Stock prices have to do with human behavior. Therefore they are unpredictable.
I think this is strongly related to the concept of free will. It's a common religious axiom: even though God is omnipotent, he so generously gave us free will so that he could hold us responsible for screwing up. Since stock prices are a product of free will, they too cannot be controlled by God or simulated by a computer. Of course, if you believe that free will is implemented by a physical system, and you believe physics can be modelled by a computer...
The unpredictability of stock prices has nothing to do with free will.
Suppose that there is a function which takes in all public information about the state of the market and then accurately predicts the change in tomorrow's stock price. Whenever the predicted price is higher than today's price, then you can buy stock today, and sell it tomorrow. (Likewise, when the price tomorrow is lower, you can short-sell.) Since this is a profit opportunity, everyone in the market will try to do this, bidding up the price of stock today until there aren't any more profit opportunities. This contradicts our assumption that you can predict future stock prices, so therefore you can't.
This argument makes no assumption at all about the amount of computational power in the prediction function; with infinite computational resources you get a random walk, and if you limit the amount of computation you can do, you'll get various computable approximations to random walks.
<< Since this is a profit opportunity, everyone in the market will try to do this >> This only follows if: * the function is known by everyone in the market * everyone in the market knows that the function accurately predicts the change in tomorrow's stock price
This is a specific instance of a much larger phenomenon: whenever you have intelligent agents interacting, randomness often shows up as an essential feature. For example, think of the rock-paper-scissors game; the Nash equilibrium in this game is to play randomly.
Stock prices can definitely be plotted according to mathematical formulas, therefore mathematical models are used in determining all kinds of parameters for stock prices (volatility, trends, relative strength, averages, retracements, support/resistance, targets). It's naive to claim that mass behaviour in the capital markets cannot be quantified mathematically.
The big problem with mathematical models of human behavior, is that humans can reason. If they know there is a model of their behavior, they can attempt to 'game' that model. Suppose the model says that, if is X is true about a company, then the stock price will increase. If I know indicator X will cause investors to buy my stock, I have an incentive to fake X by some method.
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I think this is strongly related to the concept of free will. It's a common religious axiom: even though God is omnipotent, he so generously gave us free will so that he could hold us responsible for screwing up. Since stock prices are a product of free will, they too cannot be controlled by God or simulated by a computer. Of course, if you believe that free will is implemented by a physical system, and you believe physics can be modelled by a computer...
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Suppose that there is a function which takes in all public information about the state of the market and then accurately predicts the change in tomorrow's stock price. Whenever the predicted price is higher than today's price, then you can buy stock today, and sell it tomorrow. (Likewise, when the price tomorrow is lower, you can short-sell.) Since this is a profit opportunity, everyone in the market will try to do this, bidding up the price of stock today until there aren't any more profit opportunities. This contradicts our assumption that you can predict future stock prices, so therefore you can't.
This argument makes no assumption at all about the amount of computational power in the prediction function; with infinite computational resources you get a random walk, and if you limit the amount of computation you can do, you'll get various computable approximations to random walks.
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<< Since this is a profit opportunity, everyone in the market will try to do this >>
This only follows if:
* the function is known by everyone in the market
* everyone in the market knows that the function accurately predicts the change in tomorrow's stock price
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