Forecasting Multivariate Volatilities with Exogenous Predictors: An Application to Industry Diversification Strategies

We propose a procedure to forecast the realized covariance matrix for a given set of assets within a multivariate heterogeneous autoregressive (MHAR) framework. Utilizing high-frequency data for the U.S. aggregate and industry indexes and a large set of exogenous predictors that include financial, macroeconomic, sentiment, and climate-based factors, we evaluate the out-of-sample performance of industry portfolios constructed from forecasted realized covariance matrices across various univariate and multivariate forecasting models. Our findings show that LASSO-based multivariate HAR models employing predictors that capture climate uncertainty generally yield more consistent evidence regarding the accuracy of the realized covariance forecasts, providing further support for the growing evidence that climate related factors significantly drive return and volatility dynamics in financial markets. While international summits and global warming stand out as the dominant climate predictors for realized volatility forecasts, both climate and macroeconomic predictors prove equally important for longer term correlation forecasts. In these forecasts, the U.S. EPU index and natural disasters, along with U.S. climate policy uncertainty, play dominant predictive roles. Our results suggest that the MHAR framework, coupled with DRD decomposition that splits the covariance matrix into a diagonal matrix of realized variances and realized correlations, can be utilized in a high-frequency setting to implement diversification and smart beta strategies for various investment horizons.