Constructing an optimal portfolio using Sharpe single index model
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Aug 21, 2024
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About This Presentation
We have taken automobile stocks to build an optimal portfolio using sharpe's single index model. This Dessertation was a part of our MBA project submission.
In order to form an optimal portfolio, an important step that investors or investment managers must take is portfolio analysis. In stock ...
Slide Content
Dissertation ID - 27
(A Dissertation Report Submitted in partial fulfillment of the requirements for the Degree of Master
in Business Administration under Biju Patnaik University of Technology, Odisha)
By
Soumya Ranjan Bal S Baladev Patra
Roll No. 202284016 Roll No. 202280066
Regd. No. 2206202078 Regd. No. 2206202065
Under the guidance of
Dr. Prabin Kumar Padhy
NIST INSTITUTE OF SCIENCE AND TECHNOLOGY (Autonomous )
Palur Hills, Berhampur- 761008, Odisha, India
2024
Constructing an optimal portfolio using
Sharpe single index model
(A Dissertation Report Submitted in partial fulfillment of the requirements for the Degree of Master
in Business Administration under Biju Patnaik University of Technology, Odisha)
By
Soumya Ranjan Bal S Baladev Patra
Roll No. 202284016 Roll No. 202280066
Regd. No. 2206202078 Regd. No. 2206202065
Under the guidance of
Dr. Prabin Kumar Padhy
NIST INSTITUTE OF SCIENCE AND TECHNOLOGY (Autonomous )
Palur Hills, Berhampur- 761008, Odisha, India
2024
Constructing an optimal portfolio using
Sharpe single index model
II
DECLARATION
We hereby declare that the project work entitled “Constructing an optimal portfolio using
sharpe single index model.” submitted to the Biju Patnaik University of Technology,
Odisha, Rourkela, is a record of an original work done by me under the guidance of Dr.
Prabin Kumar Padhy, Associate Professor, Dept. of Management Studies, NIST Institute of
Science and Technology, Berhampur and this project work is submitted in the partial
fulfilment of the requirements for the award of the degree of Master of Business
Administration. The results embodied in this thesis have not been submitted to any other
University or Institute for the award of any degree or diploma.
Soumya Ranjan Bal
Regd. No: 2206202078
S Baladev Patra
Regd. No: 2206202065
Signature of the Students
DECLARATION
We hereby declare that the project work entitled “Constructing an optimal portfolio using
sharpe single index model.” submitted to the Biju Patnaik University of Technology,
Odisha, Rourkela, is a record of an original work done by me under the guidance of Dr.
Prabin Kumar Padhy, Associate Professor, Dept. of Management Studies, NIST Institute of
Science and Technology, Berhampur and this project work is submitted in the partial
fulfilment of the requirements for the award of the degree of Master of Business
Administration. The results embodied in this thesis have not been submitted to any other
University or Institute for the award of any degree or diploma.
Soumya Ranjan Bal
Regd. No: 2206202078
S Baladev Patra
Regd. No: 2206202065
Signature of the Students
III
CERTIFICATE OF GUIDE
This is to certify that the project report entitled “Constructing an optimal portfolio using sharpe
single index model.” (Dissertation ID:27) submitted to NIST Institute of Science and
Technology (Autonomous), Berhampur in partial fulfilment of the requirement for the award
of the degree of MASTER OF BUSINESS ADMINISTRATION (MBA) under Biju Patnaik
University of Technology, is an authentic and original work carried out by Mr. Soumya Ranjan
Bal with University Regd. No. 2206202078 and Institute Roll No. 202284016 and Mr. S
Baladev Patra with University Regd. No. 2206202065 and Institute Roll No. 202280066 under
my guidance.
The matter embodied in this project is genuine work done by the student and has not been
submitted whether to this University or to any other University / Institute for the fulfilment of
the requirements of any course of study.
Signature of the Guide / Advisor
CERTIFICATE OF GUIDE
This is to certify that the project report entitled “Constructing an optimal portfolio using sharpe
single index model.” (Dissertation ID:27) submitted to NIST Institute of Science and
Technology (Autonomous), Berhampur in partial fulfilment of the requirement for the award
of the degree of MASTER OF BUSINESS ADMINISTRATION (MBA) under Biju Patnaik
University of Technology, is an authentic and original work carried out by Mr. Soumya Ranjan
Bal with University Regd. No. 2206202078 and Institute Roll No. 202284016 and Mr. S
Baladev Patra with University Regd. No. 2206202065 and Institute Roll No. 202280066 under
my guidance.
