量化投资 — 配对交易策略 （Pair Trading）

配对交易策略 Pair Trading

0. 引库

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

data = pd.read_csv('pair-trade-data.csv')
data.set_index('date',inplace = True)
data.head()

	000568	000858
date
2010/1/4	27.488118	26.117536
2010/1/5	27.335123	26.391583
2010/1/6	26.941707	25.694008
2010/1/7	26.388011	24.913389
2010/1/8	26.825140	24.863562

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

2. 策略开发思路

# 价差是回归的（不科学想法）
data['priceDelta'] = data['000568'] - data['000858']
data.head()

	000568	000858	priceDelta
date
2010/1/4	27.488118	26.117536	1.370582
2010/1/5	27.335123	26.391583	0.943540
2010/1/6	26.941707	25.694008	1.247699
2010/1/7	26.388011	24.913389	1.474622
2010/1/8	26.825140	24.863562	1.961578

# 图示价差及其均值
data['priceDelta'].plot(figsize=(8, 6));
plt.ylabel('Spread')
plt.axhline(data['priceDelta'].mean());

# 对价差进行标准化
data['zscore'] = (data['priceDelta'] - np.mean(data['priceDelta']))/np.std(data['priceDelta'])
data.head()

	000568	000858	priceDelta	zscore
date
2010/1/4	27.488118	26.117536	1.370582	0.569895
2010/1/5	27.335123	26.391583	0.943540	0.500520
2010/1/6	26.941707	25.694008	1.247699	0.549932
2010/1/7	26.388011	24.913389	1.474622	0.586796
2010/1/8	26.825140	24.863562	1.961578	0.665903

len(data[data['zscore'] > 1.5])

17

# 'position_1'是000568开平仓信号
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.head()

	000568	000858	priceDelta	zscore	position_1
date
2010/1/4	27.488118	26.117536	1.370582	0.569895	NaN
2010/1/5	27.335123	26.391583	0.943540	0.500520	NaN
2010/1/6	26.941707	25.694008	1.247699	0.549932	NaN
2010/1/7	26.388011	24.913389	1.474622	0.586796	NaN
2010/1/8	26.825140	24.863562	1.961578	0.665903	NaN

产生交易信号

data['position_1'] = data['position_1'].ffill().fillna(0)

data['position_1'].plot(ylim=[-1.1, 1.1], figsize=(10, 6));

# 'position_2'是000858开平仓信号（与000568符号相反）
data['position_2'] = -np.sign(data['position_1'])
data['position_2'].plot(ylim=[-1.1, 1.1], figsize=(10, 6));

3. 计算策略年化收益并可视化

data['returns_1'] = (np.log(data['000568'] / data['000568'].shift(1))).fillna(0)
data['returns_2'] = (np.log(data['000858'] / data['000858'].shift(1))).fillna(0)
data.head(10)

	000568	000858	priceDelta	zscore	position_1	position_2	returns_1	returns_2
date
2010/1/4	27.488118	26.117536	1.370582	0.569895	0.0	-0.0	0.000000	0.000000
2010/1/5	27.335123	26.391583	0.943540	0.500520	0.0	-0.0	-0.005581	0.010438
2010/1/6	26.941707	25.694008	1.247699	0.549932	0.0	-0.0	-0.014497	-0.026787
2010/1/7	26.388011	24.913389	1.474622	0.586796	0.0	-0.0	-0.020766	-0.030852
2010/1/8	26.825140	24.863562	1.961578	0.665903	0.0	-0.0	0.016430	-0.002002
2010/1/11	25.936311	24.631037	1.305274	0.559285	0.0	-0.0	-0.033696	-0.009396
2010/1/12	26.409867	25.336916	1.072951	0.521543	0.0	-0.0	0.018094	0.028255
2010/1/13	26.577433	25.137609	1.439824	0.581143	0.0	-0.0	0.006325	-0.007897
2010/1/14	28.420660	26.109231	2.311428	0.722738	0.0	-0.0	0.067054	0.037924
2010/1/15	28.253094	26.208885	2.044209	0.679327	0.0	-0.0	-0.005913	0.003810

data['strategy'] = 0.5*(data['position_1'].shift(1) * data['returns_1']) + 0.5*(data['position_2'].shift(1) * data['returns_2'])
# 计算累积收益率
data[['returns_1','returns_2','strategy']].dropna().cumsum().apply(np.exp).tail(1)

	returns_1	returns_2	strategy
date
2019/4/8	2.470158	3.837651	0.986754

# 可视化累积收益率
data[['returns_1','returns_2','strategy']].dropna().cumsum().apply(np.exp).plot(figsize=(10, 6));

Pair trading 策略 - 小范围时间（2013.6-2014.12）

data2 = pd.read_csv('pair-trade-data2.csv')
data2.set_index('date',inplace = True)
data2.head()

	000568	000858
date
2013/6/3	20.719056	20.343053
2013/6/4	20.357220	20.060867
2013/6/5	20.514540	20.274644
2013/6/6	20.113374	20.172031
2013/6/7	19.704342	19.667508

data2.plot(figsize=(8, 6));

