Dependency Network-Based Portfolio Design with Forecasting and VaR Constraints

ArXiv ID: 2507.20039 “View on arXiv”

Authors: Zihan Lin, Haojie Liu, Randall R. Rojas

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.

Keywords: Vector Autoregression (VAR), Forecast Error Variance Decomposition (FEVD), Minimum Spanning Tree (MST), Value at Risk (VaR), Network Analysis, Equities

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced econometric and statistical concepts like VAR and FEVD with detailed mathematical formulations, indicating high math complexity. It demonstrates high empirical rigor by using real-world S&P 500 data, implementing a specific backtest with concrete performance metrics (63.74% return vs. benchmark), and detailing data preprocessing and rolling-window simulations.

  flowchart TD
    subgraph Input
        A["Research Goal<br>Portfolio Optimization<br>with Network Structure"]
        B["Data: S&P 500 Daily Returns<br>2020-2024"]
    end

    subgraph Methodology
        C["1. Network Construction<br>VAR + FEVD<br>Estimate dependencies"]
        D["2. Core Structure<br>Minimum Spanning Tree MST<br>Reduce noise"]
        E["3. Selection & Forecast<br>Centrality Ranking + NNAR/ARIMA"]
        F["4. Risk Constraint<br>VaR-based Capital Allocation"]
    end

    subgraph Outcomes
        G["Dynamic Portfolio<br>Trading Simulation"]
        H["Key Findings<br>NNAR Strategy: 63.74% Return<br>Benchmark: 18.00%"]
    end

    A --> B
    B --> C
    C --> D
    D --> E
    E --> F
    F --> G
    G --> H