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Professor Xuezhong He

Biography

Prof. Xuezhong (Tony) He completed a BSc in Pure Mathematics in 1982 (Ningxia University, China), a MSc in Applied Mathematics in 1987 (Hebei Normal University, China), a PhD in Applied Mathematics in 1995 (Flinders University), and a PhD in Finance in 2001 (the University of Technology, Sydney). Tony worked as an Associated Lecturer from 1982 to 1984 and a Lecturer from 1987 to 1991 with the Department of Mathematics at Ningxia University, China. Between 1989 and 1990, he worked at Flinders University as a Visiting Scholar. Between 1995 and 1997 he was employed as an Associate Lecturer with School of Mathematics and Statistics at the University of Sydney. Tony joined the Finance Discipline Group at UTS Business School, the University of Technology, Sydney, as a Lecturer in 2001, a Senior Lecturer in 2002, an Associate Professor in 2007, and a Professor in 2011.

As a mathematician in his earlier career, Tony has established an international reputation in the field of the theory and application of nonlinear dynamical systems. He has authored/co-authored more than 40 refereed papers in this area, some of which have appeared in prestigious and high quality field journals such as SIAM and IEEE journals, Physica D, Nonlinear Analysis, Journal of Mathematical Analysis and Applications, and Journal of Mathematical Biology.

Tony’s international research profile in areas of financial market modelling, asset pricing with heterogeneous beliefs, and nonlinear economic dynamics is attested by his publications in a number of the leading international journals in economics and econometrics including Journal of Economic Dynamics and Control, Journal of Economic Behavior and Organization, Macroeconomic Dynamics, Journal of Evolutionary Economics, European Journal of Finance, Quantitative Finance, and Computational Economic.

Tony serves as the Co-Editor of the Journal of Economic Dynamics and Control, the associate editor of Journal of Economic Interaction and Coordination, Journal Differential Equations and Dynamical Systems, Discrete Dynamics in Nature and Society, and the reviewer of the Mathematics Review, American Mathematical Society.

Google scholar citation page

Professor, Finance Discipline Group
Associate Member, Advanced Analytics Institute
Associate Member, Centre for Quantum Computation and Intelligent Systems
Core Member, Quantitative Finance Research Centre
BSc (Ningxia), MSc (HBU), PhD (Flinders ), PhD (UTS)
Member, Economic Society of Australia
Download CV  (PDF 450 Kb, 2 pages)
Phone
+61 2 9514 7726

Research Interests

Financial market modelling, heterogeneous expectations and learning, nonlinear economic dynamics and bounded rationality, behavior finance and asset pricing.

Can supervise: Yes

Derivatives, Financial Economics, Nonlinear Economics, and Investment.

Books

Dieci, R., He, X.Z. & Hommes, C. 2014, Nonlinear economic dynamics and financial modelling: Essays in honour of Carl Chiarella.
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© 2014 Springer International Publishing Switzerland. All rights are reserved. This book reflects the state of the art on nonlinear economic dynamics, financial market modelling and quantitative finance. It contains eighteen papers with topics ranging from disequilibrium macroeconomics, monetary dynamics, monopoly, financial market and limit order market models with boundedly rational heterogeneous agents to estimation, time series modelling and empirical analysis and from risk management of interest-rate products, futures price volatility and American option pricing with stochastic volatility to evaluation of risk and derivatives of electricity market. The book illustrates some of the most recent research tools in these areas and will be of interest to economists working in economic dynamics and financial market modelling, to mathematicians who are interested in applying complexity theory to economics and finance and to market practitioners and researchers in quantitative finance interested in limit order, futures and electricity market modelling, derivative pricing and risk management.

Chapters

Dieci, R., He, X. & Hommes, C. 2014, 'Introduction' in Dieci, R., He, X. & Hommes, C. (eds), Nonlinear Economic Dynamics and Financial Modelling: Essays in Honour of Carl Chiarella, Springer, pp. 1-7.
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He, X. 2013, 'Recent developments in asset pricing with heterogeneous beliefs and adaptive behaviour of financial markets' in Bischi, G.I., Chiarella, C. & Sushko, I. (eds), Global analysis of dynamic models in economics and finance: Essays in honour of Laura Gardini, Springer, Germany, pp. 3-34.
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Heterogeneity and interacting among boundedly rational agents have received increasing attention in the finance and economics literature. Recent developments on the role of heterogeneous beliefs on asset pricing and the adaptive behaviour of financial markets shed light into the complex behaviour of financial markets and provide some explanations of certain market behaviour and anomalies. This paper surveys these developments, to which the author and several coauthors have contributed in several papers, and discusses the extent to which they can address market anomalies, complexity, and stylized facts in financial markets.
Böhm, V., Chiarella, C., He, X.Z. & Hüls, T. 2012, 'A homoclinic route to volatility: Dynamics of asset prices under autoregressive forecasting' in Global Analysis of Dynamic Models in Economics and Finance: Essays in Honour of Laura Gardini, pp. 289-316.
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© 2013 Springer-Verlag Berlin Heidelberg. All rights are reserved. The article investigates the impact of mean-reverting forecasts in a model of asset pricing with two groups of investors under market clearing. Fundamentalists believe that asset prices follow an exogenous stochastic process, while chartists assume that asset prices follow a stochastic geometric decay process. For high values of mean reversion a period-doubling bifurcation occurs followed by a Neimark-Sacker bifurcation, after which homoclinic points exist inducing chaotic dynamics. Before the occurrence of homoclinic points, all orbits induce significant fluctuations with recurring symmetries and nonvanishing autocorrelations in all time series of prices and returns. After the homoclinic bifurcation, prices and returns follow alternating phases with low fluctuations near the steady state followed by phases with large excursions from the steady state. This shows that nonlinearities of the deterministic model rather than random perturbations are the causes of volatility clustering and of the generation of fat tails. Autocorrelations of prices and returns vanish while those of absolute returns and squared returns persist for high-order lags. Thus, the model is able to reproduce some important empirical market features.
He, X. & Shi, L. 2011, 'Diversification effect of heterogeneous beliefs' in Dawid, H. & Semmler, W. (eds), Computational Methods in Economic Dynamics, Springer, US, pp. 57-75.
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Within the framework of Chiarella et al (2009b) on MV analysis, this paper examines the impact of the heterogeneity and bounded rationality on the market equilibrium and MV efficiency of the optimal portfolios. The heterogeneity is characterised by the heterogeneous beliefs about the returns of the risky assets, while the bounded rationality corresponds to the MV optimisation of investors based on their beliefs.
Chiarella, C., Dieci, R. & He, X.Z. 2010, 'A framework for CAPM with heterogeneous beliefs' in Nonlinear Dynamics in Economics, Finance and Social Sciences: Essays in Honour of John Barkley Rosser Jr, pp. 353-369.
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The Sharpe-Lintner-Mossin (Sharpe 1964; Lintner 1965; Mossin 1966) Capital Asset Pricing Model (CAPM) plays a central role in modern finance theory. It is founded on the paradigm of homogeneous beliefs and a rational representative agent. However, froma theoretical perspective this paradigmhas been criticized on a number of grounds, in particular concerning its extreme assumptions about homogeneous beliefs, information about the economic environment, and the computational ability on the part of the rational representative economic agent. The impact of heterogeneous beliefs among investors on the market equilibrium price has been an important focus in the CAPM literature. A number of models with investorswho have heterogeneous beliefs have been previously studied. 1 A common finding in this strand of research is that heterogeneous beliefs can affect aggregate market returns. However, the question remains as to how exactly does heterogeneity affect themarket risk of risky assets? In much of this earlier work, the heterogeneous beliefs reflect either differences of opinion among the investors2 or differences in information upon which investors are trying to learn by using some Bayesian updating rule.3 Heterogeneity has been investigated in the context of either CAPM-like mean-variancemodels (for instance, Lintner 1969; Miller 1977;Williams 1977; and Mayshar 1982) or Arrow-Debreu contingent claims models (as in Varian 1985;Abel 1989; 2002; and Calvet et al. 2004). © 2010 Springer-Verlag Berlin Heidelberg.
He, X. & Shi, L. 2010, 'Portfolio efficiency under heterogeneous beliefs' in Kijima, M., Hara, C., Tanaka, K. & Muromachi, Y. (eds), Recent Advances in Financial Engineering, World Scientific, Singapore, pp. 127-156.
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In the standard mean variance (MV) capital asset pricing model (CAPM) with homogeneous beliefs, the optimal portfolios of investors are MV efficient. It is expected that this is no longer true in general when investors have heterogeneous beliefs in the means. and variances/covariances of asset returns. This paper extends the s.tandard Black's zero-beta CAPM to incorporate heterogeneous beliefs and verifies that lhe subjectively optima) portfolios of heterogeneous investors are MV inefficient in generaL The paper then demonstrates that the traditional geometric relation of the mean variance frontiers with and Without the riskless asset under homogeneous beliefs does not hold in general under heterogelleous beliefs. The paper further examines the impact of biased beliefs among investors on the MY efficiency of their optimal portfolios. The results provide some explanalions on the risk premium puzzle, Miller's hypothesis, and underperfonnance of managed funds.
Chiarella, C., Dieci, R. & He, X. 2009, 'Heterogeneity, market mechanisms and asset price dynamics' in Hens, T. & Schenk-Hoppe, K.R. (eds), Handbook of Financial Markets: Dynamics and Evolution, Elsevier, USA, pp. 277-344.
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He, X., Hamill, P. & Li, Y. 2008, 'Can Trend Followers Survive in the Long-Run? Insights from Agent-Based Modeling' in Brabazon, A. & O'Neill, M. (eds), Natural Computing in Computational Finance, Springer, Berlin, Germany, pp. 253-269.
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This chapter uses a simple stochastic market fraction (MF) asset pricing model to investigate market dominance, profitability, and how traders adopting fundamental analysis or trend following strategies can survive under various market conditions in the long/shoft-run. This contrasts with the modern theory of finance which relies on the paradigm of utility maximizing representative agents and rational expectations assumptions which some contemporary theorists regard as extreme. This school of thought would predict that trend followers will be driven out of the markets in the long-run. Our analysis shows that in a MF framework this is not necessarily the case and that trend followers can survive in the long-run.
Chiarella, C. & He, X. 2008, 'An adaptive model of asset price and wealth dynamics in a market with heterogeneous trading strategies' in Seese, D., Weinhardt, C. & Schlottmann, F. (eds), Handbook on Information Technology in Finance, Springer, Germany, pp. 465-499.
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The traditional asset-pricing models such as the capital asset pricing model (CAPM) of [42] and [34], the arbitrage pricing theory (APT) of [40], or the intertemporal capital asset pricing model (ICAPM) of [38] have as one of their important assumptions, investor homogeneity. In particular the paradigm of the representative agent assumes that all agents are homogeneous with regard to their preferences, their expectations and their investment strategies.1 However, as already argued by Keynes in the 1930s, agents do not have sufficient knowledge of the structure of the economy to form correct mathematical expectations that would be held by all agents
Chiarella, C., He, X.Z. & Wang, D. 2006, 'Statistical properties of a heterogeneous asset pricing model with time-varying second moment', pp. 109-124.
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Stability and bifurcation analysis of deterministic systems has been widely used in modeling financial markets. However, the impact of such dynamic phenomena on various statistical properties of the corresponding stochastic model, including skewness and excess kurtosis, various autocorrelation (AC) patterns of under and over reactions, and volatility clustering characterised by the long-range dependence of ACs, is not clear and has been very little studied. This paper aims to contribute to this issue. Through a simple behavioural asset pricing model with fundamentalists and chartists, we examine the statistical properties of the model and their connection to the dynamics of the underlying deterministic model. In particular, our analysis leads to some insights into various mechanisms that may generate some of the stylised facts, such as fat tails, skewness, high kurtosis and long memory, observed in high frequency financial data. © 2006 Springer-Verlag Berlin Heidelberg.
Chiarella, C., Flaschel, P., He, X. & Hung, H. 2006, 'A stochastic model of real-financial interaction with boundedly rational heterogeneous agents' in Chiarella, C., Franke, R., Flaschel, P. & Semmler, W. (eds), Quantitative and Empirical Analysis of Nonlinear Dynamic Macromodels, Elsevier, Amsterdam, Netherlands, pp. 333-358.
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Chiarella, C. & He, X. 2005, 'An asset pricing model with adaptive heterogeneous agents and wealth effects' in Lux, T., Reitz, S. & Samanidou, E. (eds), Nonlinear Dynamics and Heterogeneous Interacting Agents, Springer, Berlin, Germany, pp. 269-285.
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The characterisation of agents' preferences by decreasing absolute risk aversion (DARA) and constant relative risk aversion (CRRA) are well documented in the literature and also supported in both empirical and experimental studies. This paper considers a financial market with heterogeneous agents having power utility functions, which are the only utility functions displaying both DARA and CRRA. By introducing a population weighted average wealth measure, we develop an adaptive model to characterise asset price dynamics as well as the evolution of population proportions and wealth dynamics. Some numerical simulations are included to illustrate the evolution of the wealth dynamics, market behaviour and market efficiency within the framework of heterogeneous agents.
Chiarella, C. & He, X.Z. 2004, 'Dynamics of beliefs and learning under a(L)-processes - The homogeneous case', pp. 363-390.
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Chiarella, C. & He, X.-.Z. 1999, 'The Dynamics of the Cobweb when Producers are Risk Averse Learners'.
In this paper we investigate the dynamics of the traditional cobweb model where producres are risk averse and seek to learn the distribution of asset prices. We consider the subjective estimates of the statistical distribution of the market prices based on L-step backward time series of market clearing prices. With constant absolute risk aversion, the cobweb model becomes nonlinear. Sufficient conditions on the local stability of the unique positive equilibrium of the nonlinear model are derived and, consequently, we show that the local stability region is proportional to the lag length L. When the equilibrium loses its local stability, we show that, for L = 2, the model has a strong 1:3 resonance bifurcation and a family of fixed points of order 3 becomes unstable on both sides of criticality. For general lag lengths, numerical simulations suggest that the model displays a variety of complex dynamics.

