Estimates from Cosine Similarity¶

We want to evaluate the feasibility of constructing optimized portfolios with the word embedding results. Our first estimate on the textual analysis is generating optimal portfolios using cosine similarity distances. We use the cosine similarity distance as correlation and sample return standard deviation to calculate the covariance estimate. We will compare the results at the end of this section to determine the feasibility.

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()

Cosine Similarity Distances¶

We conduct cosine similarity analysis with 2-to-4 grams embeddings on the business description of each company for all top 5 SIC industry. First, we generate the words counting matrix and perform cosine similarity anlaysis to calculate the distances, which will be used as the correlation between companies in the next step for generating covarince estimate.

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

Words Count¶

For this cosine similarity analysis, we generate sequences of 2 to 4 words as one term and only select the top 600 terms by frequency.

from sklearn.feature_extraction.text import CountVectorizer

Vectorizer = CountVectorizer(ngram_range = (2,4), 
                             max_features = 600)

count_data = Vectorizer.fit_transform(df['coDescription_stopwords'])
wordsCount = pd.DataFrame(count_data.toarray(),columns=Vectorizer.get_feature_names())
wordsCount = wordsCount.set_index(df['name'])
wordsCount

	ability make	accounting standard	acquire property	act act	act amended	additional information	adequately capitalized	adverse effect	adverse effect business	adverse event	...	wa million	weighted average	well capitalized	wholly owned	wholly owned subsidiary	wide range	within day	working interest	year ended	year ended december
name
MONGODB, INC.	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	3	0	0	5	0
SALESFORCE COM INC	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
SPLUNK INC	0	0	0	0	1	2	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
OKTA, INC.	0	0	0	0	0	1	0	0	0	0	...	0	0	0	0	0	1	0	0	1	0
VEEVA SYSTEMS INC	0	12	0	1	4	1	0	7	4	0	...	18	4	0	0	0	0	1	0	102	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
AMERICAN REALTY CAPITAL NEW YORK CITY REIT, INC.	0	0	1	0	0	1	0	1	0	0	...	0	0	0	0	0	0	0	0	2	2
CYCLACEL PHARMACEUTICALS, INC.	0	0	0	0	0	1	0	1	0	1	...	0	0	0	0	0	0	1	0	0	0
ZOETIS INC.	0	17	0	0	0	12	0	3	0	0	...	20	5	0	1	1	0	2	0	84	83
STAG INDUSTRIAL, INC.	0	0	1	0	1	0	0	1	1	0	...	0	0	0	0	0	0	0	0	2	2
EQUINIX INC	0	0	0	0	2	0	0	0	0	0	...	0	0	0	0	0	0	0	0	2	2

675 rows × 600 columns

Cosine Similarity Computation¶

# Compute Cosine Similarity
from sklearn.metrics.pairwise import cosine_similarity
cosine_sim = pd.DataFrame(cosine_similarity(wordsCount, wordsCount))
cosine_sim = cosine_sim.set_index(df['name'])
cosine_sim.columns = df['name']
cosine_sim

