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Abstract:
Using a dynamical microeconomic model which generalizes the classical theory of adjustment to include finite asset base and trend-based investment preference, we develop a foundation for the technical analyis (or charting) of securities. The mathematically complete system of (deterministic) ordinary differential equations that has provided a quantitative explanation of the laboratory bubbles experiments generates a broad spectrum of patterns that are used by practitioners of technical analysis. The origins of many of these patterns are classified as (i) those that can be generated by the activities of a single group, and (ii) those that can be generated by the presence of two or more groups with asymmetric information. Examples of (i) include the head and shoulders, double tops, rising wedge while (ii) includes pennants and symmetric triangles. The system of differential equations is easily generalized to stochastic ODE'S. Application is also made to Japanese candlestick analysis.

Abstract:
Using two sets of data, including daily prices (open, close, high and low) of all S&P 500 stocks between 1992 and 1996, we perform a statistical test of predictive capability of candlestick patterns. Out-of-sample tests indicate statistical significance at the level of 36 standard deviations from the null hypothesis, and indicate a profit of almost 1% during a two-day holding period. An essentially non-parametric test utilizes standard definitions of three-day candlestick patterns and removes conditions on magnitudes. The results provide evidence that traders are influenced by price behavior. To the best of our knowledge, this is the first scientific test to provide strong evidence in favor of any trading rule or pattern on a large unrestricted scale.

candlestick patterns, statistical price prediction, price pattern, technical analysis

Abstract:
We report on a large number of laboratory market experiments demonstrating that a market bubble can be reduced under the following conditions: 1) a low initial liquidity level, i.e., less total cash than value of total shares, 2) deferred dividends, and 3) a bid-ask book that is open to traders. Conversely, a large bubble arises when the opposite
conditions exist.

The first part of the article is comprised of twenty-five experiments with varying levels of total cash endowment per share (liquidity level), payment or deferral of dividends and an open or closed bid-ask book. We find that the liquidity level has a very strong influence on the mean and maximum prices during an experiment (P <1/10,000). These results suggest that within the framework of the classical bubble experiments(dividends distributed after each period and closed book), each dollar per share of additional cash results in a maximum price that is $1 per share higher.

There is also limited statistical support for the theory that deferred dividends(which also lower the cash per share during much of the experiment) and an open book lead to a reduced bubble. The three factors taken together show a striking difference in the median magnitude of the bubble ($7.30 versus $0.22 for the maximum deviation from fundamental value).

Another set of twelve experiments features a single dividend at the end of fifteen trading periods and establishes a 0.8 correlation between price and liquidity during the early periods of the experiments. As a result, calibration of prices and evolution toward equilibrium price as a function of liquidity are possible.

Abstract:
The influence of speculative stocks on value stocks is examined through a set of economics experiments. The speculative asset is designed to model a company involved in a rapidly growing market that will be saturated at some unknown point. Using a control experiment where both assets are similar value stocks, we find statistical support for the assertion that the presence of a speculative stock increases the volatility and diminishes the price of the value stock. In addition, the temporal minimum price of the value stock during the last phase of the experiment is lower in the presence of the speculative stock (when the trading price of the speculative asset is declining sharply). These results indicate that an overreaction in the speculative stock tends to divert investment capital away from other assets. An examination of the relative magnitude of monthly closing price changes confirm strong correlations between the Dow Jones Average and the more speculative Nasdaq index during the time period in 1990 to 2001 and particularly during the two years prior to the peak in March 2000 (0.72 correlation) and the March 2000 to August 2001 decline (0.79 correlation). Supplementary experiments using independent (or legally separate) markets trading the same asset show that a higher price in one market does not lead to a higher one in the other.

asset price dynamics, speculative assets, value stocks, overreaction, excess cash, volatility, legally separated markets, independent markets, Chinese A/B shares

