CAPM

6304640094

Aus Atsavakovith

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import urllib.request
import zipfile

from pandas_datareader.famafrench import get_available_datasets
import pandas_datareader.data as web
import datetime as dt


%matplotlib inline
import qeds

qeds.themes.mpl_style();
plotly_template = qeds.themes.plotly_template()
colors = qeds.themes.COLOR_CYCLE

from sklearn import (linear_model, metrics, model_selection)

Fama-French Factors (monthly)

import urllib.request
import zipfile
ff_url = "https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/F-F_Research_Data_Factors_CSV.zip"

urllib.request.urlretrieve(ff_url,'fama_french.zip')
zip_file = zipfile.ZipFile('fama_french.zip', 'r')

zip_file.extractall()
zip_file.close()

ff_factors = pd.read_csv('F-F_Research_Data_Factors.csv', skiprows = 3, nrows = 1114, index_col = 0)
ff_factors.index = pd.to_datetime(ff_factors.index, format= '%Y%m')
ff_factors.index = ff_factors.index + pd.offsets.MonthEnd()
ff_factors = ff_factors.apply(lambda x: x/ 100)
ff_factors.head()

CONCAT DATA

get_available_datasets()

['F-F_Research_Data_Factors',
 'F-F_Research_Data_Factors_weekly',
 'F-F_Research_Data_Factors_daily',
 'F-F_Research_Data_5_Factors_2x3',
 'F-F_Research_Data_5_Factors_2x3_daily',
 'Portfolios_Formed_on_ME',
 'Portfolios_Formed_on_ME_Wout_Div',
 'Portfolios_Formed_on_ME_Daily',
 'Portfolios_Formed_on_BE-ME',
 'Portfolios_Formed_on_BE-ME_Wout_Div',
 'Portfolios_Formed_on_BE-ME_Daily',
 'Portfolios_Formed_on_OP',
 'Portfolios_Formed_on_OP_Wout_Div',
 'Portfolios_Formed_on_OP_Daily',
 'Portfolios_Formed_on_INV',
 'Portfolios_Formed_on_INV_Wout_Div',
 'Portfolios_Formed_on_INV_Daily',
 '6_Portfolios_2x3',
 '6_Portfolios_2x3_Wout_Div',
 '6_Portfolios_2x3_weekly',
 '6_Portfolios_2x3_daily',
 '25_Portfolios_5x5',
 '25_Portfolios_5x5_Wout_Div',
 '25_Portfolios_5x5_Daily',
 '100_Portfolios_10x10',
 '100_Portfolios_10x10_Wout_Div',
 '100_Portfolios_10x10_Daily',
 '6_Portfolios_ME_OP_2x3',
 '6_Portfolios_ME_OP_2x3_Wout_Div',
 '6_Portfolios_ME_OP_2x3_daily',
 '25_Portfolios_ME_OP_5x5',
 '25_Portfolios_ME_OP_5x5_Wout_Div',
 '25_Portfolios_ME_OP_5x5_daily',
 '100_Portfolios_ME_OP_10x10',
 '100_Portfolios_10x10_ME_OP_Wout_Div',
 '100_Portfolios_ME_OP_10x10_daily',
 '6_Portfolios_ME_INV_2x3',
 '6_Portfolios_ME_INV_2x3_Wout_Div',
 '6_Portfolios_ME_INV_2x3_daily',
 '25_Portfolios_ME_INV_5x5',
 '25_Portfolios_ME_INV_5x5_Wout_Div',
 '25_Portfolios_ME_INV_5x5_daily',
 '100_Portfolios_ME_INV_10x10',
 '100_Portfolios_10x10_ME_INV_Wout_Div',
 '100_Portfolios_ME_INV_10x10_daily',
 '25_Portfolios_BEME_OP_5x5',
 '25_Portfolios_BEME_OP_5x5_Wout_Div',
 '25_Portfolios_BEME_OP_5x5_daily',
 '25_Portfolios_BEME_INV_5x5',
 '25_Portfolios_BEME_INV_5x5_Wout_Div',
 '25_Portfolios_BEME_INV_5x5_daily',
 '25_Portfolios_OP_INV_5x5',
 '25_Portfolios_OP_INV_5x5_Wout_Div',
 '25_Portfolios_OP_INV_5x5_daily',
 '32_Portfolios_ME_BEME_OP_2x4x4',
 '32_Portfolios_ME_BEME_OP_2x4x4_Wout_Div',
 '32_Portfolios_ME_BEME_INV_2x4x4',
 '32_Portfolios_ME_BEME_INV_2x4x4_Wout_Div',
 '32_Portfolios_ME_OP_INV_2x4x4',
 '32_Portfolios_ME_OP_INV_2x4x4_Wout_Div',
 'Portfolios_Formed_on_E-P',
 'Portfolios_Formed_on_E-P_Wout_Div',
 'Portfolios_Formed_on_CF-P',
 'Portfolios_Formed_on_CF-P_Wout_Div',
 'Portfolios_Formed_on_D-P',
 'Portfolios_Formed_on_D-P_Wout_Div',
 '6_Portfolios_ME_EP_2x3',
 '6_Portfolios_ME_EP_2x3_Wout_Div',
 '6_Portfolios_ME_CFP_2x3',
 '6_Portfolios_ME_CFP_2x3_Wout_Div',
 '6_Portfolios_ME_DP_2x3',
 '6_Portfolios_ME_DP_2x3_Wout_Div',
 'F-F_Momentum_Factor',
 'F-F_Momentum_Factor_daily',
 '6_Portfolios_ME_Prior_12_2',
 '6_Portfolios_ME_Prior_12_2_Daily',
 '25_Portfolios_ME_Prior_12_2',
 '25_Portfolios_ME_Prior_12_2_Daily',
 '10_Portfolios_Prior_12_2',
 '10_Portfolios_Prior_12_2_Daily',
 'F-F_ST_Reversal_Factor',
 'F-F_ST_Reversal_Factor_daily',
 '6_Portfolios_ME_Prior_1_0',
 '6_Portfolios_ME_Prior_1_0_Daily',
 '25_Portfolios_ME_Prior_1_0',
 '25_Portfolios_ME_Prior_1_0_Daily',
