Estimates from Sample Covariance¶

The portfolios we constructed in this notebook serve as reference to the portfolios using cosine similarity estimates and factor model estimates. Here, we simply use the sample return and sample covariance to generate portfolios for each industry.

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

r_selected = pd.read_csv("data/filtered_r.csv")
# get the mean of all 
r_selected.set_index("name", inplace = True)
mu = r_selected.mean(axis = 1)
# compute the covariance matrix 
cov = r_selected.T.cov()

Perform Mean-Variance Analysis¶

We will use one industry per time to generate a minimum-variance portfolio. In our demonstration of mean-variance analysis process, we use the industry pharmaceutical preparations whose SIC code is 2834. At the end, we will show the results for other industries.

We first get the name list of pharmaceutical preparations companies and match the names with the companies in returns data. Then, we get the sample mean and sample covariance for this specific industry. We get the efficient frontier, the set of optimal portfolios, for the industry; and recognize the minimum-variance portfolio with its performance and its weights for selected companies.

from pypfopt import EfficientFrontier
from pypfopt import risk_models
from pypfopt import expected_returns
from pypfopt import objective_functions
from pypfopt import plotting

df = pd.read_csv('../data/preprocessed.csv',
                 usecols = ['reportingDate', 'name', 'CIK',
                           'coDescription_stopwords', 'SIC', 'SIC_desc'])
df = df.set_index(df.name)

# get the names of the companies in the pharmaceutical preparations industry
Pharm = df[df.SIC == 2834]
Pharm_list = Pharm.index

# get the companies name that match return data and business description data
SET = (set(Pharm_list) & set(r_selected.index))
LIST = [*SET, ]

Sample Mean for the Pharmaceutical Preparations Industry¶

name
ALEXION PHARMACEUTICALS INC                   -0.007589
VALEANT PHARMACEUTICALS INTERNATIONAL, INC.    0.004328
ARENA PHARMACEUTICALS INC                      0.032450
THERAPEUTICSMD, INC.                          -0.016246
XENCOR INC                                     0.040986
                                                 ...   
PFIZER INC                                     0.011145
TONIX PHARMACEUTICALS HOLDING CORP.           -0.091454
ENANTA PHARMACEUTICALS INC                     0.043121
SYNTHETIC BIOLOGICS, INC.                     -0.117010
PROTHENA CORP PLC                             -0.022615
Length: 124, dtype: float64

Sample Covariance for the Pharmaceutical Preparations Industry¶

name	ALEXION PHARMACEUTICALS INC	VALEANT PHARMACEUTICALS INTERNATIONAL, INC.	ARENA PHARMACEUTICALS INC	THERAPEUTICSMD, INC.	XENCOR INC	AKORN INC	CONCERT PHARMACEUTICALS, INC.	AMICUS THERAPEUTICS INC	MERCK & CO., INC.	RXI PHARMACEUTICALS CORP	...	PACIRA PHARMACEUTICALS, INC.	RETROPHIN, INC.	WAVE LIFE SCIENCES LTD.	SERES THERAPEUTICS, INC.	ATHERSYS, INC / NEW	PFIZER INC	TONIX PHARMACEUTICALS HOLDING CORP.	ENANTA PHARMACEUTICALS INC	SYNTHETIC BIOLOGICS, INC.	PROTHENA CORP PLC
name
ALEXION PHARMACEUTICALS INC	0.012712	0.006660	0.006930	0.005225	0.001170	0.007724	-0.001042	0.006752	0.000882	-0.002845	...	0.003835	0.004225	-0.003400	0.005804	0.001423	0.001644	-0.000341	0.004035	0.007318	0.004338
VALEANT PHARMACEUTICALS INTERNATIONAL, INC.	0.006660	0.039376	0.009791	0.013252	0.001746	0.003388	-0.000155	0.008508	0.003592	0.005348	...	0.014738	-0.001323	0.006341	0.008791	0.004323	0.001972	0.018120	0.002381	0.003896	0.000611
ARENA PHARMACEUTICALS INC	0.006930	0.009791	0.016468	0.009590	0.005659	0.003093	0.002774	0.008793	-0.000367	0.007589	...	-0.001459	0.006164	0.004010	0.009748	0.003847	0.000946	-0.000497	0.006247	0.008589	0.004414
THERAPEUTICSMD, INC.	0.005225	0.013252	0.009590	0.022313	0.005284	0.005202	0.012489	0.005136	0.001250	0.014646	...	0.008701	0.006256	0.012576	0.015942	0.011200	0.002476	0.008163	0.006193	0.002654	0.000172
XENCOR INC	0.001170	0.001746	0.005659	0.005284	0.022963	0.000706	0.003764	-0.000624	0.000666	0.005584	...	-0.001834	0.006962	0.013082	0.010240	0.003081	0.001374	-0.000513	0.002233	-0.001098	0.002824
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
PFIZER INC	0.001644	0.001972	0.000946	0.002476	0.001374	0.002698	0.000957	0.000309	0.000939	0.000719	...	0.002475	0.001162	0.001007	0.001630	0.002291	0.001698	-0.000593	0.000069	0.000604	0.001456
TONIX PHARMACEUTICALS HOLDING CORP.	-0.000341	0.018120	-0.000497	0.008163	-0.000513	0.002554	0.003213	0.005606	0.000483	-0.004720	...	0.004383	-0.004944	-0.003492	0.009418	-0.000825	-0.000593	0.065843	0.007495	0.007087	0.000283
ENANTA PHARMACEUTICALS INC	0.004035	0.002381	0.006247	0.006193	0.002233	0.006631	0.003183	0.005128	0.000286	0.004438	...	-0.004859	0.008284	0.000024	0.007459	0.003778	0.000069	0.007495	0.019068	0.006687	0.005810
SYNTHETIC BIOLOGICS, INC.	0.007318	0.003896	0.008589	0.002654	-0.001098	0.017232	-0.003878	0.012808	-0.000625	0.003202	...	-0.002593	0.007492	-0.001993	0.005251	0.008775	0.000604	0.007087	0.006687	0.047660	0.009052
PROTHENA CORP PLC	0.004338	0.000611	0.004414	0.000172	0.002824	0.016777	0.005445	0.015848	0.000710	0.011297	...	0.000575	0.007092	-0.005593	-0.006159	0.005641	0.001456	0.000283	0.005810	0.009052	0.043454

