Abstract
Modern portfolio construction demands robust methods for integrating data-driven insights into asset allocation. The Black-Litterman model offers a powerful Bayesian approach to adjust equilibrium returns using investor views to form a posterior expectation along with market priors. Mainstream research mainly generates subjective views through statistical models or machine learning methods, among which hybrid models combined with decomposition algorithms perform well. However, most hybrid models do not pay enough attention to noise, and time series decomposition methods based on single variables make it difficult to fully utilize information between multiple variables. Multivariate decomposition also has problems of low efficiency and poor component quality. In this study, we propose a novel hybrid forecasting model SSA-MAEMD-TCN to automate and improve the view generation process. The proposed model combines Singular Spectrum Analysis (SSA) for denoising, Multivariate Aligned Empirical Mode Decomposition (MA-EMD) for frequency-aligned decomposition, and Temporal Convolutional Networks (TCNs) for deep sequence learning to capture complex temporal patterns across multiple financial indicators. Empirical tests on the Nasdaq 100 Index stocks show a significant improvement in forecasting performance compared to baseline models based on MAEMD and MEMD. The optimized portfolio performs well, with annualized returns and Sharpe ratios far exceeding those of the traditional portfolio over a short holding period, even after accounting for transaction costs.
Introduction: The Challenge of Portfolio Optimization
Modern portfolio management often relies on the Mean-Variance (MV) framework established by Markowitz. However, MV optimization is notoriously sensitive to input parameters—specifically expected returns. Small estimation errors in these returns can lead to erratic and extreme swings in asset weights, making the model difficult to implement in real-world trading.
The Black-Litterman (BL) model addresses these instabilities by utilizing a Bayesian approach. Instead of relying solely on historical averages, it blends market equilibrium (the "prior") with specific "investor views" (the "posterior"). While the BL framework provides a more stable mathematical structure, its effectiveness is entirely dependent on the quality of the views provided. Traditional statistical models often struggle with the non-linear, noisy, and interconnected nature of financial time series, leading to the "garbage in, garbage out" problem.
The SSA-MAEMD-TCN Framework
To generate high-quality investor views, this research introduces a multi-stage hybrid forecasting model: SSA-MAEMD-TCN.
1. Denoising with Singular Spectrum Analysis (SSA)
Financial data is inherently noisy. SSA acts as a sophisticated filter that decomposes raw time series into trend, oscillatory, and noise components. By discarding the noise before the forecasting stage, the model ensures that the subsequent layers focus on meaningful market signals rather than random fluctuations.
2. Multivariate Aligned Empirical Mode Decomposition (MA-EMD)
Standard decomposition methods like EMD often produce a different number of components for different variables (e.g., price vs. volume), making multivariate analysis difficult. MA-EMD solves this by using Kullback-Leibler (KL) divergence to align the frequency components—Intrinsic Mode Functions (IMFs)—across multiple indicators (Open, High, Low, Volume). This alignment ensures that the deep learning model receives "frequency-matched" features, allowing it to capture the lead-lag relationships between different market variables.
3. Deep Learning with Temporal Convolutional Networks (TCN)
While RNNs and LSTMs are common for time series, they often suffer from vanishing gradients and high memory requirements. The authors utilize Temporal Convolutional Networks (TCNs), which employ dilated causal convolutions.
As shown in the figure above, TCNs allow for a massive receptive field by increasing the dilation factor ($d$), enabling the model to look back further into historical data without the sequential bottlenecks of recurrent architectures. This stability is crucial for learning the complex patterns within the aligned IMFs.
Integrating Forecasts into the Black-Litterman Model
Once the SSA-MAEMD-TCN model generates price forecasts, these are converted into quantitative "investor views." These views are then integrated into the Black-Litterman equations to derive the final asset weights.
The workflow illustrated above demonstrates how the model reconciles the market's implied excess returns (derived from market weights and covariance) with the subjective return estimates (Q) and their associated reliability ($\Omega$). The resulting combined distribution $E(R) \sim N(\mu_{BL}, \Sigma_{BL})$ provides the basis for the final portfolio construction.
Empirical Results and Performance
The model was tested using daily trading data from 20 representative stocks in the Nasdaq 100 Index from January 2020 to August 2023.
Forecasting Accuracy
The SSA-MAEMD-TCN model consistently outperformed benchmarks such as MAEMD-LSTM and MEMD-TCN. For instance, in predicting Google (GOOGL) stock, the Root Mean Square Error (RMSE) dropped significantly from 1.76 (standard MAEMD-TCN) to 1.13, highlighting the critical role of SSA-based denoising.
Portfolio Performance
In a 1-day rebalancing scenario, the BL model driven by these hybrid forecasts achieved:
- Annualized Return: 103.35%
- Sharpe Ratio: 4.21
- Stability: The BL model maintained a more diversified portfolio (mean of 18.03 stocks) compared to the MV model (mean of 11.19 stocks), which tended toward extreme concentration.
Even after accounting for a 0.2% transaction cost, the strategy remained highly profitable, though its advantage was most pronounced over short holding periods (1–3 days).
Conclusion
The SSA-MAEMD-TCN framework represents a significant advancement in automating the "investor views" required for Black-Litterman optimization. By aligning multivariate frequencies and aggressively filtering noise, the model captures market dynamics that simpler models miss. Future work will explore multi-step forecasting for longer-term horizons and the integration of Reinforcement Learning to dynamically adjust risk aversion parameters.