Multi-objective carbon-energy portfolio optimization under investment horizon heterogeneity

European geopolitical risks and financial systemic risks have led to significant long-term and short-term fluctuations in global carbon and energy markets. This creates challenges for portfolio managers with different investment horizons. This study uses a multivariate variational mode decomposition (MVMD) based Vine-Copula model to perform multi-objective portfolio optimization. There are ten optimization objectives and different measures, including Mean, Variance, Skewness, Kurtosis, VaR, CVaR, and HMCR. This study analyzes carbon, natural gas, oil and coal futures assets data from December 31, 2009 to October 21, 2022, and finds the following. First, portfolios with investment horizons over 20 weeks- and less than 2 weeks-length outperform portfolios with other investment horizons. Second, the optimized Mean-Skewness-CVaR portfolio has the greatest number of optimal timings for portfolio managers at investment horizons over 20 weeks and less than 2 weeks. Portfolio performance does not necessarily improve by including more optimization objectives within portfolio strategies.