Heterogeneous expectations in the gold market: Specification and estimation

The increase in the price of gold between 2002 and 2011 appears to be a candidate for a potential asset price ‘bubble’, suggesting that chartists (feedback traders) were highly active in the gold market during this period. Hence, this paper develops and tests empirically several models incorporating heterogeneous expectations of agents, specifically fundamentalists and chartists, for the gold market. The empirical results show that both agent types are important in explaining historical gold prices but that the 10-year bull run of gold in the early 2000s is consistent with the presence of agents extrapolating long-term trends. Technically this paper is a further step toward providing an empirical foundation for certain assumptions used in the heterogeneous agents literature. For example, the empirical results presented in this paper compare the economical and statistical significance of numerous switching variable specifications that are generally only introduced ad hoc.     

Dissecting the myth of the house price in Chinese metropolises: allowing for behavioral heterogeneity among investors

This paper aims to demystify the housing boom in Chinese metropolises by allowing for behavioral heterogeneity among investors. We construct an agent-based model where investors are categorized into two groups: fundamentalists and chartists. In addition, the investment strategy switching is allowed between these two groups contingent on the historical performance. Using the data of five Chinese metropolises over the period 2008–2014, the results suggest that chartists dominate the housing market and make the house price maintain an upward trend, while fundamentalists play a stabilizing role. Specifically, fundamentalists can serve as a “price anchor” in the market, because the proportion of the fundamentalists is negatively associated with both the growth rate of the house price and the deviation relative to the fundamental value. Overall, the impact of the chartists on the house price is much greater than that of the fundamentalists, which contributes to the ever-increasing house price in Chinese metropolises.

     

Fundamentalists vs. chartists: Learning and predictor choice dynamics

In a simple, forward looking univariate model of price determination we investigate the evolution of expectations dynamics in the presence of two types of agents: fundamentalists and chartists. In particular, we combine evolutionary selection among heterogeneous classes of models through predictor choice dynamics based on a logit model, with adaptive learning in the form of parameters updating within each class of rules. We find that, for different parameterizations, it can happen that fundamentalists drive chartists completely out of the market or vice versa, and also that heterogeneous equilibria in which fundamentalists and chartists coexist are possible. Interestingly, though, only equilibria in which fundamentalists outperform chartists turn out to be adaptively learnable by agents.     

Uncertainty about fundamental,pessimistic and overconfident traders: a piecewise-linear maps approach

Decisions in Economics and Finance - We analyze a financial market model with heterogeneous interacting agents where fundamentalists and chartists are considered. We assume that fundamentalists are...     

Why a simple herding model may generate the stylized facts of daily returns: explanation and estimation

The paper proposes an elementary agent-based asset pricing model that, invoking the two trader types of fundamentalists and chartists, comprises four features: (i) price determination by excess demand; (ii) a herding mechanism that gives rise to a macroscopic adjustment equation for the market fractions of the two groups; (iii) a rush towards fundamentalism when the price misalignment becomes too large; and (iv) a stronger noise component in the demand per chartist trader than in the demand per fundamentalist trader, which implies a structural stochastic volatility in the returns. Combining analytical and numerical methods, the interaction between these elements is studied in the phase plane of the price and a majority index. In addition, the model is estimated by the method of simulated moments, where the choice of the moments reflects the basic stylized facts of the daily returns of a stock market index. A (parametric) bootstrap procedure serves to set up an econometric test to evaluate the model’s goodness-of-fit, which proves to be highly satisfactory. The bootstrap also makes sure that the estimated structural parameters are well identified.     

A heterogeneous agent model of asset price dynamics with two time delays

This study constructs a heterogeneous agents model of a financial market in a continuous-time framework. There are two types of agents, fundamentalists and chartists. The former follows the traditional efficiency market theory and has a linear demand function, whereas the latter experiences delays in the formation of price trends and possesses a S-shaped demand function. The main feature of this study is a theoretical investigation on the effects caused by two time delays in a price adjustment process. In particular, two main results are demonstrated: One is that the stability switching curves are analytically derived, and the other is that the stability losses and gains can repeatedly occur when the shape of the curves are meandering. Although it is well known that a time delay has a destabilizing effect, these results imply that multiple delays can stabilize and destabilize a market price generating persistent deviations from the stationary price.     

Equilibria,stability and asymptotic dominance in a speculative market with heterogeneous traders

We consider a pure exchange economy where one risky and one riskless security are traded in discrete time. Individual demands are expressed as fractions of individual wealth and depend on traders’ forecasts about future price movement.Introducing the ‘Equilibrium Market Line’ as the locus of all possible equilibrium returns, we show that, irrespectively of the number of traders and of their investment behavior, the economy possesses isolated equilibria where a single agent dominates the market and continuous manifolds of equilibria where many agents hold finite wealth shares. Moreover, we prove that no global dominance order relation among strategies can be defined.     

