关于长期持有风险资产收益率与风险的问题研究

发布时间：2018-05-05 12:32

本文选题：风险资产 + 卷积　；参考：《哈尔滨工业大学》2013年硕士论文

【摘要】：在进行风险投资时，风险资产收益率的分布情况对投资者的长期投资有较大的影响。若投资者计划长期投资一项风险资产，他应该知道长期投资的年平均收益率和相应的方差，而不是仅仅知道短期收益率的分布。本文重点研究了长期风险投资的平均收益率及风险的长期变化情况。首先选取了上证指数和深证综指作为样本，用正态分布拟合非参数估计方法估计出的核密度函数。之后本文运用概率论中的理论方法，依据卷积的性质和连续随机变量密度函数的定理推导出了长期持有期风险资产收益率的概率密度函数的公式。先从持有期为2年时的情形，再扩展到一般情况。在一般公式的基础上，对特殊分布如正态分布，对数正态分布等分布进行讨论，得出了一些理论结果。最后通过数值计算的方法，分别得出几种特殊分布情形下的一些结果，，并画出相应的收益率密度函数曲线和方差曲线，讨论了短期收益率特征参数的改变对长期持有风险资产收益率的影响。通过改变持有期限的长短，改变短期收益率的期望、方差、概率分布后对长期平均收益率和标准差进行进一步分析，以期对投资者的投资决策提供参考依据。为投资者提供可量化的操作指导，减小投资者的投资风险，增加投资收益。
[Abstract]:In venture capital, the distribution of return on venture assets has great influence on the long-term investment of investors. If an investor plans to invest in a risky asset in the long run, he should know the annual average rate of return and the corresponding variance of the long-term investment, not just the distribution of short-term returns. This paper focuses on the study of the average return rate and the long-term change of risk in long-term venture capital. Firstly, Shanghai and Shenzhen Composite Index are selected as samples, and the kernel density function is estimated by fitting nonparametric estimation method with normal distribution. Based on the properties of convolution and the theorem of density function of continuous random variables, this paper deduces the formula of probability density function of the rate of return of risk assets in long-term holding period by using the theoretical method of probability theory. First from the holding period of 2 years, and then extended to the general situation. Based on the general formula, the special distributions such as normal distribution and logarithmic normal distribution are discussed, and some theoretical results are obtained. Finally, some results of several special distributions are obtained by numerical calculation, and the corresponding curves of yield density function and variance are drawn. This paper discusses the influence of the change of the characteristic parameters of short-term return on the rate of return of long-term risky assets. By changing the length of the holding period, the expectation, variance and probability distribution of the short-term return rate, the paper further analyzes the long-term average return rate and standard deviation, in order to provide a reference for investors to make investment decisions. Provide quantifiable operation guidance for investors, reduce investors' investment risk and increase investment returns.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51;F224

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