Conferences

Chiarella, C., He, X.Z. & Zheng, M. 2013, 'Heterogeneous expectations and exchange rate dynamics', European Journal of Finance, pp. 392-419.
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This article presents a continuous-time model of exchange rates not only relying on macroeconomic factors but also having an investor heterogeneity component. The driving macroeconomic factor is the domestic-foreign interest rate differential, while the investor heterogeneity is described by the expectations of boundedly rational portfolio managers who use a weighted average of the expectations of fundamentalists and chartists. Within this framework, the different roles of the macroeconomic factor and investor heterogeneity in the determination of the exchange rate are examined explicitly. We show that this simple model generates very complicated market behaviour, including the existence of multiple steady-state equilibria, deviations of the market exchange rate from the fundamental one and market fluctuations. Numerical simulation of the corresponding stochastic version of the model shows that the model is able to generate typical time series and volatility clustering patterns observed in exchange rate markets. © 2013 Copyright Taylor and Francis Group, LLC.
Chiarella, C., Dieci, R. & He, X.Z. 2013, 'Time-varying beta: A boundedly rational equilibrium approach', Journal of Evolutionary Economics, pp. 609-639.
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The conditional CAPM with time-varying betas has been widely used to explain the cross-section of asset returns. However, most of the literature on time-varying beta is motivated by econometric estimation using various latent risk factors rather than explicit modelling of the stochastic behaviour of betas through agents' behaviour, such as momentum trading. Misspecification of beta risk and the lack of any theoretical guidance on how to specify risk factors based on the representative agent economy appear empirically challenging. In this paper, we set up a dynamic equilibrium model of a financial market with boundedly rational and heterogeneous agents within the mean-variance framework of repeated one-period optimisation and develop an explicit dynamic behaviour CAPM relation between the expected equilibrium returns and time-varying betas. By incorporating the two most commonly used types of investors, fundamentalists and chartists, into the model, we show that there is a systematic change in the market portfolio, risk-return relationships, and time varying betas when investors change their behaviour, such as the chartists acting as momentum traders. In particular, we demonstrate the stochastic nature of time-varying betas. We also show that the commonly used rolling window estimates of time-varying betas may not be consistent with the ex-ante betas implied by the equilibrium model. The results provide a number of insights into an understanding of time-varying beta. © 2011 Springer-Verlag.
He, X.Z. 2013, 'Recent developments in asset pricing with heterogeneous beliefs and adaptive behaviour of financial markets', pp. 3-34.
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© 2013 Springer-Verlag Berlin Heidelberg. All rights are reserved. Heterogeneity and interacting among boundedly rational agents have received increasing attention in the finance and economics literature. Recent developments on the role of heterogeneous beliefs on asset pricing and the adaptive behaviour of financial markets shed light into the complex behaviour of financial markets and provide some explanations of certain market behaviour and anomalies. This paper surveys these developments, to which the author and several coauthors have contributed in several papers, and discusses the extent to which they can address market anomalies, complexity, and stylized facts in financial markets.
He, X. 2013, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs', 19th International Conference Computing in Economics and Finance, Vancouver, Canada.
He, X. 2013, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs', 2013 Asian Finance Association Annual Meeting, Nanchang, Jiangxi, China.
He, X.-.Z., Shi, L. & Zheng, M. 2012, 'Asset Pricing Under Keeping Up With the Joneses and Heterogeneous Beliefs'.
When agents agree to disagree about the expected growth rate of the aggregate endowment process, we study the asset price dynamics under "Keeping up with the Joneses" (KUJ) meaning that each agent maximizes the expected life-time CRRA utility of his relative consumption to the other agent in the economy. By solving the optimal consumption policies analytically, we obtain the market equilibrium under heterogeneous beliefs. We provide conditions for agents' long-run survival and show that the market price of risk, risk-free rate, price-dividend ratio in market equilibrium are the consumption share weighted averages of these variables under each agent's belief. We also show the cyclical behaviour of Sharpe ratio, risk-free rate, price and dividend ratio and stock volatility. Through Monte Carlo simulations, we find that, when the less risk averse agent is relatively optimistic, allowing a small amount of disagreement between agents can explain many market characterizes including excess volatility, a high equity premium and a low risk-free rate identified in financial markets.
He, X.-.Z. & Shi, L. 2012, 'Heterogeneous Beliefs and the Cross-Section of Asset Returns'.
When agents have irrational beliefs which are rational on average, it has been shown that the effect of their trades does not cancel out in general and can lead to time variations in market price of risk and volatility. In this paper, we follow the differences-in-opinion approach and show that the impact of unbiased disagreement on market equilibrium is much stronger in a multi-asset market than in a single-asset market, in which the impact of small disagreement may be negligible. More importantly, we show that different type of disagreement contribute significantly to explain the cross-section of expected returns, volatility and covariance between asset returns. In particular, disagreement can lead to excess volatility, a positive (negative) excess covariance when optimism/pessimism are positively (negatively) correlated between assets and the level of disagreement is negatively (positively) related to expected future returns when the relatively optimistic agent has a larger (smaller) wealth share than the pessimistic agent.
He, X. & Shi, L. 2012, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs', Conference on Liquidity and Credit Risk, Freiburg, Germany.
Chiarella, C., Dieci, R. & He, X. 2012, 'Time-varying beta: A boundedly rational equilibrium approach', Seminar Presentatiom, National Cheng-Chi University, Taiwan.
Chiarella, C., Dieci, R. & He, X. 2012, 'Heterogeneity, market mechanisms, and asset price dynamics', First Meeting of COST working groups Action IS1104, Urbino, Italy.
He, X. & Treich, N. 2012, 'Heterogeneous beliefs and prediction market accuracy', 18th International Conference Computing in Economics and Finance, Prague, Czech Republic.
He, X. & Treich, N. 2012, 'Heterogeneous beliefs and prediction market accuracy', 7th World Congress of the Bachelier Finance Society, Sydney, Australia.
He, X.-.Z. & Shi, L. 2012, 'Heterogeneous Beliefs and the Performances of Optimal Portfolios'.
The market selection depends on agent's survival index, which is a function of agent's belief and risk preference. When preferences are identical, the survival index of an agent is a decreasing function of his belief accuracy and therefore agent survives if and only if he has the lowest survival index. Following this result, one maybe tempted to think that an agent is expected to perform at least as good as the market if he survives, and he is expected to outperform the market if his belief is more accurate than all other agents' beliefs. We show that the these statements are false in general. In terms of long-run performance, market outperforms those agents who do not have the minimum survival index in the long-run. When multiple agents survive, we show that no agent can outperform the market in the long-run. In terms of the expected performance, all agents are expected to underperform the market even when they all survive in the long-run. When survival indices differ, the fittest agent with the lowest survival index is expected to outperform the market consistently with any given finite investment horizons if and only if his subjective belief is much more accurate than the other agents' beliefs.
He, X. & Treich, N. 2012, 'Heterogeneous beliefs and prediction market accuracy', Asian Finance Association and Taiwan Finance Association 2012 Joint International Conference, Taipei, Taiwan.
He, X. & Treich, N. 2012, 'Heterogeneous beliefs and prediction market accuracy', Seminar Presentation, Institute of Financial Engineering and Risk Management, School of Mathematics, South China Normal University, Guangzhou, China.
He, X. & Treich, N. 2012, 'Heterogeneous beliefs and prediction market accuracy', Seminar Presentation, Tunghai University, Taiwan.
He, X. & Treich, N. 2012, 'Heterogeneous beliefs and prediction market accuracy', Seminar Presentation, China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, China.
He, X., Shi, L. & Zheng, M. 2012, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs', Seminar Presentation, National Cheng-Chi UNiversity, Taipei, Taiwan.
Bohm, V., Chiarella, C., He, X. & Huls, T. 2012, 'A homoclinic route to volatility: Dynamics of asset prices under autoregressive forecasting', Seminar Presentation, Tunghai University, Taiwan.
Chiarella, C., Dieci, R., He, X.-.Z. & Li, K. 2012, 'An Evolutionary CAPM Under Heterogeneous Beliefs'.
Heterogeneity and evolutionary behaviour of investors are two of the most important characteristics of financial markets. This papers incorporates the adaptive behaviour of agents with heterogeneous beliefs and establishes an evolutionary capital asset pricing model (ECAPM) within the mean-variance framework. We show that the rational behaviour of agents switching to better performing trading strategies can cause large deviations of the market price from the fundamental value of one asset to spill over to other assets. Also, this spill-over effect is associated with high trading volumes and persistent volatility characterized by significantly decaying autocorrelations of, and positive correlation between, price volatility and trading volume.
He, X. & Treich, N. 2012, 'Heterogeneous beliefs and prediction market accuracy', The Art of Finance 2012 FIRN Annual Conference, Hobart, Tasmania.
He, X. 2011, 'Dynamics of a continuous-time financial market model with heterogeneous beliefs', International Conference on Nonlinear Economic Dynamics and Financial Market Modelling, Guangzhou, China.
Chiarella, C., Dieci, R. & He, X. 2011, 'Time-varying beta: A boundedly rational equilibrium approach', Seminar Presentation, University of Freiburg, Germany.
Chiarella, C., Dieci, R. & He, X. 2011, 'Time-varying beta: A boundedly rational equilibrium approach', Seminar Presentation, Dublin City University, Ireland.
He, X. 2011, 'Heterogeneity, market mechanisms, and asset price dynamics', Seminar Presentation, Kunming University of Finance and Economics, China.
He, X. 2011, 'Heterogeneity, market mechanisms, and asset price dynamics', Seminar Presentation, Tianjin University of Finance and Economics, China.
He, X. 2011, 'Heterogeneity, market mechanisms, and asset price dynamics', Seminar Presentation, Peking University, China.
He, X. 2011, 'Market efficiency and moving average rules in financial markets', Seminar Presentation, Kunming University of Finance and Economics, China.
He, X. & Li, K. 2011, 'Contrarian, momentum, and market stability', 17th International Conference on Computing in Economics and Finance, San Francisco, California, USA.
He, X. 2011, 'Heterogeneous beliefs and adaptive behaviour of financial market: Recent development and challenge', Winter Workshop on Economic Heterogeneous Interacting Agents, Tianjin, China.
He, X. & Shi, L. 2011, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs', Seminar Presentation, China Institute for Actuarial Science; Central University of Finance and Economics, China.
He, X. & Shi, L. 2011, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs', Seminar Presentation, Beijing University of Foreign Language, China.
He, X. & Shi, L. 2011, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs', Seminar Presentation, Queenâs University in Belfast, UK.
He, X. & Shi, L. 2011, 'Heterogeneous beliefs and the dynamics of cross-sectional asset returns', Quantitative Methods in Finance 2011 Conference, Sydney Australia.
Chiarella, C., He, X. & Zheng, M. 2010, 'The market impact and survival of boundedly rational traders', Young Researchers Workshop in Finance, Tokyo, Japan.
He, X.Z. & Zheng, M. 2010, 'Dynamics of moving average rules in a continuous-time financial market model', Journal of Economic Behavior and Organization, pp. 615-634.
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Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used in discrete-time HAMs. The time delay represents a memory length of a moving average rule in discrete-time HAMs. Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents' behavior parameters and memory length are obtained. It is found that an increase in memory length not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize an otherwise unstable market price, leading to stability switching as the memory length increases. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized facts observed in financial markets. © 2010.
He, X. & Li, Y. 2010, 'Market maker, stability and power-law behaviour', 16th International Conference on Computing in Economics and Finance, London, UK.
He, X. & Shi, L. 2010, 'Differences in opinion and risk premium', 6th World Congress of the Bachelier Finance Society, Toronto, Canada.
He, X. 2010, 'A model of financial market with delay', 4th International Conference on Recent Advances in Applied Dynamical Systems, Jinhua, Zhejiang, China.
He, X. & Shi, L. 2010, 'Differences in opinion and risk premium', Asian Finance Association International Conference, Hong Kong.
Chiarella, C., He, X. & Zheng, M. 2009, 'Consensus investor and intertemporal asset pricing with heterogeneous beliefs', AsianFA International Conference, Brisbane, Australia.
Chiarella, C., He, X. & Zheng, M. 2009, 'Consensus investor and intertemporal asset pricing with heterogeneous beliefs', International Conference on Economic Science with Heterogeneous Interacting Agents, Beijing, China.
Chiarella, C., He, X. & Zheng, M. 2009, 'Consensus investor and intertemporal asset pricing with heterogeneous beliefs', 15th International Conference on Computing in Economics and Finance, Sydney, Australia.
Chiarella, C., Dieci, R. & He, X. 2009, 'Time-varying beta: A bounded rational equlibrium approach', Evolution and Market Behavior in Economics and Finance Workshop, Pisa, Italy.
Chiarella, C., Dieci, R. & He, X. 2009, 'Time-varying beta: A bounded rational equilibrium approach', Seminar Presentation, Bocconi University, Milan, Italy.
He, X. & Shi, L. 2009, 'Bounded rational equilibrium and risk premium', International Conference of Financial Crises, Perth, Australia.
He, X. 2009, 'Does the market maker stabilize the market?', Paul Woolley Centre for Capital Market Dysfunctionality 2009 Annual Conference, Sydney, Australia.
He, X. & Zheng, M. 2009, 'Dynamics of moving average rules in a continuous-time financial market model', Seminar Presentation, University of Adelaide, Adelaide, Australia.
Bohm, V., Chiarella, C. & He, X. 2008, 'Dynamics of asset prices in the CAPM under autoregressive forecasting and noise', International Workshop on Nonlinear Economic Dynamics and Financial Market Modelling, Beijing, China.
Bohm, V., Chiarella, C. & He, X. 2008, 'Dynamics of asset prices in the CAPM under autoregressive forecasting and noise', MDEF 2008, Urbino, Italy.
Chiarella, C., He, X. & Zheng, M. 2008, 'Consensus investor and intertemporal asset pricing with heterogeneous beliefs', International Workshop on Nonlinear Economic Dynamics and Finance, Beijing, China.
Chiarella, C., Dieci, R. & He, X. 2008, 'Heterogeneity, market mechanisms and asset price dynamics', Learning Week, Summer Workshop, Federal Reserve Bank of St Louis, St Louis, USA.
Chiarella, C., He, X. & Zheng, M. 2008, 'Heterogeneous expectations and exchange rate dynamics', 14th International Conference on Computing in Economics and Finance, Paris, France.