124 rows × 124 columns

Efficient Frontier - Pharmaceutical Preparations¶

ef1 = EfficientFrontier(mu_Pharm, cov_Pharm, weight_bounds=(0, 0.2))

fig, ax = plt.subplots()
plotting.plot_efficient_frontier(ef1, ax=ax, show_assets=True)

# Find and plot the tangency portfolio
ef2 = EfficientFrontier(mu_Pharm, cov_Pharm, weight_bounds=(0, 0.2))
# min volatility
ef2.min_volatility()
ret_tangent, std_tangent, _ = ef2.portfolio_performance()
ax.scatter(std_tangent, ret_tangent, marker="*", s=100, c="r", label="Min Volatility")

# Format
ax.set_title("Efficient Frontier - Pharmaceutical Preparations \n Sample Covariance Estimates")
ax.legend()
plt.tight_layout()
plt.savefig('images/Efficient_Frontier_Sample_Pharmaceutical_Preparations.png', dpi=200, bbox_inches='tight')
plt.show()

Efficient_Frontier_Sample_Pharmaceutical_Preparations.png

Min Volatility Portfolio¶

Performance¶

ef2.portfolio_performance(verbose=True);

Expected annual return: 1.2%
Annual volatility: 2.1%
Sharpe Ratio: -0.35

Weights¶

companies = []
weights = []
for company, weight in ef2.clean_weights().items():
    if weight != 0:
        companies.append(company)
        weights.append(weight)
        
dic = {'Company_Name':companies,'Weight':weights}
min_vol = pd.DataFrame(dic)
min_vol.to_csv("data/min_vol_sample_Pharmaceutical_Preparations.csv", index = False)

pd.read_csv("data/min_vol_sample_Pharmaceutical_Preparations.csv")

	Company_Name	Weight
0	MERCK & CO., INC.	0.20000
1	ACHAOGEN INC	0.00515
2	BRISTOL MYERS SQUIBB CO	0.12824
3	PROPHASE LABS, INC.	0.05120
4	HEAT BIOLOGICS, INC.	0.00297
5	CHEMBIO DIAGNOSTICS, INC.	0.02843
6	ORAMED PHARMACEUTICALS INC.	0.04982
7	ASSEMBLY BIOSCIENCES, INC.	0.05775
8	IMPRIMIS PHARMACEUTICALS, INC.	0.04181
9	MANNKIND CORP	0.02048
10	ARATANA THERAPEUTICS, INC.	0.03678
11	PFENEX INC.	0.03777
12	STEMLINE THERAPEUTICS INC	0.04273
13	RECRO PHARMA, INC.	0.02010
14	LIPOCINE INC.	0.00683
15	JOHNSON & JOHNSON	0.17878
16	BIODELIVERY SCIENCES INTERNATIONAL INC	0.03680
17	XENON PHARMACEUTICALS INC.	0.01350
18	ZOETIS INC.	0.01195
19	VTV THERAPEUTICS INC.	0.02372
20	CYTOMX THERAPEUTICS, INC.	0.00520

