Feature selection based index tracking: A two-stage approach for optimized sampling

Equity indices form the basis for index-oriented financial products like exchange-traded funds (ETFs). The providers of these financial products face the challenge of efficient replication. Optimized sampling is the most attractive approach for replicating an equity index. It is characterized by its cost-effectiveness, flexibility, and transparency. We propose a two-stage procedure for optimized sampling. It combines feature selection methods from machine learning to select the index constituents used for replication in the first stage and tracking error optimization to determine the weights of the tracking portfolio components in the second stage. Our approach allows explicit control over the number of tracking portfolio components, representing a significant advantage over existing machine learning-based approaches. Additionally, the optimization procedure considers important financial constraints as well as practical and statistical challenges ignored in the repeatedly suggested autoencoder approach. Based on a dataset including two major indices, S&P 500 and CSI 300, we show that our approach outperforms a state-of-the-art mixed-integer programming (MIP) solver regarding computing time for all feature selection-based approaches used in the first stage. Moreover, the autoencoder approach yields significantly higher tracking errors, higher portfolio turnover, and lower portfolio diversity and thus cannot be recommended for index tracking. Our findings have significant implications for researchers and ETF sponsors seeking to develop efficient and practical solutions for tracking portfolio construction.