Deep Learning-Based Design of Financial Index Funds Using Graph Neural Networks

In recent years, rapid development of deep learning has brought increasing attention to artificial intelligence applications in finance, especially in FinTech and quantitative finance. This talk presents a research-driven method for designing financial index funds based on deep learning.

The presentation first introduces basic concepts of financial indices and index funds, distinguishing passive (index‑tracking) and active strategies, and explains why passive funds often outperform active ones due to lower transaction costs and the efficient‑market hypothesis.

It then describes various types of stock indices—broad‑based versus narrow‑based, and weighting schemes such as price‑weighted, market‑cap‑weighted, and equal‑weighted—highlighting their role in constructing index‑tracking portfolios.

Designing an index fund is framed as a sparse portfolio selection problem: choose a small subset of assets (binary variables \(z_i\)) from a large candidate set and determine their allocation weights \(w\) under constraints (e.g., \(0 \leq w \leq 1\), \(\sum w = 1\)). This leads to a mixed‑integer programming (MIP) formulation that is computationally challenging for large‑scale problems.

To solve the MIP efficiently, a two‑stage approach is proposed. Stage 1 uses a graph neural network (GNN) to perform asset selection, converting the combinatorial problem into a binary classification task. Stage 2 solves the continuous weight allocation for the selected assets.

The GNN leverages the graph structure of financial assets, where nodes represent stocks and edges capture relationships (e.g., co‑movement). After message passing, each node obtains an embedding, which is fed into a multilayer perceptron to predict the binary selection variable.

Training data are generated by solving small instances of the MIP with the CPLEX solver, providing optimal binary labels. The network is trained with a cross‑entropy loss, allowing it to generalize to larger instances where traditional solvers become prohibitively slow.

Experimental results show that the GNN‑based method achieves tracking errors comparable to CPLEX while solving problems in seconds, even for thousands of assets. It also scales well to multi‑period settings, reducing transaction costs across rebalancing periods.

In summary, the proposed deep‑learning framework offers a fast, scalable, and accurate solution for constructing sparse index‑tracking portfolios, bridging the gap between advanced AI techniques and practical financial fund design.