well i have and i'm trying further. so feel free to ignore this thread if you don't want to help or have anything of substance to say.
Randon Walk makes perfect sense if you believe there is no ongoing consistency to price oscillations. Randon Walk makes no sense if you believe there is ongoing consistency to price oscillations. Randon Walk is confusing if you don't have enough information to form any solid beliefs. Everyone "pretty much" falls into one of these three categories and you can guarantee an argument will start when people from the first two camps try to make a case for their beliefs. IMHO - Randon Walk was grounded in solid theory when technology didn't offer a vehicle toward the destination of alternative theories or potential proofs. Times are changing and so are the advancements of our personal abilities to solve the unsolvable problems of the past. Sometimes just being open to the possibilties of those advancements will lead to conclusions never before thought possible.
Actually... Reducing "random walk" as generally understood... To "consistency of price oscillations" is a misleading oversimplification. The conclusions of "random walk" address the pricing efficiency of financial markets in the context of news dissemination. Many successful quants believe that "pricing efficiency" holds for liquid securities... Especially electronic markets not manipulated by a Specialist. You can quibble about fine points... but the net effect is that you are confronted with a random system. These same quants ** know ** that low volume exotic securities are often NOT priced efficiently. These stocks can get profitably mispriced... Even though they continue to exhibit random close-to-Normally-Distributed "price oscillations" 90% of the time. I'm detaching... (A) profitable "pricing inefficiencies" from (B) non-random "price oscillations" Just because one can profit from (A)... It does not follow that one can profit from (B). Also... Your last statement is colored by your belief in low level non-random "oscillations"... Because no amount of advancement or new technology will help predict random events. Maybe if I was "just open" to advances in Astrology... it would transform my life. rm+
You have just made my point. Oh, on a note of clarification. I don't have any beliefs that include anyone being able to "Predict" random events with any consistency, don't believe in Astrology and don't see where either of those things were mentioned in my original post but I appreciate you stretching my original post to include those absurd notions. May I ask what "low level non-random oscillations" are or at least what you "mean" by that definition?
Jerryz the math are easy to explain what the statement means. Xi are the ith step displacement. Assume step size equals S, so Xi can be either +S or –S. Total displacement after n steps is Xtot = X1 + X2 + X3 + …. + Xn Mean [Xtot] = Mean[X1 + X2 + X3 + …. + Xn] = Mean[X1] + Mean[X2] + …. +Mean[Xn] but Mean[Xi] = 0.5 * S + 0.5*(-S) = 0 for the fair tossing coin. Mean [Xtot] = 0 + 0 + …. + 0 = 0 Variance [Xtot] = Variance [X1 + X2 + X3 + …. + Xn] and because X1,X2,…,Xn independent variables you can write Variance [X1 + X2 + X3 + …. + Xn] = Variance[X1] + Variance[X2] + ... +Variance[Xn] Variance[Xi] = 0.5 * S^2 + 0.5 * (-S)^2 – (Mean[Xi])^2 = S^2 So Variance[Xtot] = S^2 + S^2 + … + S^2 = n * S^2 Standard Dev [Xtot] = sqr(n * S^2) = sqr(n) * S and that explains the "depending on the square root of the number of tosses" part of the statement.