Risk Parity: Equal Risk Contribution Portfolios

Module: Fintech AI | Difficulty: Advanced

Risk Contribution

Risk Parity Condition

All-Weather Portfolio

Leveraged Risk Parity

import numpy as np
from scipy.optimize import minimize

class RiskParity:
    def __init__(self, cov_matrix):
        self.cov = cov_matrix
    def solve(self):
        n = len(self.cov)
        def objective(w):
            portfolio_vol = np.sqrt(w @ self.cov @ w)
            risk_contributions = w * (self.cov @ w) / portfolio_vol
            target = portfolio_vol / n
            return np.sum((risk_contributions - target)**2)
        constraints = [{'type': 'eq', 'fun': lambda w: np.sum(w) - 1}]
        w0 = np.ones(n) / n
        result = minimize(objective, w0, constraints=constraints, method='SLSQP')
        return result.x

Research Insight: Risk parity is attractive because it diversifies across risk factors, not just asset classes. The key insight is that traditional 60/40 portfolios are dominated by equity risk. Risk parity achieves better risk-adjusted returns by equalizing risk contributions.