FDR-Controlled Portfolio Optimization for Sparse Financial Index Tracking

TL;DR

This paper introduces an FDR-controlled sparse index tracking method that handles correlated variables by extending the T-Rex framework with a nearest neighbors penalty, demonstrated on S&P 500 data.

Contribution

It extends the T-Rex framework to control FDR in high-dimensional, correlated variable settings for index tracking, with theoretical guarantees and practical implementation.

Findings

Successfully tracks S&P 500 with few stocks over 20 years

Provably controls FDR at specified level

Provides open-source R package implementation

Abstract

In high-dimensional data analysis, such as financial index tracking or biomedical applications, it is crucial to select the few relevant variables while maintaining control over the false discovery rate (FDR). In these applications, strong dependencies often exist among the variables (e.g., stock returns), which can undermine the FDR control property of existing methods like the model-X knockoff method or the T-Rex selector. To address this issue, we have expanded the T-Rex framework to accommodate overlapping groups of highly correlated variables. This is achieved by integrating a nearest neighbors penalization mechanism into the framework, which provably controls the FDR at the user-defined target level. A real-world example of sparse index tracking demonstrates the proposed method's ability to accurately track the S&P 500 index over the past 20 years based on a small number of stocks. An open-source implementation is provided within the R package TRexSelector on CRAN.