Asset price and wealth dynamics in a financial market with heterogeneous agents

This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics are determined by the interaction of two groups of agents, fundamentalists and chartists. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the price change over the next period: the chartists are trend extrapolators, while the fundamentalists expect that the price will return to the fundamental. We assume that investors’ optimal demand for the risky asset depends on wealth, as a result of CRRA utility. A market maker is assumed to adjust the market price at the end of each trading period, based on excess demand and on changes of the underlying reference price. The model results in a nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the long-run market dynamics are highly dependent on the parameters which characterize agents’ behaviour as well as on the initial condition. Moreover, for wide ranges of the parameters a (locally) stable fundamental steady state coexists with a stable ‘non-fundamental’ steady state, or with a stable closed orbit, where only chartists survive in the long run: such cases require the numerical and graphical investigation of the basins of attraction. Other dynamic scenarios include periodic orbits and more complex attractors, where in general both types of agents survive in the long run, with time-varying wealth fractions.     

Fundamentalists vs. chartists: Learning and predictor choice dynamics

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

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

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

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

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

     

Heterogeneous expectations in the gold market: Specification and estimation

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

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

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

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

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

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

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

Testing the efficiency of the Norwegian housing market

The question of whether or not the housing market is efficient is posed by an increasing number of economists, policymakers, homebuyers, and homesellers. This article tests the efficiency hypothesis on data from the housing market in Oslo over the period 1991–2002, employing the Case–Shiller time-structure test on a repeat-sales house price index and returns to housing. We demonstrate that both the repeat-sales house price index and returns contain time structure and that the housing market is characterized by inefficiencies. We also find, surprisingly, that the housing market consistently yields higher appreciation at lower volatility than the stock market over the period.     

关于提高住宅有效购买力的几点思考

随着我国住房制度改革的推进 ,房地产业面临着前所未有的发展机遇。然而 ,几年过去了 ,我们却不得不面对住宅潜在需求和有效需求不足的尖锐矛盾。产生这一现象的原因是多方面的 ,笔者认为最主要的原因在于商品住宅价格偏高、住房金融市场发展缓慢以及住房交易市场不健全三个方面。因此 ,要使住宅产业真正成为消费热点和新的经济增长点 ,就必须努力降低现有商品住宅价格、加快住房金融市场的发展以及完善住房交易市场     

Predicting housing prices in China based on modified Holt's exponential smoothing incorporating whale optimization algorithm

The forecast of the real estate market is an important part of studying the Chinese economic market. Most existing methods have strict requirements on input variables and are complex in parameter estimation. To obtain better prediction results, a modified Holt's exponential smoothing (MHES) method was proposed to predict the housing price by using historical data. Unlike the traditional exponential smoothing models, MHES sets different weights on historical data and the smoothing parameters depend on the sample size. Meanwhile, the proposed MHES incorporates the whale optimization algorithm (WOA) to obtain the optimal parameters. Housing price data from Kunming, Changchun, Xuzhou and Handan were used to test the performance of the model. The housing prices results of four cities indicate that the proposed method has a smaller prediction error and shorter computation time than that of other traditional models. Therefore, WOA-MHES can be applied efficiently to housing price forecasting and can be a reliable tool for market investors and policy makers.     

House Prices, Housing Investment and Demography Forecasts from the LBS/Abbey National Model of the UK Housing Market

A new housing sector has been incorporated into the London Business School model. This article outlines the new housing model, summarizes the research which has gone into its construction, and presents a forecast of the UK housing market. Using the new housing model, we forecast a moderate recovery in the housing market in the later part of 1991 and 1992. This recovery is however short-lived and does not result in such high rates of house price increase as previous house price booms (Chart 1).
Cuts in interest rates following entry to the exchange rate mechanism of the EMS prompt a recovery in house prices from the middle of 1991. House price inflation then peaks with an increase in average UK house prices in 1992 of 11 per cent over the previous year. Increases in real personal disposable income are modest, by the standards of the 1980s, and for this reason the recovery does not develop the momentum of previous house price booms. House price inflation moderates again in 1993 falling back to around 7 per cent. Housing starts and housing investment recover only slightly from their present depressed levels.
the recovery in house prices is weaker than that foreseen in our April Forecast Release. This is because real personal disposable income is now forecast to grow more slowly during 1991. Sterling's membership of the ERM is followed by a fall in interest rates, but it is the timing of interest rate cuts rather than their magnitude which differs from the earlier forecast. The changed profile of interest rates has altered the house price forecast only marginally.     

