riskparity

Risk parity portfolio optimization via the improved CCD method of Choi & Chen (2022).

Choi, J., & Chen, R. (2022). Improved iterative methods for solving risk parity portfolio. Journal of Derivatives and Quantitative Studies, 30(2). https://doi.org/10.1108/JDQS-12-2021-0031

What is risk parity?

A risk parity (equal risk contribution) portfolio chooses weights w so that every asset contributes the same fraction of total portfolio volatility:

$$\frac{w_i (\mathbf{C}\mathbf{w})_i}{\mathbf{w}^\top \mathbf{C}\mathbf{w}} = b_i \quad \forall i$$

where C is the return covariance matrix and b is the risk-budget vector (defaults to 1/N for equal risk parity).

Algorithm

The improved CCD method (Algorithm 1 in the paper) works on the correlation matrix and adds a rescaling step after each sweep, making it ~3× faster than the original CCD method and saving ~40% of iterations.

Installation

pip install riskparity

Quick start

import numpy as np
from riskparity import risk_parity

# 3-asset covariance matrix
cov = np.array([
    [0.04,  0.01,  0.002],
    [0.01,  0.09,  0.015],
    [0.002, 0.015, 0.0025],
])

result = risk_parity(cov)
print(result.weights)            # portfolio weights, sum to 1
print(result.risk_contributions) # fractional risk contributions, sum to 1
print(result.iterations)         # number of CCD iterations
print(result.converged)          # True if tolerance was met

Custom risk budgets

b = np.array([0.5, 0.3, 0.2])   # 50 / 30 / 20 % risk allocation
result = risk_parity(cov, b=b)

Standalone risk contribution utility

from riskparity import risk_contributions
rc = risk_contributions(weights, cov)  # fractional RC for any portfolio

API reference

risk_parity(cov, b=None, tol=1e-6, max_iter=1000)

Returns a RiskParityResult dataclass:

risk_contributions(weights, cov)

Compute fractional risk contributions for any portfolio.

License

MIT