name	MONGODB, INC.	SALESFORCE COM INC	SPLUNK INC	OKTA, INC.	VEEVA SYSTEMS INC	AUTODESK INC	INTERNATIONAL WESTERN PETROLEUM, INC.	DAYBREAK OIL & GAS, INC.	ETERNAL SPEECH, INC.	ETERNAL SPEECH, INC.	...	OMEGA HEALTHCARE INVESTORS INC	TABLEAU SOFTWARE INC	HORIZON PHARMA PLC	MERRIMACK PHARMACEUTICALS INC	REVEN HOUSING REIT, INC.	AMERICAN REALTY CAPITAL NEW YORK CITY REIT, INC.	CYCLACEL PHARMACEUTICALS, INC.	ZOETIS INC.	STAG INDUSTRIAL, INC.	EQUINIX INC
name
MONGODB, INC.	1.000000	0.445455	0.610272	0.620961	0.500762	0.338268	0.065380	0.052345	0.000000	0.000000	...	0.050935	0.630465	0.436327	0.143385	0.066598	0.135839	0.144678	0.189609	0.178397	0.102958
SALESFORCE COM INC	0.445455	1.000000	0.635969	0.455189	0.196053	0.418546	0.043515	0.064999	0.000000	0.000000	...	0.029326	0.492079	0.300027	0.133831	0.201221	0.201230	0.145089	0.075038	0.277952	0.354856
SPLUNK INC	0.610272	0.635969	1.000000	0.665648	0.274023	0.373142	0.019112	0.073553	0.000000	0.000000	...	0.018032	0.569939	0.330028	0.116923	0.109538	0.142041	0.128467	0.136418	0.194072	0.273502
OKTA, INC.	0.620961	0.455189	0.665648	1.000000	0.195672	0.399874	0.013240	0.093942	0.000000	0.000000	...	0.013905	0.579884	0.541775	0.163709	0.109948	0.144051	0.170361	0.111937	0.163588	0.074624
VEEVA SYSTEMS INC	0.500762	0.196053	0.274023	0.195672	1.000000	0.079927	0.074096	0.030179	0.075713	0.075713	...	0.424046	0.280852	0.153335	0.083683	0.128762	0.211695	0.060273	0.501041	0.332207	0.064207
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
AMERICAN REALTY CAPITAL NEW YORK CITY REIT, INC.	0.135839	0.201230	0.142041	0.144051	0.211695	0.106627	0.027594	0.048087	0.000000	0.000000	...	0.284525	0.114080	0.075274	0.048741	0.578793	1.000000	0.039971	0.136184	0.471651	0.042298
CYCLACEL PHARMACEUTICALS, INC.	0.144678	0.145089	0.128467	0.170361	0.060273	0.094262	0.010770	0.025407	0.000000	0.000000	...	0.015318	0.193458	0.462759	0.683597	0.047288	0.039971	1.000000	0.035694	0.080139	0.013121
ZOETIS INC.	0.189609	0.075038	0.136418	0.111937	0.501041	0.069267	0.039015	0.022235	0.065917	0.065917	...	0.159082	0.327556	0.148224	0.051060	0.163391	0.136184	0.035694	1.000000	0.207232	0.031911
STAG INDUSTRIAL, INC.	0.178397	0.277952	0.194072	0.163588	0.332207	0.169739	0.044467	0.057905	0.000000	0.000000	...	0.424106	0.242169	0.179394	0.068313	0.407758	0.471651	0.080139	0.207232	1.000000	0.038365
EQUINIX INC	0.102958	0.354856	0.273502	0.074624	0.064207	0.060531	0.002205	0.013749	0.000000	0.000000	...	0.018944	0.068787	0.035503	0.011838	0.043938	0.042298	0.013121	0.031911	0.038365	1.000000

675 rows × 675 columns

Perform Mean-Variance Analysis¶

We only use the Pharmaceutical Preparations industry data to generate portfolio based on Mean-Variance Analysis. We calculate the covariance estimate with cosine similarity distance as correlation and the sample standard deviation of returns. Then we use the sample return and estimated covariance to build efficient frontier.

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

# 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¶

mu_Pharm = mu[LIST]
mu_Pharm

name
THERAPEUTICSMD, INC.             -0.016246
PTC THERAPEUTICS, INC.            0.081859
ZYNERBA PHARMACEUTICALS, INC.    -0.003030
ACTINIUM PHARMACEUTICALS, INC.   -0.028223
ORAMED PHARMACEUTICALS INC.      -0.027747
                                    ...   
CYCLACEL PHARMACEUTICALS, INC.   -0.039404
PAIN THERAPEUTICS INC            -0.028535
CORVUS PHARMACEUTICALS, INC.     -0.017058
FIVE PRIME THERAPEUTICS INC      -0.038194
PARATEK PHARMACEUTICALS, INC.    -0.024066
Length: 124, dtype: float64