Chiarella, C., He, X. & Zheng, M. 2008, 'The stochastic dynamics of speculative prices', Bachelier Finance Society 5th World Congress, London, UK.
He, X. & Shi, L. 2008, 'Zero-beta heterogeneous CAPM', 14th International Conference on Computing in Economics and Finance, Paris, France.
He, X. & Shi, L. 2008, 'Heterogeneity, bounded rationality and market dysfunctionality', 14th International Conference on Computing in Economics and Finance, Paris, France.
Chiarella, C., Dieci, R. & He, X. 2008, 'A dynamic heterogeneous beliefs CAPM', Modelling Dynamics in Economics and Finance MDEF 08, Urbino, Italy.
Chiarella, C., Dieci, R. & He, X. 2008, 'Heterogeneity, market mechanisms and asset price dynamics', Seminar Presentation, University of Karlsruhe, Karlsruhe, Germany.
Chiarella, C., He, X. & Zheng, M. 2008, 'Consensus Investor and Intertemporal Asset Pricing with Heterogeneous Beliefs', Quantitative Methods in Finance 2008 Conference, Sydney, Australia.
Chiarella, C., He, X. & Zheng, M. 2008, 'Heterogeneous expectations and exchange rate dynamics', International Workshop on Nonlinear Economic Dynamics and Financial Market Modelling, Beijing, China.
Chiarella, C., He, X. & Zheng, M. 2008, 'Heterogeneous expectations and exchange rate dynamics', Seminar Presentation, Sydney Agents Network, Sydney, Australia.
Chiarella, C., He, X., Wang, D. & Zhu, M. 2008, 'Stock price and market maker inventory dynamics with heterogeneous beliefs', International Workshop on Nonlinear Dynamics and Financial Market Modelling, Beijing, China.
He, X. & Li, Y. 2008, 'Calibrating a market fraction model to the power-law behaviour in the DAX', International Workshop on Nonlinear Dynamics and Financial Market Modelling, Beijing, China.
He, X. & Shi, L. 2008, 'Zero-beta CAPM with heterogeneous beliefs', MDEF 2008 Conference, Urbino, Italy.
He, X. & Shi, L. 2008, 'Portfolio analysis and zero-beta heterogeneous CAPM', International Workshop on Nonlinear Economic Dynamics and Financial Market Modeling, Beijing, China.
He, X. 2008, 'Heterogeneous expectations and exchange rate dynamics', Seminar Presentation, School of Finance and Economics, University of Technology, Sydney, Sydney, Australia.
Chiarella, C., He, X. & Zheng, M. 2007, 'The stochastic price dynamics of speculative behaviour', 13th International Conference on Computing in Economics and Finance, Montreal, Canada.
He, X. 2007, 'The stochastic bifurcation of a speculative asset pricing model', 2nd International Conference on Recent Advances in Applied Dynamical Systems, Jinhua, China.
He, X. 2007, 'Aggregation of heterogeneity beliefs and asset pricing theory: A mean-variance analysis', International Symposium on Financial Engineering and Risk Management 2007, Beijing, China.
He, X. 2007, 'Aggregation of heterogeneity beliefs and asset pricing theory: A mean variance analysis', 13th International Conference on Computing in Economics and Finance, Montreal, Canada.
Chiarella, C., Dieci, R. & He, X. 2007, 'Aggregation of heterogeneous beliefs and asset pricing theory: A mean-variance analysis', ASFA/FMA Conference, Hong Kong, China.
He, X. 2007, 'Heterogeneity, bounded rationality, and market dysfunctionality', The Paul Woolley Centre for Capital Market Dysfunctionality Conference: Investing Strategies and Financial Market Inefficiency, Sydney, Australia.
He, X. & Shi, L. 2007, 'Zero-beta CAPM with heterogeneous beliefs', Australasian Finance and Banking Conference, Sydney, Australia.
Chiarella, C., He, X.-.Z. & Zheng, M. 2007, 'The Stochastic Dynamics of Speculative Prices'.
Within the framework of the heterogeneous agent paradigm, we establish a stochastic model of speculative price dynamics involving of two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the invariant measures of a random dynamical system. By conducting a stochastic bifurcation analysis, we examine the market impact of speculative behaviour. We show that, when the chartists use lagged price trends to form their expectations, the market equilibrium price can be characterised by a unique and stable invariant measure when the activity of the speculators is below a certain critical value. If this threshold is surpassed, the market equilibrium can be characterised by more than two invariant measures, of which one is completely stable, another is completely unstable and the remaining ones may exhibit various types of stability. Also, the corresponding stationary measure displays a significant qualitative change near the threshold value. We show that the stochastic model displays behaviour consistent with that of the underlying deterministic model. However, when the time lag in the formation of the price trends used by the chartists approaches zero, such consistency breaks down. In addition, the change in the stationary distribution is consistent with a number of market anomalies and stylised facts observed in financial markets, including a bimodal logarithmic price distribution and fat tails.
Chiarella, C., Dieci, R. & He, X. 2006, 'A dynamic heterogenous beliefs CAPM', Workshop on Financial Market Dynamics, Piacenza, Italy.
Chiarella, C., Dieci, R. & He, X.-.Z. 2006, 'Aggregation of Heterogeneous Beliefs and Asset Pricing Theory: A Mean-Variance Analysis'.
Within the standard mean-variance framework, this paper provides a procedure to aggregate the heterogeneous beliefs in not only risk preferences and expected payoffs but also variances/covariances into a market consensus belief. Consequently, an asset equilibrium price under heterogeneous beliefs is derived. We show that the market aggregate behavior is in principle a weighted average of heterogeneous individual behaviors. The CAPM-like equilibrium price and return relationships under heterogeneous beliefs are obtained. The impact of diversity of heterogeneous beliefs on the market aggregate risk preference, asset volatility, equilibrium price and optimal demands of investors is examined. As a special case, our result provides a simple explanation for the empirical relation between cross-sectional volatility and expected returns.
Chiarella, C., Dieci, R. & He, X. 2006, 'On the dynamic behavior of asset prices in disequilibrium: Where are we after three decades?', MDEF 2006, Urbino, Italy.
Chiarella, C., Dieci, R. & He, X. 2006, 'On the dynamic behaviour of asset prices in disequilibrium: Where are we after three decades?', WIVA 3 Conference, Sienna, Italy.
Chiarella, C., He, X.-.Z. & Hommes, C. 2006, 'A dynamic analysis of moving average rules', JOURNAL OF ECONOMIC DYNAMICS & CONTROL, pp. 1729-1753.
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Chiarella, C., He, X. & Li, Y. 2006, 'A dynamic heterogenous beliefs CAPM', 1st International Conference on Economic Science with Heterogenous Interacting Agents, Bologna, Italy.
He, X. & Li, Y. 2006, 'Long memory, heterogeneity and trend chasing', 17th Annual Asian Finance Association/ FMA Conference, 17th Annual Asian Finance Association/ FMA Conference, Asian Finance Association, Auckland, New Zealand, pp. 1-33.
Chiarella, C., Bohm, V. & He, X. 2005, 'The interaction of non-linear and stochastic elements in a one period model of asset price dynamics', Econophysics Colloquium, Econophysics Colloquium, -, Canberra, Australia.
He, X.-.Z. & Li, Y. 2005, 'Heterogeneity, Profitability and Autocorrelations'.
This paper contributes to the development of recent literature on the explanation power and calibration issue of heterogeneous asset pricing models by presenting a simple stochastic market fraction asset pricing model of two types of traders (fundamentalists and trend followers) under a market maker scenario. It seeks to explain aspects of financial market behaviour (such as market dominance, under and over-reaction, profitability and survivability) and to characterize various statistical properties (including autocorrelation structure) of the stochastic model by using the the dynamics of the underlying deterministic system, traders? behaviour and market fractions. Statistical analysis based on Monte Carlo simulations shows that the long-run behaviour and convergence of the market prices, long (short)-run profitability of the fundamental (trend following) trading strategy, survivability of chartists, and various under and over-reaction autocorrelation patterns of returns can be characterized by the stability and bifurcations of the underlying deterministic system. Our analysis underpins mechanism on various market behaviour (such as under/over-reactions), market dominance and stylized facts in high frequency financial markets.
He, X. 2005, 'Heterogeneity, profitability and autocorrelations', Quantitative Methods in Finance 2005 Conference, Quantitative Methods in Finance 2005 Conference, -, Sydney, Australia.
He, X. & Li, Y. 2005, 'Heterogeneity, profitability and autocorrelations', Proceedings of the 11th Annual Conference on Computing in Economics and Finance, 11th Annual Conference on Computing in Economics and Finance, University of Maryland, Washington, USA, pp. 1-44.
He, X.-.Z. & Li, Y. 2005, 'Long Memory, Heterogeneity and Trend Chasing'.
Long-range dependence in volatility is one of the most prominent examples of applications in financial market research involving universal power laws. Its characterization has recently spurred attempts at theoretical explanation of the underlying mechanism. This paper contributes to this recent development by analyzing a simple market fraction asset pricing model with two types of traders fundamentalists who trade on the price deviation from estimated fundamental value and trend followers who follow a trend which is updated through a geometric learning process. Our analysis shows that the heterogeneity, trend chasing through learning, and the interplay of noisy processes and a stable deterministic equilibrium can be the source of power-law distributed fluctuations. Statistical analysis based on Monte Carlo simulations are conducted to characterize the long memory. Realistic estimates of the power-law decay indices and the (FI)GARCH parameters are found.
Bird, R., He, X., Thosar, S.B. & Woolley, P.K. 2004, 'The case for market inefficiency: Investment style and market pricing', 2004 Financial Management Association Meeting, Financial Management Association Meeting, Financial Management Association, New Orleans, USA, pp. 1-24.
Chiarella, C., Flaschel, P., He, X. & Hung, H. 2004, 'A stochastic model of real-financial interaction with boundedly rational heterogeneous agents', Society for nonlinear dynamics and economics, Society for Nonlinear Dynamics and Economics, -, Atlanta, USA.
Chiarella, C., He, X.-.Z. & Hommes, C.H. 1970, 'A Dynamic Analysis of Moving Average Rules'.
The use of various moving average 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 also 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) moving average. 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 lengths used for the moving averages. By increasing the intensity of choice to switching strategies, we then examine various rational routes to randomness for different moving average rules. The price dynamics of the moving average rule is also examined and one of our main findings is that an increase of the window length of the moving average 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.
He, X. 2004, 'Economic dynamics asset pricing and nonlinear adaptive evolutionary systems', International Conference on Nonlinear Dynamics and Evolution Equations, International Conference on Nonlinear Dynamics and Evolution Equations, -, St John's Canada.
Chiarella, C. & He, X.Z. 2003, 'Heterogeneous beliefs, risk, and learning in a simple asset-pricing model with a market maker', MACROECONOMIC DYNAMICS, pp. 503-536.
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Chiarella, C. & He, X. 2003, 'Asset pricing and wealth dynamics - an adaptive model with heterogenous agents', WEHIA 2003, 8th Annual Workshop on Economics with Heterogeneous Interacting Agents, Institute of Economics, Keil, Germany, pp. 1-20.
Chiarella, C., Flaschel, P., He, X. & Hung, H. 2003, 'A stochastic model of real-financial interaction with boundedly rational heterogeneous agents', Bielefeld Workshop on Real-Financial Interaction, --, Bielefeld, Germany.
Chiarella, C. & He, X. 2003, 'An adaptive model of asset pricing and wealth dynamics with heterogeneous trading strategies', WEHIA 2003 - Annual Workshop on Economics with Heterogeneous Interacting Agents, --, Keil, Germany.
Chiarella, C., He, X. & Zhu, P. 2003, 'Fading memory learning in the cobweb model with risk averse heterogeneous producers', 9th International Conference on Computing in Economics and Finance, --, Seattle, USA.
He, X. 2003, 'Asset pricing volatility and market behaviour: a market fraction approach', Quantitative Methods in Finance 2003 Conference, --, Sydney, Australia.
He, X. 2002, 'Adaptiveness, wealth dynamics and asset pricing with heterogeneous agents', Quantitative Methods in Finance 2002 Conference, Quantitative Methods in Finance 2002 Conference, Sydney and Cairns, Australia.
Chiarella, C. & He, X. 2002, 'Adaptive models of asset pricing and wealth dynamics in economies with heterogeneous agents', Workshop on Economic Dynamics - CENDEF, Workshop on Economic Dynamics - CENDEF, University of Leiden, The Netherlands.
Chiarella, C. & He, X.-.Z. 2002, 'An Adaptive Model on Asset Pricing and Wealth Dynamics with Heterogeneous Trading Strategies'.
This paper develops an adaptive model on asset pricing and wealth dynamic of a financial market with heterogeneous agents and examines the profitability of momentum and contrarian trading strategies. In order to characterize asset price, wealth dynamics and rational adaptiveness arising from the interaction of heterogeneous agents with CRRA utility, an adaptive discrete time equilibrium model in terms of return ad wealth proportions (among heterogeneous representative agents) is established. Taking trend followers and contrarians as the main hetergeneous agents in the model, the profitability of momentum and contrarian trading strategies is analyzed. Our results show the capability of the model to characterize some of the existing evidence on many of anomailies observed in financial markets, including the profitability of momentum trading strategies over short time intervals, rational adaptiveness of agents, overconfidence and underreaction, overreaction and herd behavior, excess volatility, and volatility clustering.
Chiarella, C. & He, X. 2002, 'An adaptive model on asset pricing and wealth dynamics with heterogeneous trading systems', Asia Pacific Finance Association Conference, Asia Pacific Finance Association Conference, Tokyo, Japan.
Chiarella, C., He, X.-.Z., Dieci, R. & Sydney, U.O.T., 'A Dynamic Heterogeneous Beliefs CAPM'.
We reconsider the derivation of the traditional capital asset pricing model (CAPM) in the discrete time setting for a portfolio of one riskless asset and many risky assets. In contrast to the standard setting, it is assumed that agents are heterogeneous in their conditional means and covariances of the risky returns, and that their beliefs about future returns - based on statistical properties of past returns - induce expectations feedback. A Walrasian auctioneer scenario is used for the determination of the market clearing price. In this framework we first construct a consensus belief to represent the aggregate market beliefs about means and variances/covariances of returns, and derive a heterogeneous CAPM which relates aggregate excess return on risky assets with aggregate excess return on the market portfolio via aggregate beta coefficients. We then use this result to establish a dynamic {\em market fraction\/} model in which agents are grouped according to their beliefs. In particular, we focus on three classical heterogeneous agents types - fundamentalists, trend followers and noise traders - and investigate how some of the key agent characteristics affect the time varying behaviour of market returns and beta coefficients
Chiarella, C., Dieci, R. & He, T., 'Aggregation of Heterogeneous Beliefs and Asset Pricing: A Mean-Variance Analysis'.
The aim of this paper is to show, within the mean-variance framework, how the market belief can be constructed as the result of the aggregation of heterogeneous beliefs and how the market equilibrium prices of risky assets can thus be determined. The heterogeneous beliefs are defined in terms of not only the means but also variances and covariances. By constructing the mean and variance of the market belief, we analyze the impact of the heterogeneous beliefs on the market equilibrium asset pricing relation. In particular, we extend the standard CAPM under homogenous beliefs to the one under the heterogeneous beliefs.

