Porfolio Analysis Results
Contents
Porfolio Analysis Results¶
In this section, the porfolio performance table and weights table for each industry in terms of three kinds of estimates are displayed.
Porfolio Performance¶
Since the industry Crude Petroleum and Natural Gas cannot generate optimal portfolio selection for sample stimate and cosine similarity estimate, we do not include this industry in our performance comparison table.
| Expected Annual Return | Annual Volatility | Sharpe Ratio | ||
|---|---|---|---|---|
| Prepackaged Software | Sample | 0.600000 | 2.400000 | -0.570000 |
| Cosine Similarity | 1.100000 | 2.900000 | -0.300000 | |
| Factor Model | 1.100000 | 4.100000 | -0.210000 | |
| Pharmaceutical Preparations | Sample | 1.200000 | 2.100000 | -0.350000 |
| Cosine Similarity | 1.200000 | 2.600000 | -0.320000 | |
| Factor Model | 1.400000 | 3.300000 | -0.180000 | |
| Real Estate Investment Trusts | Sample | 0.500000 | 1.800000 | -0.800000 |
| Cosine Similarity | 0.600000 | 1.700000 | -0.810000 | |
| Factor Model | 0.600000 | 2.400000 | -0.570000 | |
| State Commercial Banks | Sample | 1.200000 | 2.700000 | -0.280000 |
| Cosine Similarity | 1.100000 | 2.200000 | -0.380000 | |
| Factor Model | 1.000000 | 3.600000 | -0.280000 |
From the above table, we can see that factor model estimated portfolios give slightly higher volatility while the cosine similarity estimated portfolios give similiar results with the sample estimated portfolios.
Next, we will look into each model’s choice of companies to determine if cosine similarity analysis and factor model can be used to construct similar portfolios as the sample estimate.
Porfolio Weights¶
We present the portfolio weights table for comparison of three estimates.
First, we highlight the companies in common as blue when comparing estimates from sample covariance and estimates from the cosine similarity of the business descriptions.
Then, we highlight the companies in common as green when comparing estimates from sample covariance and estimates from factor model based on business descriptions and return data.
Those companies that exist in all three constructed portfolios are hilighted red in the portfolio weights table.
Prepackaged Software (mass reproduction of software)¶
Sample Estimate V.S. Cosine Similarity Estimate¶
| Sample Estimate | Cosine Similarity Estimate | |||
|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | |
| 0 | BLACK KNIGHT, INC. | 0.200000 | BLACK KNIGHT, INC. | 0.200000 |
| 1 | AWARE INC /MA/ | 0.200000 | ORACLE CORP | 0.163150 |
| 2 | ACI WORLDWIDE, INC. | 0.113140 | ANSYS INC | 0.153900 |
| 3 | ORACLE CORP | 0.091700 | ULTIMATE SOFTWARE GROUP INC | 0.103500 |
| 4 | NUANCE COMMUNICATIONS, INC. | 0.086080 | NATIONAL INSTRUMENTS CORP | 0.093720 |
| 5 | COMMVAULT SYSTEMS INC | 0.073810 | Q2 HOLDINGS, INC. | 0.061900 |
| 6 | QUALYS, INC. | 0.066680 | NUANCE COMMUNICATIONS, INC. | 0.059470 |
| 7 | QUMU CORP | 0.051530 | ACI WORLDWIDE, INC. | 0.047540 |
| 8 | ENDURANCE INTERNATIONAL GROUP HOLDINGS, INC. | 0.025540 | GSE SYSTEMS INC | 0.040310 |
| 9 | MICROSTRATEGY INC | 0.021600 | REALPAGE INC | 0.029370 |
| 10 | MAJESCO | 0.019060 | AWARE INC /MA/ | 0.023160 |