# 价差是回归的（不科学想法）
data2['priceDelta'] = data['000568'] - data['000858']
data2.head()

	000568	000858	priceDelta
date
2013/6/3	20.719056	20.343053	0.376004
2013/6/4	20.357220	20.060867	0.296353
2013/6/5	20.514540	20.274644	0.239896
2013/6/6	20.113374	20.172031	-0.058657
2013/6/7	19.704342	19.667508	0.036833

# 图示价差及其均值
data2['priceDelta'].plot(figsize=(8, 6));
plt.ylabel('Spread')
plt.axhline(data2['priceDelta'].mean());

# 对价差进行标准化
data2['zscore'] = (data2['priceDelta'] - np.mean(data2['priceDelta']))/np.std(data2['priceDelta'])
data2.head()

	000568	000858	priceDelta	zscore
date
2013/6/3	20.719056	20.343053	0.376004	0.048513
2013/6/4	20.357220	20.060867	0.296353	0.000596
2013/6/5	20.514540	20.274644	0.239896	-0.033369
2013/6/6	20.113374	20.172031	-0.058657	-0.212979
2013/6/7	19.704342	19.667508	0.036833	-0.155532

len(data2[data2['zscore'] > 1.5])

40

len(data2[data2['zscore'] < -1.5])

16

# 'position_1'是000568开平仓信号
data2['position_1'] = np.where(data2['zscore'] > 1.5, -1, np.nan)
data2['position_1'] = np.where(data2['zscore'] < -1.5, 1, data2['position_1'])
data2['position_1'] = np.where(abs(data2['zscore']) < 0.5, 0, data2['position_1'])

data2.head()

	000568	000858	priceDelta	zscore	position_1
date
2013/6/3	20.719056	20.343053	0.376004	0.048513	0.0
2013/6/4	20.357220	20.060867	0.296353	0.000596	0.0
2013/6/5	20.514540	20.274644	0.239896	-0.033369	0.0
2013/6/6	20.113374	20.172031	-0.058657	-0.212979	0.0
2013/6/7	19.704342	19.667508	0.036833	-0.155532	0.0

data2['position_1'] = data2['position_1'].ffill().fillna(0)
data2['position_1'].plot(ylim=[-1.1, 1.1], figsize=(10, 6));

# 'position_2'是000858开平仓信号（与000568符号相反）
data2['position_2'] = -np.sign(data2['position_1'])
data2['position_2'].plot(ylim=[-1.1, 1.1], figsize=(10, 6));

data2['returns_1'] = (np.log(data2['000568'] / data2['000568'].shift(1))).fillna(0)
data2['returns_2'] = (np.log(data2['000858'] / data2['000858'].shift(1))).fillna(0)
data2.head(10)

	000568	000858	priceDelta	zscore	position_1	position_2	returns_1	returns_2
date
2013/6/3	20.719056	20.343053	0.376004	0.048513	0.0	-0.0	0.000000	0.000000
2013/6/4	20.357220	20.060867	0.296353	0.000596	0.0	-0.0	-0.017618	-0.013968
2013/6/5	20.514540	20.274644	0.239896	-0.033369	0.0	-0.0	0.007698	0.010600
2013/6/6	20.113374	20.172031	-0.058657	-0.212979	0.0	-0.0	-0.019749	-0.005074
2013/6/7	19.704342	19.667508	0.036833	-0.155532	0.0	-0.0	-0.020546	-0.025329
2013/6/13	19.562754	19.012515	0.550239	0.153334	0.0	-0.0	-0.007212	-0.033871
2013/6/14	19.617816	19.012515	0.605301	0.186459	0.0	-0.0	0.002811	0.000000
2013/6/17	19.255979	18.720423	0.535556	0.144501	0.0	-0.0	-0.018616	-0.015482
2013/6/18	19.405434	18.853192	0.552241	0.154539	0.0	-0.0	0.007731	0.007067
2013/6/19	19.956054	19.269202	0.686852	0.235521	0.0	-0.0	0.027979	0.021826

data2['strategy'] = 0.5*(data2['position_1'].shift(1) * data2['returns_1']) + 0.5*(data2['position_2'].shift(1) * data2['returns_2'])
# 计算累积收益率
data2[['returns_1','returns_2','strategy']].dropna().cumsum().apply(np.exp).tail(1)

	returns_1	returns_2	strategy
date
2014/12/31	0.892955	0.97347	1.12623

# 可视化累积收益率
data2[['returns_1','returns_2','strategy']].dropna().cumsum().apply(np.exp).plot(figsize=(10, 6));

# 计算年化收益率
data2[['returns_1','returns_2','strategy']].dropna().mean() * 252

returns_1   -0.073915
returns_2   -0.017554
strategy     0.077608
dtype: float64

# 计算年化风险
data2[['returns_1','returns_2','strategy']].dropna().std() * 252 ** 0.5

returns_1    0.300306
returns_2    0.280425
strategy     0.057016
dtype: float64

# 策略累积收益率
data2['cumret'] = data2['strategy'].dropna().cumsum().apply(np.exp)
# 策略累积最大值
data2['cummax'] = data2['cumret'].cummax()
# 算回撤序列
drawdown = (data2['cummax'] - data2['cumret'])
# 算最大回撤
drawdown.max()

