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I am quite new to random walk theory so please excuse my rather simply put question but I am wondering how can quant trading desks and other algorithmic trading firms exist if there is the random walk theory? Wouldn't it suggest if there is the random walk theory, noone can not outperform the market?

And as a second part of the question regarding random walks: Is there any research on random walks and the behaviour of limit order books? i.e. this Paper by Rosu models a limit-order book using Markov processes and a Markov perfect equilibirium: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=710841

Would a random walk in order book dynamics not suggest that models like this aren't of any use? To my understanding such a model makes sense, as there are agents interacting in a limit order-book that are to a substantial part algo trading driven and therefore they follow some kind of pattern that (should) make it possible to model this behaviour of such an limit order-book?

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    $\begingroup$ The 1st question: The Random Walk Theory of Fama and Samuelson is important, deserves to be studied and understood but may not be absolutely true in every respect. My view is that some people, such as Jim Simons, may have found deviations from perfect randomness. But they are difficult to discover and tend to go away (the mkt evolves toward randomness). On the other hand most of the comments on CNBC, in the WSJ and the predictions of most "experts" are not useful in predicting the market. I have tested this empirically many times. So the RWT is true to a first and maybe second approximation. $\endgroup$ – noob2 Apr 10 at 13:03
  • $\begingroup$ I'd say not necessarily that prices are random walks, but instead, Martingales with respect to the filtration that they generate on their own. That is to say roughly - past prices can't predict future prices (at the daily scale). However, if the filtration includes things that aren'r just the price of the asset in a vacuum, then I think some amount (perhaps infinitesimally small) of predictability enters the equation. $\endgroup$ – rubikscube09 Apr 10 at 17:03
  • $\begingroup$ Broke move: The market moves randomly. Woke move: The market has predictable patterns and trends, but those who discover them keep them private for their own profit, leaving everyone else to still think it’s random. $\endgroup$ – Hamish Gibson Apr 11 at 13:44
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    $\begingroup$ Individuals who do not believe prices are random, make investment decisions which makes the market random... In other words, prices are random because of people who do not believe they are random. < that’s a simplistic argument/paradox orchestrated by Grossman & Stiglitz $\endgroup$ – user28909 Apr 11 at 20:17

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