Learning to Manage Investment Portfolios beyond Simple Utility Functions

ArXiv ID: 2510.26165 “View on arXiv”

Authors: Maarten P. Scholl, Mahmoud Mahfouz, Anisoara Calinescu, J. Doyne Farmer

Abstract

While investment funds publicly disclose their objectives in broad terms, their managers optimize for complex combinations of competing goals that go beyond simple risk-return trade-offs. Traditional approaches attempt to model this through multi-objective utility functions, but face fundamental challenges in specification and parameterization. We propose a generative framework that learns latent representations of fund manager strategies without requiring explicit utility specification. Our approach directly models the conditional probability of a fund’s portfolio weights, given stock characteristics, historical returns, previous weights, and a latent variable representing the fund’s strategy. Unlike methods based on reinforcement learning or imitation learning, which require specified rewards or labeled expert objectives, our GAN-based architecture learns directly from the joint distribution of observed holdings and market data. We validate our framework on a dataset of 1436 U.S. equity mutual funds. The learned representations successfully capture known investment styles, such as “growth” and “value,” while also revealing implicit manager objectives. For instance, we find that while many funds exhibit characteristics of Markowitz-like optimization, they do so with heterogeneous realizations for turnover, concentration, and latent factors. To analyze and interpret the end-to-end model, we develop a series of tests that explain the model, and we show that the benchmark’s expert labeling are contained in our model’s encoding in a linear interpretable way. Our framework provides a data-driven approach for characterizing investment strategies for applications in market simulation, strategy attribution, and regulatory oversight.

Keywords: generative adversarial network, portfolio weights, latent strategy representation, mutual funds, Bayesian inference, Mutual Funds (Equities)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced generative modeling techniques (GANs) and explicit conditional probability formulations, indicating high mathematical complexity, while it is validated on a large, real-world dataset (1,436 U.S. mutual funds) and compared to baselines, demonstrating substantial empirical rigor.

  flowchart TD
    A["Research Goal"] --> B["Methodology: GAN Framework"]
    C["Data: 1436 U.S. Equity Funds"] --> B
    B --> D["Computational Process"]
    D --> E["Key Findings/Outcomes"]
    
    A["Research Goal<br>Learn fund strategies beyond<br>simple utility functions"]
    
    B["Methodology<br>Generative Adversarial Network<br>Model conditional prob of weights"]
    
    C["Data & Inputs<br>- Portfolio weights<br>- Stock characteristics<br>- Historical returns<br>- Previous weights"]
    
    D["Computational Process<br>1. Latent strategy encoding<br>2. Joint distribution modeling<br>3. No explicit utility spec"]
    
    E["Key Findings/Outcomes<br>- Captures 'growth' & 'value' styles<br>- Reveals implicit manager objectives<br>- Heterogeneous optimization patterns<br>- Linear interpretable encoding of benchmarks"]