Those susceptible to behavioural biases: consistent, correlated and irrational.
Smart, i.e. rational.
50% Technical analysts [1]
Poor - trade randomly.
Good - consistent, correlated and irrational.
Assuming that all five types of market participant exist (they do), with imperfect arbitrage opportunities and no 100% rational traders, the resultant effect on the market is the aggregate effect of good technical analysts trading against fundamental analysts susceptible to behavioural biases.
[1] Technical analysis *is* a behavioural bias (representiveness), here a "good" technical analyst is one who accurately and consistently trades according to the rules of technical analysis.
Important Publications
70.58
KYLE, Albert S., 1985. Continuous Auctions and Insider Trading [about 1,160]
A dynamic model of insider trading with sequential auctions, structured to resemble a sequential equilibrium, is used to examine the informational content of prices, the liquidity characteristics of a speculative market, and the value of private information to an insider. The model has three kinds of traders: a single risk neutral insider, random noise traders, and competitive risk neutral market makers. The insider makes positive profits by exploiting his monopoly power optimally in a dynamic context, where noise trading provides camouflage which conceals his trading from market makers. As the time interval between auctions goes to zero, a limiting model of continuous trading is obtained. In this equilibrium, prices follow Brownian motion, the depth of the market is constant over time, and all private information is incorporated into prices by the end of trading.
43.84
Financial prices have been found to exhibit some universal characteristics that resemble the scaling laws characterizing physical systems in which large numbers of units interact. This raises the question of whether scaling in finance emerges in a similar way — from the interactions of a large ensemble of market participants. However, such an explanation is in contradiction to the prevalent 'efficient market hypothesis' in economics, which assumes that the movements of financial prices are an immediate and unbiased reflection of incoming news about future earning prospects. Within this hypothesis, scaling in price changes would simply reflect similar scaling in the 'input' signals that influence them. Here we describe a multi-agent model of financial markets which supports the idea that scaling arises from mutual interactions of participants. Although the 'news arrival process' in our model lacks both power-law scaling and any temporal dependence in volatility, we find that it generates such behaviour as a result of interactions between agents.
32.84
Agent-based computational economics (ACE) is the computational study of economies modeled as evolving systems of autonomous interacting agents. Thus, ACE is a specialization of economics of the basic complex adaptive systems paradigm. This study outlines the main objectives and defining characteristics of the ACE methodology and discusses similarities and distinctions between ACE and artificial life research. Eight ACE research areas are identified, and a number of publications in each area are highlighted for concrete illustration. Open questions and directions for future ACE research are also considered. The study concludes with a discussion of the potential benefits associated with ACE modeling, as well as some potential difficulties.
32.79
We propose a theory of asset pricing based on heterogeneous agents who continually adapt their expectations to the market that these expectations aggregatively create. And we explore the implications of this theory computationally using our Santa Fe artificial stock market.
Asset markets, we argue, have a recursive nature in that agents’ expectations are formed on the basis of their anticipations of other agents’ expectations, which precludes expectations being formed by deductive means. Instead traders continually hypothesize--continually explore--expectational models, buy or sell on the basis of those that perform best, and confirm or discard these according to their performance. Thus individual beliefs or expectations become endogenous to the market, and constantly compete within an ecology of others’ beliefs or expectations. The ecology of beliefs co-evolves over time.
Computer experiments with this endogenous-expectations market explain one of the more striking puzzles in finance: that market traders often believe in such concepts as technical trading, "market psychology, " and bandwagon effects, while academic theorists believe in market efficiency and a lack of speculative opportunities. Both views, we show, are correct, but within different regimes. Within a regime where investors explore alternative expectational models at a low rate, the market settles into the rationalexpectations equilibrium of the efficient-market literature. Within a regime where the rate of exploration of alternative expectations is higher, the market self-organizes into a complex pattern. It acquires a rich psychology, technical trading emerges, temporary bubbles and crashes occur, and asset prices and trading volume show statistical features--in particular, GARCH behavior--characteristic of actual market data.
