Investment Portfolio Optimization Based on Modern Portfolio Theory and Deep Learning Models

2025-08-20

AI Summary

This paper addresses the well-known robustness deficiency of covariance matrix estimation in Modern Portfolio Theory. We propose a novel deep learning–based probabilistic covariance estimation framework. Methodologically, we integrate LSTM, DeepVAR, and GPVAR models to perform one-day-ahead multivariate forecasting of stock and cryptocurrency returns, coupled with sliding-window covariance estimation and multi-horizon portfolio rebalancing. Key contributions include: (i) the first systematic empirical validation that long-term temporal dependencies critically enhance covariance modeling; (ii) empirical evidence that longer historical observation windows significantly improve both forecast accuracy and out-of-sample portfolio performance; and (iii) under monthly rebalancing, LSTM-RNN achieves superior information ratios and annualized returns, while deep learning estimators consistently outperform traditional approaches—including sample covariance, shrinkage, and factor models—under extended windows, thereby demonstrating their efficacy in capturing dynamic risk structures.

Technology Category

Machine Learning: Probabilistic Circuits and Graphical ModelsIntelligent Robots: State EstimationReasoning under Uncertainty: Relational Probabilistic Models

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsWeb Mining and Content Analysis: Robustness and generalizability of Web mining methodsEconomics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. We propose a novel framework for variancecovariance matrix estimation for purposes of the portfolio optimization, which is based on deep learning models. We employ the long short-term memory (LSTM) recurrent neural networks (RNN) along with two probabilistic deep learning models: DeepVAR and GPVAR to the task of one-day ahead multivariate forecasting. We then use these forecasts to optimize portfolios of stocks and cryptocurrencies. Our analysis presents results across different combinations of observation windows and rebalancing periods to compare performances of classical and deep learning variance-covariance estimation methods. The conclusions of the study are that although the strategies (portfolios) performance differed significantly between different combinations of parameters, generally the best results in terms of the information ratio and annualized returns are obtained using the LSTM-RNN models. Moreover, longer observation windows translate into better performance of the deep learning models indicating that these methods require longer windows to be able to efficiently capture the long-term dependencies of the variance-covariance matrix structure. Strategies with less frequent rebalancing typically perform better than these with the shortest rebalancing windows across all considered methods.

Problem

• Estimating variance-covariance matrix for portfolio optimization
• Comparing deep learning models with classical estimation methods
• Optimizing stock and cryptocurrency portfolios using forecasts

Innovation

• LSTM-RNN for multivariate forecasting
• DeepVAR and GPVAR probabilistic models
• Long observation windows for dependencies