量化投資 — 移動平均及雙均線策略

SMA — 移動平均及雙均線模型

0. 引庫

%matplotlib inline
import matplotlib.pyplot as plt
import seaborn
plt.style.use('seaborn')        
import matplotlib as mpl
mpl.rcParams['font.family'] = 'serif'               # 解決一些字體顯示亂碼問題
import warnings; warnings.simplefilter('ignore')    # 忽略警告信息

import numpy as np
import pandas as pd
import tushare as ts

1. 前導知識備習

# 採用 Tushare API 獲取中信證券 600030 數據
data = ts.get_k_data('600030', start = '2010-01-01', end='2017-06-30') 

data.head()    #DataFrame數據結構

	date	open	close	high	low	volume	code
0	2010-01-04	17.016	16.639	17.176	16.612	1106207.58	600030
1	2010-01-05	16.777	17.452	17.601	16.383	2093915.41	600030
2	2010-01-06	17.548	17.250	17.628	17.229	1437889.30	600030
3	2010-01-07	17.239	16.830	17.484	16.697	1235592.34	600030
4	2010-01-08	16.718	17.154	17.208	16.644	1040929.92	600030

data.set_index('date', inplace = True)   #設置索引；替換，真實覆蓋；

data.head()

	open	close	high	low	volume	code
date
2010-01-04	17.016	16.639	17.176	16.612	1106207.58	600030
2010-01-05	16.777	17.452	17.601	16.383	2093915.41	600030
2010-01-06	17.548	17.250	17.628	17.229	1437889.30	600030
2010-01-07	17.239	16.830	17.484	16.697	1235592.34	600030
2010-01-08	16.718	17.154	17.208	16.644	1040929.92	600030

data['SMA_20'] = data['close'].rolling(20).mean()
data['SMA_60'] = data['close'].rolling(60).mean()

data.tail()

	open	close	high	low	volume	code	SMA_20	SMA_60
date
2017-06-26	16.186	16.492	16.635	16.148	2113195.0	600030	15.79700	15.467750
2017-06-27	16.482	16.349	16.511	16.301	924024.0	600030	15.83140	15.482400
2017-06-28	16.320	16.330	16.502	16.253	871050.0	600030	15.86245	15.497533
2017-06-29	16.320	16.330	16.425	16.224	668341.0	600030	15.89685	15.513783
2017-06-30	16.263	16.263	16.349	16.072	751091.0	600030	15.92745	15.528283

# 可視化
data[['close','SMA_20','SMA_60']].plot(figsize = (10,6))    

#計算股票連續收益率 returns
data['returns'] = np.log(data['close'] / data['close'].shift(1))
# 算股票離散收益率方法1
data['returns_dis'] = data['close']/data['close'].shift(1) - 1
# 算股票連續收益率方法2
data['return_dis2'] = data['close'].pct_change()

data.head()

	open	close	high	low	volume	code	SMA_20	SMA_60	returns	returns_dis	return_dis2
date
2010-01-04	17.016	16.639	17.176	16.612	1106207.58	600030	NaN	NaN	NaN	NaN	NaN
2010-01-05	16.777	17.452	17.601	16.383	2093915.41	600030	NaN	NaN	0.047705	0.048861	0.048861
2010-01-06	17.548	17.250	17.628	17.229	1437889.30	600030	NaN	NaN	-0.011642	-0.011575	-0.011575
2010-01-07	17.239	16.830	17.484	16.697	1235592.34	600030	NaN	NaN	-0.024649	-0.024348	-0.024348
2010-01-08	16.718	17.154	17.208	16.644	1040929.92	600030	NaN	NaN	0.019068	0.019251	0.019251

# 核心判斷語句（用於依策略確定決策符號）
data['position'] = np.where(data['SMA_20'] > data['SMA_60'], 1, -1)
# 可視化計算的累計收益率
data['returns'].cumsum().apply(np.exp).plot(figsize=(10, 6));     

