基于前景理论的收益率分布特征研究

发布时间：2018-08-26 06:59

【摘要】：金融资产的收益率一直是投资者最为关注的信息之一，它与投资者的切身利益息息相关。因此作为金融市场上的可观测变量之一的收益率分布成为了众多学者们的重点研究对象。充分了解收益率分布的特征和规律也有助于广大投资者合理的做出投资决策，在瞬息万变的股市中获得最佳收益。目前对收益率分布的研究工作主要是从以下两个方面展开的：一个方面是基于传统金融学理论的视角，使用现有的单个统计分布，或者多个统计分布的混合分布来对收益率的分布特征进行描述;另一个方面是从行为金融学角度入手，将投资者的某些心理因素作为解释收益率分布特征的成因。上述方法虽然可以对收益率分布的部分特征进行描绘，但并不能完整刻画出投资者所有非理性因素对收益率分布影响的全过程。本文在行为金融理论的视角下，以前景理论为理论基础，通过引入概率权重函数来描述投资者的投资行为对收益率分布的影响，构建了一个新的收益率分布模型，并在新模型的基础上，采用国际上具有代表性的10个股市综合指数数据，对股市收益率分布特征及其概率权重函数形式进行了实证研究。同时还尝试放宽收益率分布模型的假设条件，将前景理论中的价值函数概念引入到模型中来，，对新模型进行了合理扩展，并利用同样的样本数据对扩展模型也进行了实证研究，且对新模型及其扩展模型的实证结果做了对比分析。本文的主要结论有：新的收益率分布模型从投资者非理性行为的角度出发，能合理的刻画市场真实收益率的形成过程，通过对模型进行数值分析发现，新的模型能对真实收益率的“尖峰厚尾”特征做出合理的解释。新模型的理论分析和实证结果都表明，无论收益率为正还是为负，投资者都会高估小概率事件发生的概率，而低估中、高概率事件发生的概率，完整的概率权重函数是由两个相似的反S型曲线连接而成的。对新模型进行非线性最小二乘回归的结果表明，双参数概率权重函数都能够很好的刻画收益率的分布特征，且不同的概率权重函数在正、负收益条件下的参数估计值都是不相同的。通过对adjR2值进行比较发现，采用GE形式概率权重函数的收益率分布模型通常能够更好的刻画出市场上真实收益率的分布特征。本文对收益率分布扩展模型也进行了实证分析，结果发现扩展模型和新模型所得到的结论大致相同，这也从另一个角度证明了新构建的收益率分布模型的合理性和稳定性。
[Abstract]:The rate of return on financial assets is one of the most concerned information for investors, and it is closely related to the vital interests of investors. Therefore, as one of the observable variables in the financial market, the yield distribution has become the focus of many scholars. Fully understanding the characteristics and rules of yield distribution is also helpful for investors to make reasonable investment decisions and obtain the best return in the rapidly changing stock market. The current research work on the yield distribution is mainly from the following two aspects: one is based on the traditional financial theory perspective, using the existing single statistical distribution, Or the mixed distribution of multiple statistical distributions to describe the characteristics of the distribution of return; another aspect is from the perspective of behavioral finance some psychological factors of investors as the reasons for explaining the characteristics of the distribution of returns. Although the above methods can describe some characteristics of the yield distribution, it can not completely describe the whole process of the investors' influence of all irrational factors on the return distribution. In this paper, from the perspective of behavioral finance theory, based on prospect theory, a new model of return distribution is constructed by introducing probability weight function to describe the influence of investor's investment behavior on return distribution. On the basis of the new model, this paper makes an empirical study on the characteristics of the stock market return distribution and the form of the probability weight function by using the international representative 10 stock market composite index data. At the same time, we try to relax the assumptions of the return distribution model, introduce the concept of value function in the foreground theory into the model, and expand the new model reasonably, and use the same sample data to make an empirical study on the extended model. The empirical results of the new model and its extended model are compared and analyzed. The main conclusions of this paper are as follows: the new model of return distribution can reasonably depict the forming process of market real return rate from the angle of investors' irrational behavior. The new model can reasonably explain the "peak and thick tail" feature of real yield. The theoretical analysis and empirical results of the new model show that investors overestimate the probability of occurrence of small probability events regardless of whether the return rate is positive or negative, while underestimating the probability of occurrence of high probability events. The complete probabilistic weight function is connected by two similar inverse S-shaped curves. The results of nonlinear least square regression for the new model show that the probability weight functions with two parameters can well describe the distribution characteristics of the yield, and the different probability weight functions are positive. Under the condition of negative return, the parameter estimates are different. Through the comparison of the adjR2 value, it is found that the GE probability weight function model can better describe the distribution characteristics of the real return rate in the market. This paper also makes an empirical analysis of the extended model of return distribution, and finds that the extended model and the new model have the same conclusion, which also proves the rationality and stability of the new model from another angle.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9

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