Multivariate GARCH Models for Portfolio Risk Management: A Comparative Study

The research article presents an overall comparative study of multivariate GARCH M-GARCH in portfolio risk management, where three prevailing specifications VEC, CCC and DCC models are considered. We take daily closing prices of four major assets of the year 2018 through to 2023; S&P 500, NASDAQ-100, gold futures, and US Treasury Bonds, to estimate conditional variances, covariances, and dynamic correlations using maximum likelihood estimation. The descriptive statistics indicate that volatility is highly concentrated in clustering and time varying across assets with NASDAQ having the highest volatility (2.08) and significant negative skewness that shows non-normal returns. Comparison on models based on information criteria indicates that the Dynamic Conditional Correlation (DCC) specification has better performance with less computation need, fewer 8 parameters as compared to 21 (VEC) and greater log-likelihood with high improvement (164.67 units). Adequate model specification is shown through diagnostic testing using Ljung-Box test and ARCH-LM tests. Empirical results indicate that the volatility persistence (alpha + - 0 = 0.98) and the dynamics of high correlation (beta = 0.9321) are high which indicates long-memory properties and mean-reverting behavior which does not support constant correlation assumptions.