SMA策略

1. 數據準備 & 回測準備

import numpy as np
import pandas as pd
import tushare as ts

# 推薦改用 Tushare新的數據獲取接口，不然數據獲取有bug；
data = ts.get_k_data('hs300', start = '2010-01-01', end='2017-06-30')
# 把 data轉換成爲 DataFrame格式
data = pd.DataFrame(data) 

data.head()

	date	open	close	high	low	volume	code
0	2010-01-04	3592.468	3535.229	3597.75	3535.23	66101080.0	hs300
1	2010-01-05	3545.186	3564.038	3577.53	3497.66	85809641.0	hs300
2	2010-01-06	3558.700	3541.727	3588.83	3541.17	78473125.0	hs300
3	2010-01-07	3543.160	3471.456	3558.56	3452.77	80350037.0	hs300
4	2010-01-08	3456.908	3480.130	3482.08	3426.70	60790253.0	hs300

# 用字典對列改名
data.rename(columns={'close': 'price'}, inplace=True)
data.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 1819 entries, 0 to 1818
Data columns (total 7 columns):
date      1819 non-null object
open      1819 non-null float64
price     1819 non-null float64
high      1819 non-null float64
low       1819 non-null float64
volume    1819 non-null float64
code      1819 non-null object
dtypes: float64(5), object(2)
memory usage: 113.7+ KB

data.head()

	date	open	price	high	low	volume	code
0	2010-01-04	3592.468	3535.229	3597.75	3535.23	66101080.0	hs300
1	2010-01-05	3545.186	3564.038	3577.53	3497.66	85809641.0	hs300
2	2010-01-06	3558.700	3541.727	3588.83	3541.17	78473125.0	hs300
3	2010-01-07	3543.160	3471.456	3558.56	3452.77	80350037.0	hs300
4	2010-01-08	3456.908	3480.130	3482.08	3426.70	60790253.0	hs300

# 設置date項爲列，inplace=True進行覆蓋操作
data.set_index('date', inplace = True)

data.head()

	open	price	high	low	volume	code
date
2010-01-04	3592.468	3535.229	3597.75	3535.23	66101080.0	hs300
2010-01-05	3545.186	3564.038	3577.53	3497.66	85809641.0	hs300
2010-01-06	3558.700	3541.727	3588.83	3541.17	78473125.0	hs300
2010-01-07	3543.160	3471.456	3558.56	3452.77	80350037.0	hs300
2010-01-08	3456.908	3480.130	3482.08	3426.70	60790253.0	hs300

data['SMA_10'] = data['price'].rolling(10).mean()
data['SMA_60'] = data['price'].rolling(60).mean()

data.tail()

	open	price	high	low	volume	code	SMA_10	SMA_60
date
2017-06-26	3627.02	3668.09	3671.94	3627.02	134637995.0	hs300	3573.455	3475.314500
2017-06-27	3665.58	3674.72	3676.53	3648.76	97558702.0	hs300	3582.700	3478.729667
2017-06-28	3664.16	3646.17	3672.19	3644.03	97920858.0	hs300	3593.787	3481.746000
2017-06-29	3649.25	3668.83	3669.13	3644.73	85589498.0	hs300	3607.791	3485.613833
2017-06-30	3654.73	3666.80	3669.76	3646.23	81510028.0	hs300	3622.595	3489.126333

# 選擇多列進行繪製
data[['price','SMA_10','SMA_60']].plot(title='HS300 stock price | 10 & 60 days SMAs', figsize=(10, 6));

2. 策略開發思路

data['position'] = np.where(data['SMA_10'] > data['SMA_60'], 1, -1)

data.head()

	open	price	high	low	volume	code	SMA_10	SMA_60	position
date
2010-01-04	3592.468	3535.229	3597.75	3535.23	66101080.0	hs300	NaN	NaN	-1
2010-01-05	3545.186	3564.038	3577.53	3497.66	85809641.0	hs300	NaN	NaN	-1
2010-01-06	3558.700	3541.727	3588.83	3541.17	78473125.0	hs300	NaN	NaN	-1
2010-01-07	3543.160	3471.456	3558.56	3452.77	80350037.0	hs300	NaN	NaN	-1
2010-01-08	3456.908	3480.130	3482.08	3426.70	60790253.0	hs300	NaN	NaN	-1