Journal articles

He, X.Z. & Li, Y. 2015, 'Testing of a market fraction model and power-law behaviour in the DAX 30', Journal of Empirical Finance, vol. 31, pp. 1-17.
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© 2015 Elsevier B.V. This paper tests a simple market fraction asset pricing model with heterogeneous agents. By selecting a set of structural parameters of the model through a systematic procedure, we show that the autocorrelations (of returns, absolute returns and squared returns) of the market fraction model share the same pattern as those of the DAX 30. By conducting econometric analysis via Monte Carlo simulations, we characterize these power-law behaviours and find that estimates of the power-law decay indices, the (FI)GARCH parameters, and the tail index of the selected market fraction model closely match those of the DAX 30. The results strongly support the explanatory power of the heterogeneous agent models.
He, X.Z. & Li, K. 2015, 'Profitability of time series momentum', Journal of Banking and Finance, vol. 53, pp. 140-157.
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© 2015 Elsevier B.V. We propose a continuous-time heterogeneous agent model consisting of fundamental, momentum, and contrarian traders to explain the significant time series momentum. We show that the performance of momentum strategy is determined by both time horizon and the market dominance of momentum traders. Specifically, when momentum traders are more active in the market, momentum strategies with short (long) time horizons stabilize (destabilize) the market, and meanwhile the market under-reacts (over-reacts) in short-run (long-run). This provides profit opportunity for time series momentum strategies with short horizons and reversal with long horizons. When momentum traders are less active in the market, they always lose. The results provide an insight into the profitability of time series momentum documented in recent empirical studies.
Chiarella, C., He, X.Z. & Wei, L. 2015, 'Learning, information processing and order submission in limit order markets', Journal of Economic Dynamics and Control, vol. 61, pp. 245-268.
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© 2015 Elsevier B.V. By introducing a genetic algorithm learning with a classifier system into a limit order market, this paper provides a unified framework of microstructure and agent-based models of limit order markets that allows traders to determine their order submission endogenously according to market conditions. It examines how traders process and learn from market information and how the learning affects limit order markets. It is found that, measured by the average usage of different group of market information, trading rules under the learning become stationary in the long run. Also informed traders pay more attention to the last transaction sign while uninformed traders pay more attention to technical rules. Learning of uninformed traders improves market information efficiency, but not necessarily when informed traders learn. Opposite to the learning of informed traders, learning makes uninformed traders submit less aggressive limit orders and more market orders. Furthermore private values can have significant impact in the short run, but not in the long run. One implication is that the probability of informed trading (PIN) is positively related to the volatility and the bid-ask spread.
Chiarella, C., He, X.-.Z. & Zwinkels, R.C.J. 2014, 'Heterogeneous expectations in asset pricing: Empirical evidence from the S & P500', JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION, vol. 105, pp. 1-16.
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Di Guilmi, C., He, X.Z. & Li, K. 2014, 'Herding, trend chasing and market volatility', Journal of Economic Dynamics and Control, vol. 48, pp. 349-373.
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© 2014 Elsevier B.V. We introduce a heterogeneous agent asset pricing model in continuous-time to show that, although trend chasing, switching and herding all contribute to market volatility in price and return and to volatility clustering, their impacts are different. The fluctuations of the market price and return and the level of the significant autocorrelations (ACs) of the absolute and squared returns increase with the intensities of herding and trend chasing based on long time horizon. However an increase in switching intensity reduces the return volatility and in particular a low switching intensity reduces the price volatility and increases the level of the significant ACs, but the effect becomes opposite when the switching intensity is high. We also show that market noise plays a more important role than fundamental noise on the power-law behavior of returns.
Chiarella, C., ter Ellen, S., He, X.Z. & Wu, E. 2014, 'Fear or fundamentals? Heterogeneous beliefs in the European sovereign CDS market', Journal of Empirical Finance, vol. 32, pp. 19-34.
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© 2014 Elsevier B.V. This paper proposes a model for credit default swap (CDS) spreads under heterogeneous expectations to explain the escalation in sovereign European CDS spreads and the widening variations across European sovereigns following the Global Financial Crisis (GFC). In our model, investors believe that sovereign CDS spreads are determined by country-specific fundamentals and momentum. By estimating the model we find evidence that, while some of the recent movements in sovereign CDS spreads can be explained by deteriorating fundamentals for core European Union (EU) countries, momentum has also played a destabilizing role since the GFC in all sovereign credit markets studied.
Chiarella, C., He, X. & Zheng, M. 2013, 'Heterogeneous expectations and exchange rate dynamics', The European Journal of Finance, vol. 19, no. 5, pp. 392-419.
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This article presents a continuous-time model of exchange rates not only relying on macroeconomic factors but also having an investor heterogeneity component. The driving macroeconomic factor is the domestic½foreign interest rate differential, while the investor heterogeneity is described by the expectations of boundedly rational portfolio managers who use a weighted average of the expectations of fundamentalists and chartists. Within this framework, the different roles of the macroeconomic factor and investor heterogeneity in the determination of the exchange rate are examined explicitly. We show that this simple model generates very complicated market behaviour, including the existence of multiple steady-state equilibria, deviations of the market exchange rate from the fundamental one and market fluctuations. Numerical simulation of the corresponding stochastic version of the model shows that the model is able to generate typical time series and volatility clustering patterns observed in exchange rate markets.
Chiarella, C., Dieci, R. & He, X. 2013, 'Time-varying beta: A boundedly rational equlibrium approach', Journal of Evolutionary Economics, vol. 23, no. 3, pp. 609-639.
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The conditional CAPM with time-varying betas has been widely used to explain the cross-section of asset returns. However, most of the literature on time-varying beta is motivated by econometric estimation using various latent risk factors rather than explicit modelling of the stochastic behaviour of betas through agents behaviour, such as momentum trading. Misspecification of beta risk and the lack of any theoretical guidance on how to specify risk factors based on the representative agent economy appear empirically challenging. In this paper, we set up a dynamic equilibrium model of a financial market with boundedly rational and heterogeneous agents within the mean-variance framework of repeated one-period optimisation and develop an explicit dynamic behaviour CAPM relation between the expected equilibrium returns and time-varying betas. By incorporating the two most commonly used types of investors, fundamentalists and chartists, into the model, we show that there is a systematic change in the market portfolio, risk-return relationships, and time varying betas when investors change their behaviour, such as the chartists acting as momentum traders. In particular, we demonstrate the stochastic nature of time-varying betas. We also show that the commonly used rolling window estimates of time-varying betas may not be consistent with the ex-ante betas implied by the equilibrium model. The results provide a number of insights into an understanding of time-varying beta.
Chiarella, C., Dieci, R., He, X.Z. & Li, K. 2013, 'An evolutionary CAPM under heterogeneous beliefs', Annals of Finance, vol. 9, no. 2, pp. 185-215.
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Heterogeneity and evolutionary behaviour of investors are two of the most important characteristics of financial markets. This paper incorporates the adaptive behaviour of agents with heterogeneous beliefs and establishes an evolutionary capital asset pricing model (ECAPM) within the mean-variance framework. We show that the rational behaviour of agents switching to better-performing trading strategies can cause large deviations of the market price from the fundamental value of one asset to spill over to other assets. Also, this spill-over effect is associated with high trading volumes and persistent volatility characterized by significantly decaying autocorrelations of, and positive correlation between, price volatility and trading volume. © 2012 Springer-Verlag Berlin Heidelberg.
He, X.Z. & Shi, L. 2012, 'Boundedly rational equilibrium and risk premium', Accounting and Finance, vol. 52, no. 1, pp. 71-93.
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When people agree to disagree, the impact of the disagreement among agents on the market is the main concern of this paper. With the standard mean variance framework, this paper considers a market of two risky assets and two agents who have different preference and disagreement about the mean and variance/covariance of the asset returns. By constructing a consensus belief, the paper develops an concept of boundedly rational equilibrium (BRE) to characterize the market equilibrium and examines explicitly the impact of heterogeneity on the market equilibrium and risk premium when the disagreements among the two agents are mean preserved spreads of a benchmark homogeneous belief. It shows that, in market equilibrium, the biased mean preserved spreads in beliefs among the two agents have significant impact on the risk premium of the risky assets and market portfolio, and adding a riskless asset in the market magnifies the impact of the heterogeneity on the market. The results show that both optimism/pessemism and confidence/doubt can increase the market risk premium and reduce the riskfree rate. © 2011 The Authors. Accounting and Finance © 2011 AFAANZ.
He, X.Z. & Shi, L. 2012, 'Disagreement, correlation and asset prices', Economics Letters, vol. 116, no. 3, pp. 512-515.
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When people agree to disagree, how does the disagreement affect asset prices? Within an equilibrium framework with two agents, two risky assets and a riskless bond, we analyze the joint impact of disagreement about expected payoff, variance and correlation, and compare prices with benchmark prices in a market with homogeneous beliefs. © 2012 Elsevier B.V.
Chiarella, C., He, X.Z., Huang, W. & Zheng, H. 2012, 'Estimating behavioural heterogeneity under regime switching', Journal of Economic Behavior and Organization.
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Financial markets are typically characterized by high (low) price level and low (high) volatility during boom (bust) periods, suggesting that price and volatility tend to move together with different market conditions/states. By proposing a simple heterogeneous agent model of fundamentalists and chartists with Markov chain regime-dependent expectations and applying the S&P 500 data from January 2000 to June 2010, we show that the estimation of the model matches well with the boom and bust periods in the US stock market. In addition, we find evidence of time-varying behavioural heterogeneity within-group and that the model exhibits good forecasting accuracy. © 2012 Elsevier B.V. All rights reserved.
Chiarella, C., He, X. & Pellizzari, P. 2012, 'A dynamic analysis of the microstructure of moving average rules in a double auction market', Macroeconomic Dynamics, vol. 16, no. 4, pp. 556-575.
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Inspired by the theoretically oriented dynamic analysis of moving average rules in the model of Chiarella, He, and Hommes (CHH) [Journal of Economic Dynamics and Control 30 (2006), 1729-1753], this paper conducts a dynamic analysis of a more realistic microstructure model of continuous double auctions in which the probability of heterogeneous agents trading is determined by the rules of either fundamentalists mean-reverting to the fundamental or chartists choosing moving average rules based on their relative performance. With such a realistic market microstructure, the model is able not only to obtain the results of the CHH model but also to characterize most of the stylized facts including volatility clustering, insignificant autocorrelations (ACs) of returns, and significant slowly decaying ACs of the absolute returns. The results seem to suggest that a comprehensive explanation of several statistical properties of returns is possible in a framework where both behavioral traits and realistic microstructure have a role
He, X.Z. & Shi, L. 2012, 'Disagreement in a Multi-Asset Market', International Review of Finance, vol. 12, no. 3, pp. 357-373.
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This paper provides a simple framework to study the effect of disagreement in a multi-asset market equilibrium by considering two agents who disagree about expected returns, variances, and correlation of returns of two risky assets. When agents' subjective beliefs are characterized by mean preserving spreads of a benchmark homogeneous belief, we show that the effect of the disagreement does not cancel out in general and the effect in a multi-asset market can be very different from a single asset market. In particular, the market risk premium can increase and the risk-free rate can decrease significantly even when the market is overoptimistic and overconfident. © International Review of Finance Ltd. 2012.