A dynamic analysis of moving average rules

The use of various moving average (MA) rules remains popular with financial market practitioners. These rules have recently become the focus of a number empirical studies, but there have been very few studies of financial market models where some agents employ technical trading rules of the type used in practice. In this paper, we propose a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long-run) MA. Both types of traders are boundedly rational in the sense that, based on a fitness measure such as realized capital gains, traders switch from a strategy with low fitness to the one with high fitness. We characterize the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag length used for the MA. By increasing the intensity of choice to switching strategies, we then examine various rational routes to randomness for different MA rules. The price dynamics of the MA rule are also examined and one of our main findings is that an increase of the window length of the MA rule can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including temporary bubbles, sudden market crashes, price resistance and price switching between different levels.     

An analysis of the effect of noise in a heterogeneous agent financial market model

Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used, often called indirect, approach to the study of HAMs combines theoretical analysis of the underlying deterministic skeleton with numerical analysis of the stochastic model. However, it is well known that this indirect approach may not properly characterise the nature of the stochastic model. This paper aims to tackle this issue by developing a direct and analytical approach to the analysis of a stochastic model of speculative price dynamics involving two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the stationary measures of a stochastic dynamical system. Using the stochastic method of averaging and stochastic bifurcation theory, we show that the stochastic model displays behaviour consistent with that of the underlying deterministic model when the time lag in the formation of price trends used by the chartists is far away from zero. However, when this lag approaches zero, such consistency breaks down.     

Investment behaviour and “bull & bear” dynamics: modelling real and stock market interactions

In this article, we develop a simple behavioural macrodynamic model in continuous-time with the purpose of investigating the interaction of the real economy and the financial markets. Building on Westerhoff (Discret Dyn Nat Soc, 2012), we improve the specification of aggregate demand by distinguishing between consumption and investment expenditure and assuming that the latter is determined by the flexible accelerator principle. We remove the ad hoc nonlinearity in the fundamentalist behavioural rule and allow the composition of the population between chartists and fundamentalists to be endogenously determined. The resulting nonlinear dynamic systems are shown to generate various dynamic regimes, among which the coexistence of periodic attractors with interesting economic implications. Endogenous investment and stock market dynamics emerge, procyclical to each other, reflecting the interaction of induced investment with alternating waves in speculators’ sentiments. We show that a strong investment accelerator might be a crucial force generating fluctuations that, on the one hand, are transmitted and amplified by chartists and, on the other hand, are contained by fundamentalists.

     

Margin trade,short sales and financial stability

We model how leveraged trading activities constrained by dynamic funding availability affect financial stability. In the market, customers trade based on the fundamental value of the risky asset and make full payment for their transactions, while speculators take trading position based on margin, which is constantly adjusted by the financier, the fund provider, according to the price volatility. As a result of equilibrium price discontinuity triggered by dynamic margin requirements, trivial shocks to external supply, wealth or fundamental value can be transmitted into asset price crashes or jumps. We find that tightening margin requirements improves (mitigates) the market liquidity in the bull (bear) market, and that imposing short sale constraints helps prevent the price from falling further when the asset is sufficiently under-priced and accelerate price collapse when the asset is over-priced.

     

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.     

On optimal investiment strategies

Suppose an investor has a fixed decision horizon and an appropriate utility function for measuring his or her utility of wealth. If there are only two investment vehicles, a risky and a risk-free asset, then the optimal investment strategy is such that, at any time, the amount invested in the risky asset must be the product of his or her “current risk tolerance” and the risk premium on the risky asset, divided by the square of the diffusion coefficient of the risky asset. In the case of more than one risky asset, the optimal investment strategy is similar, with the ratios of the amounts invested in the different risky assets being constant over time.     

Utility indifference valuation for jump risky assets

We discuss utility maximization problems with exponential preferences in an incomplete market where the risky asset dynamics is described by a pure jump process driven by two independent Poisson processes. This includes results on portfolio optimization under an additional European claim. Value processes of the optimal investment problems, optimal hedging strategies and the indifference price are represented in terms of solutions to backward stochastic equations driven by the Poisson martingales. Via a duality result, the solution to the dual problems is derived. In particular, an explicit expression for the density of the minimal martingale measure is provided. The Markovian case is also discussed. This includes either asset dynamics dependent on a pure jump stochastic factor or claims written on a correlated non tradable asset.     

