第56讲：案例·ETF比较 (Case Study: Comparing ETFs)

# 获取2018-2020年历史数据
def fetch_comparison_data():
    tickers = ['XLK', 'XLF']
    data = yf.download(tickers, start='2018-01-01', end='2020-01-01')
    return data['Close'].dropna()  # 确保数据清洁

etf_close = fetch_comparison_data()

# 计算收益率
returns = etf_close.pct_change().dropna()
xlk_returns = returns['XLK']
xlf_returns = returns['XLF']

print("XLK收益特征:")
print(xlk_returns.describe())
print("\nXLF收益特征:")
print(xlf_returns.describe())

risk_free_rate = 0.0002  # 假设无风险利率

def sharpe_ratio(returns):
    excess_return = returns.mean() - risk_free_rate
    return excess_return / returns.std()

print(f"XLK夏普比率: {sharpe_ratio(xlk_returns):.4f}")
print(f"XLF夏普比率: {sharpe_ratio(xlf_returns):.4f}")

(etf_close / etf_close.iloc0 * 100).plot(figsize=(10,6))
plt.title('ETF价格走势标准化比较')
plt.ylabel('标准化价格（基准=100）')
plt.show()

def enhanced_normality_check(data, name):
    plt.figure(figsize=(8,4))
    stats.probplot(data, plot=plt)
    plt.title(f'{name} Q-Q图')
    plt.show()

    k2, p = stats.normaltest(data)
    print(f'{name}正态检验: p值={p:.4f}')

enhanced_normality_check(xlk_returns, 'XLK')
enhanced_normality_check(xlf_returns, 'XLF')

# 根据正态性结果选择检验方法
if stats.normaltest(xlk_returns).pvalue > 0.05 and stats.normaltest(xlf_returns).pvalue > 0.05:
    test_method = 'F-test'
    _, p_var = stats.f_oneway(xlk_returns, xlf_returns)
else:
    test_method = 'Levene'
    _, p_var = stats.levene(xlk_returns, xlf_returns)

print(f'使用{test_method}检验方差齐性: p值={p_var:.4f}')

t_stat, p_mean = stats.ttest_ind(xlk_returns, xlf_returns, equal_var=(p_var > 0.05))
print(f'均值差异检验结果: t统计量={t_stat:.2f}, p值={p_mean:.4f}')

sns.jointplot(x=xlk_returns, y=xlf_returns, kind='hex')
plt.suptitle('XLK与XLF收益联合分布')
plt.tight_layout()

window_size = 20  # 交易日窗口

plt.figure(figsize=(10,6))
xlk_returns.rolling(window_size).std().plot(label='XLK波动率')
xlf_returns.rolling(window_size).std().plot(label='XLF波动率')
plt.title('滚动20日波动率对比')
plt.legend()

def analyze_tail_risk(returns, name):
    tail_threshold = returns.quantile(0.95)
    tail_events = returns[returns > tail_threshold]
    print(f'{name}极端收益特征:')
    print(f'发生次数: {len(tail_events)}')
    print(f'平均收益: {tail_events.mean():.4f}')
    print(f'最大收益: {tail_events.max():.4f}\n')

analyze_tail_risk(xlk_returns, 'XLK')
analyze_tail_risk(xlf_returns, 'XLF')

correlation = xlk_returns.corr(xlf_returns)
print(f'收益相关系数: {correlation:.4f}')

plt.figure(figsize=(8,6))
sns.regplot(x=xlk_returns, y=xlf_returns, line_kws={'color':'red'})
plt.title('收益率散点图与回归线')

# 综合对比可视化
fig, ax = plt.subplots(2,2, figsize=(14,10))

# 收益分布对比
sns.kdeplot(xlk_returns, ax=ax[0,0], fill=True, label='XLK')
sns.kdeplot(xlf_returns, ax=ax[0,0], fill=True, label='XLF')
ax[0,0].set_title('收益分布对比')

# 累计收益对比
(etf_close/etf_close.iloc[0]).plot(ax=ax[0,1])
ax[0,1].set_title('累计收益走势')

# 波动率对比
pd.DataFrame({'XLK': xlk_returns.rolling(20).std(),
              'XLF': xlf_returns.rolling(20).std()}).plot(ax=ax[1,0])
ax[1,0].set_title('滚动波动率')

# 相关性热力图
sns.heatmap(returns.corr(), annot=True, ax=ax[1,1])
ax[1,1].set_title('收益相关性矩阵')

plt.tight_layout()