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

In recent years, rapid advances in deep learning have drawn increasing attention to artificial‑intelligence applications in finance, especially in FinTech and quantitative investing. Index funds, which aim to replicate the performance of a financial index, have historically outperformed most active funds due to lower transaction costs and the efficient‑market hypothesis.

The presentation introduces the basic concepts of financial indices and the two main fund strategies: passive (index) funds that track a predefined basket of securities, and active funds that seek excess returns through security selection and timing. It then motivates the need for a sparse, low‑cost portfolio that can closely track an index while respecting practical constraints such as weight limits and no‑short‑selling.

To address this, the authors propose a two‑stage design: first, a graph‑neural‑network (GNN) selects a small subset of assets (binary variables z_i ) from a large candidate pool; second, a continuous optimization determines the allocation weights ( w_i ) for the chosen assets. The index‑tracking objective is expressed as minimizing the loss between the portfolio return r_{ind,t} and the weighted asset returns \sum_i w_i r_{i,t} , subject to constraints l \le w_i \le h and \sum_i w_i = 1 .

The mixed‑integer programming problem is transformed into a graph‑based representation, where nodes encode asset features and edges capture relationships among assets. The GNN propagates information to produce node embeddings, which are fed into a multilayer perceptron that predicts the binary selection variables. This converts the original combinatorial optimization into a binary classification task.

Training uses solutions generated by the CPLEX solver on small‑scale instances as labels, minimizing cross‑entropy loss. Because GNNs scale well, the trained model can be applied to much larger instances, achieving near‑optimal solutions in seconds, whereas traditional solvers become prohibitively slow.

Experimental results show that the GNN‑based method matches the tracking error of exact solvers while dramatically reducing computation time, and it extends naturally to multi‑period settings where transaction costs are considered. The authors also discuss the broader applicability of GNNs to other mixed‑integer or non‑convex optimization problems.

In summary, the proposed deep‑learning approach offers an efficient, scalable alternative to classic optimization techniques for constructing financial index funds, delivering comparable tracking performance with far lower computational overhead.