ETF50 & ETF500 Pair trading 策略

Pair trading 策略

ETF50 & ETF500 小demo

import pandas as pd
import numpy as np
import tushare as ts
import seaborn
from matplotlib import pyplot as plt
plt.style.use('seaborn')
%matplotlib inline
stocks_pair = ['50ETF', '500ETF']

1. 數據準備

# 加載數據
data1 = ts.get_k_data('510050', start='2018-04-01', end='2019-04-01')[['date','close']]
data2 = ts.get_k_data('510500', start='2018-04-01', end='2019-04-01')['close']
# 按行拼接收盤價
data = pd.concat([data1, data2], axis=1)
data.set_index('date',inplace = True)
# 重命名列（'50ETF'、'500ETF'）
data.columns = stocks_pair
data.head()

	50ETF	500ETF
date
2018-04-02	2.702	6.424
2018-04-03	2.693	6.373
2018-04-04	2.694	6.321
2018-04-09	2.711	6.331
2018-04-10	2.775	6.380

畫圖

data.plot(figsize= (8,6));

2. 策略開發思路

data.corr()  # 協方差矩陣

	50ETF	500ETF
50ETF	1.000000	0.800654
500ETF	0.800654	1.000000

# 數據可視化，看相關關係
plt.figure(figsize =(8,6))
plt.title('Stock Correlation')
plt.plot(data['50ETF'], data['500ETF'], '.');
plt.xlabel('50ETF')
plt.ylabel('500ETF')
data.dropna(inplace = True)

# 對兩股票價格做線性迴歸（白噪聲項符合正態分佈）
[slope, intercept] = np.polyfit(data.iloc[:,0], data.iloc[:,1], 1).round(2)      
slope,intercept

(3.75, -4.27)

(y+4.27-3.75x) 符合Stationary

# 算出 (y+4.27-3.75x) 一列
data['spread'] = data.iloc[:,1] - (data.iloc[:,0]*slope + intercept)
data.head()

	50ETF	500ETF	spread
date
2018-04-02	2.702	6.424	0.56150
2018-04-03	2.693	6.373	0.54425
2018-04-04	2.694	6.321	0.48850
2018-04-09	2.711	6.331	0.43475
2018-04-10	2.775	6.380	0.24375

data['spread'].plot(figsize = (8,6),title = 'Price Spread');

# 對 spread 進行標準化
data['zscore'] = (data['spread'] - data['spread'].mean())/data['spread'].std()
data.head()

	50ETF	500ETF	spread	zscore
date
2018-04-02	2.702	6.424	0.56150	1.523889
2018-04-03	2.693	6.373	0.54425	1.477487
2018-04-04	2.694	6.321	0.48850	1.327522
2018-04-09	2.711	6.331	0.43475	1.182938
2018-04-10	2.775	6.380	0.24375	0.669158

# 可視化標準化後的值
data['zscore'].plot(figsize = (10,8),title = 'Z-score');
plt.axhline(1.5)
plt.axhline(0)
plt.axhline(-1.5)

<matplotlib.lines.Line2D at 0x2e8d8383c8>

產生交易信號

data['position_1'] = np.where(data['zscore'] > 1.5, 1, np.nan)
data['position_1'] = np.where(data['zscore'] < -1.5, -1, data['position_1'])
data['position_1'] = np.where(abs(data['zscore']) < 0.5, 0, data['position_1'])

data['position_1'] = data['position_1'].fillna(method = 'ffill')
data['position_1'].plot(ylim=[-1.1, 1.1], figsize=(10, 6),title = 'Trading Signal_Uptrade');

data['position_2'] = -np.sign(data['position_1'])
data['position_2'].plot(ylim=[-1.1, 1.1], figsize=(10, 6),title = 'Trading Signal_Downtrade');

3. 計算策略年化收益並可視化

# 算離散收益率
data['returns_1'] = np.log(data['50ETF'] / data['50ETF'].shift(1))
data['returns_2'] = np.log(data['500ETF'] / data['500ETF'].shift(1))

# 算策略列
data['strategy'] = 0.5*(data['position_1'].shift(1) * data['returns_1']) + 0.5*(data['position_2'].shift(1) * data['returns_2'])
# 計算累積收益率
data[['returns_1','returns_2','strategy']].dropna().cumsum().apply(np.exp).tail(1)

	returns_1	returns_2	strategy
date
2019-04-01	1.063657	0.96155	1.114828

# 畫出累積收益率
data[['returns_1','returns_2','strategy']].dropna().cumsum().apply(np.exp).plot(figsize=(10, 8),title = 'Strategy_Backtesting');

# 計算年化收益率
data[['returns_1','returns_2','strategy']].dropna().mean() * 252

returns_1    0.064263
returns_2   -0.040828
strategy     0.113192
dtype: float64

# 計算年化風險
data[['returns_1','returns_2','strategy']].dropna().std() * 252 ** 0.5

returns_1    0.236365
returns_2    0.264628
strategy     0.057670
dtype: float64

# 策略累積收益率
data['cumret'] = data['strategy'].dropna().cumsum().apply(np.exp)
# 策略累積最大值
data['cummax'] = data['cumret'].cummax()
# 算回撤序列
drawdown = (data['cummax'] - data['cumret'])
# 算最大回撤
drawdown.max()

0.053458095761447444

小結

策略的思考

1. 對多隻ETF進行配對交易，是很多實盤量化基金的交易策略；

策略的風險和問題：

1. Spread不迴歸的風險，當市場結構發生重大改變時，用過去歷史迴歸出來的Spread會發生不迴歸的重大風險；

2. 中國市場做空受到限制，策略中有部分做空的收益是無法獲得的；

3. 迴歸係數需要Rebalancing；

4. 策略沒有考慮交易成本和其他成本；