Machine Learning and Optimization for Finance: Index Replication

Indexes are baskets of stocks with specific characteristic. They provide examples for diversification in investing to mitigate the volatility of portfolios. Therefore, many investors, including institutions such as fund managers, attempt to build their portfolios to track closely major indexes. However, the effort and the transaction cost for tracking the exact constituents of indexes is not negligible, especially for indexes of many stocks (S&P500). An approach to reduce the transaction cost in index tracking is the sparse replication strategy which tries to mimic the index return through a subset of its constituents. In this project, we implement this method through the point of view of mean-variance optimization, i.e., to minimize the tracking error as a quadratic utility function. We first replicate the study in (Shi, Shu, Tian 2020) "High-dimensional index tracking based on the adaptive elastic net". This means we will implement an algorithm for sparse index replication using optimization with adaptive elastic net regularization. By implementing a Python framework and exploring possible open-source optimizers, we aim to deliver to GeomScale community a new functionality of portfolio selection, which covers data parsing and preprocessing, backtesting with configurable parameters and automated fine-tuning of hyper-parameters. The next step is to test different ideas to improve this method and calibrate the hyper-parameters to fit the market condition.