| 11 | ZEDGE, INC. | 0.017920 | ALARM.COM HOLDINGS, INC. | 0.010690 |
| 12 | ROSETTA STONE INC | 0.016470 | INTELLICHECK, INC. | 0.009380 |
| 13 | LIVEPERSON INC | 0.015190 | ZEDGE, INC. | 0.003910 |
| 14 | AVID TECHNOLOGY, INC. | 0.001290 | ||
Sample Estimate V.S. Factor Model Estimate¶
| Sample Estimate | Factor Model Estimate | |||
|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | |
| 0 | BLACK KNIGHT, INC. | 0.200000 | ORACLE CORP | 0.200000 |
| 1 | AWARE INC /MA/ | 0.200000 | ACI WORLDWIDE, INC. | 0.200000 |
| 2 | ACI WORLDWIDE, INC. | 0.113140 | BLACK KNIGHT, INC. | 0.200000 |
| 3 | ORACLE CORP | 0.091700 | NATIONAL INSTRUMENTS CORP | 0.116570 |
| 4 | NUANCE COMMUNICATIONS, INC. | 0.086080 | SALESFORCE COM INC | 0.095490 |
| 5 | COMMVAULT SYSTEMS INC | 0.073810 | AWARE INC /MA/ | 0.060640 |
| 6 | QUALYS, INC. | 0.066680 | ULTIMATE SOFTWARE GROUP INC | 0.058570 |
| 7 | QUMU CORP | 0.051530 | ANSYS INC | 0.032570 |
| 8 | ENDURANCE INTERNATIONAL GROUP HOLDINGS, INC. | 0.025540 | REALPAGE INC | 0.022550 |
| 9 | MICROSTRATEGY INC | 0.021600 | POLARITYTE, INC. | 0.010950 |
| 10 | MAJESCO | 0.019060 | MICROSTRATEGY INC | 0.002280 |
| 11 | ZEDGE, INC. | 0.017920 | Q2 HOLDINGS, INC. | 0.000380 |
| 12 | ROSETTA STONE INC | 0.016470 | ||
| 13 | LIVEPERSON INC | 0.015190 | ||
| 14 | AVID TECHNOLOGY, INC. | 0.001290 | ||
All Three Estimates¶
| Sample Estimate | Cosine Similarity Estimate | Factor Model Estimate | ||||
|---|---|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | Company Name | Weight | |
| 0 | BLACK KNIGHT, INC. | 0.200000 | BLACK KNIGHT, INC. | 0.200000 | ORACLE CORP | 0.200000 |
| 1 | AWARE INC /MA/ | 0.200000 | ORACLE CORP | 0.163150 | ACI WORLDWIDE, INC. | 0.200000 |
| 2 | ACI WORLDWIDE, INC. | 0.113140 | ANSYS INC | 0.153900 | BLACK KNIGHT, INC. | 0.200000 |
| 3 | ORACLE CORP | 0.091700 | ULTIMATE SOFTWARE GROUP INC | 0.103500 | NATIONAL INSTRUMENTS CORP | 0.116570 |
| 4 | NUANCE COMMUNICATIONS, INC. | 0.086080 | NATIONAL INSTRUMENTS CORP | 0.093720 | SALESFORCE COM INC | 0.095490 |
| 5 | COMMVAULT SYSTEMS INC | 0.073810 | Q2 HOLDINGS, INC. | 0.061900 | AWARE INC /MA/ | 0.060640 |
| 6 | QUALYS, INC. | 0.066680 | NUANCE COMMUNICATIONS, INC. | 0.059470 | ULTIMATE SOFTWARE GROUP INC | 0.058570 |
| 7 | QUMU CORP | 0.051530 | ACI WORLDWIDE, INC. | 0.047540 | ANSYS INC | 0.032570 |
| 8 | ENDURANCE INTERNATIONAL GROUP HOLDINGS, INC. | 0.025540 | GSE SYSTEMS INC | 0.040310 | REALPAGE INC | 0.022550 |
| 9 | MICROSTRATEGY INC | 0.021600 | REALPAGE INC | 0.029370 | POLARITYTE, INC. | 0.010950 |
| 10 | MAJESCO | 0.019060 | AWARE INC /MA/ | 0.023160 | MICROSTRATEGY INC | 0.002280 |
| 11 | ZEDGE, INC. | 0.017920 | ALARM.COM HOLDINGS, INC. | 0.010690 | Q2 HOLDINGS, INC. | 0.000380 |
| 12 | ROSETTA STONE INC | 0.016470 | INTELLICHECK, INC. | 0.009380 | ||
| 13 | LIVEPERSON INC | 0.015190 | ZEDGE, INC. | 0.003910 | ||
| 14 | AVID TECHNOLOGY, INC. | 0.001290 | ||||
For the industry Prepackaged Software, 6/15 of the companies in sample estimated portfolio and cosine similarity estimated portfolio are the same. 5/15 of the companies in sample estimated portfolio and factor model estimated portfolio are the same. When we compare all three porfolios, there are 4 companies in common.
