多因子選股模型
阿新 • • 發佈：2019-01-01
轉載自：https://www.joinquant.com/post/15833?tag=algorithm
多因子選股模型¶
基於《【研究】量化選股-因子檢驗和多因子模型的構建》https://zhuanlan.zhihu.com/quantstory/20634542
在原始碼的基礎上添加了一些因子，同時將時間滯後。
1.時間選取11-17年作為樣本期，並進行因子篩選及檢驗。
2.基準選取上證綜指（000001.XSHG）
模型構建及因子選取¶
擬選取以下四個方面的因子：
- 價值類因子：市盈率（PE）,市淨率（PB）,市銷率（PS）,基本每股收益（EPS）,賬面市值比（B/M)
- 成長類因子：淨資產收益率（ROE）,總資產淨利率（ROA），銷售毛利率（gross_profit_margin）,淨利潤同比增長率（inc_net_profit_year_on_year），淨利潤環比增長率（inc_net_profit_annual），營業利潤同比增長率（inc_operation_profit_year_on_year），營業利潤環比增長率（inc_operation_profit_annual）,主營毛利率（GP/R)、淨利率(P/R)
- 規模類因子：淨利潤（net_profit），營業收入（operating_revenue），總股本（capitalization），流通股本（circulating_cap），總市值（market_cap），流通市值（circulating_market_cap），資產負債（L/A)、固定資產比例（FAP）
- 交投類因子：換手率（turnover_ratio）
採用排序法對因子的有效性進行驗證。
In [1]:
import pandas as pd from pandas import Series, DataFrame import numpy as np import statsmodels.api as sm import scipy.stats as scs import matplotlib.pyplot as plt
月初取出所有因子數值，例如2018-01-01
In [2]:
factors = ['PE', 'PB', 'PS', 'EPS', 'B/M',
'ROE', 'ROA', 'gross_profit_margin', 'inc_net_profit_year_on_year', 'inc_net_profit_annual',
'inc_operation_profit_year_on_year', 'inc_operation_profit_annual', 'GP/R', 'P/R',
'net_profit', 'operating_revenue', 'capitalization', 'circulating_cap', 'market_cap', 'circulating_market_cap',
'L/A', 'FAP',
'turnover_ratio']
# 月初取出因子值
def get_factors(fdate, factors):
stock_set = get_index_stocks('000001.XSHG', fdate)
q = query(
valuation.code,
balance.total_owner_equities/valuation.market_cap/100000000,
valuation.pe_ratio,
valuation.pb_ratio,
valuation.ps_ratio,
income.basic_eps,
indicator.roe,
indicator.roa,
indicator.gross_profit_margin,
indicator.inc_net_profit_year_on_year,
indicator.inc_net_profit_annual,
indicator.inc_operation_profit_year_on_year,
indicator.inc_operation_profit_annual,
income.total_profit/income.operating_revenue,
income.net_profit/income.operating_revenue,
income.net_profit,
income.operating_revenue,
valuation.capitalization,
valuation.circulating_cap,
valuation.market_cap,
valuation.circulating_market_cap,
balance.total_liability/balance.total_assets,
balance.fixed_assets/balance.total_assets,
valuation.turnover_ratio
).filter(
valuation.code.in_(stock_set),
valuation.circulating_market_cap
)
fdf = get_fundamentals(q, date=fdate)
fdf.index = fdf['code']
fdf.columns = ['code'] + factors
return fdf.iloc[:,-23:]
fdf = get_factors('2018-01-01', factors)
fdf.head().T
Out[2]:
| code | 600000.XSHG | 600004.XSHG | 600006.XSHG | 600007.XSHG | 600008.XSHG |
|---|---|---|---|---|---|
| PE | 1.143846e+00 | 4.827871e-01 | 6.119287e-01 | 3.655787e-01 | 6.300832e-01 |
| PB | 6.804400e+00 | 2.009680e+01 | 1.093361e+02 | 2.808410e+01 | 3.863470e+01 |
| PS | 9.538000e-01 | 2.144100e+00 | 1.787800e+00 | 2.736200e+00 | 3.135900e+00 |
| EPS | 2.244700e+00 | 4.643700e+00 | 6.311000e-01 | 6.594300e+00 | 2.607200e+00 |
| B/M | 4.800000e-01 | 1.900000e-01 | -9.700000e-03 | 1.800000e-01 | 3.390000e-02 |
| ROE | 3.413200e+00 | 2.754000e+00 | -2.960000e-01 | 2.928800e+00 | 1.513400e+00 |
