第40讲：为什么要对贝塔和行业暴露进行对冲 I(Why Hedge Beta and Sector Exposures I)

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import yfinance as yf
from sklearn.covariance import LedoitWolf
import seaborn as sns
import statsmodels.api as sm

# 数据获取函数
def get_stock_data(tickers, start, end):
    data = yf.download(tickers, start=start, end=end)
    return data['Close']  # 仅使用收盘价

tickers = ['WFC', 'JPM', 'USB', 'XOM', 'BHI', 'SLB']
start = '2015-01-01'
end = '2017-02-22'

# 获取数据
prices = get_stock_data(tickers, start, end)
returns = prices.pct_change().dropna()

# 计算协方差矩阵
lw = LedoitWolf().fit(returns)
cov_matrix = lw.covariance_

# 转换为相关系数
def cov_to_corr(cov):
    d = np.sqrt(np.diag(cov))
    return cov / np.outer(d, d)

corr_matrix = cov_to_corr(cov_matrix)

# 可视化
plt.figure(figsize=(12,6))
sns.heatmap(corr_matrix, annot=True, cmap='coolwarm',
            xticklabels=tickers, yticklabels=tickers)
plt.title('无对冲策略相关系数矩阵（平均相关系数：0.56）')

tickers += ['SPY']
prices = get_stock_data(tickers, start, end)
returns = prices.pct_change().dropna()

# 分离市场收益
market_returns = returns['SPY']
stock_returns = returns.drop('SPY', axis=1)

# 计算市场Beta残差
residuals = pd.DataFrame()
for stock in stock_returns:
    model = sm.OLS(stock_returns[stock], sm.add_constant(market_returns))
    results = model.fit()
    residuals[stock] = results.resid

# 计算对冲后相关系数
lw = LedoitWolf().fit(residuals)
corr_matrix_beta = cov_to_corr(lw.covariance_)

# 可视化对比
fig, axes = plt.subplots(1,2, figsize=(16,6))
sns.heatmap(corr_matrix, ax=axes[0], cmap='coolwarm',
           annot=True, vmin=-1, vmax=1)
sns.heatmap(corr_matrix_beta, ax=axes[1], cmap='coolwarm',
           annot=True, vmin=-1, vmax=1)

sector_etf = {'金融': 'XLF', '能源': 'XLE'}
tickers = ['WFC', 'JPM', 'USB', 'XOM', 'BHI', 'SLB', 'SPY', 'XLF', 'XLE']

prices = get_stock_data(tickers, start, end)
returns = prices.pct_change().dropna()

# 市场对冲
market_ret = returns['SPY']
sector_rets = {
    '金融': returns['XLF'] - market_ret * sm.OLS(returns['XLF'], sm.add_constant(market_ret)).fit().params[1],
    '能源': returns['XLE'] - market_ret * sm.OLS(returns['XLE'], sm.add_constant(market_ret)).fit().params[1]
}

# 分行业二次对冲
final_residuals = pd.DataFrame()
for sector in ['金融', '能源']:
    sector_stocks = ['WFC','JPM','USB'] if sector == '金融' else ['XOM','BHI','SLB']
    sector_ret = sector_rets[sector]

    for stock in sector_stocks:
        # 市场对冲
        model_mkt = sm.OLS(returns[stock], sm.add_constant(market_ret))
        res_mkt = model_mkt.fit().resid

        # 行业对冲
        model_sector = sm.OLS(res_mkt, sm.add_constant(sector_ret))
        final_residuals[stock] = model_sector.fit().resid

# 计算最终相关系数
lw = LedoitWolf().fit(final_residuals)
corr_matrix_full_hedge = cov_to_corr(lw.covariance_)

def effective_breadth(N, rho):
    return N / (1 + rho*(N-1))

cases = [
    ('无对冲', 0.56),
    ('Beta对冲', 0.22),
    ('行业对冲', 0.028)
]

plt.figure(figsize=(10,6))
x = np.linspace(0, 1, 100)
for label, rho in cases:
    plt.plot(x, effective_breadth(6, x),
             label=f'{label} (实际ρ={rho})' if label else None)
plt.legend()
plt.title('不同对冲策略的有效广度对比')
plt.xlabel('平均相关系数ρ')
plt.ylabel('有效广度BR');

# 练习参考答案
# 1. 更换行业ETF代码为XLK（科技）和XLV（医疗）
# 2. 验证函数：
assert np.isclose(effective_breadth(10, 0), 10)
# 3. 苹果微软对冲分析：
tickers = ['AAPL', 'MSFT', 'SPY', 'XLK']
# ...重复上述对冲步骤...