Rethinking Portfolio Risk: Forecasting Volatility Through Cointegrated Asset Dynamics

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.