SCRIP: Successive Convex Optimization Methods for Risk Parity Portfolio Design

The traditional Markowitz portfolio optimization proposed in the 1950s has not been embraced by practitioners despite its theoretical elegance. Recently, an alternative risk parity portfolio design has been receiving significant attention from both the theoretical and practical sides due to its advantage in diversification of (ex-ante) risk contributions among assets. Such risk contributions can be deemed good predictors for the (ex-post) loss contributions, especially when there exist huge losses. Most of the existing specific problem formulations on risk parity portfolios are highly nonconvex and are solved via standard off-the-shelf numerical optimization methods, e.g., sequential quadratic programming and interior point methods. However, for nonconvex risk parity formulations, such standard numerical approaches may be highly inefficient and may not provide satisfactory solutions. In this paper, we first propose a general risk parity portfolio problem formulation that can fit most of the existing specific risk parity formulations, and then propose a family of simple and efficient successive convex optimization methods for the general formulation. The numerical results show that our proposed methods significantly outperform the existing ones.