Black-Litterman模型实战：融合市场均衡与投资者观点的资产配置

# 假设市场权重（实际应用中应从指数成分股权重获取）
market_caps = {
    'SPY': 40,   # 40%
    'EFA': 20,   # 20%
    'EEM': 15,   # 15%
    'AGG': 15,   # 15%
    'GSG': 5,    # 5%
    'VNQ': 5,    # 5%
}

w_mkt = np.array([market_caps[t] / 100 for t in tickers])

# 风险厌恶系数（通常取2.5-3）
risk_aversion = 2.5

# 逆向优化：计算隐含预期收益率
pi = risk_aversion * cov_matrix.values @ w_mkt

# 示例观点：
# 1. 美股（SPY）未来一年将上涨12%（绝对观点）
# 2. 新兴市场（EEM）将跑赢发达市场（EFA）5%（相对观点）

# 观点矩阵 P (K×N)
P = np.zeros((2, len(tickers)))
P[0, 0] = 1  # 观点1：SPY绝对收益
P[1, 2] = 1  # 观点2：EEM
P[1, 1] = -1 #       减去EFA

# 观点收益向量 Q (K×1)
Q = np.array([0.12, 0.05])

# 观点不确定性矩阵 Ω (K×K)
# 对角线元素表示观点的置信度（越小越自信）
tau = 0.05
omega = np.diag([0.1**2, 0.15**2])  # 观点1不确定性10%，观点2不确定性15%

def portfolio_vol(weights, cov_matrix):
    """计算组合波动率"""
    return np.sqrt(weights.T @ cov_matrix @ weights)

def optimize_portfolio(expected_ret, cov_matrix, risk_aversion=2.5):
    """
    均值方差优化
    """
    n_assets = len(expected_ret)
    
    # 目标函数：最大化效用 = 预期收益 - 0.5 * 风险厌恶 * 方差
    def utility(weights):
        port_ret = expected_ret @ weights
        port_vol = portfolio_vol(weights, cov_matrix)
        return -(port_ret - 0.5 * risk_aversion * port_vol**2)
    
    # 约束条件
    constraints = [
        {'type': 'eq', 'fun': lambda x: np.sum(x) - 1},  # 权重和为1
    ]
    bounds = [(0, 1) for _ in range(n_assets)]  # 不允许卖空
    
    # 优化
    result = minimize(
        utility,
        x0=np.ones(n_assets) / n_assets,
        method='SLSQP',
        bounds=bounds,
        constraints=constraints
    )
    
    return result.x

# 优化组合
optimal_weights = optimize_portfolio(posterior_ret, posterior_cov, risk_aversion)

print("优化后权重：")
for ticker, weight in zip(tickers, optimal_weights):
    print(f"{ticker}: {weight:.2%}")

import numpy as np
import pandas as pd
from scipy.optimize import minimize

# 1. 数据准备（假设已有收益率数据）
tickers = ['HS300', 'ZZ500', 'CYB', 'Bond']
returns = load_returns_data()  # 自定义函数
cov_matrix = returns.cov() * 252

# 2. 市场权重（市值加权）
market_caps = {'HS300': 50, 'ZZ500': 25, 'CYB': 15, 'Bond': 10}
w_mkt = np.array([market_caps[t] / 100 for t in tickers])

# 3. 逆向优化
risk_aversion = 2.5
pi = risk_aversion * cov_matrix.values @ w_mkt

# 4. 定义观点
P = np.array([
    [1, 0, 0, 0],        # 观点1：HS300绝对收益
    [-1, 1, 0, 0],       # 观点2：ZZ500 - HS300
    [-1, 0, 1, 0],       # 观点3：CYB - HS300
])

Q = np.array([0.15, 0.08, 0.12])

# 观点不确定性
tau = 0.05
omega = np.diag([0.05**2, 0.08**2, 0.10**2])  # 观点1最自信

# 5. 计算后验
tau_sigma = tau * cov_matrix.values
M_inv = np.linalg.inv(tau_sigma) + P.T @ np.linalg.inv(omega) @ P
M = np.linalg.inv(M_inv)

posterior_ret = M @ (np.linalg.inv(tau_sigma) @ pi + P.T @ np.linalg.inv(omega) @ Q)
posterior_cov = cov_matrix.values + M

# 6. 优化
optimal_weights = optimize_portfolio(posterior_ret, posterior_cov, risk_aversion)

print("=== Black-Litterman配置结果 ===")
for ticker, weight in zip(tickers, optimal_weights):
    print(f"{ticker}: {weight:.2%}")

# 对比：传统均值方差优化（使用历史收益率）
historical_mean = returns.mean() * 252
traditional_weights = optimize_portfolio(historical_mean.values, cov_matrix.values, risk_aversion)

print("\n=== 传统均值方差优化（对比）===")
for ticker, weight in zip(tickers, traditional_weights):
    print(f"{ticker}: {weight:.2%}")