The Sharpe-ratio-maximizing portfolio becomes questionable under non-Gaussian returns, and it rules out, by construction, systemic risk, which can negatively affect its out-of-sample performance. In the present work, we develop a new performance ratio that simultaneously addresses these two problems when building optimal portfolios. To robustify the portfolio optimization and better represent extreme market scenarios, we simulate a large number of returns via a Monte Carlo method. This is done by obtaining probabilistic return forecasts through a distributional machine learning approach in a big data setting and then combining them with a fitted copula to generate return scenarios. Based on a large-scale comparative analysis conducted on the US market, the backtesting results demonstrate the superiority of our proposed portfolio selection approach against several popular benchmark strategies in terms of both profitability and minimizing systemic risk. This outperformance is robust to the inclusion of transaction costs.