实证资产定价（Empirical asset pricing）已经发布于Github. 包的具体用法(Documentation)博主将会陆续在CSDN中详细介绍。

Github: GitHub - whyecofiliter/EAP: empirical asset pricing
模仿因子的投资组合（Factor mimicking portfolio）旨在去除研究因子外其他因子的影响，来构造模仿被研究因子的投资组合，并且由此得到被研究因子的因子风险溢价（factor risk permium）的时间序列。

本文参照Fama-French (1993) 构造方法来构造factor mimicking portfolio,并计算因子风险溢价的时间序列。

Fama-French (1993)的构造方法

1.按两个维度对股票进行分组。一个维度是规模，分为市值小于50%的小型股和市值大于50%的大型股。另一个是被研究因子，30%的尾部因子组、30%~70%的因子组和70%~100%的因子组。

2.计算市值加权投资组合收益率和因子风险溢价。

Size\Factor	Low(<=30%)	Medium(30%< & <=70%)	High(>70%)
Small(<=50%)	S/L	S/M	S/H
Big(>50%)	B/L	B/M	B/H

在Fama-French （1993）的论文中，因子是book to market ratio（账面市值比或市净率的倒数），并且之后的研究大多和他们构造因子的方式相似。投资组合的收益率是市值加权的投资组合收益率。下面是类的具体用法。

class Factor_mimicking_portfolio

def __init__(self, sample, perc_row=[0, 50, 100], perc_col=[0, 30, 70, 100], weight=True):

This function initializes the object.

input :

sample : data for analysis. The structure of the sample :

The first column is dependent variable/ test portfolio return.

The second is the first factor.

The third is the second factor.

The fourth is the timestamp.

The fifth is the weight.

perc_row : The percentiles that divide stocks by the first factor. The Default percentile is [0, 50, 100].

perc_col : The percentiles that divide stocks by the second factor. The Default percentile is [0, 30, 70, 100].

weight : Whether the portfolio return calculated by weight. The Default is True.

def portfolio_return_time(self):

This function is to construct portfolio and calculate the average return and difference matrix.

output :

diff : The differenced portfolio return matrix.

'''
TEST Factor_mimicking_portfolio
construct sample:1. 20 Periods2. 3000 Observations for each Period3. Character negative with return following the return=character*-0.5+sigma where sigma~N(0,1)
'''
import numpy as np
from fama_macbeth import Factor_mimicking_portfolio# construct sample
year=np.ones((3000,1),dtype=int)*2020
for i in range(19):year=np.append(year,(2019-i)*np.ones((3000,1),dtype=int))
character=np.random.normal(0, 1, (2, 20*3000))
weight = np.random.uniform(0, 1, (1, 20*3000))
#    print('Character:',character)
ret=np.array([-0.5,-1]).dot(character)+np.random.normal(0,1,20*3000)
sample=np.array([ret, character[0], character[1], year, weight[0]]).T    
#    print('Sample:',sample)
#    print(sample.shape)model = Factor_mimicking_portfolio(sample)
portfolio_return_time = model.portfolio_return_time()
print('portfolio_return_time:', portfolio_return_time)
print('portfolio_return_time:', np.shape(portfolio_return_time))
========================================================================
portfolio_return_time: [[[ 1.6302854   1.5920872   1.54199455  1.47560967  1.601824041.48860463  1.70067317  1.57084898  1.52938766  1.549198331.58910675  1.44369383  1.6489323   1.57230951  1.641048891.52816059  1.53197648  1.44067358  1.55358692  1.60347805][ 0.27087317  0.37938255  0.46473997  0.43118946  0.369346240.3215685   0.51716485  0.3740702   0.38663032  0.443333870.38917603  0.31347239  0.30760233  0.41415477  0.452500830.4439825   0.35821053  0.40601508  0.40495275  0.46236114][-0.77286286 -0.67348462 -0.79216628 -0.76712914 -0.73108828-0.74141791 -0.85011447 -0.65743291 -0.57583562 -0.80490414-0.64311824 -0.79901273 -0.81325556 -0.84443278 -0.80362147-0.75246184 -0.61693674 -0.69909426 -0.68554981 -0.6564971 ][-2.40314826 -2.26557182 -2.33416083 -2.24273881 -2.33291232-2.23002254 -2.55078764 -2.22828188 -2.10522328 -2.35410248-2.23222499 -2.24270656 -2.46218786 -2.41674229 -2.44467035-2.28062243 -2.14891322 -2.13976784 -2.23913673 -2.25997515]][[ 0.73368397  0.87086931  0.69626265  0.83424514  0.758258270.65550255  0.79076344  0.77316807  0.82031302  0.833209320.76971902  0.81248391  0.74568233  0.7749383   0.691688860.7511554   0.70757116  0.75320784  0.78223447  0.73699303][-0.55494493 -0.4097451  -0.42006211 -0.36317491 -0.47791724-0.40042274 -0.36004971 -0.39127871 -0.4712118  -0.33368187-0.48957933 -0.41103346 -0.46612991 -0.39504384 -0.34021312-0.41049521 -0.33209925 -0.39212119 -0.42890556 -0.40389983][-1.63941363 -1.52575966 -1.55711119 -1.45657452 -1.53325438-1.5163362  -1.4984305  -1.50929504 -1.52485715 -1.60331314-1.56591033 -1.60738805 -1.77875307 -1.4963315  -1.65246163-1.55526031 -1.40809313 -1.49853102 -1.56149388 -1.48409324][-2.3730976  -2.39662897 -2.25337384 -2.29081966 -2.29151265-2.17183875 -2.28919394 -2.28246311 -2.34517017 -2.43652246-2.33562934 -2.41987196 -2.5244354  -2.27126981 -2.34415049-2.30641572 -2.11566429 -2.25173887 -2.34372835 -2.22108628]][[-0.89660143 -0.72121789 -0.8457319  -0.64136454 -0.84356577-0.83310208 -0.90990973 -0.79768091 -0.70907464 -0.71598901-0.81938773 -0.63120993 -0.90324997 -0.7973712  -0.94936003-0.77700518 -0.82440531 -0.68746574 -0.77135245 -0.86648502][-0.82581811 -0.78912765 -0.88480208 -0.79436437 -0.84726347-0.72199124 -0.87721456 -0.7653489  -0.85784212 -0.77701574-0.87875536 -0.72450585 -0.77373224 -0.80919861 -0.79271394-0.85447771 -0.69030979 -0.79813627 -0.83385831 -0.86626098][-0.86655077 -0.85227505 -0.76494491 -0.68944538 -0.8021661-0.77491829 -0.64831603 -0.85186213 -0.94902153 -0.798409-0.92279209 -0.80837532 -0.96549751 -0.65189873 -0.84884016-0.80279847 -0.79115639 -0.79943676 -0.87594408 -0.82759615][ 0.03005066 -0.13105715  0.08078699 -0.04808085  0.041399680.05818379  0.26159369 -0.05418122 -0.23994689 -0.08241999-0.10340436 -0.17716539 -0.06224754  0.14547248  0.10051987-0.02579329  0.03324893 -0.11197102 -0.10459162  0.03888887]]]
portfolio_return_time: (3, 4, 20)