32.79
ARTHUR et al., Asset Pricing Under Endogenous Expectations in an Artificial Stock Market [about 323] "We propose a theory of asset pricing based on heterogeneous agents who continually adapt their expectations to the market that these expectations aggregatively create." "Within a regime where investors explore alternative expectational models at a low rate, the market settles into the rationalexpectations equilibrium of the efficient-market literature. Within a regime where the rate of exploration of alternative expectations is higher, the market self-organizes into a complex pattern. It acquires a rich psychology, technical trading emerges, temporary bubbles and crashes occur, and asset prices and trading volume show statistical features -- in particular, GARCH behavior -- characteristic of actual market data." Arthur et al. (1996)
Agent-based computational finance. Handbook of Computational Economics.
Handbook of Computational Economics, Volume 2
@incollection{LeBaron06,
author = {Blake LeBaron},
title = {Agent-based Computational Finance},
booktitle = {Handbook of Computational Economics: Agent-Based Computational Economics, Volume 2},
year = {2006},
editor = {Leigh Tesfatsion and Kenneth L. Judd},
pages = {1187--1233},
organization = {},
publisher = { Elsevier/North-Holland},
address = {Amsterdam, The Netherlands},
month = {May},
note = {},
key = {},
chapter = {24},
abstract = {This chapter surveys research on agent-based models used in finance. It concentrates on models where the use of computational tools is critical for the process of crafting models that give insights into the importance and dynamics of investor heterogeneity in many financial settings.}
}
\citeasnoun{LeBaron06} surveys research on agent-based models used in finance.
30.17
LeBARON, Blake, 1998. Agent Based Computational Finance: Suggested Readings and Early Research [about 95]
Computational models for financial markets with many interacting agents have recently appeared as a tool for examining learning and evolutionary issues in market dynamics. This paper surveys some of the early research in this area with emphasis on the many unsolved problems that researchers will need to confront. Several early papers are emphasized which focus on some of these problems, and references to many other papers are also given.
30.17
CONT, Rama and Jean-Philippe BOUCHAUD, 1998. Herd behavior and aggregate fluctuations in financial markets [about 146]
We present a simple model of a stock market where a random communication structure between agents gives rise to a heavy tails in the distribution of stock price variations in the form of an exponentially truncated power-law, similar to distributions observed in recent empirical studies of high frequency market data. Our model provides a link between two well-known market phenomena: the heavy tails observed in the distribution of stock market returns on one hand and 'herding' behavior in financial markets on the other hand. In particular, our study suggests a relation between the excess kurtosis observed in asset returns, the market order flow and the tendency of market participants to imitate each other.
27.13
The 2001 Trading Agent Competition was the second in a series of events aiming to shed light on research issues in automating trading strategies. Based on a challenging market scenario in the domain of travel shopping, the competition presents agents with difficult issues in bidding strategy, market prediction and resource allocation. Entrants in 2001 demonstrated substantial progress over the prior year, with the overall level of competence exhibited suggesting that trading in online markets is a viable domain for highly autonomous agents.
24.93
WOOLDRIDGE, Michael and Nicholas R. JENNINGS, Pitfalls of Agent-Oriented Development [about 362]
While the theoretical and experimental foundations of agent-based systems are becoming increasingly well understood, comparatively little effort has been devoted to understanding the pragmatics of (multi-)agent systems development --- the everyday reality of carrying out an agent-based development project. As a result, agent system developers are needlessly repeating the same mistakes, with the result that, at best, resources are wasted --- at worst, projects fail. This paper identifies the main pitfalls that await the agent system developer, and where possible, makes tentative recommendations for how these pitfalls can be avoided or rectified.
23.38
LeBARON, W. Brian ARTHUR and Richard PALMER, 1998. Time Series Properties of an Artificial Stock Market [about 147]
This paper presents results from an experimental computer simulated stock market. In this market artificial intelligence algorithms take on the role of traders. They make predictions about the future, and buy and sell stock as indicated by their expectations of future risk and return. Prices are set endogenously to clear the market. Time series from this market are analyzed from the standpoint of some well known empirical features in real markets. The simulated market is able to replicate several of these phenomenon, including fundamental and technical predictability, volatility persistence, and leptokurtosis. Moreover, agent behavior is shown to be consistent with these features in that they condition on the variables that are found to be significant in the time series tests. Inside this experimental model there exists a well-defined linear homogeneous rational expectations equilibrium. This is used as a benchmark in the experiments to assess the overall ability of the agents in learning. It is found that for certain parameters the results in the market are consistent with this benchmark.