Sample Covariance for the Pharmaceutical Preparations Industry¶

tmp = cov[LIST].T
cov_Pharm = tmp[LIST]
cov_Pharm

name	THERAPEUTICSMD, INC.	PTC THERAPEUTICS, INC.	ZYNERBA PHARMACEUTICALS, INC.	ACTINIUM PHARMACEUTICALS, INC.	ORAMED PHARMACEUTICALS INC.	CARA THERAPEUTICS, INC.	PROGENICS PHARMACEUTICALS INC	JOHNSON & JOHNSON	CHIASMA, INC	SYNDAX PHARMACEUTICALS INC	...	IRONWOOD PHARMACEUTICALS INC	AMICUS THERAPEUTICS INC	CELGENE CORP /DE/	ARQULE INC	SYNTHETIC BIOLOGICS, INC.	CYCLACEL PHARMACEUTICALS, INC.	PAIN THERAPEUTICS INC	CORVUS PHARMACEUTICALS, INC.	FIVE PRIME THERAPEUTICS INC	PARATEK PHARMACEUTICALS, INC.
name
THERAPEUTICSMD, INC.	0.022313	0.005716	0.012211	0.008953	0.001271	0.010204	0.006031	0.001142	0.010645	0.006653	...	0.008961	0.005136	0.005609	0.015417	0.002654	-0.002167	0.004205	0.014408	-0.001208	0.008331
PTC THERAPEUTICS, INC.	0.005716	0.077202	0.015773	0.004463	0.001953	0.027776	0.026502	-0.002392	0.006663	0.011031	...	0.014100	0.008482	0.007595	0.017331	0.005679	0.009276	0.006851	0.011528	0.013654	0.012638
ZYNERBA PHARMACEUTICALS, INC.	0.012211	0.015773	0.060301	0.013983	0.008395	0.025120	0.011908	0.001315	-0.002097	0.010391	...	0.017643	0.006013	0.003551	0.016136	0.003650	0.012120	-0.002097	-0.001143	0.007206	-0.002905
ACTINIUM PHARMACEUTICALS, INC.	0.008953	0.004463	0.013983	0.045604	0.002781	0.018911	0.009388	0.003213	0.002852	0.008557	...	0.008579	0.000157	0.003037	0.008916	0.006585	0.010661	0.000585	-0.002929	-0.001142	0.007948
ORAMED PHARMACEUTICALS INC.	0.001271	0.001953	0.008395	0.002781	0.012120	0.006528	-0.000530	-0.000037	0.005420	-0.002721	...	0.002220	0.005889	-0.000180	0.007738	0.011952	0.006241	0.002669	0.003121	0.005524	0.005203
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
CYCLACEL PHARMACEUTICALS, INC.	-0.002167	0.009276	0.012120	0.010661	0.006241	0.003389	0.001496	0.000655	0.004923	-0.013052	...	0.004142	-0.006834	0.000965	0.004197	0.002821	0.040065	0.011159	-0.002042	0.001104	0.012054
PAIN THERAPEUTICS INC	0.004205	0.006851	-0.002097	0.000585	0.002669	-0.001055	0.011351	0.000104	-0.009049	0.012620	...	0.002670	0.011887	0.003596	-0.002045	0.002679	0.011159	0.096589	0.012372	0.000731	0.006248
CORVUS PHARMACEUTICALS, INC.	0.014408	0.011528	-0.001143	-0.002929	0.003121	0.014182	0.016444	0.000146	0.014813	0.021624	...	0.008353	0.010539	0.004541	0.029058	0.011207	-0.002042	0.012372	0.050265	0.006850	0.018659
FIVE PRIME THERAPEUTICS INC	-0.001208	0.013654	0.007206	-0.001142	0.005524	0.009971	0.016159	0.000675	0.009991	0.001711	...	0.004857	0.004692	0.003060	-0.005347	0.011714	0.001104	0.000731	0.006850	0.022705	0.007209
PARATEK PHARMACEUTICALS, INC.	0.008331	0.012638	-0.002905	0.007948	0.005203	0.009235	0.013552	0.001234	0.014608	0.007191	...	0.005395	0.003788	0.007372	0.002726	0.013074	0.012054	0.006248	0.018659	0.007209	0.026534

124 rows × 124 columns

Cosine Similarity Distances for the Pharmaceutical Preparations Industry¶

tmp = cosine_sim[LIST].drop_duplicates().T
Pharm_cos_sim = tmp[LIST].drop_duplicates()
Pharm_cos_sim