# 去掉空值，NaN
data.dropna(inplace=True)
data['position'].plot(ylim=[-1.1, 1.1], title='Market Positioning');

3. 計算策略年化收益並可視化

data['returns'] = np.log(data['price'] / data['price'].shift(1))

data.head()

	open	price	high	low	volume	code	SMA_10	SMA_60	position	returns
date
2010-04-02	3400.139	3407.346	3412.20	3391.81	69073452.0	hs300	3322.9136	3313.538117	1	NaN
2010-04-06	3422.849	3405.145	3436.29	3386.89	65191710.0	hs300	3333.1653	3311.370050	1	-0.000646
2010-04-07	3403.088	3386.949	3404.58	3369.02	54011228.0	hs300	3344.3029	3308.418567	1	-0.005358
2010-04-08	3381.306	3346.744	3381.31	3336.16	62185322.0	hs300	3351.3104	3305.168850	1	-0.011942
2010-04-09	3348.773	3379.170	3379.40	3342.47	51280567.0	hs300	3366.3146	3303.630750	1	0.009642

# data['returns_dis'] = data['price']/data['price'].shift(1)-1    #離散計算return方法1
# data['return_dis2'] = data['price'].pct_change()                #離散計算return方法2

# 繪製收益率的直方圖
data['returns'].hist(bins=35);

# 注意進行 shift(1)，用錯一般會使得回測收益高估
data['strategy'] = data['position'].shift(1) * data['returns']
data.head()

	open	price	high	low	volume	code	SMA_10	SMA_60	position	returns	strategy
date
2010-04-02	3400.139	3407.346	3412.20	3391.81	69073452.0	hs300	3322.9136	3313.538117	1	NaN	NaN
2010-04-06	3422.849	3405.145	3436.29	3386.89	65191710.0	hs300	3333.1653	3311.370050	1	-0.000646	-0.000646
2010-04-07	3403.088	3386.949	3404.58	3369.02	54011228.0	hs300	3344.3029	3308.418567	1	-0.005358	-0.005358
2010-04-08	3381.306	3346.744	3381.31	3336.16	62185322.0	hs300	3351.3104	3305.168850	1	-0.011942	-0.011942
2010-04-09	3348.773	3379.170	3379.40	3342.47	51280567.0	hs300	3366.3146	3303.630750	1	0.009642	0.009642

# 算總的收益率
data[['returns', 'strategy']].sum()

returns     0.073386
strategy    0.727122
dtype: float64

# 測試
data[['returns','strategy']].tail()

	returns	strategy
date
2017-06-26	0.012402	0.012402
2017-06-27	0.001806	0.001806
2017-06-28	-0.007800	-0.007800
2017-06-29	0.006196	0.006196
2017-06-30	-0.000553	-0.000553

# 測試
data[['returns', 'strategy']].head()

	returns	strategy
date
2010-04-02	NaN	NaN
2010-04-06	-0.000646	-0.000646
2010-04-07	-0.005358	-0.005358
2010-04-08	-0.011942	-0.011942
2010-04-09	0.009642	0.009642

# 對收益率進行累積求和
data[['returns', 'strategy']].cumsum().tail()

	returns	strategy
date
2017-06-26	0.073737	0.727474
2017-06-27	0.075543	0.729280
2017-06-28	0.067744	0.721480
2017-06-29	0.073939	0.727676
2017-06-30	0.073386	0.727122

data[['returns', 'strategy']].sum()

returns     0.073386
strategy    0.727122
dtype: float64

# 計算累積收益率
data[['returns', 'strategy']].cumsum().apply(np.exp).tail()

	returns	strategy
date
2017-06-26	1.076524	2.069846
2017-06-27	1.078470	2.073587
2017-06-28	1.070091	2.057477
2017-06-29	1.076741	2.070263
2017-06-30	1.076145	2.069118