| ROA | 2.316000e-01 | 1.990600e+00 | -7.116000e-01 | 1.580100e+00 | 4.027000e-01 |
| gross_profit_margin | NaN | 3.798770e+01 | 1.084940e+01 | 5.062150e+01 | 3.024400e+01 |
| inc_net_profit_year_on_year | -1.588900e+00 | 8.844300e+00 | -6.544932e+02 | 6.390600e+00 | 2.954560e+01 |
| inc_net_profit_annual | -7.200000e-03 | 4.770500e+00 | -2.012624e+03 | 3.357990e+01 | -3.995000e-01 |
| inc_operation_profit_year_on_year | -1.833300e+00 | 1.868020e+01 | -6.605708e+02 | -4.675000e-01 | 1.377109e+02 |
| inc_operation_profit_annual | 2.019000e+00 | 2.919000e+00 | -1.447837e+03 | 2.506970e+01 | -2.233990e+01 |
| GP/R | 4.344424e-01 | 3.085870e-01 | -4.038174e-02 | 3.296453e-01 | 1.174919e-01 |
| P/R | 3.350075e-01 | 2.308729e-01 | -3.273438e-02 | 2.473615e-01 | 8.858635e-02 |
| net_profit | 1.387400e+10 | 3.935985e+08 | -1.587791e+08 | 1.823589e+08 | 1.900669e+08 |
| operating_revenue | 4.141400e+10 | 1.704828e+09 | 4.850528e+09 | 7.372163e+08 | 2.145555e+09 |
| capitalization | 2.935208e+06 | 2.069320e+05 | 2.000000e+05 | 1.007282e+05 | 4.820614e+05 |
| circulating_cap | 2.810376e+06 | 2.069320e+05 | 2.000000e+05 | 1.007282e+05 | 4.820614e+05 |
| market_cap | 3.695427e+03 | 3.041901e+02 | 1.170000e+02 | 1.726482e+02 | 2.477796e+02 |
| circulating_market_cap | 3.538264e+03 | 3.041901e+02 | 1.170000e+02 | 1.726482e+02 | 2.477796e+02 |
| L/A | 9.302917e-01 | 2.719476e-01 | 6.862103e-01 | 4.571281e-01 | 6.699646e-01 |
| FAP | 4.168150e-03 | 3.381332e-01 | 1.754063e-01 | 1.815366e-01 | 1.011792e-01 |
| turnover_ratio | 5.820000e-02 | 4.095000e-01 | 5.574000e-01 | 7.120000e-02 | 3.734000e-01 |
對每個因子大小排序（以流通市值為例）¶
In [3]:
score = fdf['circulating_market_cap'].order() score.head()
Out[3]:
code 603580.XSHG 5.0777 603991.XSHG 5.2659 603330.XSHG 5.3535 603041.XSHG 5.6300 603269.XSHG 5.7038 Name: circulating_market_cap, dtype: float64
股票個數¶
In [4]:
len(score)
Out[4]:
1352
按照流通市值將股票池進行五等分¶
In [5]:
startdate = '2018-01-01'
enddate = '2018-02-01'
nextdate = '2018-03-01'
df = {}
circulating_market_cap = fdf['circulating_market_cap']
port1 = list(score.index)[: len(score)/5]
port2 = list(score.index)[ len(score)/5: 2*len(score)/5]
port3 = list(score.index)[ 2*len(score)/5: -2*len(score)/5]
port4 = list(score.index)[ -2*len(score)/5: -len(score)/5]
port5 = list(score.index)[ -len(score)/5: ]
按流通市值加權計算組合月收益（例如2018-01,2018-02月收益）¶
In [6]:
def calculate_port_monthly_return(port, startdate, enddate, nextdate, circulating_market_cap):
close1 = get_price(port, startdate, enddate, 'daily', ['close'])
close2 = get_price(port, enddate, nextdate, 'daily', ['close'])
weighted_m_return = ((close2['close'].ix[0,:]/close1['close'].ix[0,:]-1)*
circulating_market_cap).sum()/(circulating_market_cap.ix[port].sum())
return weighted_m_return
calculate_port_monthly_return(port1, '2018-01-01', '2018-02-01', '2018-03-01', fdf['circulating_market_cap'])
Out[6]:
-0.09004705495088357
計算基準月收益¶
In [7]:
def calculate_benchmark_monthly_return(startdate, enddate, nextdate):
close1 = get_price(['000001.XSHG'],startdate,enddate,'daily',['close'])['close']
