SENSE is NOT ALWAYS true as we're going to see:

The theorem above is a STATIC point of view which is old of a few hundred years already - attributed to Laplace although it should be attributed to de Moivre :) - but it says nothing about the DYNAMIC point of view which is what Levy's discovery is about - and it is recent since Levy has made his discoveries after 1935 - this law, says that even in a VERY LONG GAME of two players which plays a coin toss game with SAME 1/2 PROBABILITY AT EACH BET - that is to say a FAIR game for each player - the periods of gain of each player will tend towards 0 or 1 whereas COMMON SENSE would expect 1/2 that is to say one player will appear as to be practically always the winner and the other always a loser whereas they have exactly the same chance at each bet. Most people will then think that this winner has more ability than the second one whereas in this case it is absolutlety only due to chance !

That's why this law is <font color=RED>NOT COMMON SENSE</font> and you can read that it is really not common sense in Hedge Fund Manager Peter Bertein's Book "The Improbable Origins of Modern Wall Street" where he detailed the case (sorry I'm too lazy to translate see p.144 in the french edition or the equivalent in american edition :) )
More...
 
Distinguishing trend from persistency of chance

Isn't trend something that a statistician would call the persistency of chance? And in any case, why do we need to distinguish between them anyway?
 
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