管理工程学报2024，Vol.38Issue(3)：46-57,12.DOI:10.13587/j.cnki.jieem.2024.03.004
投资者异质性、分红与资产价格的复杂动态
Heterogeneity,dividends and complex dynamics in asset pricing
摘要
Abstract
A lot of empirical researches have shown that the dividend policy can affect investor trading behaviors and price volatility.Different types of Investors may response differently to the dividend policy.For instance,individual investors are insensitive to the dividend policy,while the institutional investors usually prefer to the stocks with stable dividend.Some studies have provided evidences that the unstable dividend may lead to great fluctuations of stock price.In this paper,we attempt to develop a theoretical model based on investor behaviors,and investigate the impacts of dividend policy on price dynamics. In real financial markets,investors are heterogeneous and have asymmetric information.They make trading decisions based on the information they observe and take different trading strategies.Some investors may buy the stock and care about the dividend.Some others may trade based on the fundamentals of the stock.They estimate the fundamental value and buy the stock when the price is below the fundamental value.In this paper,investors are assumed to be boundedly rational,and their behaviors are modeled with the heterogenous agent model. In the model,we consider two types of trading strategies,i.e.,the fundamental strategy and the technical strategy.These strategies reflect the heterogeneous expectations of investors.Investors choose between the two strategies according to their performance.The better performance one strategy has,the higher probability the strategy is chosen.The strategy switching mechanism is expressed by the logit response function.It can also depict the dynamics of investor fractions in the market.The price is generated through the trading behaviors of investors.We model the price adjustment process based on the aggregate excess demand.When the aggregate excess demand is positive,the price increases,and vice versa.In Section 1,we establish the model and derive a nonlinear dynamical system,which can characterize the evolutionary dynamics of stock price and investor structure.As it shows,the dynamical system involves a variety of parameters such as investor risk appetites,the level of bounded rationality,market liquidity,trading costs,dividend,fundamental value,and risk-free rate.Using the analysis of dynamical system,we study the impacts of these factors on asset pricing and volatility. In Section 2,we investigate the equilibrium of the dynamical system with mathematical analysis.In the case with rational and homogeneous investors,the equilibrium price equals to the intrinsic value which is determined by dividends.Furthermore,we solve the equilibrium in the case with bounded rational and heterogeneous investors.The equilibrium price is a weighted average of the estimated fundamental value and the intrinsic value.When the estimated fundamental value is equal to the intrinsic value,the equilibrium price is the same as the rational equilibrium price.We study the difference between the estimated fundamental value and the intrinsic value,and analyze its impacts on asset pricing and investor structure.The fraction of fundamentalists in the market is positively correlated with the absolute difference between the estimated fundamental value and the intrinsic value.Moreover,by using the Schur-Cohn criterion,we solve the stability conditions for the equilibrium.The stability conditions are determined by the parameters such as market liquidity,risk appetites and the deviation of the fundamental value from the intrinsic value.To guarantee the stability conditions,the difference between the estimated fundamental value and the intrinsic value should be neither too great nor too small. In Section 3,the simulation analysis is implemented.Under different parameter settings,we investigate the stability region,the bifurcation diagram and the phase portrait.When the stability conditions are not satisfied,the periodic and chaotic dynamics can be observed. The results of this study can explain the empirical findings of previous literatures.If the dividend policy is unstable,the volatility of dividend is great.Then,according to our study,investors would have less demand for stocks,and fundamentalists would take a small proportion in the market.This reflects institutional investors'preference for dividend policy.In addition,if the dividend policy is unstable,the estimated fundamental value might deviate greatly from the intrinsic value,and the stability conditions cannot be satisfied.As a result,the price might fluctuate greatly.Then,the market might collapse. The findings provide some significant implications for understanding the complex phenomena in financial markets,making dividends policy and implementing market regulations.When companies formulate dividend policies,they should consider investors'fundamental valuations of stocks,and should not make dividends too low or too high.In addition,market regulators can take measures to promote the disclosure of information,guide investors to have a reasonable valuation of stocks,so as to reduce market instability.关键词
异质信念/分红/动力系统/稳定性/混沌Key words
Heterogenous beliefs/Dividends/Dynamical system/Stability/Chaos分类
管理科学引用本文复制引用
宫庆彬,刁训娣..投资者异质性、分红与资产价格的复杂动态[J].管理工程学报,2024,38(3):46-57,12.基金项目
国家自然科学基金项目(71771147、71790592) （71771147、71790592）
中国博士后科学基金项目(2021M702154) The Natural Science Foundation of China(71771147,71790592) （2021M702154）
The Postdoctoral Science Foundation of China(2021M702154) （2021M702154）