close2 = get_price(['000001.XSHG'],enddate, nextdate, 'daily',['close'])['close']
benchmark_return = (close2.ix[0,:]/close1.ix[0,:]-1).sum()
return benchmark_return
calculate_benchmark_monthly_return('2018-01-01','2018-02-01','2018-03-01')
Out[7]:
0.029462448444448563
觀察5個組合在2018年初一個月內的收益情況¶
從結果可以看出，在構建因子組合之前，前四組的收益跑輸大盤。
In [8]:
benchmark_return = calculate_benchmark_monthly_return('2018-01-01', '2018-02-01', '2018-03-01')
df['port1'] = calculate_port_monthly_return(port1,'2018-01-01', '2018-02-01', '2018-03-01', fdf['circulating_market_cap'])
df['port2'] = calculate_port_monthly_return(port2,'2018-01-01', '2018-02-01', '2018-03-01', fdf['circulating_market_cap'])
df['port3'] = calculate_port_monthly_return(port3,'2018-01-01', '2018-02-01', '2018-03-01', fdf['circulating_market_cap'])
df['port4'] = calculate_port_monthly_return(port4,'2018-01-01', '2018-02-01', '2018-03-01', fdf['circulating_market_cap'])
df['port5'] = calculate_port_monthly_return(port5,'2018-01-01', '2018-02-01', '2018-03-01', fdf['circulating_market_cap'])
print Series(df)
print 'benchmark_return %s'%benchmark_return
port1 -0.090047 port2 -0.088405 port3 -0.075064 port4 -0.060624 port5 0.068629 dtype: float64 benchmark_return 0.0294624484444
構建因子組合，計算不同組合月收益率¶
時間:2011-2017年，計算1-5組以及benchmark組合的月收益率，形成84×6的面板資料。
In [9]:
factors = ['PE', 'PB', 'PS', 'EPS', 'B/M',
'ROE', 'ROA', 'gross_profit_margin', 'inc_net_profit_year_on_year', 'inc_net_profit_annual',
'inc_operation_profit_year_on_year', 'inc_operation_profit_annual', 'GP/R', 'P/R',
'net_profit', 'operating_revenue', 'capitalization', 'circulating_cap', 'market_cap', 'circulating_market_cap',
'L/A', 'FAP',
'turnover_ratio']
#因為研究模組取fundamental資料預設date為研究日期的前一天。所以要自備時間序列。按月取
year = ['2011','2012','2013','2014','2015','2016','2017']
month = ['01','02','03','04','05','06','07','08','09','10','11','12']
result = {}
for i in range(7*12):
startdate = year[i/12] + '-' + month[i%12] + '-01'
try:
enddate = year[(i+1)/12] + '-' + month[(i+1)%12] + '-01'
except IndexError:
enddate = '2018-01-01'
try:
nextdate = year[(i+2)/12] + '-' + month[(i+2)%12] + '-01'
except IndexError:
if enddate == '2018-01-01':
nextdate = '2018-02-01'
else:
nextdate = '2018-01-01'
# print 'time %s'%startdate
fdf = get_factors(startdate,factors)
CMV = fdf['circulating_market_cap']
#5個組合，23個因子
df = DataFrame(np.zeros(6*23).reshape(6,23),index = ['port1','port2','port3','port4','port5','benchmark'],columns = factors)
for fac in factors:
score = fdf[fac].order()
port1 = list(score.index)[: len(score)/5]
port2 = list(score.index)[ len(score)/5+1: 2*len(score)/5]
port3 = list(score.index)[ 2*len(score)/5+1: -2*len(score)/5]
port4 = list(score.index)[ -2*len(score)/5+1: -len(score)/5]
port5 = list(score.index)[ -len(score)/5+1: ]
df.ix['port1',fac] = calculate_port_monthly_return(port1,startdate,enddate,nextdate,circulating_market_cap)
df.ix['port2',fac] = calculate_port_monthly_return(port2,startdate,enddate,nextdate,circulating_market_cap)
df.ix['port3',fac] = calculate_port_monthly_return(port3,startdate,enddate,nextdate,circulating_market_cap)
