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

Paper: arXiv 2508.14999

Authors: Maciej Wysocki, Paweł Sakowski

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced math including stochastic processes (LSTM, VAR, GPVAR) and rigorous portfolio optimization frameworks, and demonstrates strong empirical rigor through extensive backtesting on stocks and cryptocurrencies with various parameters, code sharing for reproducibility, and detailed performance metrics like information ratio.

Research Flowchart

  flowchart TD
  A["Research Goal<br/>Optimize Portfolio via<br/>Improved Covariance Estimation"] --> B["Data Inputs<br/>Multi-Asset (Stocks & Crypto)"]
  B --> C{"Model Comparison<br/>Observation Windows vs Rebalancing"}
  C --> D["Classical Methods<br/>e.g., Sample Covariance"]
  C --> E["Deep Learning Methods<br/>LSTM, DeepVAR, GPVAR"]
  D & E --> F["Portfolio Optimization<br/>Mean-Variance Framework"]
  F --> G["Performance Metrics<br/>Information Ratio &<br/>Annualized Returns"]
  G --> H["Key Findings<br/>LSTM Best Performance<br/>Longer Windows Preferred<br/>Less Frequent Rebalancing"]

Cited References (46)

1. Artificial intelligence in portfolio formation and forecast: Using different variance-covariance matrices (2021) — link
2. Take Bitcoin into your portfolio: a novel ensemble portfolio optimization framework for broad commodity assets (2021) — link
3. The Sharpe Ratio (2021) — link
4. PyPortfolioOpt: portfolio optimization in Python (2021) — link
5. Covariance matrix forecasting using support vector regression (2021) — link
6. Investigating the relationship between volatilities of cryptocurrencies and other financial assets (2021) — link
7. A deep Q-learning portfolio management framework for the cryptocurrency market (2020) — link
8. Deep Learning for Portfolio Optimization (2020) — link

0 of 46 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.