 '10_Portfolios_Prior_1_0',
 '10_Portfolios_Prior_1_0_Daily',
 'F-F_LT_Reversal_Factor',
 'F-F_LT_Reversal_Factor_daily',
 '6_Portfolios_ME_Prior_60_13',
 '6_Portfolios_ME_Prior_60_13_Daily',
 '25_Portfolios_ME_Prior_60_13',
 '25_Portfolios_ME_Prior_60_13_Daily',
 '10_Portfolios_Prior_60_13',
 '10_Portfolios_Prior_60_13_Daily',
 'Portfolios_Formed_on_AC',
 '25_Portfolios_ME_AC_5x5',
 'Portfolios_Formed_on_BETA',
 '25_Portfolios_ME_BETA_5x5',
 'Portfolios_Formed_on_NI',
 '25_Portfolios_ME_NI_5x5',
 'Portfolios_Formed_on_VAR',
 '25_Portfolios_ME_VAR_5x5',
 'Portfolios_Formed_on_RESVAR',
 '25_Portfolios_ME_RESVAR_5x5',
 '5_Industry_Portfolios',
 '5_Industry_Portfolios_Wout_Div',
 '5_Industry_Portfolios_daily',
 '10_Industry_Portfolios',
 '10_Industry_Portfolios_Wout_Div',
 '10_Industry_Portfolios_daily',
 '12_Industry_Portfolios',
 '12_Industry_Portfolios_Wout_Div',
 '12_Industry_Portfolios_daily',
 '17_Industry_Portfolios',
 '17_Industry_Portfolios_Wout_Div',
 '17_Industry_Portfolios_daily',
 '30_Industry_Portfolios',
 '30_Industry_Portfolios_Wout_Div',
 '30_Industry_Portfolios_daily',
 '38_Industry_Portfolios',
 '38_Industry_Portfolios_Wout_Div',
 '38_Industry_Portfolios_daily',
 '48_Industry_Portfolios',
 '48_Industry_Portfolios_Wout_Div',
 '48_Industry_Portfolios_daily',
 '49_Industry_Portfolios',
 '49_Industry_Portfolios_Wout_Div',
 '49_Industry_Portfolios_daily',
 'ME_Breakpoints',
 'BE-ME_Breakpoints',
 'OP_Breakpoints',
 'INV_Breakpoints',
 'E-P_Breakpoints',
 'CF-P_Breakpoints',
 'D-P_Breakpoints',
 'Prior_2-12_Breakpoints',
 'Developed_3_Factors',
 'Developed_3_Factors_Daily',
 'Developed_ex_US_3_Factors',
 'Developed_ex_US_3_Factors_Daily',
 'Europe_3_Factors',
 'Europe_3_Factors_Daily',
 'Japan_3_Factors',
 'Japan_3_Factors_Daily',
 'Asia_Pacific_ex_Japan_3_Factors',
 'Asia_Pacific_ex_Japan_3_Factors_Daily',
 'North_America_3_Factors',
 'North_America_3_Factors_Daily',
 'Developed_5_Factors',
 'Developed_5_Factors_Daily',
 'Developed_ex_US_5_Factors',
 'Developed_ex_US_5_Factors_Daily',
 'Europe_5_Factors',
 'Europe_5_Factors_Daily',
 'Japan_5_Factors',
 'Japan_5_Factors_Daily',
 'Asia_Pacific_ex_Japan_5_Factors',
 'Asia_Pacific_ex_Japan_5_Factors_Daily',
 'North_America_5_Factors',
 'North_America_5_Factors_Daily',
 'Developed_Mom_Factor',
 'Developed_Mom_Factor_Daily',
 'Developed_ex_US_Mom_Factor',
 'Developed_ex_US_Mom_Factor_Daily',
 'Europe_Mom_Factor',
 'Europe_Mom_Factor_Daily',
 'Japan_Mom_Factor',
 'Japan_Mom_Factor_Daily',
 'Asia_Pacific_ex_Japan_MOM_Factor',
 'Asia_Pacific_ex_Japan_MOM_Factor_Daily',
 'North_America_Mom_Factor',
 'North_America_Mom_Factor_Daily',
 'Developed_6_Portfolios_ME_BE-ME',
 'Developed_6_Portfolios_ME_BE-ME_daily',
 'Developed_ex_US_6_Portfolios_ME_BE-ME',
 'Developed_ex_US_6_Portfolios_ME_BE-ME_daily',
 'Europe_6_Portfolios_ME_BE-ME',
 'Europe_6_Portfolios_ME_BE-ME_daily',
 'Japan_6_Portfolios_ME_BE-ME',
 'Japan_6_Portfolios_ME_BE-ME_daily',
 'Asia_Pacific_ex_Japan_6_Portfolios_ME_BE-ME',
 'Asia_Pacific_ex_Japan_6_Portfolios_ME_BE-ME_daily',
 'North_America_6_Portfolios_ME_BE-ME',
 'North_America_6_Portfolios_ME_BE-ME_daily',
 'Developed_25_Portfolios_ME_BE-ME',
 'Developed_25_Portfolios_ME_BE-ME_daily',
 'Developed_ex_US_25_Portfolios_ME_BE-ME',
 'Developed_ex_US_25_Portfolios_ME_BE-ME_daily',
 'Europe_25_Portfolios_ME_BE-ME',
 'Europe_25_Portfolios_ME_BE-ME_daily',
 'Japan_25_Portfolios_ME_BE-ME',
 'Japan_25_Portfolios_ME_BE-ME_daily',
 'Asia_Pacific_ex_Japan_25_Portfolios_ME_BE-ME',
 'Asia_Pacific_ex_Japan_25_Portfolios_ME_BE-ME_daily',
 'North_America_25_Portfolios_ME_BE-ME',
 'North_America_25_Portfolios_ME_BE-ME_daily',
 'Developed_6_Portfolios_ME_OP',
 'Developed_6_Portfolios_ME_OP_Daily',
 'Developed_ex_US_6_Portfolios_ME_OP',
 'Developed_ex_US_6_Portfolios_ME_OP_Daily',
 'Europe_6_Portfolios_ME_OP',
 'Europe_6_Portfolios_ME_OP_Daily',
 'Japan_6_Portfolios_ME_OP',
 'Japan_6_Portfolios_ME_OP_Daily',
 'Asia_Pacific_ex_Japan_6_Portfolios_ME_OP',