name	THERAPEUTICSMD, INC.	PTC THERAPEUTICS, INC.	ZYNERBA PHARMACEUTICALS, INC.	ACTINIUM PHARMACEUTICALS, INC.	ORAMED PHARMACEUTICALS INC.	CARA THERAPEUTICS, INC.	PROGENICS PHARMACEUTICALS INC	JOHNSON & JOHNSON	CHIASMA, INC	SYNDAX PHARMACEUTICALS INC	...	IRONWOOD PHARMACEUTICALS INC	AMICUS THERAPEUTICS INC	CELGENE CORP /DE/	ARQULE INC	SYNTHETIC BIOLOGICS, INC.	CYCLACEL PHARMACEUTICALS, INC.	PAIN THERAPEUTICS INC	CORVUS PHARMACEUTICALS, INC.	FIVE PRIME THERAPEUTICS INC	PARATEK PHARMACEUTICALS, INC.
name
THERAPEUTICSMD, INC.	1.000000	0.311241	0.456582	0.534662	0.543275	0.363769	0.185475	0.206379	0.488301	0.675508	...	0.583528	0.429780	0.584773	0.016313	0.382713	0.652642	0.229070	0.352277	0.011227	0.257763
PTC THERAPEUTICS, INC.	0.311241	1.000000	0.327964	0.427764	0.374165	0.243474	0.057881	0.062339	0.375322	0.395880	...	0.328586	0.493302	0.407618	0.204760	0.236988	0.320797	0.236762	0.357569	0.000000	0.197942
ZYNERBA PHARMACEUTICALS, INC.	0.456582	0.327964	1.000000	0.617744	0.598029	0.195842	0.110879	0.025581	0.820874	0.708408	...	0.324872	0.281916	0.431761	0.000000	0.865089	0.645396	0.160295	0.625223	0.000000	0.418709
ACTINIUM PHARMACEUTICALS, INC.	0.534662	0.427764	0.617744	1.000000	0.691870	0.415886	0.115986	0.100493	0.739771	0.776724	...	0.457132	0.347511	0.673470	0.343720	0.552866	0.704761	0.379062	0.725817	0.000000	0.319632
ORAMED PHARMACEUTICALS INC.	0.543275	0.374165	0.598029	0.691870	1.000000	0.285224	0.156478	0.091661	0.651584	0.726614	...	0.417753	0.321514	0.555110	0.000000	0.444021	0.636782	0.137641	0.479985	0.000000	0.293768
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
CYCLACEL PHARMACEUTICALS, INC.	0.652642	0.320797	0.645396	0.704761	0.636782	0.249042	0.121401	0.060361	0.665669	0.727805	...	0.470073	0.416150	0.556812	0.012977	0.604900	1.000000	0.305312	0.524410	0.002977	0.307589
PAIN THERAPEUTICS INC	0.229070	0.236762	0.160295	0.379062	0.137641	0.291646	0.063775	0.036477	0.174156	0.288048	...	0.291563	0.231796	0.343935	0.661693	0.126259	0.305312	1.000000	0.608993	0.000000	0.179012
CORVUS PHARMACEUTICALS, INC.	0.352277	0.357569	0.625223	0.725817	0.479985	0.372136	0.088433	0.015900	0.673502	0.700044	...	0.434292	0.285891	0.503294	0.670545	0.645031	0.524410	0.608993	1.000000	0.000000	0.244997
FIVE PRIME THERAPEUTICS INC	0.011227	0.000000	0.000000	0.000000	0.000000	0.000000	0.079602	0.113822	0.003235	0.005774	...	0.022190	0.000000	0.103859	0.000000	0.002962	0.002977	0.000000	0.000000	1.000000	0.000000
PARATEK PHARMACEUTICALS, INC.	0.257763	0.197942	0.418709	0.319632	0.293768	0.181131	0.056366	0.036980	0.455409	0.285976	...	0.130570	0.215822	0.267446	0.000000	0.460032	0.307589	0.179012	0.244997	0.000000	1.000000

124 rows × 124 columns

Covariance for Cosine Similarity¶

sd = pd.DataFrame(np.sqrt(np.diag(np.diagonal(cov_Pharm))))
sd = sd.set_index(cov_Pharm.index)
sd.columns = cov_Pharm.index
cos_sim_cov = pd.DataFrame((np.dot(np.dot(sd, Pharm_cos_sim),sd))).set_index(cov_Pharm.index)
cos_sim_cov.columns = cov_Pharm.index
cos_sim_cov

