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This paper uses simulation-based portfolio optimization to mitigate the lefttail risk of the portfolio. The contribution is twofold. (i) We propose theMarkov regime-switching GARCH model with multivariate normal tempered stableinnovation (MRS-MNTS-GARCH) to accommodate fat tails, volatility clustering andregime switch. The volatility of each asset independently follows theregime-switch GARCH model, while the correlation of joint innovation of theGARCH models follows the Hidden Markov Model. (ii) We use tail risk measures,namely conditional value-at-risk (CVaR) and conditional drawdown-at-risk(CDaR), in the portfolio optimization. The optimization is performed with thesample paths simulated by the MRS-MNTS-GARCH model. We conduct an empiricalstudy on the performance of optimal portfolios. Out-of-sample tests show thatthe optimal portfolios with tail measures outperform the optimal portfolio withstandard deviation measure and the equally weighted portfolio in variousperformance measures. The out-of-sample performance of the optimal portfoliosis also more robust to suboptimality on the efficient frontier.

Portfolio Optimization on Multivariate Regime Switching GARCH Model with Normal Tempered Stable Innovation