The matter embodied in this project is genuine work done by the student and has not been
submitted whether to this University or to any other University / Institute for the fulfilment of
the requirements of any course of study.
Signature of the Guide / Advisor
IV
ACKNOWLEDGEMENT
It is our privilege to epitomize our deepest sense of gratitude and indebtedness to our advisor,
Dr. Prabin Kumar Padhy for his valuable guidance, keen and sustained interest, intuitive.
Especially we are thankful to Dr. Ratnakar Mishra, Head of the Department, School of
Management Studies for his real source of inspiration in arousing interest towards this report.
We give our sincere thanks to Dr. Pramath Nath Acharya, MBA Dissertation Coordinator, for
helping us for our report and encouraging us to complete this report.
We acknowledge with immense pleasure the sustained interest, encouraging attitude and
constant inspiration rendered by Dr. Sukant Mohapatra (Chairman) and Dr. Amarnath Padhi
(Batch Coordinator) N.I.S.T. Their continued drive for better quality in everything that happens
at N.I.S.T. and selfless inspiration has always helped us to move ahead.
Soumya Ranjan Bal
S Baladev Patra
ACKNOWLEDGEMENT
It is our privilege to epitomize our deepest sense of gratitude and indebtedness to our advisor,
Dr. Prabin Kumar Padhy for his valuable guidance, keen and sustained interest, intuitive.
Especially we are thankful to Dr. Ratnakar Mishra, Head of the Department, School of
Management Studies for his real source of inspiration in arousing interest towards this report.
We give our sincere thanks to Dr. Pramath Nath Acharya, MBA Dissertation Coordinator, for
helping us for our report and encouraging us to complete this report.
We acknowledge with immense pleasure the sustained interest, encouraging attitude and
constant inspiration rendered by Dr. Sukant Mohapatra (Chairman) and Dr. Amarnath Padhi
(Batch Coordinator) N.I.S.T. Their continued drive for better quality in everything that happens
at N.I.S.T. and selfless inspiration has always helped us to move ahead.
Soumya Ranjan Bal
S Baladev Patra
V
ABSTRACT
Portfolio construction is an important process of the investors for investment in the equity
market. A good combination of a portfolio will give a maximum return for a particular level of
risk. This research tries to construct an optimal portfolio in Indian stock market by using the
Sharpe’s single index model. In this research, 5 stocks of NSE have been selected on the basis
of their market capitalization. The data for all the stocks for the period from 2023 May to May
2024 have been considered. The proposed method formulates a unique cut-off rate and selects
those stocks or securities to construct an optimal portfolio whose excess return to beta ratio is
greater than the cut-off rate. Then, the proportion or weight of investment in each of the selected
securities is computed on the basis of beta value, unsystematic risk, and excess return to beta
ratio and cut-off rate of each of the securities is concerned.
Keywords: Beta, Portfolio, Cut-off rate, Optimal Portfolio, Systematic Risk and Unsystematic
Risk
ABSTRACT
Portfolio construction is an important process of the investors for investment in the equity
market. A good combination of a portfolio will give a maximum return for a particular level of
risk. This research tries to construct an optimal portfolio in Indian stock market by using the
Sharpe’s single index model. In this research, 5 stocks of NSE have been selected on the basis
of their market capitalization. The data for all the stocks for the period from 2023 May to May
2024 have been considered. The proposed method formulates a unique cut-off rate and selects
those stocks or securities to construct an optimal portfolio whose excess return to beta ratio is
greater than the cut-off rate. Then, the proportion or weight of investment in each of the selected
securities is computed on the basis of beta value, unsystematic risk, and excess return to beta
ratio and cut-off rate of each of the securities is concerned.
Keywords: Beta, Portfolio, Cut-off rate, Optimal Portfolio, Systematic Risk and Unsystematic
Risk
VI
TABLE OF CONTENTS
Chapter
Description
Page No.
