中文摘要：

本文将目前流行的规则化方法加入到传统指数追踪模型中,得到若干种稀疏而且稳定的资产组合,用于复制指数的收益率,并构建样本内外预测、模型一致性、资产组合稀疏性和BIC准则进行模型效果评价。基于对上证综指、沪深300指数和中证500指数的实证发现：图结构约束可以提升模型的样本外预测能力、模型一致性和资产组合稀疏性;ITM-adaL_1在资产组合稀疏性上表现远好于其他模型;结合三种指数追踪,含有自适应L_1罚函数以及图结构约束的指数追踪模型总体表现优于其他模型。本文的研究方法和结果对指数型基金管理公司、个人和投资机构者有较为重要的实际意义。

英文摘要：

This paper obtains several sparse and stable portfolio models to replicate the index returns by combining several popular regularized methods with index tracking mod- el. Based on the Shanghai Composite Index, SHSE-SZSE300 and 500SER, we find that graph-structured penalty can improve model prediction ability, consistency between in-sam- ple and out-of-sample performance and sparsity of portfolio. ITM-adaL1 performs much bet- ter in sparsity of portfolio. Considering all the index tracking, index tracking models with a- daptive-L1 penalty and graph structure perform better generally. The methods and results in this paper are of great practical significance to personal and institutional investors.