Dependency Network-Based Portfolio Design with Forecasting and VaR Constraints

Abstract: This study proposes a novel portfolio optimization framework that integrates statistical social network analysis with time series forecasting and risk management. Using daily stock data from the S&P 500 (2020-2024), we construct dependency networks via Vector Autoregression (VAR) and Forecast Error Variance Decomposition (FEVD), transforming influence relationships into a cost-based network. Specifically, FEVD breaks down the VAR's forecast error variance to quantify how much each stock's shocks contribute to another's uncertainty information we invert to form influence-based edge weights in our network. By applying the Minimum Spanning Tree (MST) algorithm, we extract the core inter-stock structure and identify central stocks through degree centrality. A dynamic portfolio is constructed using the top-ranked stocks, with capital allocated based on Value at Risk (VaR). To refine stock selection, we incorporate forecasts from ARIMA and Neural Network Autoregressive (NNAR) models. Trading simulations over a one-year period demonstrate that the MST-based strategies outperform a buy-and-hold benchmark, with the tuned NNAR-enhanced strategy achieving a 63.74% return versus 18.00% for the benchmark. Our results highlight the potential of combining network structures, predictive modeling, and risk metrics to improve adaptive financial decision-making.