• Declaration
• Certificate of guide
• Acknowledgement
• Abstract
• List of Table
ii
iii
iv
v
vii
01
INTRODUCTION
1.1 Assumptions of sharpe single index
1.2 Return and investment risk
1.3 Company Profile
1.4 Objective of the study
1-7
02
REVIEW OF LITRATURE
8-12
03
RESEARCH DESIGN AND METHODOLOGY
3.1 Design of the study
3.2 Data Collection and study period
3.3 Tools used for study
13-15
04
DATA ANALYSIS AND INTERPRETATION
16-21
05
FINDINGS, LIMITATION AND CONCLUSION
5.1 Findings
5.2 Conclusion
5.3 Managerial Applications
5.4 Future Research Directions
5.5 Limitations
5.6 References
22-27
TABLE OF CONTENTS
Chapter
Description
Page No.
• Declaration
• Certificate of guide
• Acknowledgement
• Abstract
• List of Table
ii
iii
iv
v
vii
01
INTRODUCTION
1.1 Assumptions of sharpe single index
1.2 Return and investment risk
1.3 Company Profile
1.4 Objective of the study
1-7
02
REVIEW OF LITRATURE
8-12
03
RESEARCH DESIGN AND METHODOLOGY
3.1 Design of the study
3.2 Data Collection and study period
3.3 Tools used for study
13-15
04
DATA ANALYSIS AND INTERPRETATION
16-21
05
FINDINGS, LIMITATION AND CONCLUSION
5.1 Findings
5.2 Conclusion
5.3 Managerial Applications
5.4 Future Research Directions
5.5 Limitations
5.6 References
22-27
VII
LIST OF TABLES
Table
No.
Title of the Table Page
No.
4.1 Expected Returns of Sample Companies 17
4.2 Beta Values of the Sample Companies 17
4.3 Ranking of the companies based on Excess Return to Beta Ratio 18
4.4 Sample Companies based on their Ranks and Unsystematic Risk 19
4.5 Ci of Sample Companies 20
4.6 Proportion of Investment Proposed 21
LIST OF TABLES
Table
No.
Title of the Table Page
No.
4.1 Expected Returns of Sample Companies 17
4.2 Beta Values of the Sample Companies 17
4.3 Ranking of the companies based on Excess Return to Beta Ratio 18
4.4 Sample Companies based on their Ranks and Unsystematic Risk 19
4.5 Ci of Sample Companies 20
4.6 Proportion of Investment Proposed 21
1
CHAPTER - 1
INTRODUCTION
Investment decisions must have a relevant basis in order to achieve the goal of maximizing
profits and minimizing risk, where this investment decision can be made by two parties, namely
investors or Investment managers. Investors or investment managers who invest in shares in
the capital market are important to consider several factors, including the amount of capital to
be invested, the Investment period, the level of risk that will arise, and the amount of return
that will be obtained. The level of risk factor and the factor of the amount of return (return) are
the main factors that form the basis of making investment decisions, where one of the steps to
achieve the objectives of these two factors is to have an investment portfolio as a diversification
step in minimizing investment risk.
In order to form an optimal portfolio, an important step that investors or investment managers
must take is portfolio analysis. In stock portfolio analysis, methods that can be used include
the Markowitz approach and the Single Index Model.
The Markowitz portfolio model is a portfolio optimization method introduced by Hary
Markowitz in the article Portfolio Selection in the Journal of Finance in 1952. Markowitz
model states that portfolios can be formed in two ways, namely minimizing variance or
maximizing expected return. The Markowitz procedure has several weaknesses, firstly this
model requires a very large number of estimates to fill the covariance matrix, these two models
cannot provide direction for forecasting the risk premium of securities which is fundamental to
forming an efficient frontier of risky assets.
In 1963, William Sharpe developed the Single Index Model which is a simplification of the
Markowitz Model, the Single Index Model provides an easier variance analysis solution when
compared to the Markowitz Model analysis which requires using Lagrange Multiplier analysis.
The Single Index Model can also be used to calculate expected return and portfolio risk.
The Single Index Model can be an alternative in forming an optimal portfolio that is easier for
investors or investment managers The Sharpe ratio or Sharpe index or Sharpe measure or
reward-to-variability ratio is a measure of the excess return (or Risk Premium) per unit of risk
in an investment asset or a trading strategy, named after William Forsyth Sharpe. Since its
revision by the original author in 1994. The Sharpe Index is a measure with which you may
CHAPTER - 1
INTRODUCTION
Investment decisions must have a relevant basis in order to achieve the goal of maximizing
profits and minimizing risk, where this investment decision can be made by two parties, namely
investors or Investment managers. Investors or investment managers who invest in shares in
the capital market are important to consider several factors, including the amount of capital to
be invested, the Investment period, the level of risk that will arise, and the amount of return
that will be obtained. The level of risk factor and the factor of the amount of return (return) are
the main factors that form the basis of making investment decisions, where one of the steps to
achieve the objectives of these two factors is to have an investment portfolio as a diversification
step in minimizing investment risk.
