This was discussed in a previous thread. http://www.elitetrader.com/vb/showthread.php?s=&postid=108473#post108473 In response to the comments and criticisms(mostly valid) of my original post I have done a more thorough analysis. I have calculated the mean for the differences in share or index prices given below, and then grouped the results into 2 sets N1 and N2 according to whether they were above or below the mean. I then performed the Wald-Wolfowitz runs test. Each run is a sequence of either N1 or N2. Indexes OEX between 28/8/02 and 2/8/82 OEX for 1 day interval Runs: 2580 N1: 2530 N2:2535 Expected Number of Runs: 2533.5; sd: 35.5809 z-value= 1.30695; approx. probability: 0.90439 z-val= 1.3210(continuity correct.); p: 0.90675 OEX for 20 days interval Runs: 131 N1::124 N2:126 Expected Number of Runs: 126; sd: 7.8893 z-value= 0.63478; approx. probability: 0.73722 z-val= 0.6981(continuity correct.); p: 0.75746 OEX for 200 days interval Runs:12 N1:10 N2:12 Expected Number of Runs: 11.9; sd: 2.2688 z-value= 0.04006; approx. probability: 0.51598 z-val= 0.2604(continuity correct.); p: 0.60274 exact probability of 12 or fewer runs= 0.60503 DJIA yearly interval between 02/1/53 and 13/12/91 Runs:20 N1:20 N2:16 Expected Number of Runs: 18.8; sd: 2.9193 z-value= 0.41867; approx. probability: 0.66227 z-val= 0.5899(continuity correct.); p: 0.72239 exact probability of 20 or fewer runs= 0.72244 Shares (suggested by jperl) tmpw between 16/12/96 and 8/10/02 Runs:716 N1:793 N2:659 Expected Number of Runs: 720.8; sd: 18.8837 z-value= -0.2550; approx. probability: 0.39933 z-val= -0.228(continuity correct.); p: 0.40959 aapl between 9/9/84 and 8/10/02 Runs:2258 N1:2430 N2:2131 Expected Number of Runs: 2271.7; sd: 33.6188 z-value= -0.4074; approx. probability: 0.34182 z-val= -0.392(continuity correct.); p: 0.3473 Conclusion: we cannot reject the hypothesis that the movements of the shares and indexes in these tests are random. Some of the other points raised: How is it that there are successful traders e.g. those described in The New Market Wizards by Jack Schwager? The Goddess of Chance will allow some players in a game based on luck to be profitable. On average you will be profitable 50% of the time. Schwager does not provide many figures on his wizardsâ results but I cannot resist this one observation. One trader he interviews, Paul Tudor Jones, was long on S&P futures the first time Schwager interviews him. He makes a $1 million loss. The second time he interviews him he is short and this time profitable. Thus in a sample of 2, Jones is right 50% of the time: exactly what one would predict if markets are random Are shares chaotic? No, because the number of runs in a chaotic series is higher than in a random one. www.yabz.com/random.php

Not only are you barking up the wrong tree, you aren't even in the right forest. All the calculations in the world won't change this, because you make faulty assumptions that have nothing to do with real trading. If you are going to make an example of Paul Tudor Jones, consider this quote from him (and think hard on it to figure out what is wrong with making conclusions based on generalizations drawn from a full data set): The secret to being successful from a trading perspective is to have an indefatigable and an undying and unquenchable thirst for information and knowledge. Because I think there are certain situations where you can absolutely understand what motivates every buyer and seller and have a pretty good picture of whatâs going to happen. And it just requires an enormous amount of grunt work and dedication to finding all possible bits of information. -PTJ alma mater interview