df.ix['port4',fac] = calculate_port_monthly_return(port4,startdate,enddate,nextdate,circulating_market_cap)
df.ix['port5',fac] = calculate_port_monthly_return(port5,startdate,enddate,nextdate,circulating_market_cap)
df.ix['benchmark',fac] = calculate_benchmark_monthly_return(startdate,enddate,nextdate)
# print 'factor %s'%fac
result[i+1]=df
monthly_return = pd.Panel(result)
取某個因子的5個組合月收益情況（例如市盈率PE）¶
In [11]:
monthly_return[:,:,'PE']
Out[11]:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ... | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| port1 | -0.063961 | 0.057468 | -0.003538 | 0.011939 | -0.000767 | 0.028005 | 0.048595 | -0.003958 | -0.109566 | 0.062509 | ... | 0.021345 | -0.006460 | -0.001198 | 0.049791 | 0.009338 | 0.049369 | 0.058072 | 0.069637 | -0.033160 | 0.056772 |
| port2 | -0.065009 | 0.076102 | -0.027128 | -0.018031 | -0.066994 | 0.031146 | 0.028017 | -0.046184 | -0.120076 | 0.034576 | ... | 0.037914 | -0.048666 | -0.053362 | 0.072887 | 0.040365 | 0.036833 | 0.069451 | 0.003253 | -0.022327 | 0.018349 |
| port3 | -0.056932 | 0.079801 | -0.017569 | -0.027592 | -0.073196 | 0.034040 | -0.025730 | -0.054367 | -0.129013 | 0.045660 | ... | 0.017931 | -0.045419 | -0.053020 | 0.054920 | 0.028066 | 0.018909 | 0.027487 | 0.002008 | -0.047184 | 0.006735 |
| port4 | -0.021293 | 0.046165 | -0.005278 | -0.011301 | -0.069544 | 0.019637 | -0.019397 | -0.080514 | -0.107611 | 0.081045 | ... | 0.004030 | -0.021088 | -0.005480 | 0.057372 | 0.065631 | 0.025304 | -0.005043 | 0.059699 | 0.016978 | 0.023916 |
| port5 | 0.013760 | 0.024953 | 0.050458 | 0.006419 | -0.054836 | 0.007156 | -0.035373 | -0.041296 | -0.052494 | 0.068615 | ... | 0.011837 | -0.021979 | 0.048663 | 0.021466 | 0.074965 | 0.014275 | -0.003084 | -0.003351 | 0.003836 | 0.009916 |
| benchmark | -0.018820 | 0.042859 | 0.016612 | -0.011870 | -0.064326 | 0.005755 | -0.020142 | -0.054642 | -0.082649 | 0.053409 | ... | 0.007198 | -0.038710 | -0.013070 | 0.030068 | 0.030266 | 0.022620 | 0.002156 | 0.006382 | -0.023056 | 0.009257 |
6 rows × 84 columns
總收益情況¶
In [12]:
(monthly_return[:,:,'PE'].T+1).cumprod().tail()
Out[12]:
| port1 | port2 | port3 | port4 | port5 | benchmark | |
|---|---|---|---|---|---|---|
| 80 | 2.173926 | 1.652334 | 1.708928 | 1.980452 | 2.433185 | 1.180349 |
| 81 | 2.300171 | 1.767090 | 1.755901 | 1.970465 | 2.425681 | 1.182893 |
| 82 | 2.460347 | 1.772839 | 1.759427 | 2.088099 | 2.417553 | 1.190442 |
| 83 | 2.378763 | 1.733257 | 1.676409 | 2.123552 | 2.426825 | 1.162996 |
| 84 | 2.513809 | 1.765060 | 1.687700 | 2.174338 | 2.450891 | 1.173762 |
因子檢驗量化指標¶
模型建立後，計算n個組合的年化複合收益、超額收益、不同市場情況下高收益組合跑贏benchmark和低收益組合跑輸benchmark的概率。
檢驗有效性的量化標準：
（1）序列1-n的組合，年化複合收益應滿足一定排序關係，即組合因子大小與收益具有較大相關關係。假定序列i的組合年化收益為Xi,則Xi與i的相關性絕對值Abs(Corr(Xi,i))>MinCorr。此處MinCorr為給定的最小相關閾值。
（2）序列1和n表示的兩個極端組合超額收益分別為AR1、ARn。MinARtop、MinARbottom表示最小超額收益閾值。 if AR1 > ARn #因子越小，收益越大 則應滿足AR1 > MinARtop >0 and ARn < MinARbottom < 0 if AR1 < ARn #因子越小，收益越大 則應滿足ARn > MinARtop >0 and AR1 < MinARbottom < 0 以上條件保證因子最大和最小的兩個組合，一個明顯跑贏市場，一個明顯跑輸市場。
（3）在任何市場行情下，1和n兩個極端組合，都以較高概率跑贏或跑輸市場。 以上三個條件，可以選出過去一段時間有較好選股能力的因子。
