Synthetic Data for Portfolios: A Throw of the Dice Will Never Abolish Chance (2501.03993v1)

Abstract: Simulation methods have always been instrumental in finance, and data-driven methods with minimal model specification, commonly referred to as generative models, have attracted increasing attention, especially after the success of deep learning in a broad range of fields. However, the adoption of these models in financial applications has not kept pace with the growing interest, probably due to the unique complexities and challenges of financial markets. This paper aims to contribute to a deeper understanding of the limitations of generative models, particularly in portfolio and risk management. To this end, we begin by presenting theoretical results on the importance of initial sample size, and point out the potential pitfalls of generating far more data than originally available. We then highlight the inseparable nature of model development and the desired use case by touching on a paradox: generic generative models inherently care less about what is important for constructing portfolios (in particular the long-short ones). Based on these findings, we propose a pipeline for the generation of multivariate returns that meets conventional evaluation standards on a large universe of US equities while being compliant with stylized facts observed in asset returns and turning around the pitfalls we previously identified. Moreover, we insist on the need for more delicate evaluation methods, and suggest, through an example of mean-reversion strategies, a method designed to identify poor models for a given application based on regurgitative training, i.e. retraining the model using the data it has itself generated, which is commonly referred to in statistics as identifiability.

Synthetic Data for Portfolios: A Methodological Exploration

The paper entitled "Synthetic Data for Portfolios: A Throw of the Dice Will Never Abolish Chance" by Adil Rengim Cetingoz and Charles-Albert Lehalle examines the application of generative models for producing synthetic financial data. This exploration focuses on the challenges and strategies related to using generative models for portfolio and risk management purposes. Financial markets' unique complexities, such as non-stationary environments and high-dimensional data, are at the heart of this investigation.

Generative Models in Financial Applications

Generative models have seen success across various domains, notably in generating text and images. However, their application in finance, particularly in portfolio construction and risk management, trails behind. The paper attributes this to finance-specific challenges like the inherent noisy nature of asset prices, stylized facts about returns, and the limited availability of data due to market non-stationarity. These factors complicate the use of synthetic data for financial applications. The authors propose a nuanced pipeline to generate time-series data of multivariate returns, adhering to theoretical financial analysis principles.

Theoretical Insights and Methodological Contributions

A key contribution of this paper is its theoretical insights into the use of generative models for finance, addressing the relationship between initial sample size and the amount of generated data. The authors argue that generating synthetic data that far exceeds the original data available, without considering the initial sample size, can introduce bias in estimating statistics from synthetic data—an assertion supported by the data presented. This perspective is supported by U-statistics theory, demonstrating that excessive synthetic data generation may decrease estimate accuracy unless the initial model provides a realistic approximation of the underlying stochastic process.

Additionally, the paper highlights the inherent conflict between generative models and portfolio construction. The core of this mismatch lies in the focus of typical generative models on approximating high-variance components, whereas, in financial portfolio construction, especially for long-short strategies, such components play a less prominent role than mid-to-low variance components.

Proposed Generative Pipeline

The authors propose a sophisticated generative pipeline tailored for financial data generation that aims to overcome these challenges. It involves decomposing asset returns into factor-based and residual components. For factors, generative adversarial networks (GANs) are employed, while residuals are modeled using a mixture of Student-t distributions to capture their heavy-tailed nature. This methodology explicitly acknowledges the distinct factors driving the processes and attempts to model these independently with a sensitivity to smaller variance factors critical for long-short portfolios.

Practical Evaluation and Implications

In the evaluative section, the paper provides evidence of the pipeline's application to US equities. This evaluation addresses the synthetic data's ability to replicate critical aspects of financial time-series, such as volatility clustering, leverage effects, and other stylized facts. The paper also suggests future refinements in evaluative methods, arguing for detailed consideration of the eventual application to refine the generative process further. A critical future direction proposed includes exploring the identifiability of models, assessing whether data re-generated by a trained model can be distinguished as synthetic, thereby potentially informing model design itself.

Conclusion

This paper constructs a compelling narrative on the cautious and informed application of generative models for financial data generation. By placing financial applications at the heart of generative modeling design, this paper potentially paves the way for developing more effective tools aligning with financial realities. As synthetic data applications in finance advance, such foundational work is crucial in ensuring effective model development cognizant of empirical market complexities. Future research might expand upon these methodologies, exploring novel architectures and evaluative metrics that further bridge the gap between generative models and practical financial applications.