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this is just theory, don't take it as serious, theory it's just take on approximation of reality and in this case not good one, people trade to check that strategy is profitable or trade because they think it will profitable, besides that you have many other spaces on what people compete with each other in this game


The formation of asset price bubbles, such as the recent US housing market bubble, is perhaps the clearest indication that markets are not efficient. Hundreds of bubbles have been documented for all kinds of traded assets; see the tulip mania for an extreme case. Many practitioners also routinely use trading strategies such as momentum or reversion to the ...


It's unclear what type of trading you are referring to (day trading sort of?). Also I'm not familiar with the aforementioned paradox. However, I think it's weird to say that you can't make money from trading, the semi-strong (strong) from of the EMH only states that the current share price incorporates all publicly (and non-publicly) available information. ...


Making money is not the only reasonable objective to trading. Another common reason is to manage/reallocate risk. For example, this is exactly the objective of liability-driven-investors, such as pension funds. They're specifically trying to match durations of their liabilities. It doesn't matter if pension fund managers believe there are no inefficiencies ...


In our lecture, we were told to omit the proof because it was too difficult. Maybe it will help you though if you can read it here:


After applying the theorem you can take an $Y$ orthogonal to the separation plane, pointing in the right direction, you will easily have the property $X.Y>0$ for all $X$.

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