Efficient Algorithms for Computing Risk Parity Portfolio Weights

This paper presents two simple algorithms to calculate the portfolio weights for a risk parity strategy, where asset class covariance information is appropriately taken into consideration to achieve “true” equal risk contribution. Previous implementations of risk parity either (1) used a naïve 1/vol solution, which ignores asset class correlations, or (2) computed “true” risk parity weights using relatively complicated optimizations to solve a quadratic minimization program with non-linear constraints. The two iterative algorithms presented here require only simple computations and quickly converge to the optimal solution. In addition to the technical contribution, we also compute the parity in portfolio “risk allocation” using the Gini coefficient. We confirm that portfolio strategies with parity in “asset class allocation” can actually have high concentration in its “risk allocation”.