 'Asia_Pacific_ex_Japan_6_Portfolios_ME_OP_Daily',
 'North_America_6_Portfolios_ME_OP',
 'North_America_6_Portfolios_ME_OP_Daily',
 'Developed_25_Portfolios_ME_OP',
 'Developed_25_Portfolios_ME_OP_Daily',
 'Developed_ex_US_25_Portfolios_ME_OP',
 'Developed_ex_US_25_Portfolios_ME_OP_Daily',
 'Europe_25_Portfolios_ME_OP',
 'Europe_25_Portfolios_ME_OP_Daily',
 'Japan_25_Portfolios_ME_OP',
 'Japan_25_Portfolios_ME_OP_Daily',
 'Asia_Pacific_ex_Japan_25_Portfolios_ME_OP',
 'Asia_Pacific_ex_Japan_25_Portfolios_ME_OP_Daily',
 'North_America_25_Portfolios_ME_OP',
 'North_America_25_Portfolios_ME_OP_Daily',
 'Developed_6_Portfolios_ME_INV',
 'Developed_6_Portfolios_ME_INV_Daily',
 'Developed_ex_US_6_Portfolios_ME_INV',
 'Developed_ex_US_6_Portfolios_ME_INV_Daily',
 'Europe_6_Portfolios_ME_INV',
 'Europe_6_Portfolios_ME_INV_Daily',
 'Japan_6_Portfolios_ME_INV',
 'Japan_6_Portfolios_ME_INV_Daily',
 'Asia_Pacific_ex_Japan_6_Portfolios_ME_INV',
 'Asia_Pacific_ex_Japan_6_Portfolios_ME_INV_Daily',
 'North_America_6_Portfolios_ME_INV',
 'North_America_6_Portfolios_ME_INV_Daily',
 'Developed_25_Portfolios_ME_INV',
 'Developed_25_Portfolios_ME_INV_Daily',
 'Developed_ex_US_25_Portfolios_ME_INV',
 'Developed_ex_US_25_Portfolios_ME_INV_Daily',
 'Europe_25_Portfolios_ME_INV',
 'Europe_25_Portfolios_ME_INV_Daily',
 'Japan_25_Portfolios_ME_INV',
 'Japan_25_Portfolios_ME_INV_Daily',
 'Asia_Pacific_ex_Japan_25_Portfolios_ME_INV',
 'Asia_Pacific_ex_Japan_25_Portfolios_ME_INV_Daily',
 'North_America_25_Portfolios_ME_INV',
 'North_America_25_Portfolios_ME_INV_Daily',
 'Developed_6_Portfolios_ME_Prior_12_2',
 'Developed_6_Portfolios_ME_Prior_250_20_daily',
 'Developed_ex_US_6_Portfolios_ME_Prior_12_2',
 'Developed_ex_US_6_Portfolios_ME_Prior_250_20_daily',
 'Europe_6_Portfolios_ME_Prior_12_2',
 'Europe_6_Portfolios_ME_Prior_250_20_daily',
 'Japan_6_Portfolios_ME_Prior_12_2',
 'Japan_6_Portfolios_ME_Prior_250_20_daily',
 'Asia_Pacific_ex_Japan_6_Portfolios_ME_Prior_12_2',
 'Asia_Pacific_ex_Japan_6_Portfolios_ME_Prior_250_20_daily',
 'North_America_6_Portfolios_ME_Prior_12_2',
 'North_America_6_Portfolios_ME_Prior_250_20_daily',
 'Developed_25_Portfolios_ME_Prior_12_2',
 'Developed_25_Portfolios_ME_Prior_250_20_daily',
 'Developed_ex_US_25_Portfolios_ME_Prior_12_2',
 'Developed_ex_US_25_Portfolios_ME_Prior_250_20_daily',
 'Europe_25_Portfolios_ME_Prior_12_2',
 'Europe_25_Portfolios_ME_Prior_250_20_daily',
 'Japan_25_Portfolios_ME_Prior_12_2',
 'Japan_25_Portfolios_ME_Prior_250_20_daily',
 'Asia_Pacific_ex_Japan_25_Portfolios_ME_Prior_12_2',
 'Asia_Pacific_ex_Japan_25_Portfolios_ME_Prior_250_20_daily',
 'North_America_25_Portfolios_ME_Prior_12_2',
 'North_America_25_Portfolios_ME_Prior_250_20_daily',
 'Developed_32_Portfolios_ME_BE-ME_OP_2x4x4',
 'Developed_ex_US_32_Portfolios_ME_BE-ME_OP_2x4x4',
 'Europe_32_Portfolios_ME_BE-ME_OP_2x4x4',
 'Japan_32_Portfolios_ME_BE-ME_OP_2x4x4',
 'Asia_Pacific_ex_Japan_32_Portfolios_ME_BE-ME_OP_2x4x4',
 'North_America_32_Portfolios_ME_BE-ME_OP_2x4x4',
 'Developed_32_Portfolios_ME_BE-ME_INV(TA)_2x4x4',
 'Developed_ex_US_32_Portfolios_ME_BE-ME_INV(TA)_2x4x4',
 'Europe_32_Portfolios_ME_BE-ME_INV(TA)_2x4x4',
 'Japan_32_Portfolios_ME_BE-ME_INV(TA)_2x4x4',
 'Asia_Pacific_ex_Japan_32_Portfolios_ME_BE-ME_INV(TA)_2x4x4',
 'North_America_32_Portfolios_ME_BE-ME_INV(TA)_2x4x4',
 'Developed_32_Portfolios_ME_INV(TA)_OP_2x4x4',
 'Developed_ex_US_32_Portfolios_ME_INV(TA)_OP_2x4x4',
 'Europe_32_Portfolios_ME_INV(TA)_OP_2x4x4',
 'Japan_32_Portfolios_ME_INV(TA)_OP_2x4x4',
 'Asia_Pacific_ex_Japan_32_Portfolios_ME_INV(TA)_OP_2x4x4',
 'North_America_32_Portfolios_ME_INV(TA)_OP_2x4x4',
 'Emerging_5_Factors',
 'Emerging_MOM_Factor',
 'Emerging_Markets_6_Portfolios_ME_BE-ME',
 'Emerging_Markets_6_Portfolios_ME_OP',
 'Emerging_Markets_6_Portfolios_ME_INV',
 'Emerging_Markets_6_Portfolios_ME_Prior_12_2',
 'Emerging_Markets_4_Portfolios_BE-ME_OP',
 'Emerging_Markets_4_Portfolios_OP_INV',
 'Emerging_Markets_4_Portfolios_BE-ME_INV']

