# 公募基金仓位测算方法研究Research on the Methods of Estimating the Position of Public Funds

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Fund position is the proportion of funds invested in the stock market to the assets that the fund can use. It’s a reflection of market information and represents investors’ expectations of the market. The position of the fund can be used as an indicator for investors to feel the future trend of the stock market. Public funds only disclose position information at the end of each quarter, which leads to an information asymmetry between investors and fund managers. In the paper, the daily return of public fund and CITIC industry index are taken as dependent and independent variables respectively. The coefficients of industry index are estimated by quadratic programming, stepwise regression and Lasso regression, and then the coefficients are summed up to obtain the position value of the fund. Errors of these three models are compared with the real fund positions published in the quarterly report. The results show that the errors of stepwise regression and Lasso regression are both smaller than that of quadratic programming. Therefore, the two methods are better than quadratic programming in solving such problems.

1. 引言

2. 数据及符号说明

2.1. 数据说明

2.2. 符号说明

Table 1. Symbolic explanation

3. 多元线性回归模型

${R}_{f,t}={\gamma }_{1}{R}_{1,t}+{\gamma }_{2}{R}_{2,t}+\cdots +{\gamma }_{N}{R}_{N,t}+\epsilon$

4. 二次规划

$\underset{\gamma }{\mathrm{min}}\frac{1}{2T}{\underset{t=1}{\overset{T}{\sum }}\left(\underset{t=1}{\overset{T}{\sum }}{\gamma }_{i}{R}_{i,t}-{R}_{f,t}\right)}^{2}$

${\gamma }_{d}\le \underset{i=1}{\overset{N}{\sum }}{\gamma }_{N}\le {\gamma }_{u}$

$0\le {\gamma }_{i}\le 1,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,2,\cdots ,N$

Figure 1. Error distribution of partial-equity hybrid funds

Figure 2. Error distribution of common stock funds

Figure 3. Relevance coefficient of industry index

5. 改进的模型

5.1. 逐步回归

Table 2. Estimation coefficient

5.2. Lasso回归

Lasso回归是引入L1正则化项的线性回归，是多元线性回归的有偏估计，适用于共线性数据，它可以通过将系数进行压缩直到零从而达到剔除部分自变量的目的。Lasso回归的结果对正则化系数λ取值敏感。实际使用过程中，需要通过交叉验证的方法选择合适的λ值。

$J\left(\gamma \right)=\frac{1}{2T}{{\sum }_{t=1}^{T}\left({\sum }_{i=1}^{N}{\gamma }_{i}{R}_{i,t}-{R}_{f,t}\right)}^{2}+\lambda {\sum }_{i=1}^{N}|{\gamma }_{i}|$

Figure 4. Position comparison of partial-equity hybrid funds

Figure 5. Position comparison of common stock funds

6. 模型结果对比

Table 3. Error comparison of average position

7. 结论

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