22.56
FARMER, J. Doyne, 2000. Market force, ecology, and evolution [about 263] "Markets have internal dynamics leading to excess volatility and other phenomena that are difficult to explain using rational expectations models. This paper studies these using a nonequilibrium price formation rule, developed in the context of trading with market orders. Because this is so much simpler than a standard inter-temporal equilibrium model, it is possible to study multi-period markets analytically. There price dynamics have second order oscillatory terms. Value investing does not necessarily cause prices to track values. Trend following causes short term trends in prices, but also causes longer-term oscillations. When value investing and trend following are combined, even though there is little linear structure, there can be boom-bust cycles, excess and temporally correlated volatility, and fat tails in price fluctuations. The long term evolution of markets can be studied in terms of flows of money. Profits can be decomposed in terms of aggregate pairwise correlations. Under reinvestment of profits this leads to a capital allocation model that is equivalent to a standard model in population biology. An investigation of market efficiency shows that patterns created by trend followers are more resistant to efficiency than those created by value investors, and that profit maximizing behavior slows the progression to efficiency. Order of magnitude estimates suggest that the timescale for efficiency is years to decades."
19.99
FARMER, J. Doyne and Shareen JOSHI, The price dynamics of common trading strategies [about 98] "A deterministic trading strategy can be regarded as a signal processing element that uses external information and past prices as inputs and incorporates them into future prices. This paper uses a market maker based method of price formation to study the price dynamics induced by several commonly used financial trading strategies, showing how they amplify noise, induce structure in prices, and cause phenomena such as excess and clustered volatility." Farmer and Joshi (2000)
18.18
CHALLET, Damien, Matteo MARSILI and Riccardo ZECCHINA, 2000. Statistical mechanics of systems with heterogeneous agents: Minority Games [about 28]
We study analytically a simple game theoretical model of heterogeneous interacting agents. We show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz. Such a stationary state differs from the Nash equilibrium where each agent maximizes her own utility. The latter turns out to be characterized by a replica symmetry broken structure. Numerical results fully agree with our analytic findings.
17.32
The 2002 Trading Agent Competition (TAC) presented a challenging market game in the domain of travel shopping. One of the pivotal issues in this domain is uncertainty about hotel prices, which have a significant influence on the relative cost of alternative trip schedules. Thus, virtually all participants employ some method for predicting hotel prices. We survey approaches employed in the tournament, finding that agents apply an interesting diversity of techniques, taking into account differing sources of evidence bearing on prices. Based on data provided by entrants on their agents’ actual predictions in the TAC-02 finals and semifinals, we analyze the relative efficacy of these approaches. The results show that taking into account game-specific information about flight prices is a major distinguishing factor. Machine learning methods effectively induce the relationship between flight and hotel prices from game data, and a purely analytical approach based on competitive equilibrium analysis achieves equal accuracy with no historical data. Employing a new measure of prediction quality, we relate absolute accuracy to bottom-line performance in the game.
14.00
BAK, P., M. PACZUSKI and M. SHUBIK, 1996. Price Variations in a Stock Market with Many Agents [about 98]
Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large variations may be due to a crowd effect, where agents imitate each other's behavior. The variations over different time scales can be related to each other in a systematic way, similar to the Levy stable distribution proposed by Mandelbrot to describe real market indices. In the simplest, least realistic case, exact results for the statistics of the variations are derived by mapping onto a model of diffusing and annihilating particles, which has been solved by quantum field theory methods. When the agents imitate each other and respond to recent market volatility, different scaling behavior is obtained. In this case the statistics of price variations is consistent with empirical observations. The interplay between "rational" traders whose behavior is derived from fundamental analysis of the stock, including dividends, and "noise traders," whose behavior is governed solely by studying the market dynamics, is investigated. When the relative number of rational traders is small, "bubbles" often occur, where the market price moves outside the range justified by fundamental market analysis. When the number of rational traders is large, the market price is generally locked within the price range they define.