He, X.Z. & Li, K. 2012, 'Heterogeneous beliefs and adaptive behaviour in a continuous-time asset price model', Journal of Economic Dynamics and Control, vol. 36, no. 7, pp. 973-987.
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This paper extends the analysis of the seminal work of . Brock and Hommes (1997, 1998) on heterogeneous beliefs and rational routes to randomness in discrete-time models to a continuous-time model of asset pricing. The resulting model characterised mathematically by a system of stochastic delay differential equations provides a unified approach to deal with adaptive behaviour of heterogeneous agents and market stability impact of lagged price used by chartists to form their expectations. For the underlying deterministic model, we show not only that the result of Brock and Hommes on rational routes to market instability in discrete-time holds in continuous-time but also a double edged effect of an increase in lagged price used by the chartists on market stability. For the stochastic model, we demonstrate that the interaction and boundedly rational behaviour of heterogeneous agents can generate various market phenomena such as bubbles and crashes and replicate stylised facts including volatility clustering, and long range dependence in volatility. © 2012 Elsevier B.V.
Chiarella, C., Dieci, R. & He, X.-.Z. 2011, 'Do heterogeneous beliefs diversify market risk?', EUROPEAN JOURNAL OF FINANCE, vol. 17, no. 3, pp. 241-258.
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Chiarella, C., He, X.Z. & Zheng, M. 2011, 'An analysis of the effect of noise in a heterogeneous agent financial market model', Journal of Economic Dynamics and Control, vol. 35, no. 1, pp. 148-162.
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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. © 2010 Elsevier B.V.
Chiarella, C., Dieci, R. & He, X. 2011, 'The dynamic behaviour of asset prices in disequilibrium: a survey', International Journal of Behavioural Accounting and Finance, vol. 2, no. 2, pp. 101-139.
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This article surveys boundedly rational heterogeneous agent (BRHA) models of financial markets. We give particular emphasis to the role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, and calibration of this class of models. Due to agents behavioural features and market noise, the BRHA class of models are both non-linear and stochastic. We show that BRHA models produce both a locally stable fundamental equilibrium corresponding to that of the standard paradigm, as well as instability with a consequent rich range of possible complex behaviours that are analysed by both simulation and deterministic bifurcation analysis. A calibrated model is able to reproduce quite well the stylised facts of financial markets. The BRHA framework seems able to better accommodate market features such as fat tails, volatility clustering, large excursions from the fundamental and bubbles than the standard financial market paradigm.
He, X.-.Z. & Zheng, M. 2010, 'Dynamics of moving average rules in a continuous-time financial market model', Journal of Economic Behavior & Organization, vol. 76, no. 3, pp. 615-634.
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Cao, L. & He, T. 2009, 'Developing actionable trading agents', Knowledge and Information Systems, vol. 18, no. 2, pp. 183-198.
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Trading agents are useful for developing and back-testing quality trading strategies to support smart trading actions in the market. However, most of the existing trading agent research oversimplifies trading strategies, and focuses on simulated ones. As a result, there exists a big gap between the deliverables and business needs when the developed strategies are deployed into the real life. Therefore, the actionable capability of developed trading agents is often very limited. This paper for the first time introduces effective approaches for optimizing and integrating multiple classes of strategies through trading agent collaboration. An integration and optimization approach is proposed to identify optimal trading strategy in each category, and further integrate optimal strategies crossing classes. Positions associated with these optimal strategies are recommended for trading agents to take actions in the market. Extensive experiments on a large quantity of real-life market data show that trading agents following the recommended strategies have great potential to obtain high benefits while low costs. This verifies that it is promising to develop trading agents toward workable and satisfying business needs. © Springer-Verlag London Limited 2008.
Zhu, M., Chiarella, C., He, X.Z. & Wang, D. 2009, 'Does the market maker stabilize the market?', Physica A: Statistical Mechanics and its Applications, vol. 388, no. 15-16, pp. 3164-3180.
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The market maker plays an important role in price formation, but his/her behavior and stabilizing impact on the market are relatively unclear, in particular in speculative markets. This paper develops a financial market model that examines the impact on market stability of the market maker, who acts as both a liquidity provider and an active investor in a market consisting of two types of boundedly rational speculative investors-the fundamentalists and trend followers. We show that the market maker does not necessarily stabilize the market when he/she actively manages the inventory to maximize profits, and that rather the market maker's impact depends on the behavior of the speculators. Numerical simulations show that the model is able to generate outcomes for asset returns and market inventories that are consistent with empirical findings. © 2009.
He, X., Li, K., Wei, J. & Zheng, M. 2009, 'Market stability switches in a continuous-time financial market with heterogeneous beliefs', Economic Modelling, vol. 26, no. 6, pp. 1432-1442.
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By considering a financial market of fundamentalists and trend followers in which the price trend of trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examine the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. These interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, sufficient conditions on the stability and global existence of the periodic solution are obtained.
Zheng, M., Wang, D. & He, X. 2009, 'Asymmetry of technical analysis and market price volatility', China Finance Review, vol. 61, no. 2, pp. 61-89.
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He, X.Z. & Li, Y. 2008, 'Heterogeneity, convergence, and autocorrelations', Quantitative Finance, vol. 8, no. 1, pp. 59-79.
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This paper is a contribution to the literature on the explanatory power and calibration of heterogeneous asset pricing models. We set out a new stochastic market-fraction asset pricing model of fundamentalists and trend followers under a market maker. Our model explains key features of financial market behaviour such as market dominance, convergence to the fundamental price and under- and over-reaction. We use the dynamics of the underlying deterministic system to characterize these features and statistical properties, including convergence of the limiting distribution and autocorrelation structure. We confirm these properties using Monte Carlo simulations.
Chiarella, C., He, X.Z., Wang, D. & Zheng, M. 2008, 'The stochastic bifurcation behaviour of speculative financial markets', Physica A: Statistical Mechanics and its Applications, vol. 387, no. 15, pp. 3837-3846.
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This paper establishes a continuous-time stochastic asset pricing model in a speculative financial market with fundamentalists and chartists by introducing a noisy fundamental price. By application of stochastic bifurcation theory, the limiting market equilibrium distribution is examined numerically. It is shown that speculative behaviour of chartists can cause the market price to display different forms of equilibrium distributions. In particular, when chartists are less active, there is a unique equilibrium distribution which is stable. However, when the chartists become more active, a new equilibrium distribution will be generated and become stable. The corresponding stationary density will change from a single peak to a crater-like density. The change of stationary distribution is characterized by a bimodal logarithm price distribution and fat tails. The paper demonstrates that stochastic bifurcation theory is a useful tool in providing insight into various types of financial market behaviour in a stochastic environment. © 2008 Elsevier Ltd. All rights reserved.
Gong, G., Gao, J. & He, X. 2008, 'Exchange Rate Regime and Monetary Policy: A Proposal for Small and Less Developed Economies', Jingji Yanjiu - Economic Research Journal, vol. 43, no. 6, pp. 25-36.
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He, X.Z. & Li, Y. 2007, 'Power-law behaviour, heterogeneity, and trend chasing', Journal of Economic Dynamics and Control, vol. 31, no. 10, pp. 3396-3426.
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Long-range dependence in volatility is one of the most prominent examples in financial market research involving universal power laws. Its characterization has recently spurred attempts to provide some explanations of the underlying mechanism. This paper contributes to this recent line of research by analyzing a simple market fraction asset pricing model with two types of traders - fundamentalists who trade on the price deviation from estimated fundamental value and trend followers whose conditional mean and variance of the trend are updated through a geometric learning process. Our analysis shows that agent heterogeneity, risk-adjusted trend chasing through the geometric learning process, and the interplay of noisy fundamental and demand processes and the underlying deterministic dynamics can be the source of power-law distributed fluctuations. In particular, the noisy demand plays an important role in the generation of insignificant autocorrelations (ACs) on returns, while the significant decaying AC patterns of the absolute returns and squared returns are more influenced by the noisy fundamental process. A statistical analysis based on Monte Carlo simulations is conducted to characterize the decay rate. Realistic estimates of the power-law decay indices and the (FI)GARCH parameters are presented. © 2007 Elsevier B.V. All rights reserved.
Corron, N., He, X.-.Z. & Westerhoff, F. 2007, 'Butter mountains, milk lakes and optimal price limiters', Applied Economics Letters, vol. 14, no. 15, pp. 1131-1136.
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Chiarella, C., Dieci, R. & He, X. 2007, 'Heterogeneous Expectations and Speculative Behavior in a Dynamic Multi-Asset Framework', Journal of Economic Behavior and Organization, vol. 62, no. 3, pp. 408-427.
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This paper develops a dynamic model of a financial market where heterogeneous agents invest among multiple risky assets and a risk-free asset, under a market maker scenario. Particular attention is paid to the case of two risky assets and two agent types, fundamentalists and trend chasers, whose beliefs on both first and second moments of the conditional distribution of returns are based on past observations. Conditions for the stability of the ?fundamental? equilibrium are established and the effect of the correlation between the risky assets is examined. It turns out that investors? anticipated correlation and dynamic portfolio diversification do not always have a stabilizing role, but rather may act as a source of complexity in the financial market.
Chiarella, C., He, X.Z. & Wang, D. 2006, 'A behavioral asset pricing model with a time-varying second moment', Chaos, Solitons and Fractals, vol. 29, no. 3, pp. 535-555.
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We develop a simple behavioral asset pricing model with fundamentalists and chartists in order to study price behavior in financial markets when chartists estimate both conditional mean and variance by using a weighted averaging process. Through a stability, bifurcation, and normal form analysis, the market impact of the weighting process and time-varying second moment are examined. It is found that the fundamental price becomes stable (unstable) when the activities from both types of traders are balanced (unbalanced). When the fundamental price becomes unstable, the weighting process leads to different price dynamics, depending on whether the chartists act as either trend followers or contrarians. It is also found that a time-varying second moment of the chartists does not change the stability of the fundamental price, but it does influence the stability of the bifurcations. The bifurcation becomes stable (unstable) when the chartists are more (less) concerned about the market risk characterized by the time-varying second moment. Different routes to complicated price dynamics are also observed. The analysis provides an analytical foundation for the statistical analysis of the corresponding stochastic version of this type of behavioral model. © 2005 Elsevier Ltd. All rights reserved.
Chiarella, C., He, X.Z. & Hommes, C. 2006, 'Moving average rules as a source of market instability', Physica A: Statistical Mechanics and its Applications, vol. 370, no. 1, pp. 12-17.
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Despite the pervasiveness of the efficient markets paradigm in the academic finance literature, the use of various moving average (MA) trading rules remains popular with financial market practitioners. This paper proposes a stochastic 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. Our simulations show that the MA is a source of market instability, and the interaction of the MA and market noises can lead to the tendency for the market price to take long excursions away from the fundamental. The model reveals various market price phenomena, the coexistence of apparent market efficiency and a large chartist component, price resistance levels, long memory and skewness and kurtosis of returns. © 2006 Elsevier B.V. All rights reserved.