因為開始選擇的因子較多，因此三條量化標準的選擇更加嚴格，採用如下標準進行選取：
（1）記錄因子相關性，>0.7或<-0.7合格。
（2）記錄贏家組合和輸家組合超額收益。
（3）記錄贏家組合跑贏概率>0.6和輸家組合跑輸概率>0.4合格。
In [13]:
total_return = {}
annual_return = {}
excess_return = {}
win_prob = {}
loss_prob = {}
effect_test = {}
MinCorr = 0.3
Minbottom = -0.05
Mintop = 0.05
for fac in factors:
effect_test[fac] = {}
monthly = monthly_return[:,:,fac]
total_return[fac] = (monthly+1).T.cumprod().iloc[-1,:]-1
annual_return[fac] = (total_return[fac]+1)**(1./6)-1
excess_return[fac] = annual_return[fac]- annual_return[fac][-1]
#判斷因子有效性
#1.年化收益與組合序列的相關性 大於 閾值
effect_test[fac][1] = annual_return[fac][0:5].corr(Series([1,2,3,4,5],index = annual_return[fac][0:5].index))
#2.高收益組合跑贏概率
#因子小，收益小，port1是輸家組合，port5是贏家組合
if total_return[fac][0] < total_return[fac][-2]:
loss_excess = monthly.iloc[0,:]-monthly.iloc[-1,:]
loss_prob[fac] = loss_excess[loss_excess<0].count()/float(len(loss_excess))
win_excess = monthly.iloc[-2,:]-monthly.iloc[-1,:]
win_prob[fac] = win_excess[win_excess>0].count()/float(len(win_excess))
effect_test[fac][3] = [win_prob[fac],loss_prob[fac]]
#超額收益
effect_test[fac][2] = [excess_return[fac][-2]*100,excess_return[fac][0]*100]
#因子小，收益大，port1是贏家組合，port5是輸家組合
else:
loss_excess = monthly.iloc[-2,:]-monthly.iloc[-1,:]
loss_prob[fac] = loss_excess[loss_excess<0].count()/float(len(loss_excess))
win_excess = monthly.iloc[0,:]-monthly.iloc[-1,:]
win_prob[fac] = win_excess[win_excess>0].count()/float(len(win_excess))
effect_test[fac][3] = [win_prob[fac],loss_prob[fac]]
#超額收益
effect_test[fac][2] = [excess_return[fac][0]*100,excess_return[fac][-2]*100]
#由於選擇的因子較多，test標準選取適當嚴格一些
#effect_test[1]記錄因子相關性，>0.7或<-0.7合格
#effect_test[2]記錄【贏家組合超額收益，輸家組合超額收益】
#effect_test[3]記錄贏家組合跑贏概率和輸家組合跑輸概率。【>0.6,>0.4】合格 (因實際情況，跑輸概率暫時不考慮)
DataFrame(effect_test).T
Out[13]:
| 1 | 2 | 3 | |
|---|---|---|---|
| B/M | 0.6281959 | [15.1984852636, 8.76175660448] | [0.690476190476, 0.404761904762] |
| EPS | 0.2488584 | [14.2720133294, 12.9632231367] | [0.678571428571, 0.357142857143] |
| FAP | -0.5671644 | [13.4503120268, 9.44267504971] | [0.619047619048, 0.380952380952] |
| GP/R | 0.8064658 | [13.7519085368, 9.10242336036] | [0.619047619048, 0.357142857143] |
| L/A | -0.5898578 | [16.5046555213, 12.1611504111] | [0.702380952381, 0.416666666667] |
| P/R | 0.9215462 | [13.980265264, 9.09336493425] | [0.642857142857, 0.380952380952] |
| PB | -0.8818369 | [13.9012096024, 6.71073706755] | [0.619047619048, 0.428571428571] |
| PE | 0.1328435 | [13.9001078939, 13.4085302139] | [0.607142857143, 0.369047619048] |
| PS | -0.5030761 | [14.1865783133, 9.18250270639] | [0.607142857143, 0.392857142857] |
| ROA | 0.5423133 | [19.3405425743, 9.77751849214] | [0.75, 0.380952380952] |
| ROE | 0.6386198 | [17.9776162079, 9.73910681099] | [0.654761904762, 0.404761904762] |
| capitalization | -0.7644211 | [22.4171821446, 9.86517390072] | [0.583333333333, 0.404761904762] |
| circulating_cap | -0.7761155 | [19.8132954476, 9.86514645415] | [0.571428571429, 0.369047619048] |
| circulating_market_cap | -0.8791725 | [38.1580067747, 10.3384004828] | [0.714285714286, 0.369047619048] |
