Copula-based model for portfolio of sector indices

Investigating sector indices contributes a lot to making decision of assets allocation in different sectors. In this paper, we choose CSI300HC index and CSI300CS index, whose Sharpe ratios rank the first two among the CSI 300 ten sector indices, as assets of a portfolio. ARMA-GJR-GARCH model, with Student-t innovation, is used to specify indices return series; while copula function, combined with nonparametric kernel estimation method, is used to describe dependency between the two indices returns. Moreover, employing Monte Carlo simulation method, we estimate the weights of the two indices in the optimal portfolio, which gives the minimum Value at Risk (VaR) over the next holding period at a given confidence level. The conclusion indicates that the proportion of CSI300HC index in the portfolio is significant, which is consistent with the fact that the health care sector develops favorably in recent years.