For the last time -- markets are not "random," they are chaotic. Was it random that markets went DOWN right after September 11'th? Was it random that they came back up slowly afterwards? As you zoom down on the time frame, markets become more unpredictable. Think about this: On a tick by tick basis, we can pretty much say the market is random. We don't know if Joe's order from NY will be a buy or sell and we also don't know if Sally's order from Chicago will be a buy or sell. On a tick by tick basis, we can equate market movements to resembling randomness. However, as you pull away from the smallest possible timeframe (ticks) and look at minutes, hours and days, patterns will start to emerge. It is up to the trader to isolate how he or she is going to use various time frames to make a prediction based on a future occurrence. If everyone in the world traded by flipping a coin, we could say with confidence that markets are completely random. However, traders are acting off psychology -- both fear and greed. These patterns of fear and greed show up on many time frames. How can you call a system random when the variables that make up that system are governed by non-random actions? That is absurd. The world you are looking for is chaotic and not random. Think of it in terms of spatial events. If I shoot an arrow at a grid that has 1x1 square foot blocks, I'll probably hit the square I'm shooting for most of the time. If you continue to double the number of blocks but keep the space in which the blocks are made the same, my odds of hitting the block I'm after will fall, but I will still hit it occasionally. If, however, you make it one billion blocks and ask me to hit a certain one, the arrow will appear to strike random squares near where I am aiming. However, where the arrow lands is NOT random but merely a result of chaos theory from the subtle movements in my muscles, air currents, etc. It is YOUR job to step back and look at the big picture and not concern yourself with microscopic gigablocks. You need to learn how this and that relates to each other to give yourself an EDGE over that 50% occurrence that your math is telling you is unavoidable. Get out of the math because math is deceiving. Like darkhorse said, you're looking the atoms within the bark of a tree instead of looking for paths in the forest.

Those guys might be making big money, but I'm skeptical. (Warning, this post is basically a tangent- but this doesn't look like a long lived thread anyway. How many random walkers are in here? Two? Three?) While trading requires a heavy dose of probability and mathematics, hard science types often have issues with being too rigid. When you're a product of the university system and spent years of your life earning a masters and PhD in the hard sciences, it's seared into your soul that you must have concrete proof for every assertion and that you must discard or ignore anything that you cannot quantify. There is a culture that says "if you can't conclusively prove it with a heavy duty mathematical equation, then you have no right to assert it or even to believe it." Particle physicists, for example- the top of the heap by their own lights- are known for their extreme disdain of the "soft" sciences. Most of them wouldn't be caught dead talking to anyone from the psychology or sociology or philosophy department- what an embarrassment to be associated with such losers! No different than the high school football jocks who snicker at the pimply nerd walking down the hall. Economics is a soft science that desperately wants to be a hard science- the skinny kid who isn't football material but wishes he were with all his heart. So economists analyze "rational economic man" instead of the real thing (too hard to pin down) and they try to impress the quant jocks with all manner of useless math- "See, we can do complicated equations too! We think sociology, pyschology and, bleah, PHILOSOPHY are stupid wastes of time too! Can't we be part of the club? Pleeease?" The arrogance of the hard sciences comes back to bite them when they stray off the reservation (this is obviously a generalization- no group is 100% homogenous through and through and not all science types are arrogant.) When you are arrogant you hate being wrong and you refuse to put up with partial explanations or partial solutions. When you are overly rigorous- quantitative to a fault- you refuse to go down many intuitive roads, or even to consider them- and thus many doors remain closed to you. The book about Farmer's operation- "The Predictors"- was panned pretty hard on Amazon, and rightfully so considering what little real information was presented. Basically a sycophantic puff piece with no meat on the bone. Do the Predictors have the skills to pay the bills? Maybe, maybe not. My guess is that their returns, if positive at all, are no better than the returns of countless other mechanical systems that non-PhD, non-genius traders have successfully employed. And of course, the existence of successful mechanical systems- of which there are many, and which can be easily verified- naturally begs the question: why is anyone still questioning whether the market can be beat in the first place???

I think the best trading advice / little quibit was (more or less) "Trade what you see, not what you think." Darkhorse, do you trade a mechanical system? Did you play football in highschool?

no on both counts and btw i have nothing against football players- my best friend in high school was a wide receiver- it just struck me as an apropos analogy

The only thing a man deems impossible to understand is that which he does not yet understand. Sorry, I was feeling a little philosophical. MUChris

Hmmmmm, are you sure it is the market itself that is chaotic or is it our perception of it that creates an illusion of chaos? The map is not the territory... Chaotic, random, whatever the f$ck. One thing I know for sure through direct experience is that while the market may be random, chaotic, or just my explination ---> "sponateous-organic-harmony" --- the process of consistently pulling money out is not a random act and the products of a traders actions go far beyond the realm of chance... All this philosophizing these guys do about her nature is for the birds, I can hear a birds song without having to know how it does it and my truth will be and is found through action... PEACE and good-trading, Commisso