Faster for president! Faster I enjoy and admire you sooo much that I think I may even start a website to honor you... www.FasterPussyCatIsTheShit.com!!!! PEACE and good trading, Commisso
Actually chaos theory is ultimately inadequate to explain the markets, although its a better model than coin-tossing randomness. Chaos occurs in systems with nonlinear feedback -- in particular systems with positive feedback that cause amplification of small perturbations of the system. A chaotic system (in the scientific/mathematical sense) can be 100% deterministic with no random components, noise, etc. For example, one of the simplest deterministic chaotic systems is three (or more) bodies orbiting each other under gravitational influence. This simple system has no analytic solution and the motion cannot be reliably predicted for very long. And yes, this means, that the future motion of our solar system is ultimately NOT predictable in the long-run (IIRC, the current prediction limit is only few million years into the future). For a chaotic system, doubling the quantity/quality of data about the system only adds a small amount of additional predictive power -- its a serious case of diminishing returns. <b>Controlling Chaotic Systems</b> Chaotic systems actually have some paradoxical features -- they may be unpredictable, but they can be extremely controllable. If you understand a chaotic system, you can actually control it with amazing accuracy and very little effort. If you know that a small perturbation amplifies to drive the system in a certain direction, then you can easily control the system with small inputs. Even more paradoxically, you don't even need to know the parameters of the system very accurately in order to control it. Applications include stabilizing the output of high-power lasers, enhancing the maneuverability of high-performance aircraft, and advanced heart pacemakers. If you don't believe me on this one, go out and start reading the academic literature on this topic. Perhaps the market analog of this is the games that MM and specialists play to blow-out people's stops or pump-n-dump shares. If the market were only chaotic, then a clever trader could become the boss of the market. <b> The problem is that the markets are WORSE than chaotic.</b> To understand this fact, we need to understand an important fact about the vast majority of chaotic systems that most people study. Chaotic systems may be ultimately unpredictable in the behavior, they are consistent in behavior. This consistent pattern of behavior is called the "strange attractor" of the system. The reason for the consistency of behavior is that the chaotic systems studied by chaos systems theorists have a fixed, unchanging set of equations that define the behavior (gravity in a 3-body problem is the same yesterday, today, and tomorrow. The physical properties of air, water, and land that drive the weather are the same yesterday, today, and tomorrow). <b>The changing physics of the markets</b> Where standard chaotic systems are driven by the inevitable and unchanging physics of their components (with nonlinear positive feedback loops that create chaos), the markets have a self-modifying, anticipatory element that causes the equations of motion to change over time. Its the old "traders know that other traders behave with fear and greed" so that means that "traders know that traders know that other traders behave with fear and greed"..... Traders are constantly seeking new patterns and by trading those patterns, they change the patterns. Moreover, the market structure can change as different types of trading and investing styles arrive or depart (for example trades that exploit the realignment of a stock index only work because of the current fad of stock index mutual funds). Finally, market clearing mechanisms, new markets, and regulatory changes impact the "equations of motion" of the markets (the list includes decimalization, SuperSOES, the rise of ECNs, the advent of extended hours trading, index ETFs, SSFs, etc.). <b>Humans are sufficient, but not necessary for complex behavior:</b> Although the psychological and cognitive features of humans play a major role in how markets behave, a market with nonhuman participants can also display self-modifying complex behavior. It's not humans, per se, that make the market's behave in such a complex fashion. Instead any distributed system that consists of a myriad of interacting elements can display arbitrarily complex behavior (see "A New Kind of Science" by Wolfram, or look into the Artificial Life literature for how simple interactions among dumb, emotionless objects can beget strange behavior). Even market systems that only contain negative feedback loops can be unstable if lags in the information flow interact poorly with sensitive, high-speed feedback loops (go read basic control theory to understand this one). <b>Chaos theory, better than the coin toss model, but still abysmal:</b> The people that caution about reading too much into chaos theory are right. Its an OK model for thinking about some aspects of market behavior, but, ultimately, its predictive power is low. (Likewise, I'd be very careful with all the 50:50 coin toss analogies that get "tossed" about on ET. The market is NOT a coin, market events are NOT independent, and you have no guarantee that 50:50 behavior in the past will mean 50:50 behavior in the future.) Wishing that the markets actually were chaotic, cuz then I'd be the boss, Traden4Alpha
Traden4Alpha, That about sums it up -- but I think the biggest point that needs to be made about all of this stuff (since I started down that path of wavelets, fractals, chaos theory) is that trading doesn't need to encompass a bunch of complicated esoteric formulas and techniques. Although the markets exist under very complex mathematics, it doesn't change the fact that the market usually always have some sort of "price inertia" on various time frames that a good trader can recognize and trade from. My performance was getting worse and worse as I added more and more complex variables. Then, after thinking long and hard about it, I realized that I'd never be able to trade a complex system successfully -- and I wouldn't need to when you can just use simple eyeballing and experience to trade successfully. I am just afraid that Gordon is going to spend the rest of his life researching some perfect method when none exists. We're all going to have bad days -- but if you don't get back into the ring, you aren't going to learn anything. -------- Gordon, I have a really good mentor for you. His name is Mr. Stock Market. His rates vary from person to person, but he is structured on a tier rate. The more you pay, the more you will learn, but his teaching method is the best from anyone. If you want to schedule an appointment with Mr. Stock Market, his hours are 9:30 - 4:00 and you can consult him without appointment. Good luck.
tradin4, That's worth more than 2 cents. This is where Bernsteins book Against the Gods ends up. Anyway, it was worth more than 2 cents to me. There is something to be said for quality of life, and for me, figuring out how things work is one of the most enjoyable pastimes of this business. As far as the gambling analogies go, I look at it like, my job is not to figure out if it's gonna come up red or black, my job is to figure out if people are going to bet more money on red or black. Nice post alpha, I liked that one.
The moves that really matter are a function of new information. To the extent that that information is coming in radomly the markets are random. The short term responses might be predictable b/c the info is not incorporated instantly and/or correctly, and b/c of various market frictions that get in the way (e.g. the uptick rule etc). But beyond that, it'd say they are pretty random.
Actually that one is just as good!!! Thankyou Aphex... Yes that is exactly how I will describe the nature of the universe and the microcosm of it we call "The Market"... PEACE and good trading, Commisso
Flipping a coin is a non-independent probability event -- in that each flip has exactly 50/50 odds of occuring. However, the law of large numbers says that, over a very large trial, the distribution of all flips should get closer and closer to the ratio of .50 as X (X = number of samples) becomes larger. Now, that being said, the law of large numbers would also stipulate that if you flipped a coin twice, the odds of getting two heads is one in four. Why? Because here are the possible outcomes from two flips. HT TH HH TT We see heads / heads is one possibility out of four, so it should be a 25% chance. Now, if you flipped a coin 50 times, the odds of all of them being heads it 1 possibility out of 2^50'th power. Observe: One coin flip has the possible combinations of: H T (2 possibilities) Two coin flips: HT TH HH TT (4 possibilities) 3 coin flips: HHH HHT HTH HTT THH THT TTH TTT (8 possibilities) So, the formula for the probability of getting all heads for X number of flips is 1 in 2^X (X = number of trials) So, as a betting man, I'd put my money on heads because obviously, after 1 to the 2^50'th chance that heads would do that, I'd say your coin has two heads.