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I'm trying to understand your question. To be concrete --- and trying to really putting your question in solid terms --- suppose for simplicity we are dealing with something like a standard geometric Brownian motion, $$ dS_t = \mu S_t dt + \Sigma S_t dW_t $$ where $S = (S_{1}, ..., S_{n})$ represent stock price of the $n$ risky assets at time, and $W = ...


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Philosphically, I agree with you. Sometimes you will see people like Icahn, Kohlberg Kravis... buy a majority stake in a company and take it private, selling off parts of the company, restructuring others. One interpretation of this activity is exactly what you said: there is a mispricing in the stock (compared to assets, earnings, whatever), but no way to ...


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Regarding the relationship between white noise and a random walk, I would put it this way: a random walk is integrated white noise. [And vice versa we get a white noise when we differentiate/difference a random walk]. Or to put it in quant finance terms: white noise is like the daily changes in the S&P in points, a random walk is the S&P daily level ...


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I will assume a white noise is a process $(\varepsilon_t)$ with zero mean, no autocorrelation and constant variance $\sigma^2 > 0$ while a random walk is a process $(x_t)$ defined by $$ x_{t+1} = x_t + \varepsilon_{t+1} $$ where $\varepsilon$ is a white noise. 1) No since $Var(x_{t+1}) = Var(x_t) + Var(\varepsilon_{t+1})$ is stricly increasing while ...


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Existence of arbitrage opportunities does not lead to market as inefficient. Samuelson has defined relationship between existence of arbitrage opportunities and market efficiency. He said, if market adjust quickly to arbitrage opportunities to return back to normal without cost of any other investor and through market mechanism then market can be said ...


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It seems reasonable that no-arbitrage doesn't necessarily imply EMH. If we are talking pure arbitrage opportunities, like offsetting the same contract on 2 exchanges, futures cash and carry, BS options no-arbitrage, etc. Mainly, for derivative products it's very easy to do the arbitrage trade. However, this means that you are assuming the underlying product ...


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I'll address things in order as I encountered them in the question. First, your formula for RV only makes sense if $X_{t_i}$ is the log-price, not log-return. If this was just a mistype it would probably be best if you edited the question to correct it. If it is not a mistype, let me know, because then you have bigger problems... Answer 0: I have no idea ...



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