Multivariate volatilities and distribution play an important role in portfolio selection and can be used to calculate the value-at-risk (VaR) of a multiple-asset financial position. This study proposes a new expected utility maximization (EUM) model that accounts for VaR (EUM model with a VaR constraint (EUM–VaR)). Additionally, using the EUM–VaR model, this study investigates the hedging effectiveness of short and long hedged portfolios constructed with multivariate generalized autoregressive conditional heteroscedasticity (GARCH)-type models that feature level effects and multivariate normal
and skewed distributions for stock indexes and their corresponding futures in the Greater China Region. It is found that, all else equal, portfolios constructed using the multivariate skewed distribution are far more effective in hedging than those that rely on the other distributions, and the effectiveness of hedged portfolios from the multivariate GARCH-type models with level effects outperform those without level effects. Additionally, the effectiveness of hedged portfolios from multivariate asymmetric GARCH-type models exceeds that of those from multivariate symmetric GARCH-type models. Thus, investors should select the multivariate asymmetry in volatility, multivariate asymmetry in distribution, and EUM–VaR models to construct effectively hedged portfolios. The results of this study can provide useful implications for investors looking to manage risk.