Booms,busts and behavioural heterogeneity in stock prices

We estimate a behavioural heterogeneous agents model with boundedly rational traders who know the fundamental stock price, but disagree about the persistence of deviations from the fundamental. Some agents (fundamentalists) believe in mean-reversion of stock prices, while others (chartists) expect a continuation of the trend. Agents gradually switch between the two rules, based upon their relative performance, leading to self-reinforcing regimes of mean-reversion and trend-following. For the fundamental benchmark price we use two well-known models, the Gordon model with a constant risk premium and the Campbell-Cochrane consumption-habit model with a time-varying risk premium. We estimate a two-type switching model using U.S. stock prices until 2016Q4. The estimations show an improvement over representative agent models that is both statistically and economically significant. Our model suggests that behavioural regime switching strongly amplifies booms and busts, in particular, the dot-com bubble and the financial crisis in 2008.     

Information asymmetry,sentiment interactions,and asset price

We develop an asset pricing model with sentiment interactions between institutional and individual investors under the condition of information asymmetry. Our model considers private information and investor sentiment, two imperfections in securities markets, and integrates them into a theoretical model to investigate the role of the interaction between information asymmetry and investor sentiment in asset pricing. We show that the joint effect of private information and investor sentiment deviate the price of risky assets and efficiently explains anomalies in the stock market. Investor sentiment changes the effect of information on the equilibrium price relative to a world where all investors are completely rational. Private information changes the effect of investor sentiment on the equilibrium price in comparison with a scenario with symmetric market information. In addition, the individual investors’ learning and the disclosure of information both allow private information to be better integrated into the price and simultaneously changes the effect of investor sentiment on the equilibrium price.     

Portfolio choice,behavioral preferences and equity home bias

We provide a plausible explanation of aggregate portfolio behavior, in a framework where economic agents have behavioral (narrow framing) preferences. The representative agent derives utility not only from consumption (standard models) but also from risky financial wealth fluctuations. Moreover, the investor frames the stock market risk narrowly and has loss averse preferences. We numerically solve, for the foreign equity share, a simple model of international portfolio choice, providing a possible explanation for the equity home bias puzzle. Only economic agents able to process correctly information deriving from stock markets exploit the diversification opportunities provided by international financial markets.     

Adverse effects of leverage and short-selling constraints in a financial market model with heterogeneous agents

This paper investigates the impact of leverage and short-selling constraints on financial market stability. Investors׳ demand is modelled in a well-known asset pricing model with heterogeneous beliefs. In particular, I generalise the heterogeneous agents model of Brock and Hommes (1998) and Anufriev and Tuinstra (2013) to allow for leverage constraints as well as a short-selling tax. I consider two examples of adaptive belief systems describing the coevolution of prices and investors׳ beliefs. First, if the market is inhabited by fundamentalist and chartist traders, demand constraints have potential adverse effects and may restrict the stabilising fundamentalist strategy such that mispricing and price volatility increase. Second, if the market is inhabited by fundamentalists, optimists and pessimists with fixed beliefs, demand constraints drive down price volatility, but mispricing remains. The results suggest the stabilising effects of demand constraints in financial markets are limited. Only if asset prices are too high compared to fundamentals, policy makers should consider constraining leverage ratios in order to deflate financial bubbles.     

Simple agent-based dynamical system models for efficient financial markets: Theory and examples

We propose an agent-based framework, based on simple piecewise linear time-invariant continuous-time dynamical systems models, as a means for describing efficient financial markets. We show by examples that many of the common agent-specific trading strategies occurring in the academic literature, including chartists and fundamentalists of various kinds, can be described in the proposed framework. We present definitions for weak and strong market efficiency and provide necessary and sufficient conditions for them to hold. We present minimal examples of strongly and weakly efficient markets to show that these concepts are natural and easy to satisfy in agent-based models, and that the models can reproduce both statistical and behavioral stylized facts of real markets. We provide examples to demonstrate that the framework can be extended for agents with delays in information processing, as well as for agents with time-varying strategies and for nonlinear market impact functions. We also provide a counterexample to show that the proposed market efficiency concepts may require modification in generalizations for nonlinear trading strategies.     

Evolution of heterogeneous beliefs and asset overvaluation

I analyze a model in which different agents have different non-rational expectations about the future price and cash flows of a risky asset. The beliefs in the society evolve according to a very general class of evolution functions that are monotone; that is if one type has increased its share in the population then all types with higher profit should also have increased their shares. I show that the price of the risky asset converges to the risk-neutral fundamental price even though all agents in the economy are risk-averse. The risky asset thus becomes overvalued as compared to the equilibrium with rational expectations. The overvaluation is a result of the evolution of beliefs and does not rely on such asymmetric assumptions as short-sale constraints or optimistic bias.