We propose a return based modification of the portfolio variance matrix for asset allocation using risk parity. The modification is based upon a single scalar parameter which can be tuned to tailor the allocation for desired expected risk and/or return. The present work contributes a new twist on risk parity. While classical risk parity methods are based exclusively on volatility, the new solution (Modified Risk Parity) considers both historical returns and their variance in the construction of an optimal, diversified investment portfolio. We present two examples for periods including the recent financial market crises. The results suggest that the modification may lead to significantly improved risk adjusted returns over those realized by the conventional risk parity method
