How to hedge extreme risk of natural gas in multivariate semiparametric value-at-risk portfolio?

The COVID-19 pandemic and the war in Ukraine have caused huge price changes in the natural gas market. This paper tries to minimise the extreme risk of natural gas, making two six-asset portfolios, where gas is combined with five developed and emerging European stock indices. We observe extreme risk from the aspect of classical parametric Value-at-Risk measure, but we also propose a new approach and optimise portfolios with semiparametric VaR as a target. Estimating the equicorrelation of the two portfolios, we determine that the emerging indices portfolio has a much lower level of integration, which is good for portfolio construction. Additionally, we divide the full sample into the pre-crisis and crisis periods to assess how portfolios look in the two intrinsically different subsamples. According to the results, both portfolios with the developed and emerging stock indices minimise extreme risk very well, but the latter portfolio is better. In the pre-crisis period, this advantage amounts to around 6% in the min-VaR portfolio and 3.5% in the min-mVaR portfolio. However, in the crisis period, the third and fourth moments come to the fore, meaning that hedging results increase significantly in favour of the emerging indices portfolios. In other words, the min-VaR and min-mVaR results of the emerging indices portfolio are better in amounts of more than 14% and 17%, respectively, vis-a-vis portfolios with the developed stock indices. We recommend using the semiparametric VaR metric because it is far more accurate and unbiased compared to the classical VaR since it considers all the key features of portfolio distribution.