Risk parity portfolio optimization, using expected shortfall as the risk measure, is investigated when asset returns are fat‐tailed and heteroscedastic with regime switching dynamic correlations. The conditional return distribution is modeled by an elliptical multi‐variate generalized hyperbolic distribution, allowing for fast parameter estimation via an expectation‐maximization algorithm, and a semi‐closed form of the risk contributions. A new method for efficient computation of non‐Gaussian risk parity weights sidesteps the need for numerical simulations or Cornish–Fisher‐type approximations. Accounting for fat‐tailed returns, the risk parity allocation is less sensitive to volatility shocks, thereby generating lower portfolio turnover, in particular during market turmoils such as the global financial crisis or the COVID shock. While risk parity portfolios are rather robust to the misuse of the Gaussian distribution, a sophisticated time series model can improve risk‐adjusted returns, strongly reduces drawdowns during periods of market stress and enables to use a holistic risk model for portfolio and risk management.