Equal Risk Bounding is better then Risk Parity for portfolio selection

Risk Parity (RP), also called equally weighted risk contribution, is a recent approach to risk diversification in portfolio selection. RP is based on the principle that the fractions of the capital invested in each asset should be chosen so as to make the total risk contributions of all assets equal among them. We show here that the Risk Parity approach is theoretically dominated by an alternative similar approach that does not actually require equally weighted risk contribution of all assets but only an equal upper bound on all such risks. We call it the Equal Risk Bounding (ERB) approach. This alternative approach might, and actually does in some cases, select portfolios that do not contain all assets and where the risk contributions of all assets is strictly smaller than in the RP portfolio. We prove some relations between the solutions of the ERB and of the RP models and we use such relations to provide a finite method for finding an ERB portfolio. In the case of equal correlation, a closed form solution to the ERB model is also provided. Some numerical examples illustrate the advantages of the ERB approach over the RP approach.