# 基于因子分析的基金评价研究 Research on Fund Evaluation Based on the Factor Analysis

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Factor analysis is one of the classic multivariate statistical analysis methods, which can extract few unobservable factors from the large quantity of observable variables. These factors can reveal the complex structures of the original variables. For the problem of the evaluation of fund products that the ordinary investors faced, such method could obtain explicit factor indices as the reference of evaluation from the complicated financial data. This article first introduces the basic theory of factor analysis, and then presents the general steps to analyze the financial data of fund products. Finally, an empirical analysis was taken on the yearly data of stock funds of China, 2017, aiming at providing a reference of data-based evaluation of fund products.

1. 引言

2. 因子分析基本理论

${X}_{i}={a}_{i1}{F}_{1}+{a}_{i2}{F}_{2}+\cdots +{a}_{ij}{F}_{j}+\cdots +{a}_{im}{F}_{m}+{\epsilon }_{i},\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,2,\cdots ,p;\text{\hspace{0.17em}}j=1,2,\cdots ,m$ (1)

$A=\left[\begin{array}{cccc}{a}_{11}& {a}_{12}& \cdots & {a}_{1m}\\ {a}_{21}& {a}_{22}& \cdots & {a}_{2m}\\ ⋮& ⋮& & ⋮\\ {a}_{p1}& {a}_{p2}& \cdots & {a}_{pm}\end{array}\right]=\left({A}_{1},{A}_{2},\cdots ,{A}_{m}\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}m\le p$ (2)

${h}_{i}^{2}=\underset{j=1}{\overset{m}{\sum }}{a}_{ij}^{2},\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,2,\cdots ,p$ (3)

${g}_{j}^{2}=\underset{i=1}{\overset{p}{\sum }}{a}_{ij}^{2},\text{\hspace{0.17em}}\text{\hspace{0.17em}}j=1,2,\cdots ,m$ (4)

$\stackrel{^}{F}={A}^{\text{T}}{R}^{-1}X$ (5)

3. 基于因子分析的基金投资评价的一般步骤

${W}_{j}=\frac{{V}_{j}}{{V}_{1}+{V}_{2}+\cdots +{V}_{m}}$ (6)

${T}_{k}=\underset{j=1}{\overset{m}{\sum }}{W}_{j}\cdot {S}_{ij}$ (7)

4. 实证研究

Table 1. KMO and Bartlett’s test

Table 2. Total variance explained

Table 3. Rotated Factor Matrix

Table 4. Factor score coefficient matrix

$\begin{array}{c}{F}_{1}=0.199{X}_{1}-0.153{X}_{2}+0.001{X}_{3}-0.031{X}_{4}-0.126{X}_{5}-0.128{X}_{6}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+0.01{X}_{7}+0.13{X}_{8}-0.039{X}_{9}+0.077{X}_{10}+0.24{X}_{11}+0.149{X}_{12}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-0.072{X}_{13}+0.175{X}_{14}-0.035{X}_{15}+0.067{X}_{16}+0.169{X}_{17}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+0.131{X}_{18}-0.039{X}_{19}+0.046{X}_{20}\end{array}$ (8)

Table 5. Total score of fund products

5. 结论与展望

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