Dieci, R., Foroni, I., Gardini, L. & He, X.-.Z. 2006, 'Market mood, adaptive beliefs and asset price dynamics', Chaos, Solitons & Fractals, vol. 29, no. 3, pp. 520-534.
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Ruan, D. & He, X. 2006, 'Global Stability In Chemostat-type Competition Models With Nutrient Recycling (vol 58, Pg 170, 1998)', Siam Journal On Applied Mathematics, vol. 66, no. 6, pp. 2204-2205.
This note corrects some typos and errors in the paper [S. Ruan and X.-Z. He, SIAM J. Appl. Math., 58 (1998), pp. 170-192].
Chiarella, C., He, X.Z., Hung, H. & Zhu, P. 2006, 'An analysis of the cobweb model with boundedly rational heterogeneous producers', Journal of Economic Behavior and Organization, vol. 61, no. 4, pp. 750-768.
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This paper considers the traditional cobweb model with heterogenous risk averse producers whose supply functions involve their estimates of the conditional mean and variance of the future price. The producers seek to learn these quantities by applying geometric decay processes (GDP) to past prices. The heterogeneity manifests itself in the lag lengths and memory parameters applied to past prices as well as in risk aversion coefficients. We find that each dimension of heterogeneity changes/enriches the cobweb dynamics with respect to the case of homogeneous producers. © 2006 Elsevier B.V. All rights reserved.
He, X.-.Z. & Westerhoff, F.H. 2005, 'Commodity markets, price limiters and speculative price dynamics', Journal of Economic Dynamics and Control, vol. 29, no. 9, pp. 1577-1596.
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Bird, R., (Tony) He, X.-.Z., Thosar, S. & Woolley, P. 2005, 'The case for market inefficiency: Investment style and market pricing', Journal of Asset Management, vol. 5, no. 6, pp. 365-388.
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Bird, R., He, X., Thosar, S.B. & Woolley, P.K. 2005, 'Momentum and index investing: implications for market efficiency', Journal of Financial Transformation, vol. 15, no. December, pp. 79-85.
Chiarella, C., He, T. & Hommes, C.H. 2005, 'A Dynamic Analysis of Moving Average Rules'.
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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 moving average 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.
Chiarella, C. & He, X.Z. 2003, 'Dynamics of beliefs and learning under a(L)-processes - the heterogeneous case', JOURNAL OF ECONOMIC DYNAMICS & CONTROL, vol. 27, no. 3, pp. 503-531.
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Chiarella, C. & He, X.Z. 2002, 'Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model', Computational Economics, vol. 19, no. 1, pp. 95-132.
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Trade among individuals occurs either because tastes (risk aversion)differ, endowments differ, or beliefs differ. Utilising the concept of'adaptively rational equilibrium' and a recent framework of Brock and Hommes[6, 7] this paper incorporates risk and learning schemes into a simplediscounted present value asset price model with heterogeneous beliefs. Agentshave different risk aversion coefficients and adapt their beliefs (aboutfuture returns) over time by choosing from different predictors orexpectations functions, based upon their past performance as measured byrealized profits. By using both bifurcation theory and numerical analysis, itis found that the dynamics of asset pricing is affected by the relative riskattitudes of different types of investors. It is also found that the externalnoise and learning schemes can significantly affect the dynamics. Comparedwith the findings of Brock and Hommes [7] on the dynamics caused by change ofthe intensity of choice to switch predictors, it is found that many of theirinsights are robust to the generalizations considered: however, the resultingdynamical behavior is considerably enriched and exhibits some significantdifferences. © 2002 Kluwer Academic Publishers.
Chiarella, C. & He, X.-.Z. 2001, 'Asset price and wealth dynamics under heterogeneous expectations', Quantitative Finance, vol. 1, no. 5, pp. 509-526.
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Chiarella, C. & He, X.-.Z. 2000, 'Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model with a Market Maker'.
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This paper attempts to study the dynamics of a simple discounted present value asset price model where agents have different risk attitudes and follow different expectation formulation schemes for both first and second moments of the price distribution. Instead of using a Walrasian auctioneer scenario as the market clearing mechanism, a market maker scenario is used. In particular, the paper concentrates on models of fundamentalists and trend traders who follow least squares learning processes. An analysis is made of the effects of lag lengths on the stability of the fundamental equilibrium. Some necessary and/or sufficient conditions on the stability of the fundamental equilibrium associated with the speed of the adjustment of the market maker, different risk attitudes and different risk attitudes and different values of lags (used in the learning process) are established. The results lead to the following observations: (I) Compared with the findings with the Walrasian market clearing scenario in Brock and Hommes [8] and Chiarella and He [14], different price dynamics are obtained when the speed of the adjustment of the market maker increases and, in particular, when the contrarians are involved in the model; (ii) In contrast to homogeneous beliefs, where the larger is the lag length the more stable is that in general (for both the Walrasian and the market maker equilibrium) different lag lengths can complicate the price dynamics; (iii) In the model of trend followers versus contrarians, the stability of the fundamental equilibrium is determined by risk-adjusted aggregated extrapolation rates. This indicates that although every individual forecasting rule may lead to divergence from the equilibrium, these may "cancel out" in the aggregate and the actual dynamics with learning may thus be locally stable. On the other hand, only a small group of traders with expectation functions involving significant divergence can in fact destabilize the whole system.
He, X. 2000, 'Stability And Delays In A Predator-prey System - Ii', Dynamics Of Continuous Discrete And Impulsive Systems, vol. 7, no. 2, pp. 177-187.
As a continuation of author's recent work (J. Math. Anal. Appl., 198 (1996), 355-370), a classical autonomous Lotka-Volterra predator-prey model with variable bounded delays is concerned. By means of Lyapunov functionals, we establish sufficient conditio
Li, J., Liu, Z. & He, X. 1999, 'Periodic solutions of some differential delay equations created by Hamiltonian systems', Bulletin of the Australian Mathematical Society, vol. 60, no. 03, pp. 377-377.
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Li, J. & He, X. 1999, 'Proof and generalization of Kaplan-Yorke's conjecture under the condition f ' (0) > 0 on periodic solution of differential delay equations', Science in China Series A: Mathematics, vol. 42, no. 9, pp. 957-964.
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He, X.-.Z. 1999, 'Degenerate Lyapunov functionals of a well-known prey–predator model with discrete delays', Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 129, no. 04, pp. 755-771.
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Li, J., He, X.-.Z. & Liu, Z. 1999, 'Hamiltonian symmetric groups and multiple periodic solutions of differential delay equations', Nonlinear Analysis: Theory, Methods & Applications, vol. 35, no. 4, pp. 457-474.
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He, X.-.Z. 1998, 'The Lyapunov Functionals for Delay Lotka--Volterra-Type Models', SIAM Journal on Applied Mathematics, vol. 58, no. 4, pp. 1222-1236.
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He, X.-.Z. 1998, 'Almost periodic solutions of a competition system with dominated infinite delays', Tohoku Mathematical Journal, vol. 50, no. 1, pp. 71-89.
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He, X.-.Z., Ruan, S. & Xia, H. 1998, 'Global Stability in Chemostat-Type Equations with Distributed Delays', SIAM Journal on Mathematical Analysis, vol. 29, no. 3, pp. 681-696.
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Li, J. & He, X.-.Z. 1998, 'Multiple periodic solutions of differential delay equations created by asymptotically linear Hamiltonian systems', Nonlinear Analysis: Theory, Methods & Applications, vol. 31, no. 1-2, pp. 45-54.
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He, X.-.Z. & Ruan, S. 1998, 'Global stability in chemostat-type plankton models with delayed nutrient recycling', Journal of Mathematical Biology, vol. 37, no. 3, pp. 253-271.
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Ruan, S. & He, X.-.Z. 1998, 'Global Stability in Chemostat-Type Competition Models with Nutrient Recycling', SIAM Journal on Applied Mathematics, vol. 58, no. 1, pp. 170-192.
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Chiarella, C. & He, X.Z. 1998, 'Learning about the Cobweb', Complexity International, vol. 6.
In this paper we consider how suppliers in a cobweb model may learn about their economic environment. Instead of assuming the one step backward-looking expectation scheme of the traditional linear cobweb model, we consider the subjective estimates of the statistical distribution of the market prices based on L-step backward time series of market clearing prices. With constant risk aversion, the cobweb model becomes nonlinear. Sufficient conditions on the local stability of the unique positive equilibrium of the nonlinear model are derived and, consequently, we show that the local stability region (of the parameters of the equation) is proportional to the lag length L When the equilibrium loses its local stability, we show that, for L=2, the model has strong 1:3 resonance bifurcation and a family of fixed points of order 3 becomes unstable on both sides of criticality. The numerical simulations suggest that the model has a simple global structure, it has no complicated dynamics as claimed recently by Boussard. However, complicated dynamics do appear when the model is modified with constant elasticity supply and demand.
He, X. & Gopalsamy, K. 1997, 'Persistence, Attractivity, And Delay In Facultative Mutualism', Journal Of Mathematical Analysis And Applications, vol. 215, no. 1, pp. 154-173.
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Relations between persistence and ultimate boundedness of the solutions of the Lotka-Volterra system dx(t)/dt = x(t)[r(1) - a(11)x(t - tau) + a(22)y(t - tau)] dy(t)/dt = y(t)[r(2) + a(21)x(t - tau) - a(22)y(t - tau)] modelling ''facultative mutualism'' w
Gopalsamy, K. & He, X. 1997, 'Oscillations And Convergence In An Almost Periodic Competition System', Acta Applicandae Mathematicae, vol. 46, no. 3, pp. 247-266.
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Sufficient conditions are derived for the existence of a globally attractive almost periodic solution of a competition system modelled by the nonautonomous Lotka-Volterra delay differential equations dN(1)(t)/dt = N-1(t)[r(1)(t) - a(11)(t)N-1(t-r(t)) - a
He, X. 1996, 'Stability And Delays In A Predator-prey System', Journal Of Mathematical Analysis And Applications, vol. 198, no. 2, pp. 355-370.
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Sufficient conditions for both local and global stability of the positive equilibrium in a predator-prey system with time delays are obtained by constructing suitable Lyapunov functionals. A remark on the mistake by K. N. Murty and M. A. S. Srinivas (J.
GOPALSAMY, K., HE, X.U.E.-.Z.H.O.N.G. & SUN, D.A.-.Q.I.N.G. 1995, 'On the oscillatory convergence of solutions of a neutral delay diffusion equation', International Journal of Systems Science, vol. 26, no. 3, pp. 563-576.
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He, X.Z., Zhang, B.G. & Gopalsamy, K. 1994, 'Single species dynamics in changing environments', Dynamics and Stability of Systems, vol. 9, no. 4, pp. 293-303.
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Gopalsamy, K. & Xue-Zhong, H. 1994, 'Delay-independent stability in bidirectional associative memory networks', IEEE Transactions on Neural Networks, vol. 5, no. 6, pp. 998-1002.
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He, X.Z. & Gopalsamy, K. 1994, 'Persistence, stability and level crossings in an integrodifferential system', Journal of Mathematical Biology, vol. 32, no. 5, pp. 395-426.
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Gopalsamy, K. & He, X.-.Z. 1994, 'Stability in asymmetric Hopfield nets with transmission delays', Physica D: Nonlinear Phenomena, vol. 76, no. 4, pp. 344-358.
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Gopalsamy, K., He, X.-.Z. & Sun, D.-.Q. 1993, 'Oscillations and Convergence in a Diffusive Delay Logistic Equation', Mathematische Nachrichten, vol. 164, no. 1, pp. 219-237.
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Gopalsamy, K., Wen, L., Chen, Y.-.S. & He, X.-.Z. 1993, 'Necessary and Sufficient Conditions for a Fourth Order Functional Differential Equation to be Oscillatory', Mathematische Nachrichten, vol. 164, no. 1, pp. 23-36.
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Gopalsamy, K., He, X. & Wen, L. 1991, 'Global Attractivity And Oscillations In A Periodic Logistic Integrodifferential Equation', Houston Journal Of Mathematics, vol. 17, no. 2, pp. 157-177.
Sufficient conditions are obtained for the existence of a globally attracting periodic solution of the logistic integrodifferential equation [GRAPHICS] We also derive sufficient conditions for all positive solutions of (*) to oscillate about the unique p
Gopalsamy, K., He, X.-.Z. & Wen, L. 1991, 'On a periodic neutral logistic equation', Glasgow Mathematical Journal, vol. 33, no. 03, pp. 281-281.
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Other

