Hedging effectiveness of the hedged portfolio: the expected utility maximization subject to the value-at-risk approach

摘要

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 t and skewed t 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 t 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.