介绍：Fama-French三因子模型，是Fama和French 1992年对美国股票市场决定不同股票回报率差异的因素的研究发现，股票的市场的beta值不能解释不同股票回报率的差异，而上市公司的市值、账面市值比、市盈率可以解释股票回报率的差异。Fama and French 认为，上述超额收益是对CAPM 中β未能反映的风险因素的补偿。这三个因子是:市场资产组合(Rm− Rf)、市值因子(SMB)、账面市值比因子(HMI)。这个多因子均衡定价模型可以表示为:
E(Rit)−Rft=βiE[Rmt−Rft]+siE(SMBt)+hiE(HMIi)E(R_{it})-R_{ft}=\beta_{i}E[R_{mt}-R_{ft}]+s_{i}E(SMB_{t})+h_{i}E(HMI_{i})E(Rit)−Rft=βiE[Rmt−Rft]+siE(SMBt)+hiE(HMIi)
其中，RftR_{ft}Rft 表示无风险收益率，RmtR_{mt}Rmt表示时间ttt的市场收益率，RitR_{it}Rit表示资产iii在时间ttt的收益率，
E(Rmt)−RftE(R_{mt})-R_{ft}E(Rmt)−Rft是市场风险溢价，SMBTSMB_{T}SMBT表示时间ttt的市值市值因子的模拟组合收益率，HMItHMI_{t}HMIt为时间ttt的账面市值比因子的组合收益率。βi,si,hi\beta_{i},s_{i},h_{i}βi,si,hi是三因子的系数。此外真实收益 :
Rit=E(Rit)−αiR_{it}=E(R_{it})-\alpha_{i}Rit=E(Rit)−αi
这样我们可以得到如下回归模型:
Rit−Rft=αi+βi(Rmt−Rft)+siSMBIt+hiHMIt+ϵitR_{it}-R_{ft}=\alpha_{i}+\beta_{i}(R_{mt}-R_{ft})+s_{i}SMBI_{t}+hiHMI_{t}+\epsilon_{it}Rit−Rft=αi+βi(Rmt−Rft)+siSMBIt+hiHMIt+ϵit
，我们选取市经率的倒数1/pb1/pb1/pb作为HMIHMIHMI、总市值total_mv为SMBSMBSMB和资产历史收益率RitR_{it}Rit作为三因子进行回归。
随便选一只股票查看他们的相关关系
# coding=utf-8import mathimport tushare as tsimport pandas as pdimport matplotlibimport matplotlib.pyplot as pltimport numpy as npimport talibimport pandas as pdfrom datetime import datetime, datematplotlib.rcParams['axes.unicode_minus']=Falseplt.rcParams['font.sans-serif']=['SimHei']ts.set_token('。。。。。')pro = ts.pro_api()df=pro.query('daily_basic', ts_code='600300.SH',fields='close,ts_code,ps,total_mv')df.corr()
代码运行需里获取token码
完整代码
# coding=utf-8import mathimport tushare as tsimport pandas as pdimport matplotlibimport matplotlib.pyplot as pltimport numpy as npimport talibimport pandas as pdfrom datetime import datetime, datefrom sklearn import datasetsfrom sklearn.model_selection import train_test_splitimport matplotlib.pyplot as pltfrom sklearn.linear_model import LinearRegressionmatplotlib.rcParams['axes.unicode_minus']=Falseplt.rcParams['font.sans-serif']=['SimHei']ts.set_token('f3e00efb72token 码11477')pro = ts.pro_api()############################读取数据类###################################class readData:def read_index_daily(self,code,star,end):#指数数据dsb = pro.index_daily(ts_code=code, start_date=star, end_date=end,fields='ts_code,trade_date,close,change')#默认读取三个数据return dsbdef read_daily(self,code,star,end):dsc1 = pro.daily(ts_code=code, start_date=star, end_date=end,fields='ts_code,trade_date,close')return dsc1def read_CPI(self,star,end):#时间格式start_cpi='09'dc=_cpi(start_m=star, end_m=end,fields='month,nt_yoy')return dcdef read_GDP(self,star,end):#时间格式star='Q4'df1 = _gdp(start_q=star, end_q=end,fields='quarter,gdp_yoy')return df1def read_bond(self,code,star,end):df=pro.cb_daily(ts_code=code,start_date=star,end_date=end)def read_base(self,code):df=pro.query('daily_basic', ts_code=code,fields='close,ts_code,pb,total_mv,trade_date')return df##################################################################### start_time='0110'#发布GDP需要时间，我们延迟1个月，即第一季度的GDP4月份才发布。