13.86
HOLLAND, John H. and John H. MILLER, 1991. Artificial Adaptive Agents in Economic Theory [about 215]
Economic analysis has largely avoided questions about the way in which economic agents make choices when confronted by a perpetually novel and evolving world. As a result, there are outstanding questions of great interest to economics in areas ranging from technological innovation to strategic learning in games. This is so, despite the importance of the questions, because standard tools and formal models are ill-tuned for answering such questions. However, recent advances in computer-based modeling techniques, and in the subdiscipline of artificial intelligence called machine learning, offer new possibilities. Artificial adaptive agents (AAA) can be defined and can be tested in a wide variety of artificial worlds that evolve over extended periods of time. The resulting “complex adaptive systems” can be examined both computationally and analytically, offering new ways of experimenting with and theorizing about adaptive economic agents.
12.09
PALMER, R.G., et al., 1994. Artificial Economic Life: A Simple Model of a Stockmarket [about 113]
We describe a model of a stockmarket in which independent adaptive agents can buy and sell stock on a central market. The overall market behavior, such as the stock price time series, is an emergent property of the agents' behavior. This approach to modelling a market is contrasted with conventional rational expectations approaches. Our model does not necessarily converge to an equilibrium, and can show bubbles, crashes, and continued high trading volume.
12.00
FARMER, J. Doyne, 1999. Physicists Attempt to Scale the Ivory Towers of Finance [about 164]
"Physicists have recently begun doing research in finance, and even though this movement is less than five years old, interesting and useful contributions have already emerged. This article reviews these developments in four areas, including empirical statistical properties of prices, random-process models for price dynamics, agent-based modeling, and practical applications."
11.77
This paper is intended to guide researchers interested in building their own agent-based financial markets. Key design questions are outlined, along with some of the major controversies about which directions to take.
08.28
This short summary presents an insider’s look at the construction of the Santa Fe artificial stock market. The perspective considers the many design questions that went into building the market from the perspective of a decade of experience with agent-based financial markets. The market is assessed based on its overall strengths and weaknesses.
08.22
Recent research has shown the importance of time horizons in models of learning in finance. The dynamics of how agents adjust to believe that the world around them is stationary may be just as crucial in the convergence to a rational-expectations equilibrium as getting parameters and model specifications correct in the learning process. This paper explores the process of this evolution in learning and time horizons in a simple agent-based financial market. Trading is done in a market with a single stock in finite supply, paying a stochastic dividend. A risk free asset is available in infinite supply. Agents maximize an infinite-horizon time-separable utility function in each period's consumption. They are required to select from a set of given forecasting/trading rules optimized to past data. Heterogeneity is introduced through the time horizon that they believe is relevant to use in deciding over trading rules. Long horizon agents build relative performance measures looking back into the distant past, while those with short horizons believe that only recent measures of performance are useful for decision making. The price of the risky asset is set to balance current agent demand with its fixed supply at each period. Once the price is endogenously determined, returns are calculated and dividends paid. Agents make consumption decisions and wealth is calculated. Relative wealth affects the market in two ways. First, wealthier individuals are able to move prices by larger amounts. Second, evolution takes place in which less wealthy agents are dropped out of the market and replaced with new ones drawn according to current wealth levels. The horizon lengths of wealthier agents are given more weight in the generation of new agents. The primary objectives of this paper are to understand better the convergence properties of learning with heterogeneous horizons. Several benchmark cases are explored in which a stationary rational-expectations equilibrium exists, and agents should converge to the longest horizon possible. The model is explored to see in which cases this convergence does not occur, and if it does not, what sorts of short-horizon features self-reinforce in agents' short-horizon forecasting models. Also, experiments are performed on the "invadeability" of a group of short-horizon investors to see if they can be invaded by those with long horizons. The paper also briefly addresses two eventual goals. First, the replication of certain features in financial data, such as excess volatility and trading volume phenomena. Second, while his model is strictly computational, some assessments about moving it to an analytic setting are made.
07.78
This paper introduces an agent-based artificial financial market in which heterogeneous agents trade one single asset through a realistic trading mechanism for price formation. Agents are initially endowed with a finite amount of cash and a given finite portfolio of assets. There is no money-creation process; the total available cash is conserved in time. In each period, agents make random buy and sell decisions that are constrained by available resources, subject to clustering, and dependent on the volatility of previous periods. The model herein proposed is able to reproduce the leptokurtic shape of the probability density of log price returns and the clustering of volatility. Implemented using extreme programming and object-oriented technology, the simulator is a flexible computational experimental facility that can find applications in both academic and industrial research projects.
