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****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 Periods
2. 3000 Observations for each Period
3. 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 1.60182404
1.48860463 1.70067317 1.57084898 1.52938766 1.54919833
1.58910675 1.44369383 1.6489323 1.57230951 1.64104889
1.52816059 1.53197648 1.44067358 1.55358692 1.60347805]
[ 0.27087317 0.37938255 0.46473997 0.43118946 0.36934624
0.3215685 0.51716485 0.3740702 0.38663032 0.44333387
0.38917603 0.31347239 0.30760233 0.41415477 0.45250083
0.4439825 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 0.75825827
0.65550255 0.79076344 0.77316807 0.82031302 0.83320932
0.76971902 0.81248391 0.74568233 0.7749383 0.69168886
0.7511554 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 0.04139968
0.05818379 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,)