SELECT

F-F_Research_Data_Factors

30_Industry_Portfolios

start_date = dt.datetime(1926, 7, 1)
end_date = dt.datetime(2022, 8, 1)

ff_factors = web.DataReader('F-F_Research_Data_Factors', 'famafrench', start = start_date, end = end_date)
print(ff_factors['DESCR'])

F-F Research Data Factors
-------------------------

This file was created by CMPT_ME_BEME_RETS using the 202208 CRSP database. The 1-month TBill return is from Ibbotson and Associates, Inc. Copyright 2022 Kenneth R. French

  0 : (1154 rows x 4 cols)
  1 : Annual Factors: January-December (95 rows x 4 cols)

ff_monthly = ff_factors[0]
ff_monthly

	Mkt-RF	SMB	HML	RF
Date
1926-07	2.96	-2.56	-2.43	0.22
1926-08	2.64	-1.17	3.82	0.25
1926-09	0.36	-1.40	0.13	0.23
1926-10	-3.24	-0.09	0.70	0.32
1926-11	2.53	-0.10	-0.51	0.31
...	...	...	...	...
2022-04	-9.46	-1.41	6.19	0.01
2022-05	-0.34	-1.85	8.41	0.03
2022-06	-8.43	2.09	-5.97	0.06
2022-07	9.57	2.81	-4.10	0.08
2022-08	-3.78	1.39	0.31	0.19

1154 rows × 4 columns

industry_port = web.DataReader('30_Industry_Portfolios', 'famafrench', start = start_date, end = end_date)
print(industry_port['DESCR'])

30 Industry Portfolios
----------------------

This file was created by CMPT_IND_RETS using the 202208 CRSP database. It contains value- and equal-weighted returns for 30 industry portfolios. The portfolios are constructed at the end of June. The annual returns are from January to December. Missing data are indicated by -99.99 or -999. Copyright 2022 Kenneth R. French

  0 : Average Value Weighted Returns -- Monthly (1154 rows x 30 cols)
  1 : Average Equal Weighted Returns -- Monthly (1154 rows x 30 cols)
  2 : Average Value Weighted Returns -- Annual (95 rows x 30 cols)
  3 : Average Equal Weighted Returns -- Annual (95 rows x 30 cols)
  4 : Number of Firms in Portfolios (1154 rows x 30 cols)
  5 : Average Firm Size (1154 rows x 30 cols)
  6 : Sum of BE / Sum of ME (97 rows x 30 cols)
  7 : Value-Weighted Average of BE/ME (97 rows x 30 cols)

