风险平价模型实战：超越马科维茨的配置革命

import numpy as np
import pandas as pd
import yfinance as yf
from scipy.optimize import minimize
import matplotlib.pyplot as plt

# 1. 下载数据
tickers = ['SPY', 'TLT', 'GLD', 'QQQ']  # 股票、债券、黄金、科技股
data = yf.download(tickers, start="2020-01-01", end="2025-12-31")['Adj Close']

# 2. 计算收益率
returns = data.pct_change().dropna()

# 3. 计算协方差矩阵（年化）
cov_matrix = returns.cov() * 252

# 4. 风险平价优化函数
def risk_parity_objective(weights, cov_matrix):
    """风险平价的目标函数：最小化风险贡献的差异"""
    portfolio_vol = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
    risk_contributions = weights * (np.dot(cov_matrix, weights)) / portfolio_vol
    target_risk = np.mean(risk_contributions)
    return np.sum((risk_contributions - target_risk) ** 2)

# 5. 约束条件：权重之和为1
constraints = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1})
bounds = tuple((0.01, 1) for _ in range(len(tickers)))  # 最小权重1%

# 6. 优化
initial_weights = np.array([1/len(tickers)] * len(tickers))
result = minimize(risk_parity_objective, 
                  initial_weights, 
                  args=(cov_matrix,),
                  method='SLSQP',
                  bounds=bounds,
                  constraints=constraints)

risk_parity_weights = result.x

# 7. 输出结果
print("风险平价权重分配:")
for ticker, weight in zip(tickers, risk_parity_weights):
    print(f"  {ticker}: {weight:.2%}")

# 8. 计算风险贡献
portfolio_vol = np.sqrt(np.dot(risk_parity_weights.T, np.dot(cov_matrix, risk_parity_weights)))
risk_contributions = risk_parity_weights * (np.dot(cov_matrix, risk_parity_weights)) / portfolio_vol

print("\n风险贡献:")
for ticker, rc in zip(tickers, risk_contributions):
    print(f"  {ticker}: {rc:.2%}")

# HRP的简化示例（实际需要更复杂的聚类算法）
def hierarchical_risk_parity(returns):
    """层次风险平价"""
    # 1. 计算相关性矩阵
    corr = returns.corr()
    
    # 2. 层次聚类（这里简化为按相关性排序）
    # 实际中应使用如scipy的层次聚类
    sorted_assets = corr.mean().sort_values().index
    
    # 3. 递归分配权重
    def recursive_weights(assets):
        if len(assets) == 1:
            return {assets[0]: 1.0}
        
        # 将资产分为两组
        mid = len(assets) // 2
        group1 = assets[:mid]
        group2 = assets[mid:]
        
        # 计算两组的风险贡献
        # ...（简化，实际需要计算协方差）
        w1 = 0.5  # 简化：等权
        w2 = 0.5
        
        weights = {}
        for asset, w in recursive_weights(group1).items():
            weights[asset] = w * w1
        for asset, w in recursive_weights(group2).items():
            weights[asset] = w * w2
            
        return weights
    
    hrp_weights = recursive_weights(list(sorted_assets))
    return hrp_weights