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# 金融代写|利率理论代写Portfolio Theory代考|MBA7293 MISSPECIF IED MODELS

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## 金融代写|利率理论代写Portfolio Theory代考|MISSPECIF IED MODELS

A widely held belief is that asset pricing models are likely to be misspecified and should be viewed only as approximations of the true data-generating process. Nevertheless, empirically evaluating the degree of misspecification and the relative pricing performance of candidate models through the use of actual data is useful.

There are two main problems with the econometric analyses performed in the existing asset pricing studies. First, even when a model is strongly rejected by the data (using one of the model specification tests previously described, for example), researchers still construct standard errors of parameter estimates using the theory developed for correctly specified models. This process could give rise to highly misleading inferences, especially when the degree of misspecification is large. Kan and Robotti (2009) and Gospodinov et al. (2011a) focus on the HJ-distance metric and derive misspecification-robust standard errors of the SDF parameter estimates for linear and nonlinear models. In contrast, Kan et al. (2012) focus on the beta representation of an asset pricing model and propose misspecification-robust standard errors of the second-pass risk premia estimates. For example, for linear SDF specifications, the misspecification adjustment term, which is associated with the misspecification uncertainty surrounding the model, can be decomposed into three components: (1) a pure misspecification component, which captures the degree of misspecification; (2) a spanning component that measures the degree to which the factors are mimicked by returns; and (3) a component that measures the usefulness of the factors in explaining the variation in returns. The adjustment term is zero if the model is correctly specified (component (1) is zero) and/or the factors are fully mimicked by the returns (component (2) is zero). If the factors are weakly correlated with the returns, the adjustment term could be very large. This issue will be revisited in the discussion of the case involving useless factors in the next section.

## 金融代写|利率理论代写Portfolio Theory代考|USELESS FACTORS

Consistent estimation and valid inference in asset pricing models crucially depends on the identification condition in which the covariance matrix of asset returns and risk factors is of full rank. Kan and Zhang (1999a, 1999b) study the consequences of the violation of this identification condition. In particular, they show that when the model is misspecified and one of the included factors is useless (i.e., independent of asset returns), the asymptotic properties of parameter and specification tests in GMM and two-pass cross-sectional regressions are severely affected.

The first serious implication of the presence of a useless factor is that the asymptotic distribution of the Wald test of statistical significance (a squared $t$-test) of the useless factor’s parameter (in the HJ-distance case) is chi-squared distributed with $N-K-1$ degrees of freedom instead of one degree of freedom, as in the standard case when all factors are useful. The immediate consequence of this result is that the Wald test that uses critical values from a chi-squared distribution with one degree of freedom will reject the null hypothesis too frequently when the null hypothesis is true. The false rejections are shown to become more severe as the number of test assets $N$ becomes larger and as the length of the sample increases. As a result, researchers may erroneously conclude that the useless factor is priced when, in reality, it is pure noise, uncorrelated with the stock market.

Another important implication of the presence of a useless factor is that the true risk premium associated with the useless factor is not identifiable and the estimate of this risk premium diverges at rate $\sqrt{T}$. In this case, the standard errors of the risk-premium estimates associated with the useful factors included in the model are also affected by the presence of a useless factor and the standard inference is distorted. Similar results also arise for optimal GMM estimation (Kan and Zhang 1999a) and two-pass cross-sectional regressions (Kan and Zhang 1999b).

The useless factor problem is particularly serious because the traditional model-specification tests previously described cannot reliably detect misspecification in the presence of a useless factor. This manifests itself in the failure of the specification tests to reject the null hypothesis of correct specification when the model is indeed misspecified and contains a useless factor.

# 利率理论代写

## 金融代写|利率理论代写PORTFOLIO THEORY代考|MISSPECIF IED MODELS

usingoneofthemodelspecificationtestspreviouslydescribed, forexample，研究人员仍然使用为正确指定的模型开发的理论来构建参数估计的标准误差。 如，对于线性 SDF 规范，与模型周围的错误指定不确定性相关的错误指定调整项可以分解为三个分量：1一个纯粹的错误指定组件，它捕获错误指定的程度； 2 衡量 些因膆完全被回报所模仿component (2为零) 。如果这些因表与收益的相关性较弱，则调整期限可能非常大。这个问题将在下一节涉及无用因表的安例讨论中重 新讨论。

## 金融代写|利率理论代写PORTFOLIO THEORY代考|USELESS FACTORS

KanandZhang 19996 .

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。