python线性回归 多因子模型选股思路

PB-ROE提供了一种投资的框架，这种框架是说，股票的PB和ROE之间存在近似的线性关系，ROE越高，PB越高，因此如果同时根据PB、ROE值来投资，很难选到同时满足PB最小、ROE最大的股票。但可以根据他们的线性关系进行选择，回归直线上的点可以视为合理的PB、ROE组合水平，这样位于回归线下方的股票都是PB被低估的，未来有很大的上升修复空间，而位于回归线上方的股票都是当前PB被高估的，未来会下降，因此投资可以选择位于回归线下方的股票。

使用这种方法最重要的点是回归必须是靠谱的，比如ROE应该是稳定的，确保未来可持续，比如应想办法消除行业间的差异等等。

import numpy as np
from atrader import *
import pandas as pd
set_setting('ALLOW_CONSOLE_SYSTEM_WARN', False)
import statsmodels.api as sm

#获取沪深300的成分股代码
get_code_list('hs300')

#获取PB,ROE数据
import atrader as at
dfData=get_factor_by_day(factor_list=['PB','ROE'], target_list=list(get_code_list('hs300').code), date='2019-08-30').set_index('code')
dfData

# MAD:中位数去极值
def extreme_MAD(dt,n):
    median = dt.quantile(0.5)   # 找出中位数
    new_median = (abs((dt - median)).quantile(0.5))   # 偏差值的中位数
    dt_up = median + n*new_median    # 上限
    dt_down = median - n*new_median  # 下限
    return dt.clip(dt_down, dt_up, axis=1)    # 超出上下限的值，赋值为上下限

# Z值标准化
def standardize_z(dt):
    mean = dt.mean()     #  截面数据均值
    std = dt.std()       #  截面数据标准差
    return (dt - mean)/std

# 行业中性化
shenwan_industry = {
'SWNLMY1':'sse.801010',
'SWCJ1':'sse.801020',
'SWHG1':'sse.801030',
'SWGT1':'sse.801040',
'SWYSJS1':'sse.801050',
'SWDZ1':'sse.801080',
'SWJYDQ1':'sse.801110',
'SWSPCL1':'sse.801120',
'SWFZFZ1':'sse.801130',
'SWQGZZ1':'sse.801140',
'SWYYSW1':'sse.801150',
'SWGYSY1':'sse.801160',
'SWJTYS1':'sse.801170',
'SWFDC1':'sse.801180',
'SWSYMY1':'sse.801200',
'SWXXFW1':'sse.801210',
'SWZH1':'sse.801230',
'SWJZCL1':'sse.801710',
'SWJZZS1':'sse.801720',
'SWDQSB1':'sse.801730',
'SWGFJG1':'sse.801740',
'SWJSJ1':'sse.801750',
'SWCM1':'sse.801760',
'SWTX1':'sse.801770',
'SWYH1':'sse.801780',
'SWFYJR1':'sse.801790',
'SWQC1':'sse.801880',
'SWJXSB1':'sse.801890'
}

# 构造行业哑变量矩阵
def industry_exposure(target_idx):
    # 构建DataFrame，存储行业哑变量
    df = pd.DataFrame(index = [x.lower() for x in target_idx],columns = shenwan_industry.keys())
    for m in df.columns:        # 遍历每个行业
        # 行标签集合和某个行业成分股集合的交集
        temp = list(set(df.index).intersection(set(get_code_list(m).code.tolist())))
        df.loc[temp, m] = 1      # 将交集的股票在这个行业中赋值为1
        df = df.fillna(0)
    return df        # 将 NaN 赋值为0


# 需要传入单个因子值和总市值
def neutralization(factor,MktValue,industry = True):
    Y = factor.fillna(0)
    Y.rename(index = str.lower,inplace = True)
    df = pd.DataFrame(index = Y.index, columns = Y.columns)    # 构建输出矩阵
    for i in range(Y.shape[1]):    # 遍历每一天的截面数据
        if type(MktValue) == pd.DataFrame:
            lnMktValue = MktValue.iloc[:,i].apply(lambda x:math.log(x))   # 市值对数化
            lnMktValue.rename(index=str.lower, inplace=True)
            if industry:              # 行业、市值
                dummy_industry = industry_exposure(Y.index.tolist())
                X = pd.concat([lnMktValue,dummy_industry],axis = 1,sort = False)  # 市值与行业合并
            else:                     # 仅市值
                X = lnMktValue
        elif industry:              # 仅行业
            dummy_industry = industry_exposure(factor.index.tolist())
            X = dummy_industry
      # X = sm.add_constant(X)
        result = sm.OLS(Y.iloc[:,i].astype(float),X.astype(float)).fit()   # 线性回归
        df.iloc[:,i] = result.resid  # 每日的截面数据存储到df中
    return df

dfData = dfData.loc[dfData['PB']>0]
dfData = dfData.loc[dfData['PB']<10]
dfData = dfData.loc[dfData['ROE']>0]
dfData = dfData.loc[dfData['ROE']<10]

# 去极值和标准化
data_S = standardize_z(dfData)
# 行业中性化
data_S_ID_PB = neutralization(data_S[['PB']],0)
data_S_ID_ROE = neutralization(data_S[['ROE']],0)

#回归数据准备
x = data_S_ID_ROE[['ROE']]
x['Intercept'] = 1
x_ = x[['Intercept','ROE']]
y = data_S_ID_PB['PB']

#回归
model = sm.OLS(y.astype(float),x_.astype(float))
result=model.fit()

#回归系数
result.params

#answer:
#Intercept    0.04428
#ROE          0.42821


#拟合曲线
y_fitted = data_S_ID_ROE*result.params[1]+result.params[0]

df = pd.DataFrame()
df[['PB']] = data_S_ID_PB
df['ROE'] = data_S_ID_ROE
df['y_fitted'] = y_fitted

import matplotlib.pyplot as plt
plt.figure(figsize = (8,6))
plt.plot(df['ROE'], df['PB'],'ko', label='sample')
plt.plot(df['ROE'], df['y_fitted'], 'black',label='OLS',linewidth = 2)
plt.xlabel('ROE')
plt.ylabel('PB')
plt.show()

df_choice = df.loc[df['PB']<df['y_fitted']]
df_choice.head()