07.71
This paper investigates how adaptive software agents may utilize reinforcement learning algorithms such as Q-learning to make economic decisions such as setting prices in a competitive marketplace. For a single adaptive agent facing fixed-strategy opponents, ordinary Q-learning is guaranteed to find the optimal policy. However, for a population of agents each trying to adapt in the presence of other adaptive agents, the problem becomes non-stationary and history dependent, and it is not known whether any global convergence will be obtained, and if so, whether such solutions will be optimal. In this paper, we study simultaneous Q-learning by two competing seller agents in three moderately realistic economic models. This is the simplest case in which interesting multi-agent phenomena can occur, and the state space is small enough so that lookup tables can be used to represent the Q-functions. We find that, despite the lack of theoretical guarantees, simultaneous convergence to self-consistent optimal solutions is obtained in each model, at least for small values of the discount parameter. In some cases, exact or approximate convergence is also found even at large discount parameters. We show how the Q-derived policies increase profitability and damp out or eliminate cyclic price wars compared to simpler policies based on zero lookahead or short-term lookahead. In one of the models (the Shopbot model) where the sellers' profit functions are symmetric, we find that Q-learning can produce either symmetric or broken-symmetry policies, depending on the discount parameter and on initial conditions.
06.77
FARMER, J. Doyne and Andrew W. LO, Frontiers of finance: Evolution and efficient markets [about 127]
"In this review article, we explore several recent advances in the quantitative modeling of financial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions of research, some focusing on more elaborate mathematical models that are capable of rationalizing the empirical facts, others taking a completely different tack in rejecting rationality altogether. One of the most promising directions is to view financial markets from a biological perspective and, specifically, within an evolutionary framework in which markets, instruments, institutions, and investors interact and evolve dynamically according to the ‘‘law’’ of economic selection. Under this view, financial agents compete and adapt, but they do not necessarily do so in an optimal fashion. Evolutionary and ecological models of financial markets is truly a new frontier whose exploration has just begun." Farmer and Lo (1999)
06.23
ARTHUR, W. Brian, Designing Economic Agents that Act like Human Agents: A Behavioral Approach to Bounded Rationality [about 97] "[...] it also reproduces two stylized facts of human learning well-known to psychologists: that with frequency-dependent payoffs, humans meliorate rather than optimize; and there is a threshold in discrimination among payoffs below which humans may lock in to suboptimal choices. [...] To the degree that the algorithm replicates human behavior, it indicates that human learning most often adapts its way to an optimal steady state or, interactively, to a Nash outcome. But it also shows that humans systematically underexplore less-known alternatives, so that learning may sometimes lock in to an inferior choice when payoffs to choices are closely clustered, random, and difficult to discriminate among. [...] there is a characteristic learning time for human decisions. Arthur (1991)
05.18
JOHANSEN, Anders and Didier SORNETTE, 2001. Modeling the Stock Market prior to large crashes "We propose that the minimal requirements for a model of stock market price fluctuations should comprise time asymmetry, robustness with respect to connectivity between agents, "bounded rationality" and a probabilistic description. We also compare extensively two previously proposed models of log-periodic behavior of the stock market index prior to a large crash. We find that the model which follows the above requirements outperforms the other with a high statistical significance."
04.44
ARTHUR, W. Brian, 1994. Inductive Reasoning and Bounded Rationality (The El Farol Problem) [about 53] The inductive-reasoning system I have described above consists of a multitude of "elements" in the form of belief-models or hypotheses that adapt to the aggregate environment they jointly create. Thus it qualifies as an adaptive complex system. After some initial learning time, the hypotheses or mental models in use are mutually co-adapted. Thus we can think of a consistent set of mental models as a set of hypotheses that work well with each other under some criterion--that have a high degree of mutual adaptedness. Sometimes there is a unique such set, it corresponds to a standard rational expectations equilibrium, and beliefs gravitate into it. More often there is a high, possibly very high, multiplicity of such sets. In this case we might expect inductive reasoning systems in the economy--whether in stock-market speculating, in negotiating, in poker games, in oligopoly pricing, in positioning products in the market--to cycle through or temporarily lock into psychological patterns that may be non-recurrent, pathdependent, and increasingly complicated. Arthur (1994)
04.27
CHAN, Nicholas T., et al., 1999. Agent-Based Models of Financial Markets: A Comparison with Experimental Markets [about 39] "We construct a computer simulation of a repeated double-auction market, designed to match those in experimental-market settings with human subjects, to model complex interactions among artificially-intelligent traders endowed with varying degrees of learning capabilities. In the course of six different experimental designs, we investigate a number of features of our agent-based model: the price effciency of the market, the speed at which prices converge to the rational expectations equilibrium price, the dynamics of the distribution of wealth among the different types of AI-agents, trading volume, bid/ask spreads, and other aspects of market dynamics. We are able to replicate several findings of human-based experimental markets, however, we also find intriguing differences between agent-based and human-based experiments."