Abstract:
Editorial Commentary

Abstract:
The following results are obtained. (i) It is possible to obtain a time series of market data {y(t)} in which the fluctuations in fundamental value have been compensated for. An objective test of the efficient market hypothesis (EMH), which would predict random correlations about a constant value, is thereby possible. (ii) A time series procedure can be used to determine the extent to which the differences in the data and the moving averages are significant. This provides a model of the form y(t) - y(t - 1) = 0.5{y(t - 1) - y(t - 2)} + e(t) + 0.8e(t - 1), where e(t) is the error at time t, and the coefficients 0.5 and 0.8 are determined from the data. One concludes that today's price is not a random perturbation from yesterday's; rather, yesterday's rate of change is a significant predictor of today's rate of change. This confirms the concept of momentum that is crucial to market participants. (iii) The model provides out-of-sample predictions that can be tested statistically. (iv) The model and coefficients obtained in this way can be used to make predictions on laboratory experiments to establish an objective and quantitative link between the experiments and the market data. These methods circumvent the central difficulty in testing market data, namely, that changes in fundamentals obscure intrinsic trends and autocorrelations. This procedure is implemented by considering the ratio of two similar funds (Germany and Future Germany) with the same manager and performing a set of statistical tests that have excluded fluctuations in fundamental factors. For the entire data of the first 1149 days begining with the introduction of the latter fund, a standard runs test indicates that the data is 29 standard deviations away from that which would be expected under a hypothesis of random fluctuations about the fundamental value. This and other tests provide strong evidence against the efficient market hypothesis and in favor of autocorrelations in thedata. An ARIMA time series finds strong evidence (9.6 and 21.6 standard deviations in the two coefficients) that the data is described by a model that involves the first difference, indicating that momentum is the significant factor. The first quarter's data is used to make out-of-sample predictions for the second quarter with results that are significant to 3 standard deviations. Finally, the ARIMA model and coe±cients are used to make predictions on laboratory experiments of Porter and Smith in which the intrinsic value is clear. The model's forecasts are decidedly more accurate than that of the null hypothesis of random fluctuations about the fundamental value.

Abstract:
Price volatility and investor overreactions are commonplace in experimental asset markets. Understanding the price dynamics in these markets is crucial for designing successful new trading institutions. We report on a series of experiments to test the predictions of a new momentum model using a dynamical systems approach. This model is then pitted against several standard models to predict prices, as well as against expert human forecasters. The comparative results suggest that each model has its advantages and regions of best performance. Overall, the best predictive methods are the momentum model and expert human forecasters.

Abstract:
Overreactions and other behavioral effects in stock prices can best be examined by adjusting for the changes in fundamentals. We perform this by subtracting the relative price changes in the net asset value (NAV) from that of the market price (MP) daily for 134,406 data points of closed end funds trading in US markets. We examine the days before and after a significant rise or fall in price deviation and MP return and find evidence of overreaction in the days after the change. Prior to a spike in deviation we find a gradual two or three day decline (and analogously in the other direction). Overall, there is a characteristic diamond pattern, revealing a symmetry in deviations before and after the significant change. Much of the statistical significance and the patterns disappear when the subtraction of NAV return is eliminated, suggesting that the frequent changes in fundamentals mask behavior effects. A second study subdivides the data depending on whether the NAV or MP is responsible for the spike in the relative difference. In a majority of spikes, it is the change in market price rather than NAV that is dominant. Among those spikes for which there is little or no change in NAV, the results are similar to the overall study. Furthermore, the upward spikes are preceded by one or two days of declining market price while NAV rises slightly or is relatively unchanged. This suggests that a cause of the spike may be due to over-positioning of traders in the opposite direction in anticipation.

Overreaction, Price deviation, Diamond pattern, Overpositioning, Market dynamics, Financial markets, Behavioral finance, Closed-end funds

Abstract:
Asset market experiments are analyzed by distinguishing, ex post facto, participants who trade on fundamentals versus those who trade on momentum (i.e., buying when price is rising). The distinction is made when prices are above fundamental value, so that (in each period) those who have more offers than bids (net offerers) are classified as fundamentalists while those who have more bids than offers (net bidders) are defined to be momentum players. By analyzing the data of individual behavior we are able to address a number of key questions regarding bubbles. We find evidence that the cash supply of the momentum traders diminishes and the cash supply of the fundamental traders increases as the bubble forms. This suggests that the bubble is fueled by the cash of the momentum players and the reversal is caused by inadequate cash in their possession. These data are used in conjunction with a difference equation for price dynamics for two groups. The momentum traders exhibit a positive coefficient for price derivatives and a very small negative coefficient for trading based upon the deviation from fundamental value. Surprisingly, however, the fundamental traders, who exhibit a positive coefficient for trading on valuation, also exhibit a significantly positive coefficient for trend based buying. Thus, even those who are net offerers, classified as fundamentalists, are selling less and buying more of overvalued stock when there is a strong positive recent price change. There is also evidence that some fundamentalists change strategy to momentum trading as prices soar. An additional result is that the trend coefficient of the momentum traders vanishes with the implementation of an open book that allows traders to see all trades as they are entered.

Experimental economics, Asset markets, Behavioral finance, Momentum traders, Fundamental traders

Abstract:
We develop a methodology to extract a quantitative model for behavioral effects in markets from empirical data. A set of 24 asset market experiments are utilized to derive an equation of price and its dependence on momentum, fundamental value, excess bid level and liquidity considerations. A difference equation is derived from a statistical analysis of the data. The methods are quite general and can be utilized in conjunction with other behavioral finance effects that influence price dynamics.

