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Energy markets are strategic to governments and economic development. Severalcommodities compete as substitutable energy sources and energy diversifiers.Such competition reduces the energy vulnerability of countries as well asportfolios' risk exposure. Vulnerability results mainly from price trends andfluctuations, following supply and demand shocks. Such energy price uncertaintyattracts many market participants in the energy commodity markets. First,energy producers and consumers hedge adverse price changes with energyderivatives. Second, financial market participants use commodities andcommodity derivatives to diversify their conventional portfolios. For thatreason, we consider the joint dependence between the United States (U.S.)natural gas, crude oil and stock markets. We use Gatfaoui's (2015) time varyingmultivariate copula analysis and related variance regimes. Such approachhandles structural changes in asset prices. In this light, we draw implicationsfor portfolio optimization, when investors diversify their stock portfolioswith natural gas and crude oil assets. We minimize the portfolio's variance,semi-variance and tail risk, in the presence and the absence of constraints onthe portfolio's expected return and/or U.S. stock investment. The returnconstraint reduces the performance of the optimal portfolio. Moreover, theregime-specific portfolio optimization helps implement an enhanced activemanagement strategy over the whole sample period. Under a return constraint,the semi-variance optimal portfolio offers the best risk-return tradeoff,whereas the tail-risk optimal portfolio offers the best tradeoff in the absenceof a return constraint.

Diversifying portfolios of U.S. stocks with crude oil and natural gas: A regime-dependent optimization with several risk measures