Results for the Other 4 Industries¶

Prepackaged Software (mass reproduction of software)¶

Efficient_Frontier_Sample_Covariance_Estimates_Prepackaged_Software.png

Min Volatility Portfolio¶

Performance¶

Expected annual return: 0.6%
Annual volatility: 2.4%
Sharpe Ratio: -0.57

Weights¶

	Company_Name	Weight
0	ORACLE CORP	0.09170
1	AVID TECHNOLOGY, INC.	0.00129
2	ZEDGE, INC.	0.01792
3	MAJESCO	0.01906
4	MICROSTRATEGY INC	0.02160
5	NUANCE COMMUNICATIONS, INC.	0.08608
6	QUMU CORP	0.05153
7	BLACK KNIGHT, INC.	0.20000
8	QUALYS, INC.	0.06668
9	AWARE INC /MA/	0.20000
10	ENDURANCE INTERNATIONAL GROUP HOLDINGS, INC.	0.02554
11	LIVEPERSON INC	0.01519
12	COMMVAULT SYSTEMS INC	0.07381
13	ROSETTA STONE INC	0.01647
14	ACI WORLDWIDE, INC.	0.11314

Crude Petroleum and Natural Gas¶

When we conduct the same analysis, there is no weight shown. Efficient frontier cannot be found.

Real Estate Investment Trusts¶

Efficient_Frontier_Sample_Covariance_Estimates_Real_Estate_Investment_Trusts.png

Min Volatility Portfolio¶

Performance¶

Expected annual return: 0.5%
Annual volatility: 1.8%
Sharpe Ratio: -0.80

Weights¶

	Company_Name	Weight
0	PUBLIC STORAGE	0.10950
1	GREAT AJAX CORP.	0.20000
2	CIM COMMERCIAL TRUST CORP	0.05453
3	MANHATTAN BRIDGE CAPITAL, INC	0.01480
4	BRT APARTMENTS CORP.	0.01720
5	ALEXANDERS INC	0.02292
6	LADDER CAPITAL CORP	0.04406
7	NEW YORK MORTGAGE TRUST INC	0.02065
8	ARES COMMERCIAL REAL ESTATE CORP	0.09123
9	CROWN CASTLE INTERNATIONAL CORP	0.04853
10	IMPAC MORTGAGE HOLDINGS INC	0.05104
11	HMG COURTLAND PROPERTIES INC	0.12520
12	EQUITY COMMONWEALTH	0.20000

State Commercial Banks (commercial banking)¶

Efficient_Frontier_Sample_Covariance_Estimates_State_Commercial_Banks.png

Min Volatility Portfolio¶

Performance¶

Weights¶

	Company_Name	Weight
0	RELIANT BANCORP, INC.	0.12273
1	CAROLINA TRUST BANCSHARES, INC.	0.11786
2	BANK OF THE JAMES FINANCIAL GROUP INC	0.00178
3	BANK OF NEW YORK MELLON CORP	0.09533
4	FAUQUIER BANKSHARES, INC.	0.02143
5	MACKINAC FINANCIAL CORP /MI/	0.02478
6	CITIZENS & NORTHERN CORP	0.05375
7	FIRST COMMUNITY CORP /SC/	0.05076
8	INVESTAR HOLDING CORP	0.19440
9	VILLAGE BANK & TRUST FINANCIAL CORP.	0.13994
10	GUARANTY FEDERAL BANCSHARES INC	0.17724

Analysis of Textual data from 10K Financial Reports

Estimates from Sample Covariance

Contents

Estimates from Sample Covariance¶

Perform Mean-Variance Analysis¶

Sample Mean for the Pharmaceutical Preparations Industry¶

Sample Covariance for the Pharmaceutical Preparations Industry¶

Efficient Frontier - Pharmaceutical Preparations¶

Min Volatility Portfolio¶

Performance¶

Weights¶

Results for the Other 4 Industries¶

Prepackaged Software (mass reproduction of software)¶

Min Volatility Portfolio¶

Performance¶

Weights¶

Crude Petroleum and Natural Gas¶

Real Estate Investment Trusts¶

Min Volatility Portfolio¶

Performance¶

Weights¶

State Commercial Banks (commercial banking)¶

Min Volatility Portfolio¶

Performance¶

Weights¶