Enhancing Black-Litterman Portfolio via Hybrid Forecasting Model Combining Multivariate Decomposition and Noise Reduction

TL;DR

The paper tackles noisy, single-variable time-series decomposition in Black-Litterman view generation by proposing a SSA-MAEMD-TCN hybrid that denoises data (SSA), aligns multivariate IMF components (MA-EMD), and learns complex temporal patterns with Temporal Convolutional Networks. It then feeds improved forecasts into the Black-Litterman Bayesian framework, deriving posterior returns $\mu_{post}$ and covariance $\Sigma_{post}$ for optimized weights $w_{bl}$, i.e., $\mu_{post} = \big( (\tau \Sigma)^{-1} + P^T \Omega^{-1} P \big)^{-1} \big( (\tau \Sigma)^{-1} \Pi + P^T \Omega^{-1} Q \big)$ and $\Sigma_{post} = \Sigma + \big( (\tau \Sigma)^{-1} + P^T \Omega^{-1} P \big)^{-1}$ with $w_{bl} = (\lambda \Sigma_{post})^{-1} \mu_{post}$. Empirical results on Nasdaq-100 data show that SSA-MAEMD-TCN outperforms MAEMD-TCN, MEMD-TCN, and MAEMD-LSTM in predictive accuracy (RMSE, MAPE, $R^2$) and yields more diversified, higher-performing BL portfolios, especially for short holding periods. The approach demonstrates practical benefits in generating reliable investor views and constructing robust, high-Sharpe portfolios after transaction costs, highlighting the value of noise-robust, multivariate decomposition in finance. Overall, the framework offers a data-driven pathway to enhance BL-based asset allocation with significant short-term performance gains and improved diversification.

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.

Figures (9)

• Figure 1: The process of Black-Litterman model idzorek2StepbystepGuide2007.
• Figure 2: A dilated causal convolution with dilation factors d = 1, 2, 4 and filter size k = 3 baiEmpiricalEvaluationGeneric2018.
• Figure 3: The residual block in TCNs. Left plot: an $1 \times 1$ convolution is added when the residual input and output have different dimensions. Right plot: an example of the residual connection in TCN baiEmpiricalEvaluationGeneric2018.
• Figure 4: Procedure of the complete Black-Litterman strategy.
• Figure 5: COHLV of MSFT was decomposed using MA-EMD.