# 可視化
data[['returns', 'strategy']].cumsum().apply(np.exp).plot(figsize=(10, 6));

4. 策略收益風險評估

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

returns     0.010513
strategy    0.104170
dtype: float64

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

returns     0.245468
strategy    0.245382
dtype: float64

# 計算策略累積收益率
data['cumret'] = data['strategy'].cumsum().apply(np.exp)
data['cumret'].tail()

date
2017-06-26    2.069846
2017-06-27    2.073587
2017-06-28    2.057477
2017-06-29    2.070263
2017-06-30    2.069118
Name: cumret, dtype: float64

# 計算策略累積最大值
data['cummax'] = data['cumret'].cummax()
data['cummax'].head(6)

date
2010-04-02         NaN
2010-04-06    0.999354
2010-04-07    0.999354
2010-04-08    0.999354
2010-04-09    0.999354
2010-04-12    0.999354
Name: cummax, dtype: float64

data.tail()

	open	price	high	low	volume	code	SMA_10	SMA_60	position	returns	strategy	cumret	cummax
date
2017-06-26	3627.02	3668.09	3671.94	3627.02	134637995.0	hs300	3573.455	3475.314500	1	0.012402	0.012402	2.069846	2.731778
2017-06-27	3665.58	3674.72	3676.53	3648.76	97558702.0	hs300	3582.700	3478.729667	1	0.001806	0.001806	2.073587	2.731778
2017-06-28	3664.16	3646.17	3672.19	3644.03	97920858.0	hs300	3593.787	3481.746000	1	-0.007800	-0.007800	2.057477	2.731778
2017-06-29	3649.25	3668.83	3669.13	3644.73	85589498.0	hs300	3607.791	3485.613833	1	0.006196	0.006196	2.070263	2.731778
2017-06-30	3654.73	3666.80	3669.76	3646.23	81510028.0	hs300	3622.595	3489.126333	1	-0.000553	-0.000553	2.069118	2.731778

# 繪製累積收益率和累積最大值
data[['cumret', 'cummax']].plot(figsize=(10, 6));

# 算回撤序列
drawdown = (data['cummax'] - data['cumret'])

# 算最大回撤
drawdown.max()

0.7744165301748813

# 算所有drawdown==0項
temp = drawdown[drawdown == 0]
temp.head()

date
2010-04-06    0.0
2010-05-06    0.0
2010-05-07    0.0
2010-05-11    0.0
2010-05-17    0.0
dtype: float64

temp.index[1:]

Index(['2010-05-06', '2010-05-07', '2010-05-11', '2010-05-17', '2010-06-07',
       '2010-06-29', '2010-06-30', '2010-07-01', '2010-07-05', '2010-10-15',
       '2010-10-19', '2010-10-20', '2010-10-25', '2010-11-05', '2010-11-08',
       '2014-12-04', '2014-12-05', '2014-12-08', '2014-12-16', '2014-12-17',
       '2014-12-19', '2014-12-22', '2014-12-26', '2014-12-29', '2014-12-30',
       '2014-12-31', '2015-01-05', '2015-01-07', '2015-03-16', '2015-03-17',
       '2015-03-18', '2015-03-20', '2015-03-23', '2015-03-24', '2015-03-30',
       '2015-04-01', '2015-04-02', '2015-04-03', '2015-04-07', '2015-04-08',
       '2015-04-10', '2015-04-13', '2015-04-14', '2015-04-16', '2015-04-17',
       '2015-04-21', '2015-04-22', '2015-04-23', '2015-04-27', '2015-05-21',
       '2015-05-22', '2015-05-25', '2015-05-26', '2015-06-05', '2015-06-08',
       '2015-07-08', '2015-08-21', '2015-08-24', '2015-08-25', '2015-08-26'],
      dtype='object', name='date')

temp.index[:-1]