Experimental economics, Asset markets, Behavioral finance

Abstract:
A system of nonlinear asset flow differential equations (AFDE) gives rise to an inverse problem involving optimization of parameters that characterize an investor population. The optimization procedure is used in conjunction with daily market prices and net asset values to determine the parameters for which the AFDE yield the best fit for the previous n days. Using these optimal parameters the equations are computed and solved to render a forecast for market prices for the following days. For a number of closed-end funds, the results are statistically closer to the ensuing market prices than the default prediction of random walk. In particular, we perform this optimization by a nonlinear computational algorithm that combines a quasi-Newton weak line search with the BFGS formula. We develop a nonlinear least-square technique with an initial value problem (IVP) approach for arbitrary stream data by focusing on the market price variable P since any real data for the other three variables B, zeta_1 and zeta_2 in the dynamical system is not available explicitly. We minimize the sum of exponentially weighted squared differences F[K] between the true trading prices from day i to day i n-1 and the corresponding computed market prices obtained from the first row vector of the numerical solution U of the IVP with AFDE for ith optimal parameter vector where {K} is an initial parameter vector. Here, the gradient (F(x))is approximated by using the central difference formula and step length s is determined by the backtracking line search. One of the novel components of the proposed asset flow optimization forecast algorithm is a dynamic initial parameter pool which contains most recently used successful parameters, besides the various fixed parameters from a set of grid points in a hyper-box.

numerical nonlinear optimization, inverse problem of parameter estimation, asset flow differential equations, financial market dynamics, market return prediction algorithm, data analysis in mathematical finance and economics, out-of-sample prediction

Abstract:
We use basic conservation and microeconomic identities to derive a nonlinear first-order ordinary differential equation for a market system with a prescribed number of shares and cash supply (including additions in time).

The equation incorporates the ideas of the niteness of assets and preference that is influenced by price momentum and discount from fundamental value. The concept of a 'liquidity value,' defined as the total cash in the system divided by the number of shares, emerges as a key price along with the fundamental value. In the absence of a clear focus on fundamentals, the price evolves into the liquidity value. This is consistent with the belief of some market analysts who feel that liquidity, or a large sum of cash available for investment, is a primary factor in moving asset prices higher.

These equations can also be derived from the system of equations used in previous work by considering a closed system and taking the limit of short time-scale in the preference or transition function as well as some linearization.

Finally, the full system of equations is generalized to include randomness. The resulting stochastic system is studied numerically. In particular, when the deterministic equations are complemented with randomness, the solutions generate a range of stochastic patterns, such as the head and shoulders with certain characteristics in common.

Abstract:
A series of experiments, in which nine participants trade an asset over 15 periods, test the hypothesis that an initial imbalance of asset/cash will influence the trading price over an extended time. Participants know at the outset that the asset or "stock" pays a single dividend with fixed expectation value at the end of the 15th period. In experiments with a greater total value of cash at the start, the mean prices during the trading periods are higher, compared to those with greater amount of asset, with a high degree of statistical significance. The difference is most significant at the outset and gradually tapers near the end of the experiment. The results are very surprising from a rational expectations and classical game theory perspective, since the possession of a large amount of cash does not lead to a simple motivation for a trader to bid excessively on a financial instruments. The gradual erosion of the difference toward the end of trading, however, suggests that fundamental value is approached belatedly, offering some consolation to the rational expectations theory. It also suggests that there is a time scale on which an evolution toward fundamental value occurs.

Abstract:
We consider financial market using mathematical models which incorporate an excess demand function that depends not only upon the price but on the price derivative. The classical (value-based) motivation for purchasing the equity is augmented with a trend-based strategy of buying due to rising prices. An analysis (based on money flow and the finiteness of assets) of the supply, demand and price as a function of time leads to a system of ordinary differential equations which is mathematically complete. The numerical study of our equations exhibits overshooting, abrupt reversals and oscillations in prices. We examine our models with the context of real markets and economic laboratory experiments by comparing its predictions with a set of Porter and Smith experiments and with all US stock market crashes since 1929.

