Multivariate GARCH and portfolio variance prediction: A forecast reconciliation perspective

TL;DR

This paper investigates how combining univariate and multivariate GARCH-based portfolio risk forecasts using forecast reconciliation can improve variance predictions, especially under model misspecification and noisy data.

Contribution

It demonstrates that forecast reconciliation enhances portfolio variance forecasts in simulations and real data, even with model misspecification and noisy covariance proxies.

Findings

Forecast reconciliation improves variance prediction when the true covariance is known.

Reconciliation provides benefits even with misspecified models and noisy proxies.

Empirical results show improved forecasts using real data with reconciliation.

Abstract

We assess the advantage of combining univariate and multivariate portfolio risk forecasts with the aid of forecast reconciliation techniques. In our analyzes, we assume knowledge of portfolio weights, a standard for portfolio risk management applications. With an extensive simulation experiment, we show that, if the true covariance is known, forecast reconciliation improves over a standard multivariate approach, in particular when the adopted multivariate model is misspecified. However, if noisy proxies are used, correctly specified models and the misspecified ones (for instance, neglecting spillovers) turn out to be, in several cases, indistinguishable, with forecast reconciliation still providing improvements. The noise in the covariance proxy plays a crucial role in determining the improvement of both the forecast reconciliation and the correct model specification. An empirical analysis shows how forecast reconciliation can be adopted with real data to improve traditional GARCH-based portfolio variance forecasts.