Realized Variances vs. Correlations: Unlocking the Gains in Multivariate Volatility Forecasting

This paper disentangles the added value of using high-frequency-based (realized) covariance measures on multivariate volatility forecasting into two pillars: the realized variances and realized correlations and quantifies the corresponding economic gains using a broad set of portfolio performance metrics. Using state-of-the-art models based on daily returns and realized (co)variances, we predict the conditional covariance matrix on a daily, weekly, biweekly, and monthly frequency, both for dimensions 30 and 50. We evaluate the forecasts statistically using various loss functions and economically by constructing Global Minimum Variance (GMV) portfolios. Using a data set of 50 liquid U.S. stocks from 2001 to 2019, we find that the inclusion of realized variances largely accounts for the improvement in statistical forecast performance (between 65% and at least 78%). The results on the GMV portfolios show that realized covariance models exhibit lower ex-post volatility but tend to produce substantially lower ex-post mean returns compared to models with realized variances and daily returns. Consequently, Sharpe Ratios increase roughly by 35%, leading to significant utility gains, equivalent to up to 500 basis points per year. Combined, our results indicate that there is no economic gain by modeling correlations dynamically, either using daily returns or realized correlations.