> 1.Mkt isn't like BM. BM permits -ve values & any market index say SPY must be non-negative. That's one reason everybody models log-returns, which map non-neg

> 1.Mkt isn't like BM. BM permits -ve values & any market index say SPY must be non-negative. That's one reason everybody models log-returns, which map non-negative prices onto the whole real line. > 2. We (quants) model market indices like SPY as a log-normal process like so : dS = rSdt + sigmaSdz ... But that doesn't make S itself Brownian. That's a geometric Brownian motion with drift. It is in fact the model developed by Louis Bachelier in his thesis of 1900 that presented the first mathematical description of Brownian motion. Much of the argument you're trying to make can be made better, in my opinion, simply by pointing people to the Grossman-Stiglitz paradox [1]: markets cannot be fully informationally efficient or no one would have the incentive to provide information to them through trading. 1 - [PDF] http://www.math.ku.dk/kurser/2003-1/invfin/GrossmanStiglitz.pdf http://www.math.ku.dk/kurser/2003-1/invfin/GrossmanStiglitz....