This paper develops a version of risk-parity portfolio construction that targets tail risk instead of plain volatility. The authors replace standard volatility with Entropic Value-at-Risk (EVaR), a risk measure that focuses on the worst losses and is defined through an exponential transform of the loss distribution. They build two rules: EVaR-based inverse risk parity (IRP), which scales weights by standalone EVaR, and EVaR-based equal risk contribution (ERC), which equalizes each asset’s contribution to portfolio EVaR.

To make these rules practical, the researchers fit parametric return models that can capture skewness and heavy tails. They use multivariate normal tempered stable (MNTS) models and an independent component analysis (ICA) approach where the components follow tempered stable laws. From those models they derive formulas for each asset’s EVaR contribution and for a centered version called the EVaR deviation, which removes the fitted mean so that contributions reflect distributional risk rather than location.

A useful finding is that the EVaR-deviation approach connects back to familiar volatility rules when returns are Gaussian. In that special case the EVaR-deviation becomes proportional to variance, and the EVaR-based IRP and ERC rules reduce to conventional volatility-based IRP and ERC. This link helps show how the new method generalizes the standard practice by adding sensitivity to skewness and heavy tails.

The paper evaluates the resulting portfolios in three investment universes: cross-asset exchange-traded funds (ETFs), momentum-sorted portfolios, and U.S. sector ETFs. The empirical statement reported in the excerpt is that EVaR-based ERC portfolios achieved positive Sharpe-ratio differences relative to equal-weight portfolios across these universes. The authors also compare their tempered-stable EVaR results to a Gaussian EVaR benchmark, consider matched EVaR and CVaR constructions, and look at the role of transaction costs and the difference between raw EVaR and EVaR-deviation ERC rules.