Pharmaceutical Preparations¶
Sample Estimate V.S. Cosine Similarity Estimate¶
| Sample Estimate | Cosine Similarity Estimate | |||
|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | |
| 0 | MERCK & CO., INC. | 0.200000 | ZOETIS INC. | 0.200000 |
| 1 | JOHNSON & JOHNSON | 0.178780 | PFIZER INC | 0.200000 |
| 2 | BRISTOL MYERS SQUIBB CO | 0.128240 | JOHNSON & JOHNSON | 0.187560 |
| 3 | ASSEMBLY BIOSCIENCES, INC. | 0.057750 | MERCK & CO., INC. | 0.137530 |
| 4 | PROPHASE LABS, INC. | 0.051200 | BIOSPECIFICS TECHNOLOGIES CORP | 0.073940 |
| 5 | ORAMED PHARMACEUTICALS INC. | 0.049820 | BIOMARIN PHARMACEUTICAL INC | 0.045720 |
| 6 | STEMLINE THERAPEUTICS INC | 0.042730 | BRISTOL MYERS SQUIBB CO | 0.037190 |
| 7 | IMPRIMIS PHARMACEUTICALS, INC. | 0.041810 | LILLY ELI & CO | 0.035620 |
| 8 | PFENEX INC. | 0.037770 | XENCOR INC | 0.021080 |
| 9 | BIODELIVERY SCIENCES INTERNATIONAL INC | 0.036800 | PACIRA PHARMACEUTICALS, INC. | 0.018830 |
| 10 | ARATANA THERAPEUTICS, INC. | 0.036780 | FIVE PRIME THERAPEUTICS INC | 0.017820 |
| 11 | CHEMBIO DIAGNOSTICS, INC. | 0.028430 | PERRIGO CO PLC | 0.014970 |
| 12 | VTV THERAPEUTICS INC. | 0.023720 | HERON THERAPEUTICS, INC. /DE/ | 0.009060 |
| 13 | MANNKIND CORP | 0.020480 | ARQULE INC | 0.000680 |
| 14 | RECRO PHARMA, INC. | 0.020100 | ||
| 15 | XENON PHARMACEUTICALS INC. | 0.013500 | ||
| 16 | ZOETIS INC. | 0.011950 | ||
| 17 | LIPOCINE INC. | 0.006830 | ||
| 18 | CYTOMX THERAPEUTICS, INC. | 0.005200 | ||
| 19 | ACHAOGEN INC | 0.005150 | ||
| 20 | HEAT BIOLOGICS, INC. | 0.002970 | ||
Sample Estimate V.S. Factor Model Estimate¶
| Sample Estimate | Factor Model Estimate | |||
|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | |
| 0 | MERCK & CO., INC. | 0.200000 | JOHNSON & JOHNSON | 0.200000 |
| 1 | JOHNSON & JOHNSON | 0.178780 | PFIZER INC | 0.200000 |
| 2 | BRISTOL MYERS SQUIBB CO | 0.128240 | ZOETIS INC. | 0.200000 |
| 3 | ASSEMBLY BIOSCIENCES, INC. | 0.057750 | MERCK & CO., INC. | 0.200000 |
| 4 | PROPHASE LABS, INC. | 0.051200 | LILLY ELI & CO | 0.182500 |
| 5 | ORAMED PHARMACEUTICALS INC. | 0.049820 | BIOSPECIFICS TECHNOLOGIES CORP | 0.017500 |
| 6 | STEMLINE THERAPEUTICS INC | 0.042730 | ||
| 7 | IMPRIMIS PHARMACEUTICALS, INC. | 0.041810 | ||
| 8 | PFENEX INC. | 0.037770 | ||
| 9 | BIODELIVERY SCIENCES INTERNATIONAL INC | 0.036800 | ||
| 10 | ARATANA THERAPEUTICS, INC. | 0.036780 | ||
| 11 | CHEMBIO DIAGNOSTICS, INC. | 0.028430 | ||
| 12 | VTV THERAPEUTICS INC. | 0.023720 | ||
