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

Energy markets are strategic to governments and economic development. Several commodities compete as substitutable energy sources and energy diversifiers. Such competition reduces the energy vulnerability of countries as well as portfolios' risk exposure. Vulnerability results mainly from price trends and fluctuations, following supply and demand shocks. Such energy price uncertainty attracts many market participants in the energy commodity markets. First, energy producers and consumers hedge adverse price changes with energy derivatives. Second, financial market participants use commodities and commodity derivatives to diversify their conventional portfolios. For that reason, we consider the joint dependence between the United States (U.S.) natural gas, crude oil and stock markets. We use Gatfaoui's (2015) time varying multivariate copula analysis and related variance regimes. Such approach handles structural changes in asset prices. In this light, we draw implications for portfolio optimization, when investors diversify their stock portfolios with 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 on the portfolio's expected return and/or U.S. stock investment. The return constraint reduces the performance of the optimal portfolio. Moreover, the regime-specific portfolio optimization helps implement an enhanced active management 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 absence of a return constraint.