Risk parity is an approach to investing that aims to balance risk evenly across assets within a given universe. The aim of this study is to unify the most commonly-used approaches to risk parity within a single framework. Links between these approaches have been identified in the published literature. A key point in risk parity is being able to identify and control the contribution of each asset to the risk of the portfolio. With alpha risk parity, risk contributions are given by a closed-form formula. There is a form of antisymmetry-or self-duality-in alpha risk portfolios that lie between risk budgeting and minimum-risk portfolios. Techniques from information geometry play a key role in establishing these properties.
Keywords: diversification; generalized entropy; information theory; investment risk; portfolio optimization; portfolio selection; risk budgeting; risk parity; statistical divergence.