Paper: arXiv 2509.23533

Authors: Gabriele Casto

Abstract

We introduce the Historical and Dynamic Volatility Ratios (HVR/DVR) and show that equity and index volatilities are cointegrated at intraday and daily horizons. This allows us to construct a VECM to forecast portfolio volatility by exploiting volatility cointegration. On S&P 500 data, HVR is generally stationary and cointegration with the index is frequent; the VECM implementation yields substantially lower mean absolute percentage error (MAPE) than covariance-based forecasts at short- to medium-term horizons across portfolio sizes. The approach is interpretable and readily implementable, factorizing covariance into market volatility, relative-volatility ratios, and correlations.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced econometric methods including cointegration analysis and VECM modeling, requiring significant mathematical sophistication. Empirical validation is demonstrated on S&P 500 data with quantitative metrics like MAPE, indicating strong practical implementation.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Forecast portfolio volatility<br>exploiting cointegrated dynamics"] --> B["Data & Inputs<br>S&P 500 intraday & daily data<br>Equity & index volatilities"]
  B --> C["Methodology: Historical Volatility Ratio<br>Compute relative variance ratios<br>Check for stationarity & cointegration"]
  C --> D["Methodology: Dynamic Volatility Ratio<br>VECM estimation<br>Exploit cointegration for forecasts"]
  D --> E["Key Findings/Outcomes"]
  subgraph E ["Outcomes"]
      F1["HVR is typically stationary<br>Volatilities are cointegrated"]
      F2["VECM forecasts reduce MAPE<br>vs. covariance benchmarks<br>at short-medium horizons"]
      F3["Interpretable decomposition<br>Market Volatility +<br>Relative Ratios + Correlations"]
  end

  %% Styling
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  classDef data fill:#fff3e0,stroke:#e65100,stroke-width:2px
  classDef method fill:#f3e5f5,stroke:#4a148c,stroke-width:2px
  classDef outcome fill:#e8f5e9,stroke:#1b5e20,stroke-width:2px

  class A goal
  class B data
  class C,D method
  class E,F1,F2,F3 outcome