How do precious and industrial metals hedge oil in a multi-frequency semiparametric CVaR portfolio?

•This paper reduces extreme risk of Brent oil by constructing multivariate portfolios.•Gold dominates in precious metal portfolios, because gold has the lowest second, third and fourth moments.•Precious metals portfolio is better than industrials metals portfolio in all the time-horizons when CVaR is target. This paper tries to reduce extreme risk of Brent oil by constructing multivariate portfolios with precious and industrial metals in a multi-frequency framework. Extreme risk is measured by the parametric CVaR and more elaborate semiparametric CVaR measure, while the wavelet technique is used to build portfolios in different time-horizons. The results indicate that gold dominates in the precious metal portfolios, creating the lowest downside risk in most cases. The back-testing results reveal that the raw data CVaR portfolio with precious metals is the best, while the midterm mCVaR portfolio with industrial metals has upper hand. In terms of forecasting, CVaR portfolios with precious and industrial metals are the best in the short- and midterm horizons, respectively. In the long-term horizon, none of the portfolios is good in back-testing and forecasting, which means that CVaR and mCVaR models are not adequate risk functions for identifying realized risk in the long term. In the oil-dominated portfolios, the CVaR portfolios with gold are the best in terms of the lowest risk as well as back-testing and forecasting performances. When Brent is replaced by WTI oil, the share of WTI is somewhat smaller in the portfolios because WTI has higher risk. When the US 10Y bond is added to the portfolios, the portfolio risk is reduced because the bonds are very weakly correlated with the commodities.