It is a random process but you know that over the long run it will be close to 50/50. You also know that the probability to be furthest from 50/50 is at the middle and highest probability to be closest to 50/50 is at the start or end of the series of tosses. Using this information you could create a positive expectancy game on coin tossing. But it doesnt have much to do with trading.
It appears that I need to post more, so here you go. By looking at a (lognormal) random walk, my eye can't tell if it's a real chart or a r.w. . Still what my eyes tell me is highly subjective. The real question is to what extent does the random walk theory exclude the existence of patterns, Let's look at the basic Black-Scholes lognormal process, dS/S = mu*dt+sigma*dW, (Eq 1) where dW is the brownian component and mu is the deterministic component. Assume mu = mu(t) and sigma is a constant to make things easier. The whole point in this formalism is not that there are no patterns in the stock chart. mu(t) can have patterns, it can even have momentum. None of this is conflicting (Eq 1). All the brownian component is adding is noise to that bit. Now, from a hedging perspective, mu is replaced by the risk free rate and becomes irrelevant but a buy-side trader has absolutely no reason to do this, he's not interested in "killing" the brownian component of his options position in order to be hedged. It makes perfect sense to look for patterns, the existence of a brownian component just makes his job harder as instead of a real pattern he may come up with something created by noise. All the above is irrespective of whether the existing TA, as published by several authors in popular books is valid or not, but the results of trend following funds do hint that looking for patterns is a viable approach to trading.
Some people, especially university theorists, believe randomness means you can't make any profits. This is totally wrong. If you can spot random processes with a very small winning bias then you can make a lot of money by simply buying and holding assets. You exit when the bias slowly evaporates. The author of the blog post below demonstrates that the bias in the gold market and GLD was less than 5% on the average during the past 7 years but it was enough to cause a spectacular trend that made some players very wealthy: Games with Fancy Names
Could the Nature of short term Trends be simply a streak of consecutive heads or tails contained within the randomness cloud surrounding an "entropy increasing" true long term trend e.g, decreasing value of currency or inflation will cause dow index to increase on a up trend certainly over time? http://www.investopedia.com/articles/trading/07/stationary.asp Does anyone how to apply the concept & math of "stationary" for mean reverting pairs trading?
Coin tossing has no memory. The market does. When you place a limit or stop order after you go long or short you essentially destroy any link to coin tossing. Are you people ever going to get that?
You have got to be kidding! A young Bulgarian girl writes a very poor master's thesis with a lot of mathematical errors and literally no understanding of RWs and you want to follow her???? Oh, boy .. "Tzveta Iordanova started her career at the Investment Supervision Division of the Financial Supervision Commission in Bulgaria. Since 2004 she has been working for DSK Bank OTP Group, specializing in strategic planning and research, market and macroeconomic analyses. Currently she is pursuing a master's degree in finance at the University of Skovde in Sweden"
This is an exceptionally wrong statement; it illustrates a very common mistake of mixing the cause and effect. Not a first time I have seen it. Theory of Random Walks is by far different than majority of people here imagine it. The above link to an article by a novice researcher from Bulgaria is a good illustration of it.