| 13 | MANNKIND CORP | 0.020480 | ||
| 14 | RECRO PHARMA, INC. | 0.020100 | ||
| 15 | XENON PHARMACEUTICALS INC. | 0.013500 | ||
| 16 | ZOETIS INC. | 0.011950 | ||
| 17 | LIPOCINE INC. | 0.006830 | ||
| 18 | CYTOMX THERAPEUTICS, INC. | 0.005200 | ||
| 19 | ACHAOGEN INC | 0.005150 | ||
| 20 | HEAT BIOLOGICS, INC. | 0.002970 | ||
All Three Estimates¶
| Sample Estimate | Cosine Similarity Estimate | Factor Model Estimate | ||||
|---|---|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | Company Name | Weight | |
| 0 | MERCK & CO., INC. | 0.200000 | ZOETIS INC. | 0.200000 | JOHNSON & JOHNSON | 0.200000 |
| 1 | JOHNSON & JOHNSON | 0.178780 | PFIZER INC | 0.200000 | PFIZER INC | 0.200000 |
| 2 | BRISTOL MYERS SQUIBB CO | 0.128240 | JOHNSON & JOHNSON | 0.187560 | ZOETIS INC. | 0.200000 |
| 3 | ASSEMBLY BIOSCIENCES, INC. | 0.057750 | MERCK & CO., INC. | 0.137530 | MERCK & CO., INC. | 0.200000 |
| 4 | PROPHASE LABS, INC. | 0.051200 | BIOSPECIFICS TECHNOLOGIES CORP | 0.073940 | LILLY ELI & CO | 0.182500 |
| 5 | ORAMED PHARMACEUTICALS INC. | 0.049820 | BIOMARIN PHARMACEUTICAL INC | 0.045720 | BIOSPECIFICS TECHNOLOGIES CORP | 0.017500 |
| 6 | STEMLINE THERAPEUTICS INC | 0.042730 | BRISTOL MYERS SQUIBB CO | 0.037190 | ||
| 7 | IMPRIMIS PHARMACEUTICALS, INC. | 0.041810 | LILLY ELI & CO | 0.035620 | ||
| 8 | PFENEX INC. | 0.037770 | XENCOR INC | 0.021080 | ||
| 9 | BIODELIVERY SCIENCES INTERNATIONAL INC | 0.036800 | PACIRA PHARMACEUTICALS, INC. | 0.018830 | ||
| 10 | ARATANA THERAPEUTICS, INC. | 0.036780 | FIVE PRIME THERAPEUTICS INC | 0.017820 | ||
| 11 | CHEMBIO DIAGNOSTICS, INC. | 0.028430 | PERRIGO CO PLC | 0.014970 | ||
| 12 | VTV THERAPEUTICS INC. | 0.023720 | HERON THERAPEUTICS, INC. /DE/ | 0.009060 | ||
| 13 | MANNKIND CORP | 0.020480 | ARQULE INC | 0.000680 | ||
| 14 | RECRO PHARMA, INC. | 0.020100 | ||||
| 15 | XENON PHARMACEUTICALS INC. | 0.013500 | ||||
| 16 | ZOETIS INC. | 0.011950 | ||||
| 17 | LIPOCINE INC. | 0.006830 | ||||
| 18 | CYTOMX THERAPEUTICS, INC. | 0.005200 | ||||
| 19 | ACHAOGEN INC | 0.005150 | ||||
| 20 | HEAT BIOLOGICS, INC. | 0.002970 | ||||
For the industry Pharmaceutical Preparations, 4/21 of the companies in sample estimated portfolio and cosine similarity estimated portfolio are the same. 3/21 of the companies in sample estimated portfolio and factor model estimated portfolio are the same. When we compare all three porfolios, there are 3 companies in common.