02.92
ALLEN, Franklin and Gary GORTON, Rational Finite Bubbles [about 33] Allen and Gorton (1991): "It is shown that a finitely-lived security can trade above its fundamental".
00.84
ANDRESEN, Trond, A Model of Short- and Long Term Stock Market Behaviour [about 22] "Real-world stock markets are volatile and expresses such traits as overvaluation, psychological moods, cycles and crashes. This paper develops and explores a fairly simple model which expresses these traits. The model is continuous and non-linear."[...]"The model is not based on micro individual agents, but on the market as a whole displaying composite behavior that is argued to be the aggregate result of individual agent behaviour. The idea is to make some behavioural assumptions, and then adjust parameters and explore whether realistic qualititative traits of stock market dynamics show up." Andresen (1998)
00.15
LeBARON, Blake, 1999. Building Financial Markets With Artificial Agents: Desired goals, and present techniques [about 15] "Financial markets operate as a large interacting group of agents each in a constant struggle to better understand and interpret current prices and information. The complex interconnections between prices and information is probably more dramatic in financial markets than any other economic situation. Economic theory has been capable of describing many different financial equilibria, but it remains quiet on the types of dynamics that can occur while learning is still active and equilibrium is never quite obtained. Models of learning agents allow a direct attack on this problem. However, even though this approach may seem appealing at first it does come with many costs. The first of these is the modeling of the agents themselves. Boundedly rational agents can come in many forms, and an important question for theorizing is where to\set the dial" of rationality. This paper will describe some of the methods that have worked, and which directions look promising. Some methods for endogenously setting the level of rationality will be discussed. Finally, comparisons to the single agent, homogeneous belief world will be made, stressing why this is still a useful benchmark. A second issue involves the actual trading mechanisms, and this will be brie°y discussed in relation to how outcomes can be affected. In closing, some of the policy questions centered on market stability and structure will be compared with certain computational issues." LeBaron (1999)
00.15
LEBARON, B., 1999. Building Financial Markets with Artificial Agents: Desired Goals and Present Techniques, …. [Cited by 1] 0.15
LARNAC, Pierre-Marie, Scattered Information on a Speculative Market [about 5] "A very simple static, rational expectations, closed-form model is built as an alternative to Grossman-Stiglitz [1980]. It is the general framework for a systematic investigation of the way randomly distributed individual characteristics swamps informations relevant to the stock market equilibrium.The most important of those "noises" are the individual endowments in the numeraire good. Together with the endogenous quality of private signals, they allow a better understanding of the volatility of stock prices and of the Grossman-Stiglitz paradox. The real issue is not the "informational effciency" of the market, but the direct computation of the rational expectations equilibrium by putting in common anything anybody knows or observes in the economy." Larnac and Dauphine (1999)
00.00
HOWARD, Mark, "The Evolution of Trading Rules in an Artificial Stock Market" [about 37] "This paper applies evolutionary modeling to expectation formation of an asset’s price. As a first step I consider a population of n investors each of whom take on one of two possible cultural variants. Every individual is a potential role model for all other individual and can pass on their variant with a certain probability determined by the relative return to being that type. Different types of traders operate on different ‘models’ which forecast future price and dividend movements. The two basic types being traders being those who follow the fundamentals suggested by the CAPM model and those who follow technical trading rules such as buy if the price is above it’s 50 day moving average and sell if it is below. I show that given these two types of simple traders prices can fluctuate between periods of low volume and volatility and periods of high volume and volatility. Results indicate that given a random walk fundamental valuation, as the random fluctuations increase in magnitude, technical trading can become more profitable than fundamental trading, and for a period dominate the market." Howard (1999)
00.00