He, X.-.Z., Li, K. & Li, Y. 2015, 'Optimal Time Series Momentum'.
We develop a continuous-time asset price model to capture the time series momentum documented recently. The underlying stochastic delay differential system facilitates the analysis of effects of different time horizons used by momentum trading. By studying an optimal asset allocation problem, we find that the performance of time series momentum strategy can be significantly improved by combining with market fundamentals and timing opportunity with respect to market trend and volatility. Furthermore, the results also hold for different time horizons, the out-of-sample tests and with short-sale constraints. The outperformance of the optimal strategy is immune to market states, investor sentiment and market volatility.
Chu, L., He, X.-.Z., Li, K. & Tu, J. 2015, 'Market Sentiment and Paradigm Shifts'.
The equity premium forecasting literature provides ample evidence of predictability for both fundamental economic variables and non-fundamental variables, such as time-series momentum. In this paper, we study the role of investor setiment in equity premium predictability. Consistent with the theory of investor sentiment, we ?nd that although economic variables can have strong predicting power when investor sentiment is low, their predictability tends to become insigni?cant when investor sentiment is high and the fundamental link between economic variables and equity premium is weakened. In contrast, the predictability of non-fundamental variables can be strong in high sentiment periods while tends to vanish away when sentiment is low and behavioural actions boosting the predictability of non-fundamental variables are moderated. Moreover, about 80% (20%) times can be classi?ed as low (high) sentiment periods in our framework, which idicates that economic variables could be a more prevalent force than non-fundamental variables in terms of predicting equity premium
Chiarella, C., He, X.-.Z., Shi, L. & Wei, L. 2014, 'A Behavioural Model of Investor Sentiment in Limit Order Markets'.
This paper examines the effect of behavioral sentiment in a limit order market when agents are risk averse and arrive in the market with different time horizons. The order submission rules with respect to order type and size are determined by maximizing the expected utility of agents with heterogeneous beliefs on the fundamental price and investment horizon. We show that behavioral sentiment has a double-edge impact on market quality: it improves market liquidity by reducing bid-ask spread and market volatility but increasing trading volume; however, it reduces pricing ef?ciency by increasing the price deviation from the fundamental value. Consistent with empirical observations, the model is able to replicate a number of stylized facts and limit book phenomena, including insigni?cant autocorrelations in returns, but signi?cant and decaying autocorrelations in the absolute returns, the bid-ask spread and the trading volume, hump shaped order books, a concave relationship between trade imbalance and average mid-price returns, and event clustering in order submissions. More important, the behavioral sentiment plays a very important role in explaining the positive autocorrelation in trading volume and also event clustering.
He, X.-.Z. & Li, K. 2014, 'Time Series Momentum and Market Stability'.
We propose a continuous-time heterogeneous agent model consisting of fundamental, momentum, and contrarian traders to explain the significant time series momentum. We show that the market under-reacts in short-run and overreacts in long-run when momentum traders dominate the market, which provides profit opportunity for time series momentum strategies with short-time horizons and reversal with long-time horizons. We find momentum strategies with short horizons stabilise the market while the effect becomes opposite with longer horizons. The results provide an insight into the profitability of time series momentum documented in recent empirical studies.
Wei, L., Zhang, W., He, X.-.Z. & Zhang, Y. 2013, 'Learning and Information Dissemination in Limit Order Markets'.
What can traders learn and how does learning affect the market? When information is asymmetric, short-lived, and uninformed traders learn, we present an artificial limit order market model to examine the effect of learning, information value, and order aggressiveness on information dissemination efficiency, bid-ask spread, order submission, and order profit of traders. We find that learning helps the uninformed traders to acquire private information more effectively and hence improves market information dissemination. Also the informed traders in general consume liquidity while the uninformed traders mainly supply liquidity. More interestingly, due to the learning and short-lived information, the bid-ask spread and its volatility are positively related to the probability of informed trading. The results help us to understand the behavior of uninformed traders and provide substantial insight and intuition into the trading process.
Chiarella, C., He, X.-.Z. & Pellizzari, P. 2012, 'A DYNAMIC ANALYSIS OF THE MICROSTRUCTURE OF MOVING AVERAGE RULES IN A DOUBLE AUCTION MARKET'.
He, X.-.Z. & Shi, L. 2010, 'Differences in Opinion and Risk Premium'.
When people agree to disagree, this paper examines the impact of the disagreement among agents on market equilibrium and equity premium. Within the standard mean variance framework, we consider a market of two risky assets, a riskless asset and two (and then a continuum of) agents who have different preferences and heterogeneous beliefs in the means and variance/covariances of the asset returns. By constructing a consensus belief, we introduce a boundedly rational equilibrium (BRE) to characterize the market equilibrium and derive a CAPM under heterogeneous beliefs. When the differences in opinion are formed as mean-preserving spreads of a benchmark homogeneous belief, we analyz eexplicitly the impact on the market equilibrium and risk premium, showing that the risk tolerance, optimism/pessimism and confidence/doubt can jointly generate high risk premium and low risk-free rate.
He, X. & Zheng, M. 2010, 'Dynamics of moving average rules in a continuous-time financial market model', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 268 Abstract: Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used indiscrete-time HAMs. The time delay represents a memory length of a moving average rule indiscrete-time HAMs.Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents' behavior parameters and memory length are obtained. It is found that an increase in memory length not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize another wise unstable market price, leading to stability switching as the memory length increases. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized factso bserved in financial markets.
Chiarella, C., Dieci, R. & He, X.Z. 2009, 'Heterogeneity, Market Mechanisms, and Asset Price Dynamics', Handbook of Financial Markets: Dynamics and Evolution.
Although there might be agreement that the standard paradigm does not fully explain what is causing the evolution of speculative asset prices, there may be less agreement on where to start to build an improved paradigm. By and large, the view that has been adopted in the boundedly rational heterogeneous agent literature is to retain expected utility maximization as the goal of each agent but to allow the agents to have different risk preferences and different expectations, rather than the single homogeneous rational expectation, about future possible returns. The expectations differ since agents are assumed to have different information and beliefs. Thus the asset price modeling framework is based on the fact that trading is driven more by differences in expectations than by the random arrival of news events. Within this framework, a simple market of one risky asset and one risk-free asset, with agents having different expectations, is considered with two different types of utility functions and two different market-clearing mechanisms. The framework provides the basic elements and structure of the various models. The basic building blocks of this framework are portfolio optimization, agents' utility functions, the market-clearing mechanism, and expectations feedback. © 2009 Elsevier Inc. All rights reserved.
Chiarella, C., He, X. & Zheng, M. 2009, 'Heterogeneous Expectations and Exchange Rate Dynamics (243)', Quantitative Finance Research Paper Series.
This paper presents a continuous-time model of exchange rates relying not only on macroeconomic factors but also having a market microstructure component. The driving macroeconomic factor is the interest rate differential, while the market microstructure element is described by the expectations of boundedly rational portfolio managers who use a weighted average of the expectations of fundamentalists and chartists. Within this framework, the different roles of the macroeconomic factors and market microstructure elements on the determination of the exchange rate are examined explicitly. We show that this simple model generates very complicated market behaviour, including the existence of multiple steady state equilibria, the deviations of the market exchange rate from the fundamental, and market fluctuations. Numerical simulation of the corresponding stochastic version of the model shows that the model is able to generate typical time series and volatility clustering patterns observed in exchange rate markets.
He, X.Z., Li, K., Wei, J. & Zheng, M. 2009, 'Market stability switches in a continuous-time financial market with heterogeneous beliefs'.
By considering a financial market of fundamentalists and trend followers in which the price trend of trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examine the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. These interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, sufficient conditions on the stability and global existence of the periodic solution are obtained. © 2009 Elsevier B.V. All rights reserved.
He, X.-.Z. & Shi, L. 2009, 'Portfolio Analysis and Zero-Beta CAPM with Heterogeneous Beliefs'.
With the standard mean variance framework, by assuming heterogeneity and bounded rationality of investors, this paper examines their impact on the market equilibrium and implications to the portfolio analysis. By constructing a market consensus belief, we establish market equilibrium prices of risky assets and show that the standard Black's zero-beta CAPM under homogeneous beliefs holds under the heterogeneous belief. We demonstrate that the biased belief (from the market consensus belief) of investors makes their optimal portfolio not necessarily locate on the market mean-variance frontier. We show that the traditional geometric relation of the mean variance frontiers with and without the riskless asset under the homogeneous beliefs does not hold under the heterogeneous beliefs. The results shed light on the risk premium puzzle, Miller's hypothesis, the lower market performance when the access to the riskfree asset is impossible, and the empirical finding that managed funds under-perform comparing to the market indices on average.
Chiarella, C., Dieci, R. & He, X. 2009, 'A framework for CAPM with heterogenous beliefs', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 254 Abstract: We introduce heterogeneous beliefs in to the mean-variance framework of the standard CAPM, in contrast to the standard approach which assumes homogeneous beliefs. By assuming that agents form optimal portfolios based upon their heterogeneous beliefs about conditional means and covariances of the risky asset returns, we set up a framework for the CAPM that incorporates the heterogeneous beliefs when the market is in equilibrium. In this framework we first construct a consensus belief (with respect to the means and covariances of the risky asset returns) to represent the aggregate market belief when the market is in equilibrium. We then extend the analysis to a repeated one-period set-up and establish a framework for a dynamic CAPM using a market fraction model in which agents are grouped according to their beliefs. The exact relation between heterogeneous beliefs, the market equilibrium returns and the ex-ante beta-coeffcients is obtained. CAPM and Heterogeneous beliefs.
He, X.-.Z. & Shi, L. 2008, 'Heterogeneity, Bounded Rationality and Market Dysfunctionality'.
As the main building blocks of the modern finance theory, homogeneity and rational expectation have faced difficulty in explaining many market anomalies, stylized factors, and market inefficiency in empirical studies. As a result, heterogeneity and bounded rationality have been used as an alterative paradigm of asset price dynamics and this paradigm has been widely recognized recently in both academic and financial market practitioners. Within the framework of Chiarella, Dieci and He (2006a, 2006b) on mean-variance analysis under heterogeneous beliefs in terms of either the payoffs or returns of the risky assets, this paper examines the effect of the heterogeneity. We first demonstrate that, in market equilibrium, the standard one fund theorem under homogeneous belief does not held under heterogeneous belief in general, however, the optimal portfolios of investors are very close to the market efficient frontier. By imposing certain distribution assumption on the heterogeneous beliefs, we then use Monte Carlo simulations to show that certain heterogeneity among investors can improve the Sharpe and Treynor ratios of the portfolios and investors can benefit from the diversity in investors' beliefs. We also show that non-normality of market equilibrium return distributions is an outcome of the market aggregation of individual investors who make rational decisions based on their beliefs. Our results explain the empirical funding that that managed funds under-perform the market index on average and show that heterogeneity can improve the market efficiency.
Chiarella, C., Dieci, R. & He, X.-.Z. 2007, 'Heterogeneous expectations and speculative behavior in a dynamic multi-asset framework'.
Chiarella, C., He, X. & Zheng, M. 2007, 'The Stochastic Dynamics of Speculative Prices (208)', Quantitative Finance Research Paper Series.
