追踪市场指数的投资组合策略——以上证50指数为例

A Portfolio Strategy for Tracks Market Indices—Taking the SSE 50 Index as an Example

摘要: 指数追踪是一种用少量的成分股来追踪某一市场指数走势的方法，它是消极投资组合管理策略中的一种。本文通过逐步回归、岭回归、两步回归和分位数回归等构建指数追踪模型，并通过Cp准则、CV准则得到了两个样本股空间，在这两个样本股空间上对模型进行实证分析。本文选取了2021年8月1日到2022年7月1日的上证50指数的日线收盘价数据，划分2/3训练集和1/3测试集，最后通过残差平方和、平均残差平方和、残差标准差等评价指标进行对比分析。本文得到的主要结论如下：1) 在Cp准则下，LASSO保留了49个变量(成分股)，且在测试集上的残差平方和、平均残差平方和和残差标准差三种指标都优于逐步回归和岭回归；在LASSO变量选择方法下，进一步运用刘估计进行回归，得到较好的外预测效果。2) 在CV准则下，LASSO只保留了36个变量，外预测效果明显都次于Cp准则；在CV准则下，LASSO测试集上的残差平方和、平均残差平方和和残差标准差三种指标都优于逐步回归和岭回归；两步估计中，岭估计外预测效果也是较好的。3) 在CV准则下，LASSO测试集上的残差平方和、平均残差平方和和残差标准差三种指标都优于逐步回归和岭回归；两步估计中，0.5分位数回归外预测效果也是最好的，0.05分位数回归的效果最差。4) 在不同的选股法下数值的改变对模型的影响不同。

Abstract: Index tracking is a method of tracking the movement of a market index with a small number of constituent stocks. It is one of the passive portfolio management strategies. In this paper, the index tracking model is constructed by stepwise regression, ridge regression, two-step regression and quantile regression, and two sample stock Spaces are obtained by Cp criteria and CV criteria, and empirical analysis is conducted on these two sample stock Spaces. This paper selects the daily closing price data of the Shanghai Stock Exchange 50 Index from August 1, 2021 to July 1, 2022, divides the 2/3 training set and 1/3 test set, finally, the evaluation indexes such as sum of squares of residuals, average sum of squares of residuals and standard deviation of residuals are compared and analyzed. The main conclusions of this paper are as follows: 1) under the Cp criteria, 49 variables (component stocks) are retained in LASSO, and the three indexes of residual sum of squares, mean residual sum of squares and residual standard deviation on the test set are better than stepwise regression and ridge regression; under the LASSO variable selection method, Liu estimation is further used for regression, and better external prediction results are obtained. 2) Under the CV criterion, LASSO retains only 36 variables, and the external prediction effect is obviously inferior to the Cp criterion; under the CV criterion, the sum of squares of residuals, sum of squares of mean residuals and standard deviation of residuals on LASSO test set are better than stepwise regression and ridge regression. In the two-step estimation, the prediction effect outside the ridge estimation is also better. 3) Under CV criteria, the three indexes of the sum of squares of residuals, the sum of squares of mean residuals and the standard deviation of residuals on LASSO test set are better than stepwise regression and ridge regression; in the two-step estimation, the effect of 0.5 quantile regression is the best, and the effect of 0.05 quantile regression is the worst. 4) The change of values under different stock selection methods has different impacts on the model.