风险平价策略在中国市场的实证：从理论到实践

import numpy as np
from scipy.optimize import minimize

def risk_parity_weights(returns, risk_target='vol', max_leverage=1.0):
    """
    计算风险平价权重
    
    Parameters:
    -----------
    returns : DataFrame
        各资产的收益率序列
    risk_target : str
        风险目标：'vol'（波动率）或 'corr'（相关性）
    max_leverage : float
        最大杠杆倍数
    
    Returns:
    --------
    weights : array
        风险平价权重
    """
    cov_matrix = returns.cov() * 252  # 年化协方差矩阵
    n_assets = returns.shape[1]
    
    def risk_contribution(weights):
        """计算各资产的风险贡献"""
        portfolio_vol = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
        marginal_risk = np.dot(cov_matrix, weights) / portfolio_vol
        risk_contrib = weights * marginal_risk / portfolio_vol
        return risk_contrib
    
    def objective(weights):
        """目标函数：最小化风险贡献的方差"""
        rc = risk_contribution(weights)
        return np.sum((rc - rc.mean()) ** 2)
    
    # 约束条件
    constraints = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1.0})
    bounds = tuple((0, max_leverage) for _ in range(n_assets))
    
    # 初始权重：等风险贡献
    init_weights = np.ones(n_assets) / n_assets
    
    # 优化
    result = minimize(objective, init_weights, method='SLSQP', 
                     bounds=bounds, constraints=constraints)
    
    return result.x

def ewma_covariance(returns, lambda=0.94):
    """
    指数加权移动平均协方差矩阵
    
    Parameters:
    -----------
    returns : DataFrame
        收益率序列
    lambda : float
        衰减因子（0.94对应约30天半衰期）
    
    Returns:
    --------
    cov_matrix : DataFrame
        时变协方差矩阵（最新一期）
    """
    n_observations, n_assets = returns.shape
    
    # 标准化收益率
    standardized_returns = (returns - returns.mean()) / returns.std()
    
    # 初始化协方差矩阵
    cov_matrix = np.eye(n_assets)
    
    # 递归更新
    for t in range(1, n_observations):
        weighted_returns = standardized_returns.iloc[t].values
        cov_matrix = lambda * cov_matrix + (1 - lambda) * np.outer(weighted_returns, weighted_returns)
    
    # 缩放回实际波动率
    actual_vol = returns.std() * np.sqrt(252)
    cov_matrix = cov_matrix * np.outer(actual_vol, actual_vol)
    
    return pd.DataFrame(cov_matrix, index=returns.columns, columns=returns.columns)

def leveraged_risk_parity(weights, leverage=1.5, funding_cost=0.03):
    """
    带杠杆的风险平价
    
    Parameters:
    -----------
    weights : array
        无杠杆风险平价权重
    leverage : float
        杠杆倍数（1.5表示50%杠杆）
    funding_cost : float
        融资成本（年化）
    
    Returns:
    --------
    leveraged_weights : array
        加杠杆后的权重
    expected_return : float
        期望收益率（扣除融资成本后）
    """
    # 加杠杆
    leveraged_weights = weights * leverage
    
    # 剩余资金投资于现金（或无风险资产）
    cash_weight = 1 - leverage
    
    # 计算期望收益（简化模型）
    asset_expected_return = 0.08  # 假设资产期望收益8%
    expected_return = leverage * asset_expected_return + cash_weight * funding_cost
    
    return leveraged_weights, expected_return