def portfolio_return(self):

This function is to construct factor risk premium.

output :

return_row : The first factor risk premium. The Default is size factor.

return_col : The second factor risk premium.

# Continue the previous code
portfolio_return = model.portfolio_return()
print('portfolio_return_row: \n', portfolio_return[0])
print('portfolio_return_row:', np.shape(portfolio_return[0]))
print('portfolio_return_col: \n', portfolio_return[1])
print('portfolio_return_col:', np.shape(portfolio_return[1]))
==============================================================
portfolio_return_row: 1970-01-01 00:00:00.000002001   -0.639730
1970-01-01 00:00:00.000002002   -0.623419
1970-01-01 00:00:00.000002003   -0.603673
1970-01-01 00:00:00.000002004   -0.543314
1970-01-01 00:00:00.000002005   -0.612899
1970-01-01 00:00:00.000002006   -0.567957
1970-01-01 00:00:00.000002007   -0.543462
1970-01-01 00:00:00.000002008   -0.617268
1970-01-01 00:00:00.000002009   -0.688971
1970-01-01 00:00:00.000002010   -0.593458
1970-01-01 00:00:00.000002011   -0.681085
1970-01-01 00:00:00.000002012   -0.585314
1970-01-01 00:00:00.000002013   -0.676182
1970-01-01 00:00:00.000002014   -0.528249
1970-01-01 00:00:00.000002015   -0.622599
1970-01-01 00:00:00.000002016   -0.615019
1970-01-01 00:00:00.000002017   -0.568156
1970-01-01 00:00:00.000002018   -0.599252
1970-01-01 00:00:00.000002019   -0.646437
1970-01-01 00:00:00.000002020   -0.630363
dtype: float64
portfolio_return_row: (20,)
portfolio_return_col: 1970-01-01 00:00:00.000002001   -1.582065
1970-01-01 00:00:00.000002002   -1.597753
1970-01-01 00:00:00.000002003   -1.502249
1970-01-01 00:00:00.000002004   -1.527213
1970-01-01 00:00:00.000002005   -1.527675
1970-01-01 00:00:00.000002006   -1.447892
1970-01-01 00:00:00.000002007   -1.526129
1970-01-01 00:00:00.000002008   -1.521642
1970-01-01 00:00:00.000002009   -1.563447
1970-01-01 00:00:00.000002010   -1.624348
1970-01-01 00:00:00.000002011   -1.557086
1970-01-01 00:00:00.000002012   -1.613248
1970-01-01 00:00:00.000002013   -1.682957
1970-01-01 00:00:00.000002014   -1.514180
1970-01-01 00:00:00.000002015   -1.562767
1970-01-01 00:00:00.000002016   -1.537610
1970-01-01 00:00:00.000002017   -1.410443
1970-01-01 00:00:00.000002018   -1.501159
1970-01-01 00:00:00.000002019   -1.562486
1970-01-01 00:00:00.000002020   -1.480724
dtype: float64
portfolio_return_col: (20,)