Multivariate GARCH and portfolio variance prediction: A forecast reconciliation perspective

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.

Figures (5)

• Figure 1: Average relative MSE where the reference forecast is the univariate GARCH fitted on simulated portfolio returns with equally weighted portfolios (the $1/N$ case), and the DGP is a Scalar BEKK. The fitted MGARCH models are: the DCC-GARCH (first row, DCC) and the Scalar BEKK (second row, SBEKK). The columns indicates the sample size ($T$): $T=500$ left, $T=1000$ center and $T=2000$ right column. All values are averages across the 500 experiments.
• Figure 2: Average relative MSE where the reference forecast is the univariate GARCH fitted on simulated portfolio returns with equally weighted portfolios (the $1/N$ case), and the DGP is a DCC-GARCH. The fitted MGARCH models are: the DCC-GARCH (first row, DCC) and the Scalar BEKK (second row, SBEKK). The columns indicates the sample size ($T$): $T=500$ left, $T=1000$ center and $T=20000$ right column. All values are averages across the 500 experiments.
• Figure 3: Average relative MSE where the reference forecast is the univariate GARCH fitted on simulated portfolio returns with equally weighted portfolios (the $1/N$ case), and the DGP is a EDCC-GARCH. The fitted MGARCH models are: the DCC-GARCH (first row, DCC), the EDCC-GARCH (second row, EDCC) and the Scalar BEKK (third row, SBEKK). The columns indicates the sample size ($T$): $T=500$ left, $T=1000$ center and $T=2000$ right column. All values are averages across the 500 experiments.
• Figure 4: Average relative MSE where the reference forecast is the univariate GARCH fitted on simulated portfolio returns with equally weighted portfolios (the $1/N$ case), and the DGP is a Full BEKK. The fitted MGARCH models are: the DCC-GARCH (first row, DCC) and the Scalar BEKK (second row, SBEKK). The columns indicates the sample size ($T$): $T=500$ left, $T=1000$ center and $T=2000$ right column. All values are averages across the 500 experiments.
• Figure 5: Average relative MSE where the reference forecast is the univariate GARCH fitted on simulated portfolio returns with equally weighted portfolios (the $1/N$ case) for 24 assets, and the DGP is reported in each column (BEKK, DCC, EDCC and SBEKK). The fitted MGARCH models are: the DCC-GARCH (first row, DCC) and the Scalar BEKK (second row, SBEKK). All values are averages across the 500 experiments.