Real Estate Investment Trusts¶
Sample Estimate V.S. Cosine Similarity Estimate¶
| Sample Estimate | Cosine Similarity Estimate | |||
|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | |
| 0 | GREAT AJAX CORP. | 0.200000 | EQUITY COMMONWEALTH | 0.163270 |
| 1 | EQUITY COMMONWEALTH | 0.200000 | SUN COMMUNITIES INC | 0.149070 |
| 2 | HMG COURTLAND PROPERTIES INC | 0.125200 | GREAT AJAX CORP. | 0.138060 |
| 3 | PUBLIC STORAGE | 0.109500 | EQUINIX INC | 0.070680 |
| 4 | ARES COMMERCIAL REAL ESTATE CORP | 0.091230 | GAMING & LEISURE PROPERTIES, INC. | 0.067340 |
| 5 | CIM COMMERCIAL TRUST CORP | 0.054530 | PUBLIC STORAGE | 0.063390 |
| 6 | IMPAC MORTGAGE HOLDINGS INC | 0.051040 | DUKE REALTY CORP | 0.053690 |
| 7 | CROWN CASTLE INTERNATIONAL CORP | 0.048530 | HIGHWOODS PROPERTIES INC | 0.053470 |
| 8 | LADDER CAPITAL CORP | 0.044060 | MFA FINANCIAL, INC. | 0.051010 |
| 9 | ALEXANDERS INC | 0.022920 | ANNALY CAPITAL MANAGEMENT INC | 0.050940 |
| 10 | NEW YORK MORTGAGE TRUST INC | 0.020650 | HMG COURTLAND PROPERTIES INC | 0.031870 |
| 11 | BRT APARTMENTS CORP. | 0.017200 | CROWN CASTLE INTERNATIONAL CORP | 0.026340 |
| 12 | MANHATTAN BRIDGE CAPITAL, INC | 0.014800 | HEALTHCARE TRUST OF AMERICA, INC. | 0.020520 |
| 13 | STARWOOD PROPERTY TRUST, INC. | 0.018510 | ||
| 14 | EASTGROUP PROPERTIES INC | 0.017850 | ||
| 15 | ALEXANDERS INC | 0.014870 | ||
| 16 | RAYONIER INC | 0.008760 | ||
| 17 | LTC PROPERTIES INC | 0.000360 | ||
Sample Estimate V.S. Factor Model Estimate¶
| Sample Estimate | Factor Model Estimate | |||
|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | |
| 0 | GREAT AJAX CORP. | 0.200000 | GREAT AJAX CORP. | 0.200000 |
| 1 | EQUITY COMMONWEALTH | 0.200000 | EQUITY COMMONWEALTH | 0.200000 |
| 2 | HMG COURTLAND PROPERTIES INC | 0.125200 | STARWOOD PROPERTY TRUST, INC. | 0.200000 |
| 3 | PUBLIC STORAGE | 0.109500 | ARES COMMERCIAL REAL ESTATE CORP | 0.093570 |
| 4 | ARES COMMERCIAL REAL ESTATE CORP | 0.091230 | ALEXANDRIA REAL ESTATE EQUITIES INC | 0.072070 |
| 5 | CIM COMMERCIAL TRUST CORP | 0.054530 | SUN COMMUNITIES INC | 0.059740 |
| 6 | IMPAC MORTGAGE HOLDINGS INC | 0.051040 | TWO HARBORS INVESTMENT CORP. | 0.059210 |
| 7 | CROWN CASTLE INTERNATIONAL CORP | 0.048530 | GAMING & LEISURE PROPERTIES, INC. | 0.041730 |
| 8 | LADDER CAPITAL CORP | 0.044060 | ESSEX PROPERTY TRUST INC | 0.031640 |
| 9 | ALEXANDERS INC | 0.022920 | UDR, INC. | 0.020510 |