Within the framework of the heterogeneous agent paradigm, we establish a stochastic model of speculative price dynamics involving of two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the invariant measures of a random dynamical system. By conducting a stochastic bifurcation analysis, we examine the market impact of speculative behaviour. We show that, when the chartists use lagged price trends to form their expectations, the market equilibrium price can be characterised by a unique and stable invariant measure when the activity of the speculators is below a certain critical value. If this threshold is surpassed, the market equilibrium can be characterised by more than two invariant measures, of which one is completely stable, another is completely unstable and the remaining ones may exhibit various types of stability. Also, the corresponding stationary measure displays a significant qualitative change near the threshold value. We show that the stochastic model displays behaviour consistent with that of the underlying deterministic model. However, when the time lag in the formation of the price trends used by the chartists approaches zero, such consistency breaks down. In addition, the change in the stationary distribution is consistent with a number of market anomalies and stylised facts observed in financial markets, including a bimodal logarithmic price distribution and fat tails.
Gao, J., Gong, G. & He, X.-.Z. 2007, 'Monetary Policy and Exchange Rate Regime: Proposal for a Small and Less Developed Economy'.
We investigate monetary policy under the assumption that a country's capital market is 'open' under the WTO framework while the exchange rate is fixed. Our purpose is to determine if it is possible in this case for the economy to maintain an effective monetary policy for stabilizing the domestic economy. For this, we suggest two institutional restrictions. Given the restrictions, we demonstrate within a macro-dynamic model that monetary policy can still be effective. The implication of such an institutional design for an exchange rate regime is also discussed with special reference to small and less development economies.
Chiarella, C. & He, X. 2006, 'Aggregation of heterogeneous beliefs and asset pricing theory: A mean-variance analysis', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Paper Number: 186
Corron, N., He, X. & Westerhoff, F.H. 2005, 'Butter mountains, milk lakes and optimal price limiters (QFRC paper #158)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp158.pdf
Dieci, R., Foroni, I., Gardini, L. & He, X. 2005, 'Market mood, adaptive beliefs and asset price dynamics (QFRC paper #162)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp162.pdf
He, X. & Li, Y. 2005, 'Long memory, heterogeneity and trend chasing (QFRC paper #148)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp148.pdf
He, X. & Li, Y. 2005, 'Heterogeneity, profitability and autocorrelations (QFRC paper #147)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp147.pdf
Chiarella, C., He, X. & Hommes, C. 2004, 'A dynamic analysis of moving average rules (QFRC paper #133)'.
He, X.-.Z. & Westerhoff, F.H. 2004, 'Commodity Markets, Price Limiters and Speculative Price Dynamics'.
We develop a behavioral commodity market model with consumers, producers and heterogeneous speculators to characterize the nature of commodity price fluctuations and to explore the efectiveness of price stabilization schemes. Within our model, nonlinear interactions between market participants can create either bull or bear markets, or irregular price fluctuations between bulland bear markets. Both the imposition of a bottoming price level (to support producers) or a topping price level (to protect consumers) can reduce market price volatility. However, simple policy rules, such as price limiters, may have unexpected consequences in a complex environment: a minimum price level decreases the average price while a maximum price limit increases the average price. In addition, price limiters influence the price dynamics in an intricate way and may cause volatility clustering.
Chiarella, C., He, X. & Hommes, C. 2004, 'A dynamic analysis of moving average rules (Centre for Nonlinear Dynamics in Economics & Finance, University of Amsterdam, paper #04-14)', 10th International conference on computing in economics and finance.
Chiarella, C., He, X. & Wang, D. 2004, 'Statistical Properties of a Heterogeneous Asset Price Model with Time-Varying Second Moment', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 142 Abstract: Stability and bifurcation analysis of deterministic systems has been widely used in modeling financial markets. However, the impact of such dynamic phenomena on various statistical properties of the corresponding stochastic model, including skewness and excess kurtosis, various autocorrelation (AC) patterns of under and over reactions, and volatility clustering characterised by the long-range dependence of ACs, is not clear and has been very little studied. This paper aims to study this issue. Through a simple behavioural asset pricing model with fundamentalists and chartists, we examine the statistical properties of the model and their connection to the dynamics of the underlying deterministic model. In particular, our analysis leads to some insights into the type of mechanism that may be generating some of the stylised facts, such as fat tails, skewness, high kurtosis and long memory, observed in high frequency financial data.
Chiarella, C., He, X. & Wang, D. 2004, 'A behavioural asset pricing model with a time-varying second moment', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 141 Abstract: We develop a simple behavioural asset pricing model with fundamentalists and chartists to study price behaviour in financial markets. Within our model, the market impact of the weighting process of the conditional mean and variance of the chartists and investors' reactions are analysed. Price dynamics of the deterministic model under/over-reactions are analyzed. It shows different price dynamics and routes to complicated price behaviour when the chartists act as either trend followers or contrarians. It is found that (in a separate paper Chiarella et al (2004)) this analysis can be used to establish some connections between the statistical properties of the nonlinear stochastic system (such as distribution density and autocorrelation patterns of returns, in particular the stylised facts, such as fat tails, skewness, high kurtosis and long memory, observed in high frequency financial data) and the stability and bifurcation of the underlying deterministic system are established.
Chiarella, C., He, X.-.Z. & Zhu, P. 2003, 'Fading Memory Learning in the Cobweb Model with Risk Averse Heterogeneous Producers'.
This paper studies the dynamics of the traditional cobweb model with risk averse heterogeneous producers who seek to learn the distribution of asset prices using a geometric decay processes (GDP) - the expected mean and variance are estimated as a geometric weighted average of past observations - with either finite or infinite fading memory. With constant absolute risk aversion, the dynamics of the model can be characterized with respect to the length of memory window and the memory decay rate of the learning GPD. The dynamics of such heterogeneous learning processes and capability of producers' learning are discussed. It is found that the learning memory decay rate of the GDP of heterogeneous producers plays a complicated role on the pricing dynamics of the nonlinear cobweb model. In general, an increase of the memory decay rate plays stabilizing role on the local stability of the steady state price when the memory is infinite, but this role becomes less clear when the memory is finite. It shows a double edged effect of the heterogeneity on the dynamics. It is shown that (quasi)periodic solutions and strange (or even chaotic) attractors can be created through Neimark-Hopf bifurcation when the memory is infinite and through flip bifucation as well when the memory is finite.
He, X.-.Z. 2003, 'Asset Pricing, Volatility and Market Behaviour: A Market Fraction Approach'.
Motivated by recent development in structural agent models on asset pricing, explanation power and calibration issue of those models, this paper presents a simple market fraction model of two types of traders - fundamentalists and trend followers - under a market maker scenario. It is found that asset prices, wealth dynamics and market behaviour are characterised by the dynamics of the underlying deterministic system. The model is able to explain various market behaviour, and generate some of the stylized facts. By introducing two measures on wealth dynamics, we are able to show the limitations of profitability and rationality of different trading strategies. Six significant autocorrelation coefficients (ACs) patterns are charaterized by different types of bifurcation of the underlying deterministic system. In particular, an oscillating and decaying AC pattern with positive ACs for even lags and negative for odd lags can only be generated when the market is dominated by the fundamentalists (that is when the parameters are near the flip bifurcation boundary), and a positive decaying AC pattern with long memory can only be generated when the market is dominated by the trend followers with high decay memory (that is when the parameters are near the Hopf bifurcation boundary). The results show a promising power of stability analysis and bifurcation theory in explaining and calibrating asset price and wealth dynamics, markt behaviour, and generating various econometric properties of financial data.
Chiarella, C. & He, X. 2002, 'An adaptive model on asset pricing and wealth dynamics with heterogeneous trading strategies', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 84 Abstract: This paper develops an adaptive model on asset pricing and wealth dynamic of a financial market with heterogeneous agents and examines the profitability of momentum and contrarian trading strategies. In order to characterize asset price, wealth dynamics and rational adaptiveness arising from the interaction of heterogeneous agents with CRRA utility, an adaptive discrete time equilibrium model in terms of return ad wealth proportions (among heterogeneous representative agents) is established. Taking trend followers and contrarians as the main hetergeneous agents in the model, the profitability of momentum and contrarian trading strategies is analyzed. Our results show the capability of the model to characterize some of the existing evidence on many of anomailies observed in financial markets, including the profitability of momentum trading strategies over short time intervals, rational adaptiveness of agents, overconfidence and underreaction, overreaction and herd behavior, excess volatility, and volatility clustering.
Chiarella, C. & He, X.-.Z. 2001, 'Asset Price and Wealth Dynamics Under Heterogeneous Expectations'.
In order to characterize asset price and wealth dynamics arising from the interaction of heterogeneous agents with CRRA utility, a discrete time stationary model in terms of return and wealth proportions (among different types of agents) is established. When fundamentalists and chartists are the main heterogeneous agents in the model, it is found that in the presence of heterogeneous agents the stationary model can have multiple steady-states. The steady-state is unstable when the chartists extrapolate strongly and (locally) stable when they extrapolate weakly. The convergence to steady-state follows an optimal selection principle - the return and wealth proportions tend to the steady-state which has relatively higher return. More importantly, heterogeneity can generate instability which, under the stochastic processes of the dividend yield and extrapolation rates, results in switching of the return among different states, such as steady-state, periodic and aperiodic cycles from time to time. To model that is finally developed displays the essential characteristics of the standard asset price dynamics model assumed in continuous time finance, in that the asset price is fluctuating around a geometrically growing trend. The model also displays the volatility clustering that is an essential feature of empirically observed assets returns.
Chiarella, C. & He, X. 2001, 'Dynamics of beliefs and learning under aL processes - The heterogeneous case', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 55 Abstract: This paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some recursive processes with bounded memory. Under the assumptions of heterogeneous expectations (or beliefs) and that the agents update their expectations by recursive L- and general aL-processes, the dynamics of the resulting expectations and learning schemes are analyzed. It is shown that the dynamics of the system, including stability, instability and bifurcation, are affected differently by the recursive processes. The cobweb model with a simple heterogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics. In particular, the double edged effect of heterogeneity on the dynamics of the model is demonstrated.
Chiarella, C. & He, X. 2001, 'Dynamics of beliefs and learning under aL processes - The homogeneous case', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 53 Abstract: This paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some learning process. Under the assumptions that agents have homogeneous expectations (or beliefs) and that they update their expectations by least-squares L- and general aL - processes, the dynamic of the resulting expectations and learning schemes are analyzed. It is shown how the dynamics of the system, including stability, instability and bifurcation, are affected by the learning processes. The cobweb model with a simple homogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics.
Chiarella, C. & He, X.-.Z. 2000, 'Stability of Competitive Equilibria with Heterogeneous Beliefs and Learning'.
The paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some learning processes. Situations of both homogeneous and heterogeneous beliefs are considered. In both cases agents update their expectations by general ah - and least-squares h-processes and the stability of the resulting dynamics in both cases is analysed. It is shown how the stability of the actual dynamics is affected by the heterogeneous expectations and different least-squares h-processes.
Chiarella, C. & He, X. 2000, 'Heterogeneous beliefs, risk and learning in a simple asset pricing model with a market maker', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 35