Self-organized criticality in a herd behavior model of financial markets

This paper explains the fat-tail distribution of asset transaction volumes and prices by a model of rational herd behavior of traders. Each trader decides whether to buy an asset by observing private information and other traders’ actions. A trader’s buying action reveals his positive private information and affects the other traders’ beliefs in favor of buying, leading to strategic complementarity. A power-law distribution emerges for the number of buying actions in a static Nash equilibrium. This model provides an economic reason as to why the stock market has to exhibit a criticality in the connectivity of the traders’ actions. I am benefited by comments from the seminar participants at University of Tokyo and the Econophysics Colloquium 2006 at International Christian University, the editors of the special issue, and particularly an anonymous referee.     

Informational cascades with endogenous prices: The role of risk aversion

In this paper, we show that long run market informational inefficiency and informational cascades can easily happen when trades occur at market clearing prices. We consider a sequential trade model where: (i) the investors’ set of actions is discrete; (ii) dealers and investors differ in risk aversion; (iii) investors’ information is bounded. We show that informational cascade occurs as soon as traders’ beliefs do not differ too sharply. Thus, prices cannot fully incorporate the private information dispersed in the economy.     

Are day traders bias free?—evidence from internet stock message boards

This study addresses the issue whether day traders’ recommendations on stocks are biasfree. We test whether on average day traders’ “Hold” sentiment is skewed and different from a neutral opinion. Posted messages and mature text classifier technology provide a novel approach to analyze the content of these “Hold” sentiment postings among day traders. Findings indicate that the self-disclosed “Hold” sentiment conveys an optimistic opinion and significantly differs from neutral. These results help both investors and researchers to better understand day traders’ psychology and behaviors when they recommend stocks. The paper also provides insight into the construction of future online sentiment indexes based on stock message boards.     

Efficient trading with restriction

In a classical paper by Cramton, Gibbons, and Klemperer (CGK) (Econometrica 55:615–632, 1987), it is shown that an efficient trading mechanism exists if traders’ initial endowments are not too asymmetric. In this paper, we extend the CGK model by assuming that traders are not allowed to consume more than a given amount (upper bound) of the good. In the CGK model, instead the only restriction is that no agent can consume more than the entire endowment in the economy. By varying this upper bound, we characterize the set of endowments (efficient region) in which efficient trading mechanisms exist in terms of this upper bound. We show that the efficient region becomes smaller when the upper bound decreases. On the other hand, when this upper bound becomes the entire endowment of the economy, we obtain the result in CGK as a special case.     

Transaction taxes, greed and risk aversion in an agent-based financial market model

Recent agent-based financial market models came to the result that taxing financial transactions does not per se increase financial stability and that the response of volatility and misalignments to rising tax rates seem to be u-shaped. Moreover, greed and the risk appetite of traders are often blamed for financial instability and there is no evidence how greed and risk aversion affect the effectiveness of regulations in financial markets. We aim to add to this gap in the literature by analyzing how the effectiveness of transaction taxes depend on different behavioral patterns within an agent-based framework. Our simulations indicate that a tax rate of 0.1% demarcates the stabilizing tax regime from the destabilizing one. We figure out that transaction taxes are less effective, either when chartists trade more aggressively, fundamentalists trade less aggressively, agents switch more frequently between trading strategies or only have short memory in their fitness measures. Lower risk aversion of agents, however, makes higher tax rates more effective as indicated by a flatter volatility response curve. We conclude that additional regulations should concentrate on the traders’ responsibilities for their risk-exposure.     

Survival in Cournot games

In a model that encompasses a general equilibrium framework, we consider a monopolist (a producer) with subjective beliefs that endogenously hedges against fluctuations in input prices in a complete market. We allow for entries and Cournot competition in this economy, and we study how erroneous beliefs affect long-run survival for those firms. We introduce a notion of entropy of beliefs, and we use it to characterize the class of beliefs for which the monopolist eventually disappears almost surely. When disappearance occurs, the whole market power switches to the entrant making the most accurate predictions in our sense. The class of beliefs for which survival occurs is much broader than that of perfectly competitive settings.     

Detecting speculative bubbles in an IT-intensive stock market

Using a battery of unit root test procedures and cointegration analysis with alternative null hypotheses we find some evidence of speculative bubbles in the Finnish stock market for monthly data on industry portfolio stock prices and returns from the 1990s. When analyzing the time series behavior of stock market prices and returns against the development of certain macroeconomic fundamentals, the bubbles seem to be present especially in the information technology (IT) prices and only during the latter half of the decade. (JEL C22, G12)     

