核心思想

风险平价 (Risk Parity) 是一种资产配置方法，使每个资产对组合总风险的贡献相等。传统的 $60/40$ 股债组合中，股票通常贡献 >80% 的风险。风险平价通过杠杆平衡实现等风险分配。

$\text{RC}_i = w_i \cdot \frac{\Sigma w}{\sqrt{w^\top \Sigma w}}$

目标是：$\text{RC}_1 = \text{RC}_2 = \dots = \text{RC}_n$

计算框架

import numpy as np
from scipy.optimize import minimize

def risk_parity_weights(cov_matrix, target_vol=0.05):
    """风险平价优化：最小化各资产风险贡献的差异"""
    n = len(cov_matrix)
    
    def objective(w):
        w = np.abs(w)  # 确保权重非负
        w /= w.sum()   # 归一化
        port_vol = np.sqrt(w.T @ cov_matrix @ w)
        
        # Marginal risk contribution
        mrc = cov_matrix @ w
        # Risk contribution
        rc = w * mrc / port_vol
        
        # 最小化 RC 的差异
        target_rc = np.ones(n) / n * port_vol
        return np.sum((rc - target_rc)**2)
    
    result = minimize(objective, x0=np.ones(n)/n, 
                      bounds=[(0, 1)]*n)
    return result.x

def leverage_adjusted_target(cov_matrix, base_weights, target_vol):
    """杠杆调整：使用风险平价权重 + 杠杆达到目标波动率"""
    w_rp = risk_parity_weights(cov_matrix)
    rp_vol = np.sqrt(w_rp.T @ cov_matrix @ w_rp)
    
    leverage = target_vol / rp_vol
    return w_rp * leverage, leverage

局限与风险

• ⚠️ 杠杆风险：通常需要低杠杆（1.5-2x），利率上升时成本增加
• ⚠️ 股债同跌：极端情况下股票和债券同时下跌（如 2022）
• ⚠️ 估计误差敏感：协方差矩阵的误设直接影响权重

变体

参考文献

1. Qian, E., 2005. “Risk Parity Portfolios: Efficient Portfolios Through True Risk Diversification.”
2. Maillard, S., Roncalli, T. & Teiletche, J., 2010. “The Properties of Equally Weighted Risk Contribution Portfolios.”