Risk parity for mixed tempered stable distributed sources of risk

In this paper we discuss a detailed methodology for dealing with Risk parity in a parametric context. In particular, we use the Independent Component Analysis for a linear decomposition of portfolio risk factors. Each Independent Component is modeled with the Mixed Tempered Stable distribution. Risk parity optimal portfolio weights are calculated for three risk measures: Volatility, modified Value At Risk and modified Expected Shortfall. Empirical analysis is discussed in terms of out-of-sample performance and portfolio diversification.