Mechanisms that efficiently verify the optimality of a proposed action

The best known achievement of the literature on resource-allocating mechanisms and their message spaces is the first rigorous proof of the competitive mechanism's informational efficiency. In an exchange economy withN persons andK+1 commodities (including a numeraire), that mechanism announcesK prices as well as aK-compenent trade vector for each ofN−1 persons, making a total ofNK message variables. Trial messages are successively announced and after each announcement each personprivately determines, usingprivate information, whether she finds the proposed trades acceptable at the announced prices. When a message is reached with which all are content, then the trades specified in that message take place, and they satisfy Pareto optimality and individual rationality. The literature shows that no (suitably regular) mechanism can achieve the same thing with fewer thanNK message variables. In the classic proof, all the candidate mechanisms have the privacy property, and the proof uses that property in a crucial way. ‘Non-private’ mechanisms are, however, well-defined. We present a proof that forN>K,NK remains a lower bound even when we permit ‘non-private’ mechanisms. Our new proof does not use privacy at all. But in a non-private mechanism, minimality of the number of message variables can hardly be defended as the hallmark of informational efficiency, since a non-private mechanism requires some persons to know something about the private information of othersin addition to the information contained in the messages. The new proof of the lower boundNK invites a new interpretation of the competitive mechanism's informational efficiency. We provide a new concept of efficiency which the competitive mechanism exhibits and which does rest on privacy even whenN>K. To do so, we first define a class ofprojection mechanisms, wherein some of the message variables are proposed values of the action to be taken, and the rest are auxiliary variables. The competitive mechanism has the projection property, with a trade vector as its action and prices as the auxiliary variables. A projection mechanism proposes an action; for each proposal, the agents then use the auxiliary variables, together with their private information, to verify that the proposed action meets the mechanism's goal (Pareto optimality and individual rationality for the competitive mechanism) if, indeed, it does meet that goal. For a given goal, we seek projection mechanisms for which theverification effort (suitably measured) is not greater than that of any other projection mechanism that achieves the goal. We show the competitive mechanism to be verification-minimal within the class of private projection mechanisms that achieve Pareto optimality and individual rationality; that proofdoes use the privacy of the candidate mechanisms. We also show, under certain conditions, that a verification-minimal projection mechanism achieving a given goal has smallest ‘total communication effort’ (which is locally equivalent to the classic ‘message-space size’) among all private mechanisms that achieve the goal, whether or not they have the projection property.     

On the impossibility of insider trade in rational expectations equilibria

Existing no trade results are based on the common prior assumption (CPA). This paper identifies a strictly weaker condition than the CPA under which speculative trade is impossible in a rational expectations equilibrium (REE). As our main finding, we demonstrate the impossibility of speculative asset trade in an REE whenever an insider is involved who knows the asset's true value. To model insider trade as an equilibrium phenomenon an alternative equilibrium concept than the REE is thus required.     

Fundamentals, Feedback Trading, and Housing Market Speculation: Evidence from California

Housing market researchers have long suspected that the market for single family homes is not efficient. The apparent predictability in housing prices, at least in the short run, leaves open the possibility of speculative purchases in the housing market. The purpose of this paper is to investigate the relative influence of speculative and economic demand on median house price on the Santa Barbara South Coast. An empirical model is presented that allows for decomposition of house price appreciation into that driven by economic and demographic forces and that resulting from speculative demand. The decomposition reveals a speculative bubble in the housing market forming in late 1987 and collapsing in mid 1990.     

The behavior of speculative prices and the consistency of economic models

Modern financial economic theory suggest that changes in speculative prices should follow simple ‘fair game’ processes in an informationally efficient capital market. The observation that changes in speculative prices follow simple time series processes both supports this theoretical proposition and suggest restrictions on the transfer functions of structural econometric models in which speculative prices appear as output variables. The simplicity of the time series processes for observed changes in speculative prices are shown to impose strong restrictions on potential equilibrium models of asset pricing, informational disequilibrium models of financial markets, and many monetary and macroeconomic models as well.     

Prediction market prices under risk aversion and heterogeneous beliefs

In this paper, we examine the properties of prediction market prices when risk averse traders have heterogeneous beliefs in state probabilities. We show that the equilibrium state prices equal the mean beliefs of traders about that state if and only if the traders’ common utility function is logarithmic. We also provide a necessary and sufficient condition ensuring that the state prices are systematically below or above the mean beliefs of traders, thus providing a rational explanation to the favorite-longshot bias in prediction markets.     

Market undervaluation of risky convertible offerings: Evidence from the airline industry

We assess market valuation of airline convertible preferred stocks using a contingent claims valuation model that was extensively tested by Ramanlal et al. (Rev Quant Financ Account 10:303–319, 1998). Our sample consists of 4,096 daily price observations of 11 convertible preferred stocks issued by the U.S. airlines in 1980–1991. For each convertible we estimate daily model prices for 2 years after issuance and compare them with market prices by calculating pricing errors. While the entire sample’s mean pricing error is found to be negative 3.8%, the panel data analysis and the mean pricing errors of the sub-samples indicate that the undervaluation is much more severe in the first 6 months of trading. The results suggest that airlines leave about 10% on the table when they raise capital by issuing convertible securities.     