| gross_profit_margin | 0.7770139 | [15.5893122733, 9.22929383936] | [0.642857142857, 0.452380952381] |
| inc_net_profit_annual | 0.6899743 | [14.9827068239, 9.99043264863] | [0.678571428571, 0.392857142857] |
| inc_net_profit_year_on_year | 0.8082138 | [13.825611634, 3.32909642528] | [0.630952380952, 0.416666666667] |
| inc_operation_profit_annual | 0.5963116 | [13.1949471333, 9.79858245467] | [0.654761904762, 0.404761904762] |
| inc_operation_profit_year_on_year | 0.8663793 | [14.0478401847, 3.17046201915] | [0.654761904762, 0.404761904762] |
| market_cap | -0.8262643 | [44.3574164544, 10.5284689923] | [0.738095238095, 0.369047619048] |
| net_profit | 0.04857344 | [12.1195026493, 8.12374126557] | [0.642857142857, 0.380952380952] |
| operating_revenue | -0.7751005 | [23.9766654178, 11.219895262] | [0.630952380952, 0.345238095238] |
| turnover_ratio | -0.6218568 | [10.175151521, 4.22831336907] | [0.619047619048, 0.511904761905] |
有效因子¶
同時滿足上述三個條件的有：
（1）價值類因子：市盈率（B/M）
（2）成長類因子：主營毛利率（P/R），銷售毛利率（gross_profit_margin），淨利潤同比增長率（inc_net_profit_year_on_year），營業利潤同比增長率（ inc_operation_profit_year_on_year）
（3）規模類因子：營業收入（operating_revenue），總股本（capitalization），流通股本（circulating_cap），總市值（market_cap），流通市值（circulating_market_cap），資產負債（L/A）
有效因子總收益¶
In [14]:
effective_factors = ['B/M','L/A','P/R', 'capitalization', 'circulating_cap', 'circulating_market_cap', 'gross_profit_margin',
'inc_net_profit_year_on_year', 'inc_operation_profit_year_on_year', 'market_cap', 'operating_revenue']
DataFrame(total_return).ix[:,effective_factors].T
Out[14]:
| port1 | port2 | port3 | port4 | port5 | benchmark | |
|---|---|---|---|---|---|---|
| B/M | 0.918228 | 1.480658 | 1.142045 | 1.148155 | 1.686498 | 0.173762 |
| L/A | 1.870086 | 1.526532 | 0.843702 | 1.124105 | 1.297099 | 0.173762 |
| P/R | 0.952724 | 1.060859 | 1.183619 | 1.649951 | 1.524196 | 0.173762 |
| capitalization | 2.837346 | 1.656063 | 1.372731 | 1.964715 | 1.035016 | 0.173762 |
| circulating_cap | 2.382449 | 1.692737 | 1.170379 | 1.747633 | 1.035013 | 0.173762 |
| circulating_market_cap | 6.812751 | 2.619596 | 1.248171 | 1.063917 | 1.086887 | 0.173762 |
| gross_profit_margin | 0.967012 | 1.086652 | 0.899555 | 1.183325 | 1.740373 | 0.173762 |
| inc_net_profit_year_on_year | 0.421356 | 0.994127 | 1.055084 | 2.446268 | 1.504189 | 0.173762 |
| inc_operation_profit_year_on_year | 0.408645 | 0.801897 | 1.381442 | 2.183790 | 1.532979 | 0.173762 |
| market_cap | 9.116529 | 1.863749 | 1.864567 | 0.896007 | 1.108029 | 0.173762 |
| operating_revenue | 3.133399 | 1.325240 | 1.267816 | 1.006326 | 1.186449 | 0.173762 |
有效因子年化收益¶
In [15]:
DataFrame(annual_return).ix[:,effective_factors].T
Out[15]:
| port1 | port2 | port3 | port4 | port5 | benchmark | |
|---|---|---|---|---|---|---|
| B/M | 0.114680 | 0.163486 | 0.135372 | 0.135911 | 0.179047 | 0.027062 |
| L/A | 0.192109 | 0.167045 | 0.107342 | 0.133781 | 0.148674 | 0.027062 |
| P/R | 0.117996 | 0.128084 | 0.139015 | 0.176358 | 0.166865 | 0.027062 |
| capitalization | 0.251234 | 0.176810 | 0.154892 | 0.198571 | 0.125714 | 0.027062 |