Abstract:
We study overreaction and the cumulative effect of the consecutive local overreaction patterns in financial markets. The 'overreaction diamond' pattern [1] is one of the key components of a financial market bubble. The cumulative effect of the consecutive short term overreactions arising from the deviation of stock prices from their fundamentals can be explained by attribution theory, feedback traders, affect and representativeness theories, and reference points in investments. We study large set of financial data and propose a data mining method by exploiting the relative cumulative sentiment of the investors. This leads to a potential for the implementation of suitable algorithms and the preparation of software packages that can be useful for prediction of various stages of overreaction and bubbles.

data mining, overreaction, computational finance software, financial bubble, prediction, financial markets

Abstract:
A system of ordinary differential equations is used to study the price dynamics of an asset under various conditions. One of these involves the introduction of new information that is interpreted differently by two groups. Another studies the price change due to a change in the number of shares. The steady state is examined under these conditions to determine the changes in the price due to these phenomena. Numerical studies are also performed to understand the transition between the regimes. The differential equations naturally incorporate the effects due to the finiteness of assets (rather than assuming unbounded arbitrage) in addition to investment strategies that are based on either price momentum (trend) or valuation considerations. The numerical studies are compared with closed-end funds that issue additional shares, and offers insight into the strategies of investors.

Asset, price, dynamics, heterogeneous information, investment strategies, differential equations, modeling, stock prices

Abstract:
A set of experiments tests the hypothesis that a market discovers price even though no individual trader has all of the necessary information. Participants trade an asset that can have a single payout of $1, $2 or $3. In each experiment there are three groups: one receives information, for example that the payout is not $3, another that it is not $2, and the third receives no additional information. With participants chosen from economics graduate students, prices evolve toward the payout price under neutral cash conditions. However, when there is a large or small amount of cash compared with asset value in the system, the price converges to the wrong price that is favored by the cash/asset ratio.

Abstract:
Laboratory asset markets provide an experimental setting in which to observe investor behavior. Over more than a decade, numerous studies have found that participants in laboratory experiments frequently drive asset prices far above fundamental value, after which the prices crash. This bubble-and-crash behavior is robust to variations in a number of variables, including liquidity (the amount of cash available relative to the value of the assets being traded), short-selling, certainty or uncertainty of dividendpayments, brokerage fees, capital gains taxes, buying on margin, and others.

This paper attempts to model the behavior of asset prices in experimental settings by proposing a "momentum model" of asset price changes. The model assumes that investors follow a combination of two factors when setting prices: fundamental value, and the recent price trend. The predictions of the model, while still far from perfect, are superior to those of a rational expectations model, in which traders consider only fundamental value. In particular, the momentum model predicts that higher levels of liquidity lead to larger price bubbles, a result that is confirmed in the experiments. The similarity between laboratory results and data from field (real-world) markets suggests that the momentum model may be applicable there as well.

Abstract:
The neoclassical price adjustment equation stipulates that prices move toward equilibrium at rate that is proportional to the excess demand, i.e., the difference between the demand and supply divided by the demand (at that price). However, the demand and supply are generally nonlinear functions of price. We show that the information on this nonlinear variation of demand and supply leads to a more accurate description of price evolution toward equilibrium. With this additional information the optimal forecast for the price of the good or asset is given by a nonlinear equation. This yields an advantage to traders utilizing all of the available information on supply and demand functions, rather than simply their value at the current price.

Price adjustment, dynamical price equation, nonlinear supply and demand, asset price, optimal forecast, trading price

Abstract:
This article generalizes the asset flow model of the dynamics of equity prices to multiple groups of investors with distinct strategies and assessments of value. Applications include the closed-end fund puzzle, government privatizations, and marketing of initial and secondary offerings of equities. The generalized model is used to provide a theoretical foundation for the practice of technical analysis, in which price history and patterns are examined in order to obtain an indication of future prices.

The asset flow model, which is an extension of price adjustment due to disequilibria, tracks the finite assets of each group and involves a preference function that is governed by the price trend in addition to the fundamental value of the equity. The system, which consists of a system of ordinary differential equations, uses four parameters that characterize the extent to which investors' preferences are governed by trend versus fundamental value, and the time scales associated with each motivation. The evolution toward equilibrium is found to be much more complex than the monotonic change that is implied by standard price theories. Finally, the time scale for the return to equilibrium, a concept crucial to securities marketing, is considered in a precise quantitative context. The asset flow approach provides a unified explanation for many of the basic patterns of technical analysis and market phenomena. In particular, the origin of a typical bubble can be explained on the basis of trend-based investors entering a market hitherto dominated by value-based investors. Thus, a channel of increasing prices yields to a breakout from a trend line. The formation of triangle patterns in prices has its origin in the emergence of a second group of investors, with a different assessment of value, that offers fresh supply or demand near a particular price. The article also considers applications to the marketing of securities, consumer preferences which are logically influenced by the popular trend (e.g., VHS versus Beta or long-distance telephone companies) and (particularly three-way) elections.