ind_monthly = industry_port[0]
ind_monthly

	Food	Beer	Smoke	Games	Books	Hshld	Clths	Hlth	Chems	Txtls	...	Telcm	Servs	BusEq	Paper	Trans	Whlsl	Rtail	Meals	Fin	Other
Date
1926-07	0.56	-5.19	1.29	2.93	10.97	-0.48	8.08	1.77	8.14	0.39	...	0.83	9.22	2.06	7.70	1.91	-23.79	0.07	1.87	-0.02	5.20
1926-08	2.59	27.03	6.50	0.55	10.01	-3.58	-2.51	4.25	5.50	7.97	...	2.17	2.02	4.39	-2.38	4.85	5.39	-0.75	-0.13	4.47	6.76
1926-09	1.16	4.02	1.26	6.58	-0.99	0.73	-0.51	0.69	5.33	2.30	...	2.41	2.25	0.19	-5.54	0.07	-7.87	0.25	-0.56	-1.61	-3.86
1926-10	-3.06	-3.31	1.06	-4.76	9.47	-4.68	0.12	-0.57	-4.76	1.00	...	-0.11	-2.00	-1.09	-5.08	-2.61	-15.38	-2.20	-4.11	-5.51	-8.49
1926-11	6.35	7.29	4.55	1.66	-5.80	-0.54	1.87	5.42	5.20	3.10	...	1.63	3.77	3.64	3.84	1.61	4.67	6.52	4.33	2.34	4.00
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2022-04	3.01	3.03	6.37	-25.22	-10.76	2.04	-7.00	-6.80	-2.28	6.63	...	-10.70	-12.59	-12.26	-0.74	-10.93	-2.14	-11.41	-5.47	-7.99	-7.65
2022-05	-1.68	-1.60	2.67	-2.93	-7.40	-5.12	-6.45	0.99	4.52	2.38	...	8.54	-3.35	-0.75	-0.66	-4.59	1.03	-5.64	-3.29	2.80	-1.19
2022-06	-1.64	-0.02	-11.63	-11.33	-12.53	-2.56	-12.00	-2.05	-15.65	-11.17	...	-6.72	-6.79	-10.19	-8.51	-7.14	-6.43	-8.50	-9.02	-9.05	-11.78
2022-07	3.67	5.49	0.56	14.62	12.10	0.76	11.86	2.75	7.66	6.86	...	-0.40	8.60	15.68	7.22	9.33	9.08	16.33	11.89	7.38	9.19
2022-08	-1.61	-1.87	-0.12	-2.95	-4.97	-2.16	-6.01	-5.07	-1.39	-12.20	...	-3.00	-4.72	-5.89	-7.66	-1.46	-1.60	-3.46	-1.47	-2.24	-3.65

1154 rows × 30 columns

df = pd.concat([ff_monthly, ind_monthly], axis = 1, join = 'inner')
df

	Mkt-RF	SMB	HML	RF	Food	Beer	Smoke	Games	Books	Hshld	...	Telcm	Servs	BusEq	Paper	Trans	Whlsl	Rtail	Meals	Fin	Other
Date
1926-07	2.96	-2.56	-2.43	0.22	0.56	-5.19	1.29	2.93	10.97	-0.48	...	0.83	9.22	2.06	7.70	1.91	-23.79	0.07	1.87	-0.02	5.20
1926-08	2.64	-1.17	3.82	0.25	2.59	27.03	6.50	0.55	10.01	-3.58	...	2.17	2.02	4.39	-2.38	4.85	5.39	-0.75	-0.13	4.47	6.76
1926-09	0.36	-1.40	0.13	0.23	1.16	4.02	1.26	6.58	-0.99	0.73	...	2.41	2.25	0.19	-5.54	0.07	-7.87	0.25	-0.56	-1.61	-3.86
1926-10	-3.24	-0.09	0.70	0.32	-3.06	-3.31	1.06	-4.76	9.47	-4.68	...	-0.11	-2.00	-1.09	-5.08	-2.61	-15.38	-2.20	-4.11	-5.51	-8.49
1926-11	2.53	-0.10	-0.51	0.31	6.35	7.29	4.55	1.66	-5.80	-0.54	...	1.63	3.77	3.64	3.84	1.61	4.67	6.52	4.33	2.34	4.00
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2022-04	-9.46	-1.41	6.19	0.01	3.01	3.03	6.37	-25.22	-10.76	2.04	...	-10.70	-12.59	-12.26	-0.74	-10.93	-2.14	-11.41	-5.47	-7.99	-7.65
2022-05	-0.34	-1.85	8.41	0.03	-1.68	-1.60	2.67	-2.93	-7.40	-5.12	...	8.54	-3.35	-0.75	-0.66	-4.59	1.03	-5.64	-3.29	2.80	-1.19
2022-06	-8.43	2.09	-5.97	0.06	-1.64	-0.02	-11.63	-11.33	-12.53	-2.56	...	-6.72	-6.79	-10.19	-8.51	-7.14	-6.43	-8.50	-9.02	-9.05	-11.78
2022-07	9.57	2.81	-4.10	0.08	3.67	5.49	0.56	14.62	12.10	0.76	...	-0.40	8.60	15.68	7.22	9.33	9.08	16.33	11.89	7.38	9.19
2022-08	-3.78	1.39	0.31	0.19	-1.61	-1.87	-0.12	-2.95	-4.97	-2.16	...	-3.00	-4.72	-5.89	-7.66	-1.46	-1.60	-3.46	-1.47	-2.24	-3.65