| circulating_cap | 0.225195 | 0.179503 | 0.137861 | 0.183477 | 0.125714 | 0.027062 |
| circulating_market_cap | 0.408642 | 0.239110 | 0.144559 | 0.128363 | 0.130446 | 0.027062 |
| gross_profit_margin | 0.119355 | 0.130425 | 0.112864 | 0.138990 | 0.182955 | 0.027062 |
| inc_net_profit_year_on_year | 0.060353 | 0.121912 | 0.127556 | 0.229018 | 0.165318 | 0.027062 |
| inc_operation_profit_year_on_year | 0.058767 | 0.103117 | 0.155598 | 0.212897 | 0.167540 | 0.027062 |
| market_cap | 0.470636 | 0.191669 | 0.191726 | 0.112517 | 0.132347 | 0.027062 |
| operating_revenue | 0.266829 | 0.151007 | 0.146220 | 0.123053 | 0.139261 | 0.027062 |
各個因子6組收益的時間序列圖：¶
In [16]:
def draw_return_picture(df):
plt.figure(figsize =(10,4))
plt.plot((df.T+1).cumprod().ix[:,0], label = 'port1')
plt.plot((df.T+1).cumprod().ix[:,1], label = 'port2')
plt.plot((df.T+1).cumprod().ix[:,2], label = 'port3')
plt.plot((df.T+1).cumprod().ix[:,3], label = 'port4')
plt.plot((df.T+1).cumprod().ix[:,4], label = 'port5')
plt.plot((df.T+1).cumprod().ix[:,5], label = 'benchmark')
plt.xlabel('return of factor %s'%fac)
plt.legend(loc=0)
for fac in effective_factors:
draw_return_picture(monthly_return[:,:,fac])
冗餘因子的剔除¶
有些因子，因為內在的邏輯比較相近等原因，選出來的組合在個股構成和收益等方面相關性較高。所以要對這些因子做冗餘剔除，保留同類因子中收益最好、區分度最高的因子。 由於本人能力有限，未完成此步驟，具體方法：
（1）對不同因子的n個組合打分。收益越大分值越大。分值達到好將分值賦給每月該組合內的所有個股。
if AR1 > ARn #因子越小，收益越大
則組合i的分值為（n-i+1)
if AR1 < ARn #因子越小，收益越小
則組合i的分值為i
（2）按月計算個股不同因子得分的相關性矩陣。得到第t月個股的因子得分相關性矩陣Score_Corrt,u,v。u,v為因子序號。
（3）計算樣本期內相關性矩陣的平均值。即樣本期共m個月，加總矩陣後取1/m。
（4）設定得分相關性閾值MinScoreCorr。只保留與其他因子相關性較小的因子。
模型建立和選股¶
根據選好的有效因子，每月初對市場個股計算因子得分，按一定權重求得所有因子的平均分。如遇因子當月無取值時，按剩下的因子分值求加權平均。通過對個股的加權平均得分進行排序，選擇排名靠前的股票交易。
以下程式碼段等權重對因子分值求和，選出分值最高的股票進行交易
In [17]:
def score_stock(fdate):
#B/M, L/A, P/R, capitalization, circulating_cap, circulating_market_cap, market_cap, operating_revenue
#八個因子越小收益越大,分值越大，應降序排；gross_profit_margin, inc_net_profit_year_on_year,
#inc_operation_profit_year_on_year三個因子越大收益越大應順序排
effective_factors = {'inc_net_profit_year_on_year':True,'gross_profit_margin':True,'inc_operation_profit_year_on_year':True,
'B/M':False,'L/A':False,'P/R':False, 'capitalization':False, 'circulating_cap':False,
'circulating_market_cap':False, 'market_cap':False, 'operating_revenue':False}
fdf = get_factors(fdate)
score = {}
for fac,value in effective_factors.items():
score[fac] = fdf[fac].rank(ascending = value,method = 'first')
print DataFrame(score).T.sum().order(ascending = False).head(5)
score_stock = list(DataFrame(score).T.sum().order(ascending = False).index)
return score_stock,fdf['circulating_market_cap']
def get_factors(fdate):
factors = ['B/M','L/A','P/R', 'capitalization', 'circulating_cap', 'circulating_market_cap', 'gross_profit_margin',
'inc_net_profit_year_on_year', 'inc_operation_profit_year_on_year', 'market_cap', 'operating_revenue']
stock_set = get_index_stocks('000001.XSHG',fdate)
q = query(
valuation.code,
balance.total_owner_equities/valuation.market_cap/100000000,
balance.total_liability/balance.total_assets,