In order to form an optimal portfolio, an important step that investors or investment managers
must take is portfolio analysis. In stock portfolio analysis, methods that can be used include
the Markowitz approach and the Single Index Model.
The Markowitz portfolio model is a portfolio optimization method introduced by Hary
Markowitz in the article Portfolio Selection in the Journal of Finance in 1952. Markowitz
model states that portfolios can be formed in two ways, namely minimizing variance or
maximizing expected return. The Markowitz procedure has several weaknesses, firstly this
model requires a very large number of estimates to fill the covariance matrix, these two models
cannot provide direction for forecasting the risk premium of securities which is fundamental to
forming an efficient frontier of risky assets.
In 1963, William Sharpe developed the Single Index Model which is a simplification of the
Markowitz Model, the Single Index Model provides an easier variance analysis solution when
compared to the Markowitz Model analysis which requires using Lagrange Multiplier analysis.
The Single Index Model can also be used to calculate expected return and portfolio risk.
The Single Index Model can be an alternative in forming an optimal portfolio that is easier for
investors or investment managers The Sharpe ratio or Sharpe index or Sharpe measure or
reward-to-variability ratio is a measure of the excess return (or Risk Premium) per unit of risk
in an investment asset or a trading strategy, named after William Forsyth Sharpe. Since its
revision by the original author in 1994. The Sharpe Index is a measure with which you may
2
measure the performance of your portfolio over a given period of time. The important aspect
of the Sharpe Index is that this performance indicator takes into consideration the risk of the
portfolio. The Markowitz Model was theoretically elegant and conceptually sounds in
analyzing the risk and returns of portfolio. However, its serious limitation was that it related
each security to every other security in the portfolio. Another problem is that a number of co-
variances have to be estimated. (N2-N)/2 correlation coefficients are needed to be calculated
every time. So, the need for sophistication arises, which reduces the volume of work. Then,
William F. Sharpe published a simplified model to analyses the portfolio. This model needs
(3N+2) bits of information in compilation to (N [N+3]/2) bits of information in Markowitz
analysis
By using the Single Index Model approach, we can determine the efficient set of portfolios
more simply because the Single Index Model simplifies the amount and type of input (data),
as well as the analysis procedure to determine the optimal portfolio. The Single Index Model
assumes that the correlation of the returns for each stock occurs because of the security's
response to changes in a particular index.
1.1: Assumptions of Sharpe single index
1. The expectations of all investors are homogeneous in nature.
2. A uniform holding period is used in estimating risk and return for each security.
3. The price movements of a security are not only dependent upon the nature of the other
securities. They are also dependent on the general business and economic conditions.
4. The indices, to which the returns of each security are correlated, are likely to be some
securities’ market proxy.
5. The random disturbance terms ‘ei ’ has an expected value zero (0) and a finite variance. It
is not correlated with the return on market portfolio (Rm) as well as with the error term (ei)
for any other securities.
measure the performance of your portfolio over a given period of time. The important aspect
of the Sharpe Index is that this performance indicator takes into consideration the risk of the
portfolio. The Markowitz Model was theoretically elegant and conceptually sounds in
analyzing the risk and returns of portfolio. However, its serious limitation was that it related
each security to every other security in the portfolio. Another problem is that a number of co-
variances have to be estimated. (N2-N)/2 correlation coefficients are needed to be calculated
every time. So, the need for sophistication arises, which reduces the volume of work. Then,
William F. Sharpe published a simplified model to analyses the portfolio. This model needs
(3N+2) bits of information in compilation to (N [N+3]/2) bits of information in Markowitz
analysis
By using the Single Index Model approach, we can determine the efficient set of portfolios
more simply because the Single Index Model simplifies the amount and type of input (data),
as well as the analysis procedure to determine the optimal portfolio. The Single Index Model
assumes that the correlation of the returns for each stock occurs because of the security's
response to changes in a particular index.
1.1: Assumptions of Sharpe single index
1. The expectations of all investors are homogeneous in nature.
2. A uniform holding period is used in estimating risk and return for each security.
3. The price movements of a security are not only dependent upon the nature of the other
securities. They are also dependent on the general business and economic conditions.
