Generative Machine Learning for Multivariate Equity Returns

Paper: arXiv 2311.14735

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10 (capped from 7.0: transaction costs only partially modelled; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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).

Research Flowchart

  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

Cited References (418)

1. UK List of \TeX Frequently Asked Questions (2019)
2. The \textsf amsart , \textsf amsproc , and \textsf amsbook document~classes (2004)
3. a lgorithm2e.sty—package for algorithms (2015)
4. The algorithms bundle (2009)
5. The Listings Package (2015)
6. Publication quality tables in \LaTeX (2005)
7. ACM Visual Identity Standards (2007)
8. The subcaption package (2013)

0 of 418 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.