income.net_profit/income.operating_revenue,
valuation.capitalization,
valuation.circulating_cap,
valuation.circulating_market_cap,
indicator.gross_profit_margin,
indicator.inc_net_profit_year_on_year,
indicator.inc_operation_profit_year_on_year,
valuation.market_cap,
income.operating_revenue
).filter(
valuation.code.in_(stock_set)
)
fdf = get_fundamentals(q,date = fdate)
fdf.index = fdf['code']
fdf.columns = ['code'] + factors
return fdf.iloc[:,-11:]
[score_result,circulating_market_cap] = score_stock('2017-01-01')
code 603859.XSHG 10554 603189.XSHG 10521 600817.XSHG 10451 600385.XSHG 10372 603518.XSHG 10326 dtype: float64
6個組合和benchmark在7年中的月收益率¶
計算port1-port5以及TOP20和benchmark的月收益率，時間跨度為7×12=84個月，並將所有資料儲存在panel中。
In [18]:
year = ['2011','2012','2013','2014','2015','2016','2017']
month = ['01','02','03','04','05','06','07','08','09','10','11','12']
factors = ['B/M','L/A','P/R', 'capitalization', 'circulating_cap', 'circulating_market_cap', 'gross_profit_margin',
'inc_net_profit_year_on_year', 'inc_operation_profit_year_on_year', 'market_cap', 'operating_revenue']
result = {}
for i in range(7*12):
startdate = year[i/12] + '-' + month[i%12] + '-01'
try:
enddate = year[(i+1)/12] + '-' + month[(i+1)%12] + '-01'
except IndexError:
enddate = '2018-01-01'
try:
nextdate = year[(i+2)/12] + '-' + month[(i+2)%12] + '-01'
except IndexError:
if enddate == '2018-01-01':
nextdate = '2018-02-01'
else:
nextdate = '2018-01-01'
print 'time %s'%startdate
#綜合11個因子打分後，劃分幾個組合
df = DataFrame(np.zeros(7),index = ['Top20','port1','port2','port3','port4','port5','benchmark'])
[score,circulating_market_cap] = score_stock(startdate)
port0 = score[:20]
port1 = score[: len(score)/5]
port2 = score[ len(score)/5+1: 2*len(score)/5]
port3 = score[ 2*len(score)/5+1: -2*len(score)/5]
port4 = score[ -2*len(score)/5+1: -len(score)/5]
port5 = score[ -len(score)/5+1: ]
print len(score)
df.ix['Top20'] = calculate_port_monthly_return(port0,startdate,enddate,nextdate,circulating_market_cap)
df.ix['port1'] = calculate_port_monthly_return(port1,startdate,enddate,nextdate,circulating_market_cap)
df.ix['port2'] = calculate_port_monthly_return(port2,startdate,enddate,nextdate,circulating_market_cap)
df.ix['port3'] = calculate_port_monthly_return(port3,startdate,enddate,nextdate,circulating_market_cap)
df.ix['port4'] = calculate_port_monthly_return(port4,startdate,enddate,nextdate,circulating_market_cap)
df.ix['port5'] = calculate_port_monthly_return(port5,startdate,enddate,nextdate,circulating_market_cap)
df.ix['benchmark'] = calculate_benchmark_monthly_return(startdate,enddate,nextdate)
result[i+1]=df
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In [19]:
df = pd.Panel(result)
繪製六個組合的月超額收益率¶
In [20]:
matplotlib.rcParams['axes.unicode_minus']=False
index = ['Top20','port1','port2','port3','port4','port5']
def draw_backtest_picture(ind):
plt.figure(figsize =(10,4))
plt.plot(df.ix[:,ind,0]-df.ix[:,'benchmark',0], label = 'excess return: %s'%ind)
plt.xlabel('backtest excess return of factor %s'%ind)
plt.legend(loc=0)
grid()
for ind in index:
draw_backtest_picture(ind)
