Abstract: Overreaction, as an expression of investor bias in uncertain environments, significantly impacts the accuracy of investment decision-making and the cyclical fluctuations in market trends. When investors generally overreact to market information, it will increase market uncertainty, causing greater deviations in market prices from an unbiased state. In situations where investors commonly underreact to market information, market prices exhibit a lag in response to information, resulting in smoother price trends compared to an unbiased state. The market price discrepancies resulting from the characteristic of widespread investor reactions reduce the actual efficiency of rational decision-making. Simultaneously, the transaction costs associated with frequent entry and exit from investment markets, based on return expectations, are not only non-negligible in practice but also offset net investment returns. In summary, determining the measurement of the volatile market state and seeking a balance between investment returns and transaction costs are a pressing issue in this study.
This passage discusses the construction of an initial measurement model for investment market response characteristics in the context of irrationality. It iteratively estimates parameters and predicts trends, ultimately creating updated optimized decisions based on investor response characteristics. This approach addresses the shortcomings of traditional decision-making in expressing the relationship between investor responses and price mapping, while also resolving the issue of updating transaction costs in practice. In the study of dynamic trading decisions, the following methods are primarily employed to address the challenges of the ever-changing market response states and transaction cost constraints: (1)Using regression and run test methods to determine the directional features of market reactions and the strength of information, and based on this, accomplishing the measurement of market reaction states. (2)Employing Hidden Markov models to project market reaction states into observable states and predict the observed values at time t+1. (3)Utilizing the Expectation-Maximization (EM) algorithm to estimate the parameters of the Hidden Markov model. (4)Constructing a dual-objective multi-round optimization model to update the weights of the investment portfolio in each round of trading decisions, and achieving the optimal objective of investment while satisfying capital and trading cost constraints.
To demonstrate the effectiveness of the trading decision in practice, this paper employs a stock fund scheme to conduct a comparative analysis of the trading decision proposed in this paper and existing decision-making methods in terms of returns, risk, and investment efficiency. Built upon this analysis, a general validation is performed. The research results indicate: (1)Individual decisions formulated based on market reactions are more effective than price-oriented investment decisions. (2)Multi-round updating decisions that incorporate transaction costs are more valuable in practical applications. (3)The degree of abnormal reaction displayed by investors to price-oriented information reduces the efficiency of investment decisions. (4)When investors are in an irrational state, conservative holding is more likely to yield better results than overreacting.
　Further research can be extended to the impact of high-frequency trading and market overreactions on asset value stability, the analysis of differences in overreactions among investors from different countries, and the practical analysis of round-based investment decisions in the context of cross-regional influences. Shifting the research focus of trading decisions from individual returns enhancement to market environment optimization holds more profound significance for the exploration and development in this field.

Key words: overreaction; round-update; projection effect; hidden Markov

摘要： 以往研究着重于讨论投资市场过度反应的来源,本文在投资市场反应特征非理性的背景下,借鉴游程测试法的思路构建投资市场反应特征的初始测度模型,利用Expectation Maximization算法完成参数的迭代估计与趋势预测,并在此基础上根据投资者反应特征构建回合更新优化决策,弥补了传统决策在投资者反应与价格映射关系表达上的空白,同时解决了实践中交易成本的更新问题。结果表明:包含交易成本的多回合更新决策在实践中更具参考价值;当投资者反应特征非理性时,保守持有相比过度作为更可能获得好的收益结果。

关键词: 过度反应, 回合更新, 投射效应, 隐马尔科夫