name	THERAPEUTICSMD, INC.	PTC THERAPEUTICS, INC.	ZYNERBA PHARMACEUTICALS, INC.	ACTINIUM PHARMACEUTICALS, INC.	ORAMED PHARMACEUTICALS INC.	CARA THERAPEUTICS, INC.	PROGENICS PHARMACEUTICALS INC	JOHNSON & JOHNSON	CHIASMA, INC	SYNDAX PHARMACEUTICALS INC	...	IRONWOOD PHARMACEUTICALS INC	AMICUS THERAPEUTICS INC	CELGENE CORP /DE/	ARQULE INC	SYNTHETIC BIOLOGICS, INC.	CYCLACEL PHARMACEUTICALS, INC.	PAIN THERAPEUTICS INC	CORVUS PHARMACEUTICALS, INC.	FIVE PRIME THERAPEUTICS INC	PARATEK PHARMACEUTICALS, INC.
name
THERAPEUTICSMD, INC.	0.022313	0.012918	0.016748	0.017055	0.008934	0.011408	0.005667	0.001378	0.016164	0.023595	...	0.010360	0.008472	0.008508	0.000654	0.012480	0.019514	0.010634	0.011798	0.000253	0.006272
PTC THERAPEUTICS, INC.	0.012918	0.077202	0.022377	0.025382	0.011445	0.014203	0.003290	0.000775	0.023109	0.025721	...	0.010851	0.018087	0.011032	0.015277	0.014375	0.017841	0.020445	0.022274	0.000000	0.008959
ZYNERBA PHARMACEUTICALS, INC.	0.016748	0.022377	0.060301	0.032395	0.016167	0.010097	0.005569	0.000281	0.044669	0.040677	...	0.009482	0.009135	0.010327	0.000000	0.046377	0.031723	0.012233	0.034422	0.000000	0.016749
ACTINIUM PHARMACEUTICALS, INC.	0.017055	0.025382	0.032395	0.045604	0.016266	0.018646	0.005066	0.000960	0.035008	0.038786	...	0.011603	0.009793	0.014008	0.019710	0.025775	0.030125	0.025158	0.034750	0.000000	0.011119
ORAMED PHARMACEUTICALS INC.	0.008934	0.011445	0.016167	0.016266	0.012120	0.006592	0.003524	0.000451	0.015896	0.018705	...	0.005466	0.004671	0.005952	0.000000	0.010671	0.014032	0.004709	0.011847	0.000000	0.005268
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
CYCLACEL PHARMACEUTICALS, INC.	0.019514	0.017841	0.031723	0.030125	0.014032	0.010465	0.004970	0.000540	0.029526	0.034065	...	0.011183	0.010992	0.010856	0.000698	0.026433	0.040065	0.018993	0.023533	0.000090	0.010029
PAIN THERAPEUTICS INC	0.010634	0.020445	0.012233	0.025158	0.004709	0.019029	0.004054	0.000507	0.011994	0.020933	...	0.010770	0.009506	0.010411	0.055221	0.008566	0.018993	0.096589	0.042433	0.000000	0.009063
CORVUS PHARMACEUTICALS, INC.	0.011798	0.022274	0.034422	0.034750	0.011847	0.017516	0.004055	0.000159	0.033461	0.036700	...	0.011573	0.008458	0.010991	0.040369	0.031571	0.023533	0.042433	0.050265	0.000000	0.008947
FIVE PRIME THERAPEUTICS INC	0.000253	0.000000	0.000000	0.000000	0.000000	0.000000	0.002453	0.000767	0.000108	0.000203	...	0.000397	0.000000	0.001524	0.000000	0.000097	0.000090	0.000000	0.000000	0.022705	0.000000
PARATEK PHARMACEUTICALS, INC.	0.006272	0.008959	0.016749	0.011119	0.005268	0.006194	0.001878	0.000269	0.016439	0.010893	...	0.002528	0.004639	0.004243	0.000000	0.016359	0.010029	0.009063	0.008947	0.000000	0.026534

124 rows × 124 columns

Efficient Frontier - Pharmaceutical Preparations¶

ef1 = EfficientFrontier(mu_Pharm, cos_sim_cov, 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, cos_sim_cov, 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 Cosine Similarity Estimates")
ax.legend()
plt.tight_layout()
plt.savefig('images/Efficient_Frontier_Cos_Sim_Pharmaceutical_Preparations.png', dpi=200, bbox_inches='tight')
plt.show()

Efficient_Frontier_Cos_Sim_Pharmaceutical_Preparations.png

Min Volatility Portfolio¶

Performance¶

ef2.portfolio_performance(verbose=True);

Expected annual return: 1.2%
Annual volatility: 2.6%
Sharpe Ratio: -0.32

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 = pd.DataFrame(dic)
min_vol.to_csv("data/min_vol_cos_sim_Pharmaceutical_Preparations.csv", index = False)

