华东理工大学《Python与金融计算》¶

单因子资产定价模型的实证检验（单资产）¶

蒋志强 2022-03-17 18:00-21:00¶

In [1]:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import statsmodels.api as sm

In [2]:

stock_data = pd.read_csv('1EShowData_data_stock_daily_price_2001-2018.csv', encoding='GB2312', usecols=[1, 5, 10])
stock_data

Out[2]:

	日期_Date	收盘价_Clpr	日无风险收益率_DRfRet
0	2001/8/27	35.55	0.000054
1	2001/8/28	36.86	0.000054
2	2001/8/29	36.38	0.000054
3	2001/8/30	37.10	0.000054
4	2001/8/31	37.01	0.000054
...	...	...	...
4232	2018/12/24	568.00	0.000088
4233	2018/12/25	565.79	0.000090
4234	2018/12/26	560.08	0.000091
4235	2018/12/27	563.00	0.000091
4236	2018/12/28	590.01	0.000092

4237 rows × 3 columns

In [3]:

stock_data.columns = ['date', 'close', 'rfreturn']
stock_data

Out[3]:

	date	close	rfreturn
0	2001/8/27	35.55	0.000054
1	2001/8/28	36.86	0.000054
2	2001/8/29	36.38	0.000054
3	2001/8/30	37.10	0.000054
4	2001/8/31	37.01	0.000054
...	...	...	...
4232	2018/12/24	568.00	0.000088
4233	2018/12/25	565.79	0.000090
4234	2018/12/26	560.08	0.000091
4235	2018/12/27	563.00	0.000091
4236	2018/12/28	590.01	0.000092

4237 rows × 3 columns

In [4]:

stock_data.dropna(inplace=True)
stock_data

Out[4]:

	date	close	rfreturn
0	2001/8/27	35.55	0.000054
1	2001/8/28	36.86	0.000054
2	2001/8/29	36.38	0.000054
3	2001/8/30	37.10	0.000054
4	2001/8/31	37.01	0.000054
...	...	...	...
4232	2018/12/24	568.00	0.000088
4233	2018/12/25	565.79	0.000090
4234	2018/12/26	560.08	0.000091
4235	2018/12/27	563.00	0.000091
4236	2018/12/28	590.01	0.000092

4135 rows × 3 columns

In [5]:

stock_data['return'] = np.log(stock_data['close']) - np.log(stock_data['close'].shift(periods=1))
stock_data

Out[5]:

	date	close	rfreturn	return
0	2001/8/27	35.55	0.000054	NaN
1	2001/8/28	36.86	0.000054	0.036187
2	2001/8/29	36.38	0.000054	-0.013108
3	2001/8/30	37.10	0.000054	0.019598
4	2001/8/31	37.01	0.000054	-0.002429
...	...	...	...	...
4232	2018/12/24	568.00	0.000088	0.001039
4233	2018/12/25	565.79	0.000090	-0.003898
4234	2018/12/26	560.08	0.000091	-0.010143
4235	2018/12/27	563.00	0.000091	0.005200
4236	2018/12/28	590.01	0.000092	0.046860

4135 rows × 4 columns

In [6]:

stock_data.dropna(inplace=True)
stock_data

Out[6]:

	date	close	rfreturn	return
1	2001/8/28	36.86	0.000054	0.036187
2	2001/8/29	36.38	0.000054	-0.013108
3	2001/8/30	37.10	0.000054	0.019598
4	2001/8/31	37.01	0.000054	-0.002429
5	2001/9/3	36.99	0.000054	-0.000541
...	...	...	...	...
4232	2018/12/24	568.00	0.000088	0.001039
4233	2018/12/25	565.79	0.000090	-0.003898
4234	2018/12/26	560.08	0.000091	-0.010143
4235	2018/12/27	563.00	0.000091	0.005200
4236	2018/12/28	590.01	0.000092	0.046860

4134 rows × 4 columns

In [7]:

stock_data['return'].plot()

Out[7]:

<matplotlib.axes._subplots.AxesSubplot at 0x7fbc711fe2d0>

In [8]:

ind = (stock_data['return'] >= -0.1) & (stock_data['return'] <= 0.1)
stock_data = stock_data.loc[ind, :]
stock_data['return'].plot()

Out[8]:

<matplotlib.axes._subplots.AxesSubplot at 0x7fbc71132250>

In [9]:

stock_data

Out[9]:

	date	close	rfreturn	return
1	2001/8/28	36.86	0.000054	0.036187
2	2001/8/29	36.38	0.000054	-0.013108
3	2001/8/30	37.10	0.000054	0.019598
4	2001/8/31	37.01	0.000054	-0.002429
5	2001/9/3	36.99	0.000054	-0.000541
...	...	...	...	...
4232	2018/12/24	568.00	0.000088	0.001039
4233	2018/12/25	565.79	0.000090	-0.003898
4234	2018/12/26	560.08	0.000091	-0.010143
4235	2018/12/27	563.00	0.000091	0.005200
4236	2018/12/28	590.01	0.000092	0.046860

4125 rows × 4 columns

In [10]:

index_data = pd.read_csv('1EShowData_data_Index_daily_price_2001-2018.csv', encoding = 'GB2312', usecols=[1, 5])
index_data

Out[10]:

	交易日期_TrdDt	收盘价(元/点)_ClPr
0	2005/1/4	982.79
1	2005/1/5	992.56
2	2005/1/6	983.17
3	2005/1/7	983.96
4	2005/1/10	993.88
...	...	...
3397	2018/12/24	3038.20
3398	2018/12/25	3017.28
3399	2018/12/26	3002.03
3400	2018/12/27	2990.51
3401	2018/12/28	3010.65