| 10 | NEW YORK MORTGAGE TRUST INC | 0.020650 | PUBLIC STORAGE | 0.015510 |
| 11 | BRT APARTMENTS CORP. | 0.017200 | RAYONIER INC | 0.005130 |
| 12 | MANHATTAN BRIDGE CAPITAL, INC | 0.014800 | MFA FINANCIAL, INC. | 0.000890 |
All Three Estimates¶
| Sample Estimate | Cosine Similarity Estimate | Factor Model Estimate | ||||
|---|---|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | Company Name | Weight | |
| 0 | GREAT AJAX CORP. | 0.200000 | EQUITY COMMONWEALTH | 0.163270 | GREAT AJAX CORP. | 0.200000 |
| 1 | EQUITY COMMONWEALTH | 0.200000 | SUN COMMUNITIES INC | 0.149070 | EQUITY COMMONWEALTH | 0.200000 |
| 2 | HMG COURTLAND PROPERTIES INC | 0.125200 | GREAT AJAX CORP. | 0.138060 | STARWOOD PROPERTY TRUST, INC. | 0.200000 |
| 3 | PUBLIC STORAGE | 0.109500 | EQUINIX INC | 0.070680 | ARES COMMERCIAL REAL ESTATE CORP | 0.093570 |
| 4 | ARES COMMERCIAL REAL ESTATE CORP | 0.091230 | GAMING & LEISURE PROPERTIES, INC. | 0.067340 | ALEXANDRIA REAL ESTATE EQUITIES INC | 0.072070 |
| 5 | CIM COMMERCIAL TRUST CORP | 0.054530 | PUBLIC STORAGE | 0.063390 | SUN COMMUNITIES INC | 0.059740 |
| 6 | IMPAC MORTGAGE HOLDINGS INC | 0.051040 | DUKE REALTY CORP | 0.053690 | TWO HARBORS INVESTMENT CORP. | 0.059210 |
| 7 | CROWN CASTLE INTERNATIONAL CORP | 0.048530 | HIGHWOODS PROPERTIES INC | 0.053470 | GAMING & LEISURE PROPERTIES, INC. | 0.041730 |
| 8 | LADDER CAPITAL CORP | 0.044060 | MFA FINANCIAL, INC. | 0.051010 | ESSEX PROPERTY TRUST INC | 0.031640 |
| 9 | ALEXANDERS INC | 0.022920 | ANNALY CAPITAL MANAGEMENT INC | 0.050940 | UDR, INC. | 0.020510 |
| 10 | NEW YORK MORTGAGE TRUST INC | 0.020650 | HMG COURTLAND PROPERTIES INC | 0.031870 | PUBLIC STORAGE | 0.015510 |
| 11 | BRT APARTMENTS CORP. | 0.017200 | CROWN CASTLE INTERNATIONAL CORP | 0.026340 | RAYONIER INC | 0.005130 |
| 12 | MANHATTAN BRIDGE CAPITAL, INC | 0.014800 | HEALTHCARE TRUST OF AMERICA, INC. | 0.020520 | MFA FINANCIAL, INC. | 0.000890 |
| 13 | STARWOOD PROPERTY TRUST, INC. | 0.018510 | ||||
| 14 | EASTGROUP PROPERTIES INC | 0.017850 | ||||
| 15 | ALEXANDERS INC | 0.014870 | ||||
| 16 | RAYONIER INC | 0.008760 | ||||
| 17 | LTC PROPERTIES INC | 0.000360 | ||||
For the industry Real Estate Investment Trusts, 6/13 of the companies in sample estimated portfolio and cosine similarity estimated portfolio are the same. 4/13 of the companies in sample estimated portfolio and factor model estimated portfolio are the same. When we compare all three porfolios, there are 3 companies in common.
