1. I think this is the part that is not intuitive. Could you explain the insights/the whys? Explanations that do not need the law itself can be educational and useful in trading, as they can instill insights. 2. The arc sine law is a distribution. The ratio of times satisfy it. Other variables could also satisfy it. Is Ninna trying to say that other variables satisfy that law?
My understanding is that the arc sine law describes a variable that takes continuous values between 0 and 1. Your variable is between 0 and infinity, and is discrete. Could you provide further comments?
The arc sine law assumes a normal stationary process. It has been shown that this assumption does not apply to many markets. Then, there are at least 3 different definitions of probability. Most results in the field are wrong because they apply the wrong definition of probability. People in the literature are coming out of the woods slowly and start questioning our concepts and definitions of probability. Now, as far as your question. This reason this is observed often in the market, although it is not a result of the arc sine law as some clowns believe, is that some big players follow/create the momentum of prolonged trends, usually big funds, while retailers attempt to short it for a quick profit. Few speculators go with the funds and also win.
My question was aimed at explaining it in the context of coin flipping so that the questions of applicability of laws/etc is not an issue. So the questions related to arc sine law in the context of coin flipping remains.
The issue of laws is important because the arc sine law is a counter-intuitive result. It says basically that the expected first return time to zero is infinite! Let us try to understand the contradiction here. As n , the number of tosses, becomes very large, the number of head events and the number of tail events should both approach n/2 for a fair coin. Winnings should be equal to losses in the case of two players. The arc sine law considers the fraction of time during which gains remain positive. The result is that it must be either close to 0 or close to 1 but not equal to 1/2, the intuitive result, as the clowns claim it to be. I claim the result is wrong.. I further claim that the correct answer is that we do not know the fraction of the interval gains will be positive because ... ...answer deleted I deleted my answer above because I do not plan to give food for thought and for publishing another paper to some clowns when if I write the same paper they will not publish it because they control the peer review process. One thing I can tell you. Science, in particular mathematics and physics, is full of clowns who have an ego problem, cannot make a buck running business, cannot even run a deli store but they think they can discover the secrets of the world. 99.99% of physicists and mathematicians have some type of autism disorder http://en.wikipedia.org/wiki/Asperger_syndrome If you want to make money, forget those clowns and use your intuition. Their "intuition defying results" is a by product of their inability to understand the self-evident principles that govern math and physics, and as a consequences, physical reality.
Who states such claims? Does not the arc sine law probability implies that the prob that the fraction of positive time is less than or equal to 50%, is o.5. The density of the law is such that when the fraction of positive time approaches zero or one, the density slope goes to infinity. The density looks like a U. This means that the probability distribution (which is the integral of the density) should have a slope that is decreasing when fraction of time is between 0 and 0.5, and rising when it is beyond 0.5. It should approach 1 with a sharp up slope. Maybe what they mean to say is the prob. that the fraction of positive time is between say 0.8 and 0.90 is higher than the prob than the fraction of time is between say 0.5 and 0.6.
The above sentence is not in proper English systax. I basically do not understand what you want to say there. Please try to use standard syntax. The concepts are difficult to grasp and the use of not proper syntal makes things exremely complicated.
Coin flipping is purely binary. You'd be better served will varying weights to outcomes for expample with a pile of slips of paper -4-3-2-1/+1+2+3+4. Closer approximation to reality and provides a clearer insight to "risk of ruin". Your descretion in trading, ie cutting losses/wating for entry partially offsets the randomness. Any mechancial endeavor, coin flipping, paper trading, etc. is not going to embrace the emotional element when real moola is at stake. Postion size is for another day.
I tried to make "heads or tails" about what the researchers are trying to prove on this thread and still come to the same conclusion. Its all bs, there is no applicability to trading and anyone spending time trying to prove it is wasting their time. There are so many better areas to research. The expected value of coin flipping in trading is break even minus commissions. Eventually the commissions will overwhelm you. Even if you luck out and start winning immediately then you face the decision to stop and keep your winnings ( lucky guy or gal ). Then what ? Your trading career with coin flipping is over. Same strategy works for roulette.