Generative Machine Learning for Multivariate Equity Returns

ArXiv ID: 2311.14735 “View on arXiv”

Authors: Unknown

Abstract

The use of machine learning to generate synthetic data has grown in popularity with the proliferation of text-to-image models and especially large language models. The core methodology these models use is to learn the distribution of the underlying data, similar to the classical methods common in finance of fitting statistical models to data. In this work, we explore the efficacy of using modern machine learning methods, specifically conditional importance weighted autoencoders (a variant of variational autoencoders) and conditional normalizing flows, for the task of modeling the returns of equities. The main problem we work to address is modeling the joint distribution of all the members of the S&P 500, or, in other words, learning a 500-dimensional joint distribution. We show that this generative model has a broad range of applications in finance, including generating realistic synthetic data, volatility and correlation estimation, risk analysis (e.g., value at risk, or VaR, of portfolios), and portfolio optimization.

Keywords: Generative Models, Equities, Risk Analysis, Value at Risk (VaR), Portfolio Optimization

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced deep learning architectures (conditional IWAEs, normalizing flows) with rigorous mathematical formulations, while also providing substantial empirical validation on real-world S&P 500 data and comparing against classical financial models (GARCH, factor models).

  flowchart TD
    A["Research Goal"] --> B["Data Preparation"]
    B --> C["Model Selection"]
    C --> D["Model Training"]
    D --> E["Generative Process"]
    E --> F["Key Outcomes"]

    A:::goal
    B:::data
    C:::method
    D:::process
    E:::process
    F:::outcome

    subgraph Goal
        A["Model 500-dimensional joint<br/>distribution of S&P 500 returns"]
    end

    subgraph Input
        B["Multivariate Equity Return Data<br/>(High Dimensionality)"]
    end

    subgraph Methodology
        C["Conditional Variational Autoencoder<br/>(CIWAE)"]
        D["Learn Conditional<br/>Distributions"]
        E["Generate Synthetic Data<br/>& Statistical Moments"]
    end

    subgraph Outcomes
        F["1. Realistic Synthetic Data<br/>2. Volatility & Correlation Estimation<br/>3. Risk Analysis (VaR)<br/>4. Portfolio Optimization"]
    end

    classDef goal fill:#e1f5fe,stroke:#01579b
    classDef data fill:#fff3e0,stroke:#ef6c00
    classDef method fill:#e8f5e8,stroke:#2e7d32
    classDef process fill:#f3e5f5,stroke:#7b1fa2
    classDef outcome fill:#fce4ec,stroke:#c2185b