0.03645280148896235

Pair trading 策略 - 考虑时间序列平稳性

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

1. 数据准备

data3 = pd.read_csv('pair-trade-data2.csv')
data3.set_index('date',inplace = True)
data3.head()

	000568	000858
date
2013/6/3	20.719056	20.343053
2013/6/4	20.357220	20.060867
2013/6/5	20.514540	20.274644
2013/6/6	20.113374	20.172031
2013/6/7	19.704342	19.667508

data3.plot(figsize=(8,6));

2. 策略开发思路

data3.corr()  # 协方差矩阵

	000568	000858
000568	1.000000	0.552409
000858	0.552409	1.000000

# 可视化看相关关系
plt.figure(figsize =(10,8))
plt.title('Stock Correlation')
plt.plot(data['000568'], data['000858'], '.');
plt.xlabel('000568')
plt.ylabel('000858')
data.dropna(inplace = True)

# 对两股票价格做线性回归（白噪声项符合正态分布）
[slope, intercept] = np.polyfit(data3.iloc[:,0], data3.iloc[:,1], 1).round(2)      
slope,intercept 

(0.51, 7.82)

data3['spread'] = data3.iloc[:,1] - (data3.iloc[:,0]*slope + intercept)
data3.head()

	000568	000858	spread
date
2013/6/3	20.719056	20.343053	1.956334
2013/6/4	20.357220	20.060867	1.858684
2013/6/5	20.514540	20.274644	1.992228
2013/6/6	20.113374	20.172031	2.094210
2013/6/7	19.704342	19.667508	1.798294

data3['spread'].plot(figsize = (10,8),title = 'Price Spread');

data3['zscore'] = (data3['spread'] - data3['spread'].mean())/data3['spread'].std()
data3.head()

	000568	000858	spread	zscore
date
2013/6/3	20.719056	20.343053	1.956334	1.452385
2013/6/4	20.357220	20.060867	1.858684	1.382488
2013/6/5	20.514540	20.274644	1.992228	1.478078
2013/6/6	20.113374	20.172031	2.094210	1.551075
2013/6/7	19.704342	19.667508	1.798294	1.339261

data3['zscore'].plot(figsize = (10,8),title = 'Z-score')
plt.axhline(1.5)
plt.axhline(0)
plt.axhline(-1.5)

产生交易信号

data3['position_1'] = np.where(data3['zscore'] > 1.5, 1, np.nan)
data3['position_1'] = np.where(data3['zscore'] < -1.5, -1, data3['position_1'])
data3['position_1'] = np.where(abs(data3['zscore']) < 0.5, 0, data3['position_1'])

data3['position_1'] = data3['position_1'].ffill().fillna(0)
data3['position_1'].plot(ylim=[-1.1, 1.1], figsize=(10, 6),title = 'Trading Signal_Uptrade');

data3['position_2'] = -np.sign(data3['position_1'])

data3['position_2'].plot(ylim=[-1.1, 1.1], figsize=(10, 6),title = 'Trading Signal_Downtrade');

3. 计算策略年化收益并可视化

data3['returns_1'] = np.log(data3['000568'] / data3['000568'].shift(1))
data3['returns_2'] = np.log(data3['000858'] / data3['000858'].shift(1))
data3['strategy'] = 0.5*(data3['position_1'].shift(1) * data3['returns_1']) + 0.5*(data3['position_2'].shift(1) * data3['returns_2'])

# 计算累积收益率
data3[['returns_1','returns_2','strategy']].dropna().cumsum().apply(np.exp).tail(1)

	returns_1	returns_2	strategy
date
2014/12/31	0.892955	0.97347	1.174494

data3[['returns_1','returns_2','strategy']].dropna().cumsum().apply(np.exp).plot(figsize=(10, 8),title = 'Strategy_Backtesting');

# 计算年化收益率
data3[['returns_1','returns_2','strategy']].dropna().mean() * 252

returns_1   -0.073915
returns_2   -0.017554
strategy     0.105002
dtype: float64

# 计算年化风险
data3[['returns_1','returns_2','strategy']].dropna().std() * 252 ** 0.5

returns_1    0.300306
returns_2    0.280425
strategy     0.068639
dtype: float64

# 策略累积收益率
data3['cumret'] = data3['strategy'].dropna().cumsum().apply(np.exp)
# 策略累积最大值
data3['cummax'] = data3['cumret'].cummax()
# 算回撤序列
drawdown = (data3['cummax'] - data3['cumret'])
# 算最大回撤
drawdown.max()

0.038159777097367176

策略的思考

1. 对多只ETF进行配对交易，是很多实盘量化基金的交易策略；

策略的风险和问题：

1. Spread不回归的风险，当市场结构发生重大改变时，用过去历史回归出来的Spread会发生不回归的重大风险；

2. 中国市场做空受到限制，策略中有部分做空的收益是无法获得的；

3. 回归系数需要Rebalancing；

4. 策略没有考虑交易成本和其他成本；