Index(['2010-04-06', '2010-05-06', '2010-05-07', '2010-05-11', '2010-05-17',
       '2010-06-07', '2010-06-29', '2010-06-30', '2010-07-01', '2010-07-05',
       '2010-10-15', '2010-10-19', '2010-10-20', '2010-10-25', '2010-11-05',
       '2010-11-08', '2014-12-04', '2014-12-05', '2014-12-08', '2014-12-16',
       '2014-12-17', '2014-12-19', '2014-12-22', '2014-12-26', '2014-12-29',
       '2014-12-30', '2014-12-31', '2015-01-05', '2015-01-07', '2015-03-16',
       '2015-03-17', '2015-03-18', '2015-03-20', '2015-03-23', '2015-03-24',
       '2015-03-30', '2015-04-01', '2015-04-02', '2015-04-03', '2015-04-07',
       '2015-04-08', '2015-04-10', '2015-04-13', '2015-04-14', '2015-04-16',
       '2015-04-17', '2015-04-21', '2015-04-22', '2015-04-23', '2015-04-27',
       '2015-05-21', '2015-05-22', '2015-05-25', '2015-05-26', '2015-06-05',
       '2015-06-08', '2015-07-08', '2015-08-21', '2015-08-24', '2015-08-25'],
      dtype='object', name='date')

temp.index[1:].to_datetime() - temp.index[:-1].to_datetime()

TimedeltaIndex([  '30 days',    '1 days',    '4 days',    '6 days',
                  '21 days',   '22 days',    '1 days',    '1 days',
                   '4 days',  '102 days',    '4 days',    '1 days',
                   '5 days',   '11 days',    '3 days', '1487 days',
                   '1 days',    '3 days',    '8 days',    '1 days',
                   '2 days',    '3 days',    '4 days',    '3 days',
                   '1 days',    '1 days',    '5 days',    '2 days',
                  '68 days',    '1 days',    '1 days',    '2 days',
                   '3 days',    '1 days',    '6 days',    '2 days',
                   '1 days',    '1 days',    '4 days',    '1 days',
                   '2 days',    '3 days',    '1 days',    '2 days',
                   '1 days',    '4 days',    '1 days',    '1 days',
                   '4 days',   '24 days',    '1 days',    '3 days',
                   '1 days',   '10 days',    '3 days',   '30 days',
                  '44 days',    '3 days',    '1 days',    '1 days'],
               dtype='timedelta64[ns]', freq=None)

periods = temp.index[1:].to_datetime() - temp.index[:-1].to_datetime()
periods

TimedeltaIndex([  '30 days',    '1 days',    '4 days',    '6 days',
                  '21 days',   '22 days',    '1 days',    '1 days',
                   '4 days',  '102 days',    '4 days',    '1 days',
                   '5 days',   '11 days',    '3 days', '1487 days',
                   '1 days',    '3 days',    '8 days',    '1 days',
                   '2 days',    '3 days',    '4 days',    '3 days',
                   '1 days',    '1 days',    '5 days',    '2 days',
                  '68 days',    '1 days',    '1 days',    '2 days',
                   '3 days',    '1 days',    '6 days',    '2 days',
                   '1 days',    '1 days',    '4 days',    '1 days',
                   '2 days',    '3 days',    '1 days',    '2 days',
                   '1 days',    '4 days',    '1 days',    '1 days',
                   '4 days',   '24 days',    '1 days',    '3 days',
                   '1 days',   '10 days',    '3 days',   '30 days',
                  '44 days',    '3 days',    '1 days',    '1 days'],
               dtype='timedelta64[ns]', freq=None)

# 算持續最長時間
periods.max()

Timedelta('1487 days 00:00:00')

5. 策略優化的一種思路

hs300 = ts.get_k_data('hs300','2010-01-01', '2017-06-30')[['date','close']]
hs300 = pd.DataFrame(hs300)   # 一般不用
hs300.rename(columns={'close': 'price'}, inplace=True) 
hs300.set_index('date',inplace = True)
hs300.head()

	price
date
2010-01-04	3535.229
2010-01-05	3564.038
2010-01-06	3541.727
2010-01-07	3471.456
2010-01-08	3480.130

hs300['SMA_10'] = hs300['price'].rolling(10).mean()
hs300['SMA_60'] = hs300['price'].rolling(60).mean()
hs300[['price', 'SMA_10', 'SMA_60']].tail()

	price	SMA_10	SMA_60
date
2017-06-26	3668.09	3573.455	3475.314500
2017-06-27	3674.72	3582.700	3478.729667
2017-06-28	3646.17	3593.787	3481.746000
2017-06-29	3668.83	3607.791	3485.613833
2017-06-30	3666.80	3622.595	3489.126333

