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 via spectral decomposition 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. While the climate and sentiment-based forecasting models generally yield more accurate forecasts of realized covariance compared to the macroeconomic and financial based models, particularly at the short forecast horizon, we find that the models that include industry-level information, generally yield better economic outcomes, in line with the established evidence of the predictive information captured at the industry level. 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; however, the choice of the predictors should be aligned with the target investment horizon.