  This article develops a model that takes into account skewness risk in risk
parity portfolios. In this framework, asset returns are viewed as stochastic
processes with jumps or random variables generated by a Gaussian mixture
distribution. This dual representation allows us to show that skewness and jump
risks are equivalent. As the mixture representation is simple, we obtain
analytical formulas for computing asset risk contributions of a given
portfolio. Therefore, we define risk budgeting portfolios and derive existence
and uniqueness conditions. We then apply our model to the
equity/bond/volatility asset mix policy. When assets exhibit jump risks like
the short volatility strategy, we show that skewness-based risk parity
portfolios produce better allocation than volatility-based risk parity
portfolios. Finally, we illustrate how this model is suitable to manage the
skewness risk of long-only equity factor portfolios and to allocate between
alternative risk premia.
