Machine Learning and Optimization for Finance: Index Replication

Goal:

Replicate the payouts (profits and losses (P&L)) of a certain stock market index (i.e., a portfolio of stocks) with only a limited number of liquid (i.e., highly traded) stocks. Index replication is an important tool for portfolio managers seeking returns of indices that are not directly investable for most people by mimicking the performance of such indices with investable stocks.

Task:

Develop a learner to create a portfolio based on a given set of stocks and their respective characteristics, with the goal of mimicking a predefined index as closely as possible. A major challenge is to define a meaningful objective function that serves as a measure of similarity to the index and to optimize a payoff that reflects the performance of the index. Evaluate different methods by comparing their computational efficiency and accuracy, taking into account computational resources and economic outcomes.

Data:

Stock market data will be provided.

Methods:

The replication task can be accomplished through various methods, each affecting the complexity of the optimization program differently. Depending on the chosen method or objective function, the optimization program can range from linear to quadratic to highly non-linear, thereby influencing the complexity of the solver method, which can range from straightforward to challenging. Feel free to employ any machine learning tool or solver of your preference.

Difficulty: Medium

Size

Large (350 hours)

Skills

• Required: Python, R, linear algebra, optimization
• Preferred: Experience with mathematical software and/or knowledge in computational finance is a plus

Expected impact

Index replication is an important tool for portfolio managers seeking returns of indices that are not directly investable for most people by mimicking the performance of such indices with investable stocks. That would be a great enhancement for GeomScale packages.

Mentors

• Bachelard Cyril <cyril.bachelard at quantarea.ch> He serves as the Head of Quant Engineering and is a founding partner at Quantarea, a quantitative Asset Manager in Switzerland. He has 12+ years of experience in quantitative portfolio management and systematic equity research. His areas of expertise include high-dimensional portfolio optimization, machine learning, and signal processing for dynamic asset allocation.

• Apostolos Chalkis <tolis.chal at gmail.com> is a Research Engineer at Quantagonia GmbH. He is an expert in statistical software, computational geometry, and optimization, and has previous GSoC student experience (2018 & 2019) and mentoring experience with GeomScale (from 2020 to 2023).

• Vissarion Fisikopoulos <vissarion.fisikopoulos at gmail.com> is an expert in mathematical software, computational geometry, and optimization, and has previous GSOC mentoring experience with Boost C++ libraries (2016-2017) and the R-project (2017).