货币和税收政策对我国住房价格的影响——基于VAR模型的实证研究

基于我国1999-2010年房地产市场季度数据,本文建立向量自回归模型(VAR)和向量误差修正模型(VEC),将住房供给和需求同时纳入模型,分析我国利率政策、信贷政策和税收政策对住房价格的影响。结果显示,贷款利率在短期内对住房供给有负效应,但长期效应不明显;贷款规模对住房价格的短期冲击明显,二者之间存在正相关关系;针对保有环节征税可以通过影响住房供给,从而有效抑制住房价格上升。根据我国住房供求特点,应优先选择税收工具,通过促进住房供给实现控制房价的政策目标。     

A dynamic analysis of moving average rules

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

On the welfare cost of rare housing disasters

This paper examines the welfare cost of rare housing disasters characterized by large drops in house prices. I construct an OLG general equilibrium model with recursive preferences and housing disaster shocks. The likelihood and magnitude of housing disasters are inferred from historical housing market experiences in the OECD. The model shows that despite the rarity of housing disasters, Canadian households would willingly give up 6 percent of their non-housing consumption each year to eliminate the housing disaster risk. The welfare evaluation of this risk, however, varies considerably across age groups. The risk translates into a welfare loss of as much as 16 percent of annual non-housing consumption for the old, but a welfare gain of 2 percent for the young. This asymmetry stems from the fact that, compared to the old, younger households suffer less from house price declines in disaster periods, due to smaller holdings of housing assets, and benefit from lower house prices in normal periods, due to the negative price effect of disaster risk.     

基于信息不对称房价博弈模型的优化均衡研究

目前我国住宅市场存在严重的信息不对称,如何进行规制引起多方关注。首先利用房价博弈模型研究我国住宅市场信息不对称下的非理性均衡和精炼优化的序贯均衡,进而探求政府对市场房价经济优化规制后的理性序贯均衡,以此提出政府对住宅产业的规制方式和对策建议。     

Arbitrage,speculation and futures price fluctuations with boundedly rational and heterogeneous agents

This paper proposes a dynamic model for the futures market with three types of investors. The bounded rationality and heterogeneity of investors are taken into consideration. The equilibrium of the system and its stability conditions are derived with mathematical analysis. In the equilibrium, the futures price and the spot price converge to the equilibrium simultaneously. The equilibrium is determined by many factors, including the risk appetite and the rationality of investors, the trading costs, the arbitrage basis price and the fundamental price. When the stability conditions are violated, complex dynamics will emerge in the market. As shown by the simulations, the arbitrage is likely to destabilize the market. Moreover, when investors have the high degree of rationality, the equilibrium will become unstable and the futures market is inefficient. Statistical analysis indicates that the model can reproduce the stylized facts observed in the futures market, such as long memory, volatility clustering and fat tail of returns.

     

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

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

House prices and consumer welfare

We develop a new approach to measuring changes in consumer welfare due to changes in the price of owner-occupied housing. In our approach, an agent's welfare adjustment is defined as the transfer required to keep expected discounted utility constant given a change in current house prices. We demonstrate that, up to a first-order approximation, there is no aggregate change in welfare due to price increases in the existing housing stock. This follows from a simple market clearing condition where capital gains experienced by sellers are exactly offset by welfare losses to buyers. We show that this result holds (approximately) even in a model that accounts for changes in consumption and investment plans prompted by current house price changes. There can, however, be changes in welfare due to additions to the stock of housing, or to changes in the price of renovating and upgrading the existing stock of housing. For the United States, we estimate the welfare cost of house price appreciation to be an average of $127 per household per year over the 1984–1998 period.     

Heterogeneous expectations,boom-bust housing cycles,and supply conditions: A nonlinear economic dynamics approach

We combine a standard stock-flow housing market model, incorporating explicit relationships between house prices, the housing stock, and the rent level, with a parsimonious expectation formation scheme of housing market investors, reflecting an evolving mix of extrapolative and regressive expectation rules. The model results in a two-dimensional discrete-time nonlinear dynamical system. Based on realistic parameters, the model is able to generate endogenous boom-bust housing market dynamics with lasting periods of overvaluation and overbuilding. We thus exploit our model to investigate how real forces, in particular supply conditions, interact with expectations-driven housing market fluctuations.