Improved iterative methods for solving risk parity portfolio

TL;DR

This paper enhances iterative algorithms for risk parity portfolio optimization, significantly improving their speed and efficiency through methodological refinements and better initial guesses.

Contribution

It introduces simplified formulations and rescaling in CCD, along with an improved initial guess for Newton, leading to faster convergence in risk parity solutions.

Findings

Improved CCD method is about three times faster.

Enhanced methods save over 40% of iterations.

Numerical experiments confirm superior performance.

Abstract

Risk parity, also known as equal risk contribution, has recently gained increasing attention as a portfolio allocation method. However, solving portfolio weights must resort to numerical methods as the analytic solution is not available. This study improves two existing iterative methods: the cyclical coordinate descent (CCD) and Newton methods. We enhance the CCD method by simplifying the formulation using a correlation matrix and imposing an additional rescaling step. We also suggest an improved initial guess inspired by the CCD method for the Newton method. Numerical experiments show that the improved CCD method performs the best and is approximately three times faster than the original CCD method, saving more than 40% of the iterations.