Markowitz space: A more stationary representation for efficient portfolio selection

Efficient portfolio selection remains a central challenge in financial markets due to the dynamic nature of asset returns, influenced by external shocks and interdependencies among assets. To address this, we introduce the Markowitz Space, a novel representation of financial data derived from the Markowitz model. Each point in this space represents the optimal asset allocation for a specific time window, capturing the evolving risk–return trade-off. From a theoretical perspective, we prove that when return volatility exhibits reversing patterns – a common phenomenon in real markets – the Markowitz Space is more stationary and temporally consistent than the traditional Return space. Practically, we evaluate the Markowitz Space using historical data from stock markets, currency pairs, and cryptocurrencies during financial crises. Stationarity is confirmed through Dickey–Fuller (DF) and Augmented Dickey–Fuller (ADF) tests, demonstrating higher stability compared to the Return space. Portfolio selection is performed in both spaces, and predictive modeling with the Kalman Filter (KF) and Decomposition-Based Neural Dynamics (DBND) shows that the Markowitz Space enhances forecasting accuracy. Results indicate that leveraging this space allows for improved portfolio management by providing more stable and reliable predictions of optimal asset weights, particularly in volatile market conditions. Overall, the Markowitz Space offers a theoretically sound and empirically validated framework for improving prediction and portfolio performance, highlighting the benefits of incorporating the underlying Markowitz model structure into temporal financial analysis.