8. 确定股票收益的正态值

#  加载亚马逊的股票数据，使用Data作为行索引
 In[57]: amzn = pd.read_csv('data/amzn_stock.csv', index_col='Date', parse_dates=['Date'])
         amzn.head()
Out[57]:

#  选取Close收盘价，用pct_change()计算每日回报率
 In[58]: amzn_daily_return = amzn.Close.pct_change()
         amzn_daily_return.head()
Out[58]: Date
         2010-01-04         NaN
         2010-01-05    0.005900
         2010-01-06   -0.018116
         2010-01-07   -0.017013
         2010-01-08    0.027077
         Name: Close, dtype: float64

#  去掉缺失值，画一张柱状图，查看分布情况
 In[59]: amzn_daily_return = amzn_daily_return.dropna()
         amzn_daily_return.hist(bins=20)
Out[59]: <matplotlib.axes._subplots.AxesSubplot at 0x1174b3128>

#  计算平均值和标准差
 In[60]: mean = amzn_daily_return.mean()  
         std = amzn_daily_return.std()
#  计算每个数据的z-score的绝对值：z-score是远离平均值的标准差值得个数
 In[61]: abs_z_score = amzn_daily_return.sub(mean).abs().div(std)
#  计算位于1，2，3个标准差之内的收益率的比例
 In[62]: pcts = [abs_z_score.lt(i).mean() for i in range(1,4)]
         print('{:.3f} fall within 1 standard deviation. '
               '{:.3f} within 2 and {:.3f} within 3'.format(*pcts))
         0.787 fall within 1 standard deviation. 0.956 within 2 and 0.985 within 3

更多

#  将上面的方法整合成一个函数
 In[63]: def test_return_normality(stock_data):
             close = stock_data['Close']
             daily_return = close.pct_change().dropna()
             daily_return.hist(bins=20)
             mean = daily_return.mean() 
             std = daily_return.std()
             abs_z_score = abs(daily_return - mean) / std
             pcts = [abs_z_score.lt(i).mean() for i in range(1,4)]
             print('{:.3f} fall within 1 standard deviation. '
                   '{:.3f} within 2 and {:.3f} within 3'.format(*pcts))
 In[64]: slb = pd.read_csv('data/slb_stock.csv', 
                           index_col='Date', parse_dates=['Date'])
         test_return_normality(slb)
         0.742 fall within 1 standard deviation. 0.946 within 2 and 0.986 within 3