	Company_Name	Weight
0	JOHNSON & JOHNSON	0.18756
1	BIOSPECIFICS TECHNOLOGIES CORP	0.07394
2	BIOMARIN PHARMACEUTICAL INC	0.04572
3	MERCK & CO., INC.	0.13753
4	BRISTOL MYERS SQUIBB CO	0.03719
5	ZOETIS INC.	0.20000
6	HERON THERAPEUTICS, INC. /DE/	0.00906
7	PERRIGO CO PLC	0.01497
8	XENCOR INC	0.02108
9	PACIRA PHARMACEUTICALS, INC.	0.01883
10	LILLY ELI & CO	0.03562
11	PFIZER INC	0.20000
12	ARQULE INC	0.00068
13	FIVE PRIME THERAPEUTICS INC	0.01782

Results for the Other 4 Industries¶

Prepackaged Software (mass reproduction of software)¶

Efficient_Frontier_Cosine_Similarity_Estimates_Prepackaged_Software.png

Min Volatility Portfolio¶

Performance¶

Expected annual return: 1.1%
Annual volatility: 2.9%
Sharpe Ratio: -0.30

Weights¶

	Company_Name	Weight
0	ALARM.COM HOLDINGS, INC.	0.01069
1	Q2 HOLDINGS, INC.	0.06190
2	ORACLE CORP	0.16315
3	INTELLICHECK, INC.	0.00938
4	ZEDGE, INC.	0.00391
5	NUANCE COMMUNICATIONS, INC.	0.05947
6	AWARE INC /MA/	0.02316
7	NATIONAL INSTRUMENTS CORP	0.09372
8	GSE SYSTEMS INC	0.04031
9	ULTIMATE SOFTWARE GROUP INC	0.10350
10	ACI WORLDWIDE, INC.	0.04754
11	BLACK KNIGHT, INC.	0.20000
12	ANSYS INC	0.15390
13	REALPAGE INC	0.02937

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_Cosine_Similarity_Estimates_Real_Estate_Investment_Trusts.png

Min Volatility Portfolio¶

Performance¶

Expected annual return: 0.6%
Annual volatility: 1.7%
Sharpe Ratio: -0.81

Weights¶

	Company_Name	Weight
0	GREAT AJAX CORP.	0.13806
1	EQUITY COMMONWEALTH	0.16327
2	RAYONIER INC	0.00876
3	EQUINIX INC	0.07068
4	HIGHWOODS PROPERTIES INC	0.05347
5	HEALTHCARE TRUST OF AMERICA, INC.	0.02052
6	STARWOOD PROPERTY TRUST, INC.	0.01851
7	MFA FINANCIAL, INC.	0.05101
8	EASTGROUP PROPERTIES INC	0.01785
9	LTC PROPERTIES INC	0.00036
10	ANNALY CAPITAL MANAGEMENT INC	0.05094
11	SUN COMMUNITIES INC	0.14907
12	GAMING & LEISURE PROPERTIES, INC.	0.06734
13	HMG COURTLAND PROPERTIES INC	0.03187
14	DUKE REALTY CORP	0.05369
15	CROWN CASTLE INTERNATIONAL CORP	0.02634
16	PUBLIC STORAGE	0.06339
17	ALEXANDERS INC	0.01487

State Commercial Banks (commercial banking)¶

Efficient_Frontier_Cosine_Similarity_Estimates_State_Commercial_Banks.png

Min Volatility Portfolio¶

Performance¶

Expected annual return: 1.1%
Annual volatility: 2.2%
Sharpe Ratio: -0.38

Weights¶

	Company_Name	Weight
0	INVESTAR HOLDING CORP	0.16789
1	CITIZENS & NORTHERN CORP	0.11305
2	S&T BANCORP INC	0.05201
3	BANNER CORP	0.20000
4	BANK OF NEW YORK MELLON CORP	0.09816
5	ENTERPRISE FINANCIAL SERVICES CORP	0.07078
6	EAST WEST BANCORP INC	0.08342
7	HOWARD BANCORP INC	0.02931
8	BANK OF HAWAII CORP	0.04935
9	UNITY BANCORP INC /NJ/	0.01179
10	CB FINANCIAL SERVICES, INC.	0.02883
11	INDEPENDENT BANK CORP /MI/	0.09540

Analysis of Textual data from 10K Financial Reports

Estimates from Cosine Similarity

Contents

Estimates from Cosine Similarity¶

Cosine Similarity Distances¶

Words Count¶

Cosine Similarity Computation¶

Perform Mean-Variance Analysis¶

Sample Mean for the Pharmaceutical Preparations Industry¶

Sample Covariance for the Pharmaceutical Preparations Industry¶

Cosine Similarity Distances for the Pharmaceutical Preparations Industry¶

Covariance for Cosine Similarity¶

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¶