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
  classDef goal fill:#e1f5fe,stroke:#01579b,stroke-width:2px
  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

Cited References (16)

  1. Portfolio selection (1952)
  2. Generalized autoregressive conditional heteroskedasticity (1986)
  3. Dynamic conditional correlation: A simple class of multivariate GARCH models (2002)
  4. Co-integration and error correction: Representation, estimation, and testing (1987)
  5. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models (1991)
  6. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection (2003)
  7. A well-conditioned estimator for large-dimensional covariance matrices (2004)
  8. The Markowitz optimization enigma: Is ``optimized’’ optimal? (1989)
and 8 more
  1. The distribution of realized exchange rate volatility (2001)
  2. Distribution of the estimators for autoregressive time series with a unit root (1979)
  3. Likelihood ratio statistics for autoregressive time series with a unit root (1981)
  4. Testing the null hypothesis of stationarity against the alternative of a unit root (1992)
  5. Testing for a unit root in time series regression (1988)
  6. Lag length selection and the construction of unit root tests with good size and power (2001)
  7. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix (1987)
  8. Automatic time series forecasting: The forecast package for R (2008)

0 of 16 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.