State Commercial Banks (commercial banking)¶
Sample Estimate V.S. Cosine Similarity Estimate¶
| Sample Estimate | Cosine Similarity Estimate | |||
|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | |
| 0 | INVESTAR HOLDING CORP | 0.194400 | BANNER CORP | 0.200000 |
| 1 | GUARANTY FEDERAL BANCSHARES INC | 0.177240 | INVESTAR HOLDING CORP | 0.167890 |
| 2 | VILLAGE BANK & TRUST FINANCIAL CORP. | 0.139940 | CITIZENS & NORTHERN CORP | 0.113050 |
| 3 | RELIANT BANCORP, INC. | 0.122730 | BANK OF NEW YORK MELLON CORP | 0.098160 |
| 4 | CAROLINA TRUST BANCSHARES, INC. | 0.117860 | INDEPENDENT BANK CORP /MI/ | 0.095400 |
| 5 | BANK OF NEW YORK MELLON CORP | 0.095330 | EAST WEST BANCORP INC | 0.083420 |
| 6 | CITIZENS & NORTHERN CORP | 0.053750 | ENTERPRISE FINANCIAL SERVICES CORP | 0.070780 |
| 7 | FIRST COMMUNITY CORP /SC/ | 0.050760 | S&T BANCORP INC | 0.052010 |
| 8 | MACKINAC FINANCIAL CORP /MI/ | 0.024780 | BANK OF HAWAII CORP | 0.049350 |
| 9 | FAUQUIER BANKSHARES, INC. | 0.021430 | HOWARD BANCORP INC | 0.029310 |
| 10 | BANK OF THE JAMES FINANCIAL GROUP INC | 0.001780 | CB FINANCIAL SERVICES, INC. | 0.028830 |
| 11 | UNITY BANCORP INC /NJ/ | 0.011790 | ||
Sample Estimate V.S. Factor Model Estimate¶
| Sample Estimate | Factor Model Estimate | |||
|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | |
| 0 | INVESTAR HOLDING CORP | 0.194400 | INVESTAR HOLDING CORP | 0.200000 |
| 1 | GUARANTY FEDERAL BANCSHARES INC | 0.177240 | MACKINAC FINANCIAL CORP /MI/ | 0.177680 |
| 2 | VILLAGE BANK & TRUST FINANCIAL CORP. | 0.139940 | BANK OF THE JAMES FINANCIAL GROUP INC | 0.124670 |
| 3 | RELIANT BANCORP, INC. | 0.122730 | HOPFED BANCORP INC | 0.090230 |
| 4 | CAROLINA TRUST BANCSHARES, INC. | 0.117860 | GUARANTY FEDERAL BANCSHARES INC | 0.088860 |
| 5 | BANK OF NEW YORK MELLON CORP | 0.095330 | BANK OF HAWAII CORP | 0.084090 |
| 6 | CITIZENS & NORTHERN CORP | 0.053750 | CB FINANCIAL SERVICES, INC. | 0.062010 |
| 7 | FIRST COMMUNITY CORP /SC/ | 0.050760 | COMMERCE BANCSHARES INC /MO/ | 0.046340 |
| 8 | MACKINAC FINANCIAL CORP /MI/ | 0.024780 | OLD LINE BANCSHARES INC | 0.036410 |
| 9 | FAUQUIER BANKSHARES, INC. | 0.021430 | CITIZENS & NORTHERN CORP | 0.034830 |
| 10 | BANK OF THE JAMES FINANCIAL GROUP INC | 0.001780 | VILLAGE BANK & TRUST FINANCIAL CORP. | 0.031400 |
| 11 | BANK OF NEW YORK MELLON CORP | 0.023480 | ||
All Three Estimates¶
| Sample Estimate | Cosine Similarity Estimate | Factor Model Estimate | ||||
|---|---|---|---|---|---|---|
| Company Name | Weight | Company Name | Weight | Company Name | Weight | |
| 0 | INVESTAR HOLDING CORP | 0.194400 | BANNER CORP | 0.200000 | INVESTAR HOLDING CORP | 0.200000 |
| 1 | GUARANTY FEDERAL BANCSHARES INC | 0.177240 | INVESTAR HOLDING CORP | 0.167890 | MACKINAC FINANCIAL CORP /MI/ | 0.177680 |
| 2 | VILLAGE BANK & TRUST FINANCIAL CORP. | 0.139940 | CITIZENS & NORTHERN CORP | 0.113050 | BANK OF THE JAMES FINANCIAL GROUP INC | 0.124670 |
| 3 | RELIANT BANCORP, INC. | 0.122730 | BANK OF NEW YORK MELLON CORP | 0.098160 | HOPFED BANCORP INC | 0.090230 |
| 4 | CAROLINA TRUST BANCSHARES, INC. | 0.117860 | INDEPENDENT BANK CORP /MI/ | 0.095400 | GUARANTY FEDERAL BANCSHARES INC | 0.088860 |