# 繪圖
hs300[['price', 'SMA_10', 'SMA_60']].plot(grid=True, figsize = (8,6));

# 算10日SMA和60日SMA差值
hs300['10-60'] = hs300['SMA_10'] - hs300['SMA_60']
hs300['10-60'].tail()

date
2017-06-26     98.140500
2017-06-27    103.970333
2017-06-28    112.041000
2017-06-29    122.177167
2017-06-30    133.468667
Name: 10-60, dtype: float64

SD = 20  # 設置閾值                   
hs300['regime'] = np.where(hs300['10-60'] > SD, 1,0)
hs300['regime'] = np.where(hs300['10-60'] < -SD, -1,hs300['regime']) # 重要
hs300['regime'].value_counts()

 1    792
-1    751
 0    276
Name: regime, dtype: int64

hs300.tail(20)

	price	SMA_10	SMA_60	10-60	regime
date
2017-06-05	3468.75	3457.542	3448.415500	9.126500	0
2017-06-06	3492.88	3466.445	3449.064167	17.380833	0
2017-06-07	3533.87	3478.708	3450.483167	28.224833	1
2017-06-08	3560.98	3492.387	3452.717167	39.669833	1
2017-06-09	3576.17	3507.587	3455.188500	52.398500	1
2017-06-12	3574.39	3516.460	3457.126667	59.333333	1
2017-06-13	3582.27	3526.644	3459.219667	67.424333	1
2017-06-14	3535.30	3530.886	3460.414000	70.472000	1
2017-06-15	3528.79	3533.991	3461.202000	72.789000	1
2017-06-16	3518.76	3537.216	3462.417833	74.798167	1
2017-06-19	3553.67	3545.708	3464.152167	81.555833	1
2017-06-20	3546.49	3551.069	3465.487833	85.581167	1
2017-06-21	3587.96	3556.478	3467.786333	88.691667	1
2017-06-22	3590.34	3559.414	3469.925667	89.488333	1
2017-06-23	3622.88	3564.085	3472.147000	91.938000	1
2017-06-26	3668.09	3573.455	3475.314500	98.140500	1
2017-06-27	3674.72	3582.700	3478.729667	103.970333	1
2017-06-28	3646.17	3593.787	3481.746000	112.041000	1
2017-06-29	3668.83	3607.791	3485.613833	122.177167	1
2017-06-30	3666.80	3622.595	3489.126333	133.468667	1

hs300['Market'] = np.log(hs300['price']/hs300['price'].shift(1))
hs300['Strategy'] = hs300['regime'].shift(1) * hs300['Market']
hs300[['Market','Strategy']].cumsum().apply(np.exp).plot(grid=True, figsize = (8,6));

hs300.head()

	price	SMA_10	SMA_60	10-60	regime	Market	Strategy
date
2010-01-04	3535.229	NaN	NaN	NaN	0	NaN	NaN
2010-01-05	3564.038	NaN	NaN	NaN	0	0.008116	0.0
2010-01-06	3541.727	NaN	NaN	NaN	0	-0.006280	-0.0
2010-01-07	3471.456	NaN	NaN	NaN	0	-0.020040	-0.0
2010-01-08	3480.130	NaN	NaN	NaN	0	0.002496	0.0

# 算總收益
hs300[['Market', 'Strategy']].sum()

Market      0.036541
Strategy    0.896131
dtype: float64

# 算優化策略年化收益
hs300[['Market', 'Strategy']].mean() * 252

Market      0.005065
Strategy    0.124216
dtype: float64

# 算優化策略年化風險
hs300[['Market', 'Strategy']].std() * 252 ** 0.5

Market      0.244318
Strategy    0.235367
dtype: float64