An equilibrium model of insider trading in continuous time

We study a Bayesian–Nash equilibrium model of insider trading in continuous time. The supply of the risky asset is assumed to be stochastic. This supply can be interpreted as noise from nonrational traders (noise traders). A rational informed investor (the insider) has private information on the growth rate of the dividend flow rewarded by the risky asset. She is risk averse and maximizes her inter-temporal utility rate over an infinite time-horizon. The market is cleared by a risk neutral market maker who sets the price of the risky asset competitively as the conditional present value of future dividends, given the information supplied by the dividend history and the cumulative order flow. Due to the presence of noise traders, the market demand does not fully reveal the insider’s private information, which slowly becomes incorporated in prices. An interesting result of the paper is that a nonstandard linear filtering procedure gives an a priori form for the equilibrium strategy to be postulated. We show the existence of a stationary linear equilibrium where the insider acts strategically by taking advantage of the camouflage provided by the noise which affects the market maker’s estimates on private information. In this equilibrium, we find that the insider’s returns on the stock are uncorrelated over long periods of time. Finally, we show that the instantaneous variance of the price under asymmetric information lies between the instantaneous variance of the price under complete and incomplete information. The converse inequalities hold true for the unconditional variance of the price.     

Consumption optimization for recursive utility in a jump-diffusion model

In this paper, we consider a market model with prices and consumption following a jump-diffusion dynamics. In this setting, we first characterize the optimal consumption plan for an investor with recursive stochastic differential utility on the basis of his/her own beliefs, then we solve the inverse problem to find what beliefs make a given consumption plan optimal. The problem is viewed in general for a class of homogeneous recursive utility, and later we choose a logarithmic model for the utility aggregator as an explicitly computable example. When beliefs, represented via Girsanov’s theorem, get incorporated into the model, the change of measure gives rise, up to a transformation, to a backward stochastic differential equation whose generator exhibits a quadratic behavior in the Brownian component and a locally Lipschitz one in the jump component, which is solvable on the basis of some recent results.     

On the behavior of commodity prices when speculative storage is bounded

This paper investigates the implications of bounded speculative storage, storage bounded from below at zero and above at a capacity, on commodity prices. Binding capacity mirrors the non-negativity constraint on storage and leads to negative price spiking and higher volatility when the market is in deep contango, i.e. low current prices at high stock levels. With bounded storage there is no need to restrict storage to be costly to ensure a rational expectations equilibrium. This allows the model to cover a wide range of storage technologies, including free and productive storage. We also provide an alternative expression for speculative prices that highlights the key role of the storage boundaries. The competitive equilibrium price is the sum of discounted future probability weighted boundary prices. The boundary prices can be viewed as dividends on commodities in storage reflecting the realization of economic profits from storage.     

Accounting contagion: The case of Enron

The Enron scandal offers the opportunity to assess the degree to which misleading accounting can affect connected firms and industry rivals. While the market was inept at detecting the inaccuracy of Enron’s financial statements, it swiftly punished many connected firms once Enron's faulty accounting was publicized. A cross-sectional analysis documents that the market punished connected firms that had greater exposure to Enron’s business, whose financial statements were viewed as more complex, and that had greater financial leverage. Most of the negative news indicating concern with Enron’s accounting corresponded with a significant decline in the stock prices of firms in the energy and natural gas (ENG) industry, regardless of an explicit connection to Enron. Furthermore, rival firms with direct exposure to Enron and more aggressive earnings-reporting methods also experienced more detrimental effects.     

The pricing of callable preferred stock

In this study, the authors use both the Black/Scholes European option model and the Barone-Adesi/Whaley American option model to estimate call option values implicit in seasoned callable preferred stock issues. Consistent with the finding that call features increase bond yields, a significant relationship is found between estimated option values and discounts of these securities’ market prices from their estimated income values. However, the size of the discount is only a fraction of what would be predicted by the American option model. Specifically, the market does not appear to take the “early exercise premium” into account. Furthermore, this discount seems to be isolated to in-the-money call features that have evolved to their final call price. Thus, incorporation of a call feature into a security’s indentures, with a deferment period and an initial premium call price, appears to represent a pure gain for the issuing corporation.     

Countervailing power? Collusion in markets with decentralized trade

We consider the collective incentives of buyers and sellers to form cartels in markets with decentralized trade and pairwise bargaining. Cartels are coalitions of buyers or sellers that limit market participation and compensate inactive members for their abstention. In stable market outcomes, cartels set Nash equilibrium quantities and cartel memberships are immune to deviations. The set of stable market outcomes is non-empty and its full characterization is provided. Stable market outcomes are of two types: (i) at least one cartel restrains trade and market participation is balanced; (ii) only one cartel is active and it reduces trade slightly below the opponent’s.     

Incorporating positions into asset pricing models with order-based strategies

The paper addresses the problem of agent-based asset pricing models with order-based strategies that the implied positions of the agents remain indeterminate. To overcome this inconsistency, two easily applicable risk aversion mechanisms are proposed which modify the original actions of a market maker and the speculative agents, respectively. Here the concepts are incorporated into the classical Beja–Goldman model. For the deterministic version of the thus enhanced model a four-dimensional mathematical stability analysis is provided. In a stochastic version it is demonstrated that jointly the mechanisms are indeed able to keep the agents’ positions within bounds, provided the corresponding risk aversion coefficients are neither too low nor too high. A similar result holds for the misalignment of the market price. We wish to thank two anonymous referees for their observations and detailed comments. Financial support from EU STREP ComplexMarkets, contract number 516446, is gratefully acknowledged.