| 5 | BANK OF NEW YORK MELLON CORP | 0.095330 | EAST WEST BANCORP INC | 0.083420 | BANK OF HAWAII CORP | 0.084090 |
| 6 | CITIZENS & NORTHERN CORP | 0.053750 | ENTERPRISE FINANCIAL SERVICES CORP | 0.070780 | CB FINANCIAL SERVICES, INC. | 0.062010 |
| 7 | FIRST COMMUNITY CORP /SC/ | 0.050760 | S&T BANCORP INC | 0.052010 | COMMERCE BANCSHARES INC /MO/ | 0.046340 |
| 8 | MACKINAC FINANCIAL CORP /MI/ | 0.024780 | BANK OF HAWAII CORP | 0.049350 | OLD LINE BANCSHARES INC | 0.036410 |
| 9 | FAUQUIER BANKSHARES, INC. | 0.021430 | HOWARD BANCORP INC | 0.029310 | CITIZENS & NORTHERN CORP | 0.034830 |
| 10 | BANK OF THE JAMES FINANCIAL GROUP INC | 0.001780 | CB FINANCIAL SERVICES, INC. | 0.028830 | VILLAGE BANK & TRUST FINANCIAL CORP. | 0.031400 |
| 11 | UNITY BANCORP INC /NJ/ | 0.011790 | BANK OF NEW YORK MELLON CORP | 0.023480 | ||
For the industry State Commercial Banks, 3/11 of the companies in sample estimated portfolio and cosine similarity estimated portfolio are the same. 8/11 of the companies in sample estimated portfolio and factor model estimated portfolio are the same. When we compare all three porfolios, there are 3 companies in common.
Crude Petroleum and Natural Gas¶
Since there is no optimal portfolio generated for the Crude Petroleum and Natural Gas industry, we do not include this industry.
Conclusion¶
Overall, cosine similarity analysis has a better performance on estimating covariance close to the sample covariance. From the performance table, we can conclude that sample estimate and cosine similarity estimate give more similar results on expected returns and annual volatility for the minimum-variance portfolio.
For all portfolios constructed, the industry Prepackaged Software and Pharmaceutical Preparations, the sample portfolios have a larger selection of companies while the other two industries generate similar size of portfolio from all three estimates.
Most portfolios generated from cosine similarity estimate and factor model estimate contain less than half of the companies that are in common with sample estimate portfolio being the reference. However, for the industry State Commercial Banks, 8/11 of the companies in sample estimated portfolio and factor model estimated portfolio are the same. Factor model estimate has a better performance in consturcting a similar portfolio than cosine similarity estimate for this industry only.
To sum up, the feasibility of constructing similar portfolios using the document embeddings of the company’s business description in SEC filings is low but it indeed illustrates the possibility of constructing similar portfolios through textual analysis.
Our research has certain limitations, such as the accrucy of topic selection in factor model, due to unsupervised learning. Moreover, the informativeness of the words we used in word embedding is not confirmed.
For future research, we may apply topic modeling on the risk disclosure section of SEC filings and use the risk factors in the factor model. Business description of the companies may not explain much of their returns and correlation with other companies. Risk disclosure of the companies may reveal more information.