1154 rows × 34 columns

1.1) Run the following Regression

Create blank dataframe

ind_name = ind_monthly.columns

beta = pd.DataFrame(data = np.nan, index = ind_name, columns = ['BETAs'])
beta

	BETAs
Food	NaN
Beer	NaN
Smoke	NaN
Games	NaN
Books	NaN
Hshld	NaN
Clths	NaN
Hlth	NaN
Chems	NaN
Txtls	NaN
Cnstr	NaN
Steel	NaN
FabPr	NaN
ElcEq	NaN
Autos	NaN
Carry	NaN
Mines	NaN
Coal	NaN
Oil	NaN
Util	NaN
Telcm	NaN
Servs	NaN
BusEq	NaN
Paper	NaN
Trans	NaN
Whlsl	NaN
Rtail	NaN
Meals	NaN
Fin	NaN
Other	NaN

y = Ri - Rf

x = E(Rm) - Rf

from sklearn import linear_model

for i in range(len(ind_name)):
    model = linear_model.LinearRegression()
    model = model.fit(df[['Mkt-RF']], pd.DataFrame(df[ind_name[i]]-df['RF'])) 
    beta.iloc[i,:][0] = model.coef_
beta

	BETAs
Food	0.729095
Beer	0.924026
Smoke	0.623424
Games	1.385464
Books	1.110920
Hshld	0.884306
Clths	0.831563
Hlth	0.833813
Chems	1.043679
Txtls	1.145560
Cnstr	1.181354
Steel	1.361442
FabPr	1.239619
ElcEq	1.288733
Autos	1.286918
Carry	1.188716
Mines	0.913507
Coal	1.278337
Oil	0.889536
Util	0.763865
Telcm	0.664651
Servs	0.823919
BusEq	1.080205
Paper	0.948937
Trans	1.138238
Whlsl	1.086695
Rtail	0.967677
Meals	0.946614
Fin	1.158976
Other	1.055502

1.2) Plot 30 beta's against premium

exp_ri = pd.DataFrame(data = np.nan, index = ind_name, columns = ['Average Excess Return'])
for i in range(len(ind_name)):
    exp_ri.iloc[i] = np.sum(df[ind_name[i]]-df['RF'])/df.shape[0]

exp_ri

	Average Excess Return
Food	0.699220
Beer	0.929593
Smoke	0.866482
Games	0.835659
Books	0.631750
Hshld	0.655269
Clths	0.664896
Hlth	0.807920
Chems	0.777340
Txtls	0.675537
Cnstr	0.694168
Steel	0.677374
FabPr	0.800849
ElcEq	0.896854
Autos	0.923614
Carry	0.850295
Mines	0.640659
Coal	0.828094
Oil	0.773960
Util	0.618354
Telcm	0.566352
Servs	0.953033
BusEq	0.903787
Paper	0.721256
Trans	0.655191
Whlsl	0.575069
Rtail	0.777964
Meals	0.800208
Fin	0.742305
Other	0.522088

plt.scatter(beta, exp_ri)
plt.xlabel('Beta')
plt.ylabel('Excess Return')
plt.title('Beta and Excess Return')
plt.ylim(0.1,2)
plt.xlim(0.1,2)
plt.show()

plt.savefig('Beta and Excess Return.png')

<Figure size 432x288 with 0 Axes>

ax = sns.regplot(x = beta, y = exp_ri) 
ax.set_title("Beta and Excess Return", fontsize=10)
ax.set_xlabel("Beta", fontsize = 10)
ax.set_ylabel("Excess Return", fontsize = 10)

plt.savefig("REG - Beta and Excess Return.png")

CONCLUSION

we cannot observe SML right away because they are lots of error terms from the linear line.

1.3) Cross-validation for CAPM ( 10-fold, RMSE, MAE )

create blank dataframe

metric_CAPM = pd.DataFrame(data = np.nan, index = ind_name, columns = ['RMSE','MAE'])
metric_CAPM

	RMSE	MAE
Food	NaN	NaN
Beer	NaN	NaN
Smoke	NaN	NaN
Games	NaN	NaN
Books	NaN	NaN
Hshld	NaN	NaN
Clths	NaN	NaN
Hlth	NaN	NaN
Chems	NaN	NaN
Txtls	NaN	NaN
Cnstr	NaN	NaN
Steel	NaN	NaN
FabPr	NaN	NaN
ElcEq	NaN	NaN
Autos	NaN	NaN
Carry	NaN	NaN
Mines	NaN	NaN
Coal	NaN	NaN
Oil	NaN	NaN
Util	NaN	NaN
Telcm	NaN	NaN
Servs	NaN	NaN
BusEq	NaN	NaN
Paper	NaN	NaN
Trans	NaN	NaN
Whlsl	NaN	NaN
Rtail	NaN	NaN
Meals	NaN	NaN
Fin	NaN	NaN
Other	NaN	NaN

from sklearn.model_selection import KFold
kf = KFold(n_splits=10,shuffle=False)

for i in range(len(ind_name)):
    err_rmse_test = 0
    err_mae_test = 0
    mkt = df['Mkt-RF'].to_numpy()
    ri_rf = (df[ind_name[i]]-df['RF']).to_numpy()
    for train,test in kf.split(mkt):
        lr=linear_model.LinearRegression()
        reg=lr.fit(mkt[train].reshape(-1, 1),ri_rf[train])
        ri_rf_pred_test =reg.predict(mkt[test].reshape(-1, 1))
        e_test = ri_rf[test]-ri_rf_pred_test
        err_rmse_test += np.sqrt(np.mean(e_test*e_test))
        err_mae_test += np.mean(np.abs(e_test))
    rmse_10cv_test = err_rmse_test/10
    mae_10cv_test = err_mae_test/10
    metric_CAPM.iloc[i][0] = rmse_10cv_test
    metric_CAPM.iloc[i][1] = mae_10cv_test
metric_CAPM

