[Paper Review] Dynamic Mean-Variance Portfolio Optimisation

Xiang Meng|arXiv (Cornell University)|Jul 6, 2019

Stochastic processes and financial applications8 references4 citations

TL;DR

This paper proposes a time-consistent dynamic mean-variance portfolio optimization strategy using a game-theoretic approach to resolve time-inconsistency in dynamic MVO. It derives explicit solutions under CEV-driven dynamics, validates performance using real and simulated market data, and shows the strategy outperforms LSTM-based methods in return and risk-adjusted metrics, particularly under realistic market assumptions.

ABSTRACT

The portfolio optimisation problem, first raised by Harry Markowitz in 1952, has been a fundamental and central topic to understanding the stock market and making decisions. There has been plenty of works contributing to development of the mean-variance optimisation (MVO) so far. In this paper, one kind of them, namely, dynamic mean-variance optimisation (DMVO) is mainly discussed. One can apply either precommitment or game-theoritical approach to address time-inconsistency in DMVO. We use the second approach to seek for a time-consistent strategy. After obtaining the optimal strategy, we extend the result to a CEV-driven economy. In order to prove the usefulness of them, strategies are fit into both real market data and simulated data. It turns out that the strategy whose assumptions are close to market conditions generally gives a better result. Lastly, a selected strategy is chosen to compare with another strategy came up by deep learning technique.

Motivation & Objective

• To address time-inconsistency in dynamic mean-variance portfolio optimization (DMVO) using a game-theoretic approach instead of precommitment.
• To derive a time-consistent optimal strategy by formulating the problem as a Nash equilibrium game between successive decision periods.
• To extend the theoretical solution to a CEV-driven market model to better reflect real market volatility patterns.
• To empirically validate the strategy using both real-world and simulated market data across different volatility regimes.
• To compare the performance of the proposed dynamic strategy against deep learning-based LSTM portfolio strategies in terms of terminal return, drawdown, and volatility.

Proposed method

• Applies a game-theoretic framework to model the investor's dynamic preferences as a non-cooperative game across time periods.
• Uses the total variance formula to transform the time-inconsistent DMVO objective into a time-consistent one.
• Employs the Hamilton-Jacobi-Bellman (HJB) equation to derive explicit analytical solutions under Brownian motion and CEV processes.
• Incorporates CEV dynamics with a negative elasticity parameter (α = -0.1) to model stochastic volatility that matches empirical stock price behavior.
• Calibrates the strategy using 10-year historical data from 25 stocks listed on the Singapore Exchange (SGX).
• Compares performance against LSTM-based portfolio strategies trained on the same data, using terminal wealth, max drawdown, and standard deviation as evaluation metrics.

Experimental results

Research questions

• RQ1 How can time-inconsistency in dynamic mean-variance portfolio optimization be resolved using a game-theoretic framework?
• RQ2 What is the analytical form of the time-consistent optimal portfolio strategy under CEV-driven asset dynamics?
• RQ3 How does the performance of the proposed dynamic strategy compare to deep learning-based LSTM strategies in real and simulated market environments?
• RQ4 To what extent do model assumptions that align with real market conditions improve portfolio performance?
• RQ5 What trade-offs exist between risk, return, and stability between the dynamic mean-variance strategy and LSTM-based approaches?

Key findings

• The CEV-based dynamic mean-variance strategy achieved a terminal return of 47.90% with a maximum drawdown of -83.82% and standard deviation of 29.03% on real SGX data.
• LSTM strategies with 1000 training epochs produced lower terminal returns (e.g., -4.42%) but significantly lower volatility (2.72%) and smaller drawdowns (e.g., -12.37%) compared to the CEV strategy.
• Within the same LSTM architecture, longer training (1000 epochs) led to more stable predictions that closely followed lagged price patterns, reducing return variability.
• The CEV strategy exhibited higher risk and return than LSTM strategies, indicating a higher potential for gains but also greater downside risk.
• The game-theoretic approach successfully produced a time-consistent strategy that outperformed LSTM in terminal return under realistic market assumptions.
• Strategies with assumptions closer to actual market dynamics (e.g., CEV with negative α) delivered better performance than those based purely on pattern prediction.