Deep Reinforcement Learning for Optimal Portfolio Allocation: A Comparative Study with Mean-Variance Optimization

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Deep Reinforcement Learning for Optimal Portfolio Allocation: A Comparative Study with Mean-Variance Optimization

Srijan Sood
Kassiani Papasotiriou
Marius Vaiciulis
Tucker Balch
Published on 2/19/2026
Equities
Cross-asset
Reinforcement learning
Deep learning
Machine learning
Risk management
Backtesting
Factor allocation

This paper presents a comprehensive comparison between Deep Reinforcement Learning (DRL) and traditional Mean-Variance Optimization (MVO) for portfolio allocation. The authors design a DRL framework using Proximal Policy Optimization (PPO) with a Differential Sharpe Ratio reward function, which optimizes risk-adjusted returns at each timestep. The environment uses market replay of S&P 500 sector indices, with state features including historical log returns, current portfolio weights, and volatility indicators. For MVO, they use a 60-day lookback with Ledoit-Wolf shrinkage for covariance estimation and optimize for maximum Sharpe ratio. Both methods are tested on 10 annual backtests from 2012 to 2021, with DRL agents trained on rolling 5-year windows and validated on a burn year.

The results show that DRL significantly outperforms MVO across multiple metrics: average annual return (12.11% vs 6.53%), Sharpe ratio (1.17 vs 0.68), and maximum drawdown (-32.96% vs -33.03%). DRL also exhibits more consistent monthly returns and lower portfolio turnover, which implies lower transaction costs in practice. The study addresses common shortcomings in prior work by ensuring both methods optimize for the same objective (risk-adjusted returns) and providing detailed implementation details. The findings suggest that DRL can be a viable alternative to classical portfolio optimization, especially in dynamic market conditions.

Highlights

  • 1Designs a simple DRL environment using market replay for multi-asset portfolio allocation.
  • 2Provides a thorough comparison of DRL (PPO) with traditional Mean-Variance Optimization (MVO) under equal conditions.
  • 3Demonstrates DRL outperforms MVO in Sharpe ratio, annual returns, max drawdown, and portfolio turnover across 10 backtests.
  • 4Uses Differential Sharpe Ratio as reward to optimize risk-adjusted returns online.
  • 5Employs a sliding window training approach with seed policy transfer to handle non-stationary data.

Methods

  • M
    Deep Reinforcement Learning with Proximal Policy Optimization (PPO) and Differential Sharpe Ratio reward.
  • M
    Mean-Variance Optimization with Ledoit-Wolf shrinkage covariance estimation and Sharpe ratio maximization.
  • M
    Market replay environment with state features including log returns, portfolio weights, and volatility indicators.
  • M
    Sliding window training: 5 years training, 1 year validation, 1 year backtest, with seed policy transfer.

Results

  • R
    DRL achieves average annual return of 12.11% vs MVO's 6.53% over 2012-2021.
  • R
    DRL Sharpe ratio is 1.17 vs MVO's 0.68, a 72% improvement.
  • R
    DRL has lower maximum drawdown (-32.96% vs -33.03%) and higher Calmar ratio (2.31 vs 1.16).
  • R
    DRL portfolio turnover is lower, especially during market stress (e.g., March 2020).
  • R
    DRL produces more consistent monthly returns with lower volatility and positive mean.
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