多因子選股模型 —— 因子間相關性檢驗和等權因子法

1. import package  and download data

from atrader import *
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import math
import statsmodels.api as sm
import datetime as dt
import scipy.stats as stats
import seaborn as sns

# 獲取因子數據
# 單日多標的多因子
# 4個月的動量類因子
names = ['REVS60','REVS120','BIAS60','CCI20','PVT','MA10Close','DEA','RC20','RSTR63','DDI']

factors1 = get_factor_by_day(factor_list= names, target_list=list(get_code_list('hs300',date='2019-02-01').code), date='2019-02-28')

factors2 = get_factor_by_day(factor_list= names, target_list=list(get_code_list('hs300',date='2019-02-01').code), date='2019-03-29')

factors3 = get_factor_by_day(factor_list= names, target_list=list(get_code_list('hs300',date='2019-02-01').code), date='2019-04-30')

factors4 = get_factor_by_day(factor_list= names, target_list=list(get_code_list('hs300',date='2019-02-01').code), date='2019-05-31')

2. factors preprocess

# MAD:中位數去極值
def extreme_MAD(dt,n = 5.2):
    median = dt.quantile(0.5)   # 找出中位數
    new_median = (abs((dt - median)).quantile(0.5))   # 偏差值的中位數
    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，賦值爲上下限

# Z值標準化
def standardize_z(dt):
    mean = dt.mean()     #  截面數據均值
    std = dt.std()       #  截面數據標準差
    return (dt - mean)/std

# 行業中性化
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'
}

# 構造行業啞變量矩陣
def industry_exposure(target_idx):
    # 構建DataFrame，存儲行業啞變量
    df = pd.DataFrame(index = [x.lower() for x in target_idx],columns = shenwan_industry.keys())
    for m in df.columns:        # 遍歷每個行業
        # 行標籤集合和某個行業成分股集合的交集
        temp = list(set(df.index).intersection(set(get_code_list(m).code.tolist())))
        df.loc[temp, m] = 1      # 將交集的股票在這個行業中賦值爲1
    return df.fillna(0)         # 將 NaN 賦值爲0

# 需要傳入單個因子值和總市值
def neutralization(factor,MktValue,industry = True):
  Y = factor.fillna(0)
  df = pd.DataFrame(index = Y.index, columns = Y.columns)    # 構建輸出矩陣
  for i in range(Y.shape[1]):    # 遍歷每一天的截面數據
      if type(MktValue) == pd.DataFrame:
          lnMktValue = MktValue.iloc[:,i].apply(lambda x:math.log(x))   # 市值對數化
          lnMktValue = lnMktValue.fillna(0)
          if industry:              # 行業、市值
              dummy_industry = industry_exposure(Y.index.tolist())
              X = pd.concat([lnMktValue,dummy_industry],axis = 1,sort = False)  # 市值與行業合併
          else:                     # 僅市值
              X = lnMktValue
      elif industry:              # 僅行業
          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()   # 線性迴歸
      df.iloc[:,i] = result.resid  # 每日的截面數據存儲到df中
  return df

3. corr（mean） test

# 計算因子的相關係數矩陣函數
def factor_corr(factors):
    factors = factors.set_index('code')
    factors_process = standardize_z(extreme_MAD(factors.fillna(0)))
    result = factors_process.fillna(0).corr()
    return result

# 獲取相關係數矩陣
factors_corr1 = factor_corr(factors1)
factors_corr2 = factor_corr(factors2)
factors_corr3 = factor_corr(factors3)
factors_corr4 = factor_corr(factors4)
factors_corr = (factors_corr1+factors_corr2+factors_corr3+factors_corr4).div(4)  # 矩陣均值檢驗

# 相關係數檢驗
abs(factors_corr).mean()
abs(factors_corr).median()

4. corr hot map plot

# 畫圖二
fig = plt.figure()
plt.subplots(figsize=(8, 6.4))  # 設置畫面大小
sns.heatmap(factors_corr, annot=True, vmax=1, vmin=-1, square=True, cmap="CMRmap_r",)
plt.show()

5. factors equal combine

# 因子合成
# 等權法
corrnames = ['REVS60','REVS120','BIAS60','CCI20','MA10Close','DEA','RC20','DDI']
collinear_factors = factors4.loc[:,corrnames]         # 共線的因子矩陣
composite_factor = collinear_factors.mul(1/len(corrnames)).sum(axis=1)
print(composite_factor)