Risk Budgeting: Allocating Risk Across Portfolios

Module: Fintech AI | Difficulty: Advanced

Risk Budget

Risk Budgeting Problem

Equal Risk Contribution

import numpy as np
from scipy.optimize import minimize

class RiskBudgetOptimizer:
    def __init__(self, cov_matrix, risk_budgets):
        self.cov = cov_matrix; self.budgets = risk_budgets
    def optimize(self):
        n = len(self.budgets)
        def objective(w):
            portfolio_vol = np.sqrt(w @ self.cov @ w)
            risk_contributions = w * (self.cov @ w) / portfolio_vol
            target_rc = self.budgets * portfolio_vol
            return np.sum((risk_contributions - target_rc)**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 budgeting allows investors to allocate risk based on conviction rather than capital. The key insight is that traditional equal-weight or market-cap-weight portfolios have unintended risk concentrations. Risk budgeting provides explicit control over risk allocation.