	RMSE	MAE
Food	2.538109	1.898086
Beer	4.636514	3.384528
Smoke	4.526541	3.521301
Games	4.874197	3.623334
Books	3.861875	2.956903
Hshld	3.213406	2.409892
Clths	4.235036	3.093844
Hlth	3.229728	2.437323
Chems	2.905301	2.200431
Txtls	4.653665	3.403551
Cnstr	2.829698	2.153414
Steel	4.417177	3.314934
FabPr	2.817130	2.186627
ElcEq	3.274492	2.547459
Autos	4.572182	3.280924
Carry	4.224256	3.154163
Mines	5.255009	4.125605
Coal	8.114324	5.838560
Oil	4.139266	3.138144
Util	3.519019	2.705937
Telcm	2.901631	2.226987
Servs	5.632045	3.950464
BusEq	3.421839	2.596730
Paper	2.839679	2.148962
Trans	3.515633	2.602099
Whlsl	3.747144	2.795816
Rtail	2.954227	2.257817
Meals	3.997552	3.018501
Fin	2.691408	2.016012
Other	3.483393	2.651443

mean_rmse_CAPM = np.mean(metric['RMSE'])
mean_mae_CAPM = np.mean(metric['MAE'])
print(f"RMSE: {mean_rmse_CAPM}")
print(f"MAE: {mean_mae_CAPM}")

RMSE: 3.900715824121209
MAE: 2.9213263884838936

1.4) Fama-Factors

Blank dataframe

beta_ff = pd.DataFrame(data = np.nan, index = ind_name, columns = ['MKT', 'SMB', 'HML'])
beta_ff

	MKT	SMB	HML
Food	NaN	NaN	NaN
Beer	NaN	NaN	NaN
Smoke	NaN	NaN	NaN
Games	NaN	NaN	NaN
Books	NaN	NaN	NaN
Hshld	NaN	NaN	NaN
Clths	NaN	NaN	NaN
Hlth	NaN	NaN	NaN
Chems	NaN	NaN	NaN
Txtls	NaN	NaN	NaN
Cnstr	NaN	NaN	NaN
Steel	NaN	NaN	NaN
FabPr	NaN	NaN	NaN
ElcEq	NaN	NaN	NaN
Autos	NaN	NaN	NaN
Carry	NaN	NaN	NaN
Mines	NaN	NaN	NaN
Coal	NaN	NaN	NaN
Oil	NaN	NaN	NaN
Util	NaN	NaN	NaN
Telcm	NaN	NaN	NaN
Servs	NaN	NaN	NaN
BusEq	NaN	NaN	NaN
Paper	NaN	NaN	NaN
Trans	NaN	NaN	NaN
Whlsl	NaN	NaN	NaN
Rtail	NaN	NaN	NaN
Meals	NaN	NaN	NaN
Fin	NaN	NaN	NaN
Other	NaN	NaN	NaN

#the same as industry but 3 columns
from sklearn import linear_model

for i in range(len(ind_name)):
    model = linear_model.LinearRegression()
    model = model.fit(df[['Mkt-RF','SMB','HML']], pd.DataFrame(df[ind_name[i]]-df['RF']))
   
    beta_ff.iloc[i] = model.coef_
beta_ff

	MKT	SMB	HML
Food	0.747453	-0.140384	0.052259
Beer	0.866732	0.196442	0.133388
Smoke	0.649355	-0.216873	0.096605
Games	1.287535	0.408923	0.138250
Books	1.012498	0.372491	0.186158
Hshld	0.906274	-0.088170	-0.035378
Clths	0.761506	0.422109	-0.060045
Hlth	0.878894	-0.085659	-0.189481
Chems	1.068119	-0.151514	0.026175
Txtls	0.982731	0.563268	0.372973
Cnstr	1.118341	0.247742	0.107824
Steel	1.259659	0.232049	0.380399
FabPr	1.173377	0.261550	0.111985
ElcEq	1.295485	-0.035460	-0.000616
Autos	1.247708	0.055086	0.188627
Carry	1.097555	0.218124	0.328079
Mines	0.842647	0.258731	0.145621
Coal	1.084163	0.485378	0.673339
Oil	0.878785	-0.179207	0.290080
Util	0.755451	-0.166903	0.259715
Telcm	0.694991	-0.131654	-0.036739
Servs	0.832129	0.368626	-0.505840
BusEq	1.121167	0.153322	-0.455735
Paper	0.952825	-0.057684	0.045355
Trans	1.038001	0.163473	0.454423
Whlsl	0.972969	0.550152	0.068217
Rtail	0.979982	0.041639	-0.131479
Meals	0.896939	0.289515	-0.030568
Fin	1.121536	-0.057539	0.315218
Other	0.999547	0.283097	0.018335

1.5) Plot of those 3 betas

import matplotlib.pyplot as plt

plt.scatter(beta_ff['MKT'], exp_ri)
plt.xlabel('MKT_FF')
plt.ylabel('Excess Return')
plt.title('MKT_FF and Excess Return')
plt.ylim(0.1,2)
plt.xlim(0.1,2)
plt.show()

plt.savefig('MKT_FF and Excess Return.png')