end_time="2031"dc=readData()dsc1=readData()dsb1=readData()def alpha_fun(code):dsb=dsb1.read_base(code) .fillna(0) dsc=dsc1.read_index_daily('000300.SH',start_time,end_time)dsc.set_index(['trade_date'],inplace=True)dsb.set_index(['trade_date'],inplace=True)df=pd.merge(dsc, dsb, on='trade_date').fillna(0)R=np.reshape( np.array([df.close_y]) , (-1,1) )R_f=np.reshape(np.array([ (df.change/(df.close_x.shift(-1))).fillna(0) ]) , (-1,1))#用0 填充nanHMI=np.reshape( np.array([ (1/df.pb).fillna(0) ]), (-1,1) )SMB=np.reshape( np.array([ df.total_mv]) , (-1,1) )X=np.concatenate(( R_f-4/252, HMI,SMB ),axis=1) y1=np.reshape(R,(1,-1)).TX_train, X_test, y_train, y_test = train_test_split(X, y1, test_size=0.3, random_state=0)linear = LinearRegression()linear.fit(X_train, y_train)alpha=linear.intercept_-4/252return alpha,linear.intercept_ ,linear.coef_,linear.score(X_test, y_test),dfdef Sy_function(df1,star,end):df=pro.query('daily', ts_code=df1, start_date=star, end_date=end,fields='') df=df.sort_index()df.index=pd.to_datetime(df.trade_date,format='%Y-%m-%d')#设置日期索引ret=df.change/df.close.shift(-1)dd=pd.Series(1,index=df.close.index)cumqq=ret*dd.shift(1).fillna(0)cum=(np.cumprod(1+ret[cumqq.index[0:]])-1)#等权重配置一篮子股票return cum.fillna(0),ret.fillna(0)co=pro.query('daily_basic', ts_code="",trade_date="0203",fields='ts_code')code_list=[]N=300#股票池k=0ret=0cum=0for i in co.ts_code.values[0:N]:try:if alpha_fun(i)[0]<-10:k+=1ret=Sy_function( str(i) ,start_time,end_time)[1]+retexcept ValueError:passcontinue ret=ret.sort_index(axis=0,ascending=True)cum=np.cumprod(1+ret)-1# RET=ret/k####################计算收益率函数，如沪深300#####################################def JZ_function(code,star,end):df12 = pro.index_daily( ts_code=code, start_date=star, end_date=end)df12=df12.sort_index( )df12.index=pd.to_datetime(df12.trade_date,format='%Y-%m-%d')#设置日期索引ret12=df12.change/df12.close.shift(-1)#将顺序颠倒aq=pd.Series(1,index=df12.close.index) SmaRet=ret12*aq.shift(1).dropna()cum12=np.cumprod(1+ret12[SmaRet.index[0:]])-1return cum12#############################策略的年化统计######################################def Tongji(RET,cum):RET1 = RET*100 - (4/252)NH=cum[-2]*100*252/len(RET.index)BD=np.std(RET)*100*np.sqrt(252)SR=(NH-400/252)/BDfor i in range(len(cum)):if cum[cum.index[i]]==cum.max():MHC=(cum.max()-cum[cum.index[i:]].min())*100/cum.max()print("年化收益率：{:.2f}%:，年化夏普率：{:.2f},波动率为：{:.2f}%,最大回撤：{:.2f}%".format( NH,SR,BD,MHC))############################################################################if __name__=="__main__":cum12=JZ_function('000300.SH',start_time,end_time)Tongji(RET,cum)plt.plot(cum12,label="沪深300",color='b')plt.plot(cum,label="股票组合",color='r')plt.title("alpha股+指期对冲策略")plt.legend()#a=alpha_fun('600300.SH') #print("alpha:{}".format( a[0] ))#print('f截距：{}'.format(a[1]))#print(f'系数：{a[2]}')#print(f'准确率：{a[3]:.4f}')
FF三因子（改进代码+结果）
参考资料：
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