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# Arcsinus law: distinguishing trend from persistency of chance

Discussion in 'Technical Analysis' started by harrytrader, Sep 15, 2003.

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.

2. ### AsaFce

Reminds me of "Rosencrantz & Guildenstern Are Dead" in which they are constantly flipping a coin and it always lands the same way (of which they repeatedly note the oddity of).

Your writing is barely decipherable - at least you are trying to learn english.

I'm not sure what you are saying: if you are saying that pseudo-patterns can occur in large data sets then yes, this is true. Look long enough in a large set of "random" events and islands of pattern develop but over the whole universe of data these are not significant.

Cite your sources like any other professional would in a publication. Otherwise nobody will bother listening ...

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

5. ### maxpi

Wow, if the casinos find out about this they will limit the maximum bet!! Jeez, if some trader had a good system but he had an unusually bad run of luck he would blow out his account!! Better tell everybody Harry, you owe it to them all.
:eek:

6. ### GIG

Maybe I'm not understanding the significance of the text, but I don't see anything new with the arcsinus theory.

Flipping a coin:

Law of large numbers states: 50/50 chance, period.

In a million coin tosses, look at 100 tosses at a time as a smaller data set.

Then, calculate:

Probability of 0 heads in 100 tosses
Probability of 1 head in 100 tosses
Probability of 2 heads in 100 tosses
...
...
...
Probability of 99 heads in 100 tosses
Probability of 100 heads in 100 tosses

Graphing the results will generate a probability distribution curve, similar to bell curves you've seen in school.

Although the probability of getting 0/100 heads or 100/100 heads is small, it does happen.

So, yes, sometimes you will get 'lucky streaks', this is the nature of a probability distribution curve. And yes, the longer you play, the higher the probability that your (acuracy, winnings, whatever) will ultimatley reach the probability generated from the law of large numbers (in this case 50/50).

But, this is like grade 12 math, isn't it?

Let me know if I've missed something here.

Brandon

7. ### Bolts

So, Harry, you're saying that this Arcsinus law tells us that trends can be illusions. And yet some people abuse this law by saying that the Arcsinus law can actually explain the existence of real trends where none should exist. Did I follow that correctly?

Of course they do: there is generally a minimum bet (which will accelerate the probability of ruin for small traders) and a maximum bet for preventing too lucky players. Also some casinos will ask you to quit when you are too lucky.

Now don't dream because at long term the Central Theorem Limit will play against you. That's why for this to succeed the player must hurry up and don't stay too long and so not play too low a bet - since he also fears the risk of ruin. For example at roulette let's say you have a capital of 10000\$ and will stop when you will win 1000\$ (1/10th) by betting on red or black: the probability of success is more than 88% ! But remember that probability is not all since if you lose although the probability is low you will lose 10000\$.

In stock market, if you are a pure player (using only money management that is too say a martingale - let's remark at passage that so called "anti-martingale" doubling when winning and the contrary when losing is in fact also a martingale mathematically so the name anti-martingale is mistakingly aimed at people believing that it is more reasonable than a martingale) you will be in the same case than a casino game except that it can be amplified because of Market Asymetry. But if you are not a pure player Stock Market is more advantageous than Casino especially small players have interest to apply martingale rules because there is true trend in stock market. The market's organiser know that so for efficiency of market they will adjust capital requirement, fees, margin call, liquidity etc. to prevent too lucky traders also. PDT rule is an example, higher fees and worser liquidity will also chase traders from lower scale to higher scale which would create a change in their profile risk, etc. But contrary to casinos Market organisers can't chase too lucky traders if they retire quickly - if not they will relose with probability of one although it can take much time if they really win big.

At school you must have learned to calculate the parameters of a brownian motion. You know that if game coin is fair
the mean m is 0 and that the standard deviation of m is SQRT(n) which is to say there is a non negligeable probability of finding m not equal to 0 after n steps. Nevertheless it doesn't imply that the most probable case is to be far from 0. To be more visual let's say 100 hundred players play at this game you would expect intuitively about 50 players losing and 50 players winning whereas it is not the most probable case: in most case there will be much more players losing ... or much more players winning so a sort of desequilibrium ... in apparence only because with probability of 1 it will reverse one day but it can take a long time that's what the law is about and justify its name of persistency of chance (or bad luck) or fundamental injustice of nature.

This means that some traders that are losers could have undergone also this phenomena and aren't more bad or more good than other winner traders and so shouldn't obligatory give up if they know they can progress.