3402 rows × 2 columns

In [11]:

index_data.columns = ['date', 'close']
index_data

Out[11]:

	date	close
0	2005/1/4	982.79
1	2005/1/5	992.56
2	2005/1/6	983.17
3	2005/1/7	983.96
4	2005/1/10	993.88
...	...	...
3397	2018/12/24	3038.20
3398	2018/12/25	3017.28
3399	2018/12/26	3002.03
3400	2018/12/27	2990.51
3401	2018/12/28	3010.65

3402 rows × 2 columns

In [12]:

index_data.dropna(inplace=True)
index_data

Out[12]:

	date	close
0	2005/1/4	982.79
1	2005/1/5	992.56
2	2005/1/6	983.17
3	2005/1/7	983.96
4	2005/1/10	993.88
...	...	...
3397	2018/12/24	3038.20
3398	2018/12/25	3017.28
3399	2018/12/26	3002.03
3400	2018/12/27	2990.51
3401	2018/12/28	3010.65

3402 rows × 2 columns

In [13]:

index_data['return'] = np.log(index_data['close']) - np.log(index_data['close'].shift(periods=1))
index_data

Out[13]:

	date	close	return
0	2005/1/4	982.79	NaN
1	2005/1/5	992.56	0.009892
2	2005/1/6	983.17	-0.009505
3	2005/1/7	983.96	0.000803
4	2005/1/10	993.88	0.010031
...	...	...	...
3397	2018/12/24	3038.20	0.002901
3398	2018/12/25	3017.28	-0.006909
3399	2018/12/26	3002.03	-0.005067
3400	2018/12/27	2990.51	-0.003845
3401	2018/12/28	3010.65	0.006712

3402 rows × 3 columns

In [14]:

index_data.dropna(inplace=True)
index_data

Out[14]:

	date	close	return
1	2005/1/5	992.56	0.009892
2	2005/1/6	983.17	-0.009505
3	2005/1/7	983.96	0.000803
4	2005/1/10	993.88	0.010031
5	2005/1/11	997.13	0.003265
...	...	...	...
3397	2018/12/24	3038.20	0.002901
3398	2018/12/25	3017.28	-0.006909
3399	2018/12/26	3002.03	-0.005067
3400	2018/12/27	2990.51	-0.003845
3401	2018/12/28	3010.65	0.006712

3401 rows × 3 columns

In [15]:

merge_data = pd.merge(left=stock_data[['date', 'return', 'rfreturn']],
                      right=index_data[['date', 'return']],
                      on='date',
                      how='inner')
merge_data

Out[15]:

	date	return_x	rfreturn	return_y
0	2005/1/5	0.021442	0.000073	0.009892
1	2005/1/6	-0.017335	0.000071	-0.009505
2	2005/1/7	0.008163	0.000071	0.000803
3	2005/1/10	0.035932	0.000071	0.010031
4	2005/1/11	0.001306	0.000071	0.003265
...	...	...	...	...
3321	2018/12/24	0.001039	0.000088	0.002901
3322	2018/12/25	-0.003898	0.000090	-0.006909
3323	2018/12/26	-0.010143	0.000091	-0.005067
3324	2018/12/27	0.005200	0.000091	-0.003845
3325	2018/12/28	0.046860	0.000092	0.006712

3326 rows × 4 columns

In [16]:

merge_data.columns = ['date', 'return_stk', 'rfreturn', 'return_ind']
merge_data

Out[16]:

	date	return_stk	rfreturn	return_ind
0	2005/1/5	0.021442	0.000073	0.009892
1	2005/1/6	-0.017335	0.000071	-0.009505
2	2005/1/7	0.008163	0.000071	0.000803
3	2005/1/10	0.035932	0.000071	0.010031
4	2005/1/11	0.001306	0.000071	0.003265
...	...	...	...	...
3321	2018/12/24	0.001039	0.000088	0.002901
3322	2018/12/25	-0.003898	0.000090	-0.006909
3323	2018/12/26	-0.010143	0.000091	-0.005067
3324	2018/12/27	0.005200	0.000091	-0.003845
3325	2018/12/28	0.046860	0.000092	0.006712

3326 rows × 4 columns

In [17]:

stk_ret = merge_data['return_stk'].values
rf_ret = merge_data['rfreturn'].values
ind_ret = merge_data['return_ind'].values

In [19]:

plt.plot(ind_ret - rf_ret, stk_ret - rf_ret, 'o', ms=5, mfc='w', lw=2)
plt.xlabel(r'$r_m - r_f$', fontsize = 20)
plt.ylabel(r'$r_i - r_f$', fontsize = 20)

Out[19]:

Text(0, 0.5, '$r_i - r_f$')

In [20]:

x = sm.add_constant(ind_ret-rf_ret)
y = stk_ret - rf_ret
model = sm.OLS(y, x)
results = model.fit()
print(results.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.248
Model:                            OLS   Adj. R-squared:                  0.248
Method:                 Least Squares   F-statistic:                     1097.
Date:                Thu, 17 Mar 2022   Prob (F-statistic):          3.53e-208
Time:                        18:44:08   Log-Likelihood:                 8498.5
No. Observations:                3326   AIC:                        -1.699e+04
Df Residuals:                    3324   BIC:                        -1.698e+04
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0011      0.000      3.391      0.001       0.000       0.002
x1             0.6159      0.019     33.125      0.000       0.579       0.652
==============================================================================
Omnibus:                      437.950   Durbin-Watson:                   1.838
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1855.618
Skew:                           0.583   Prob(JB):                         0.00
Kurtosis:                       6.468   Cond. No.                         57.0
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.