<Figure size 432x288 with 0 Axes>

ax = sns.regplot(x = beta_ff[['MKT']], y = exp_ri) 
ax.set_title("MKT_FF and Excess Return", fontsize=10)
ax.set_xlabel("MKT_FF", fontsize = 10)
ax.set_ylabel("Excess Return", fontsize = 10)

plt.savefig("REG - MKT_FF and Excess Return.png")

import matplotlib.pyplot as plt

plt.scatter(beta_ff['SMB'], exp_ri)
plt.xlabel('SMB_FF')
plt.ylabel('Excess Return')
plt.title('SMB_FF and Excess Return')
plt.ylim(0.1,2)
plt.xlim(0.1,2)
plt.show()

plt.savefig('SMB_FF and Excess Return.png')

<Figure size 432x288 with 0 Axes>

ax = sns.regplot(x = beta_ff[['SMB']], y = exp_ri) 
ax.set_title("SMB_FF and Excess Return", fontsize=10)
ax.set_xlabel("SMB_FF", fontsize = 10)
ax.set_ylabel("Excess Return", fontsize = 10)

plt.savefig("REG - SMB_FF and Excess Return.png")

import matplotlib.pyplot as plt

plt.scatter(beta_ff['HML'], exp_ri)
plt.xlabel('HML_FF')
plt.ylabel('Excess Return')
plt.title('HML_FF and Excess Return')
plt.ylim(0.1,2)
plt.xlim(-1,1)
plt.show()

plt.savefig('HML_FF and Excess Return.png')

<Figure size 432x288 with 0 Axes>

ax = sns.regplot(x = beta_ff[['HML']], y = exp_ri) 
ax.set_title("HML_FF and Excess Return", fontsize=10)
ax.set_xlabel("HML_FF", fontsize = 10)
ax.set_ylabel("Excess Return", fontsize = 10)

plt.savefig("REG - HML_FF and Excess Return.png")

CONCLUSION

Since I plot a regplot that obviously show the linear line, but as can be seen, only MKT_FF show the positive relationship with the excess return while another 2 roughly show the negative relationship but there are many outliers.

Easily compared, when we use the CAPM to analyze the relationship, SML reveals that the linear is more obvious rather than CAPM. Therefore the Three factors model is more suitable than CAPM.

1.6) Cross-validation for Three factors model ( 10-fold, RMSE, MAE )

metric_ff = pd.DataFrame(data = np.nan, index = ind_name, columns = ['RMSE','MAE'])
metric_ff

	RMSE	MAE
Food	NaN	NaN
Beer	NaN	NaN
Smoke	NaN	NaN
Games	NaN	NaN
Books	NaN	NaN
Hshld	NaN	NaN
Clths	NaN	NaN
Hlth	NaN	NaN
Chems	NaN	NaN
Txtls	NaN	NaN
Cnstr	NaN	NaN
Steel	NaN	NaN
FabPr	NaN	NaN
ElcEq	NaN	NaN
Autos	NaN	NaN
Carry	NaN	NaN
Mines	NaN	NaN
Coal	NaN	NaN
Oil	NaN	NaN
Util	NaN	NaN
Telcm	NaN	NaN
Servs	NaN	NaN
BusEq	NaN	NaN
Paper	NaN	NaN
Trans	NaN	NaN
Whlsl	NaN	NaN
Rtail	NaN	NaN
Meals	NaN	NaN
Fin	NaN	NaN
Other	NaN	NaN

from sklearn.model_selection import KFold
kf = KFold(n_splits=10,shuffle=False)

for i in range(len(ind_name)):
    err_rmse_test = 0
    err_mae_test = 0
    FFs = df[['Mkt-RF','SMB','HML']].to_numpy()
    ri_rf = (df[ind_name[i]]-df['RF']).to_numpy()
    for train,test in kf.split(mkt):
        lr=linear_model.LinearRegression()
        reg=lr.fit(FFs[train],ri_rf[train])
        ri_rf_pred_test =reg.predict(FFs[test])
        e_test = ri_rf[test]-ri_rf_pred_test
        err_rmse_test += np.sqrt(np.mean(e_test*e_test))
        err_mae_test += np.mean(np.abs(e_test))
    rmse_10cv_test = err_rmse_test/10
    mae_10cv_test = err_mae_test/10
    metric_ff.iloc[i][0] = rmse_10cv_test
    metric_ff.iloc[i][1] = mae_10cv_test
metric_ff

	RMSE	MAE
Food	2.583992	1.950460
Beer	4.727382	3.441337
Smoke	4.534637	3.511960
Games	4.822235	3.520520
Books	3.725951	2.855786
Hshld	3.235331	2.434792
Clths	4.197140	2.975686
Hlth	3.197743	2.386017
Chems	2.943988	2.243567
Txtls	4.255104	3.106636
Cnstr	2.807713	2.112981
Steel	4.192168	3.179183
FabPr	2.690331	2.090893
ElcEq	3.334103	2.592332
Autos	4.564839	3.317047
Carry	4.102379	3.079451
Mines	5.209853	4.070646
Coal	7.683888	5.632237
Oil	4.087016	3.117979
Util	3.389365	2.590805
Telcm	2.908926	2.232419
Servs	5.143993	3.536210
BusEq	3.147124	2.411187
Paper	2.924536	2.204255
Trans	3.201444	2.472775
Whlsl	3.581311	2.605731
Rtail	2.952258	2.250535
Meals	4.032527	3.011346
Fin	2.514929	1.901121
Other	3.480490	2.631941

mean_rmse_ff = np.mean(metric['RMSE'])
mean_mae_ff = np.mean(metric['MAE'])
print(f"RMSE: {mean_rmse_ff}")
print(f"MAE: {mean_mae_ff}")

RMSE: 3.900715824121209
MAE: 2.9213263884838936