Risk parity with expectiles

A recent popular approach to portfolio selection aims at diversifying risk by looking for the so called Risk Parity portfolios. These are defined by the condition that the risk contributions of all assets to the global risk of the portfolio are equal. The Risk Parity approach has been originally introduced for the volatility risk measure. In this paper we consider expectiles as risk measures, we refine results on their differentiability and additivity, and we show how to define Risk Parity portfolios when the expectiles are used. Furthermore, we propose three different classes of methods for practically finding Risk Parity portfolios with respect to expectiles, and we compare the accuracy and efficiency of these methods on real-world data. Expectiles are also used as risk measures in the classical risk-return approach to portfolio selection, where we present a new linear programming formulation.