4. The indices, to which the returns of each security are correlated, are likely to be some
securities’ market proxy.
5. The random disturbance terms ‘ei ’ has an expected value zero (0) and a finite variance. It
is not correlated with the return on market portfolio (Rm) as well as with the error term (ei)
for any other securities.
3
1.2: Return and Investment Risk
According to Brigham et al (1999), stated that Return is: "measure the financial performance
of an investment." return is used in an investment to measure the financial results of an
investment. According to (Jogiyanto, 2008) returns can be divided into:
i. Return Realization
The process of turning investment earnings into cash or its equivalents, or return realization,
denotes the actual receipt of investment profits. Return is calculated based on historical data.
Realized return is important because it is used as a measure of company performance. This
historical return is also useful as a basis for determining the expected return and risk in the
future. The calculation of realized return here uses total return. Total return is the total of an
investment in a certain period.
ii. Return Expected
A return that is used for making investment decisions. This return is important compared to
historical returns because the expected return is the expected return on the investment made.
Expected return can be calculated using the expectation value method, which is to multiply
each future outcome by its probability of occurrence and add up all the products of this product.
Understanding risk according to Keown (1999), risk is the possibilities that a return will be
different from the expected rate of return. According to Jones (2002), there are two types of
risk, namely:
a. Systematic risk:
Risk related to conditions that occur on the market in general, namely interest rate risk,
political risk, inflation risk, exchange rate risk and market risk. Also called the risk of not
diversification.
b. unsystematic risk:
The risk associated with the condition of the company that occurs individually, namely
business risk, leverage risk and liquidity risk. Also called diversification risk, residual risk,
unique risk, or company-specific risk. So, it can be concluded that risk is the possibility of a
real deviation of the rate of return against the expected rate of return. The amount of the risk
value can be found by calculating the standard deviation, or by calculating the variance.
1.2: Return and Investment Risk
According to Brigham et al (1999), stated that Return is: "measure the financial performance
of an investment." return is used in an investment to measure the financial results of an
investment. According to (Jogiyanto, 2008) returns can be divided into:
i. Return Realization
The process of turning investment earnings into cash or its equivalents, or return realization,
denotes the actual receipt of investment profits. Return is calculated based on historical data.
Realized return is important because it is used as a measure of company performance. This
historical return is also useful as a basis for determining the expected return and risk in the
future. The calculation of realized return here uses total return. Total return is the total of an
investment in a certain period.
ii. Return Expected
A return that is used for making investment decisions. This return is important compared to
historical returns because the expected return is the expected return on the investment made.
Expected return can be calculated using the expectation value method, which is to multiply
each future outcome by its probability of occurrence and add up all the products of this product.
Understanding risk according to Keown (1999), risk is the possibilities that a return will be
different from the expected rate of return. According to Jones (2002), there are two types of
risk, namely:
a. Systematic risk:
Risk related to conditions that occur on the market in general, namely interest rate risk,
political risk, inflation risk, exchange rate risk and market risk. Also called the risk of not
diversification.
b. unsystematic risk:
The risk associated with the condition of the company that occurs individually, namely
business risk, leverage risk and liquidity risk. Also called diversification risk, residual risk,
unique risk, or company-specific risk. So, it can be concluded that risk is the possibility of a
real deviation of the rate of return against the expected rate of return. The amount of the risk
value can be found by calculating the standard deviation, or by calculating the variance.
4
1.2.1: Other types of risk
i. Credit risk
Credit risk is the possibility that a borrower would miss payments on their debt, resulting in
losses for the investor or lender. Particularly with regard to bonds, loans, and other credit
instruments, this kind of risk is pertinent.
ii. Risk to Liquidity
When an asset cannot be sold on the market quickly enough to stop or lessen a loss, liquidity
risk results. This may occur as a result of a dearth of market participants or because an asset is
highly specialized and difficult to transfer.
iii. Risk Related to Operations
Operational risk is the chance of suffering a loss as a result of insufficient or unsuccessful
systems, personnel, internal processes, or outside circumstances. Fraud, system malfunctions,
human mistake, and natural disasters are a few examples.
iv. Risk of Regulation and Compliance
The danger of losing money as a result of modifications to laws, rules, or policies that have an
impact on a company or investment is known as regulatory risk. The danger of financial loss
and legal or regulatory repercussions for breaking laws, rules, codes of behavior, or standards
is known as compliance risk.
v. Risk of Interest Rates
The possibility that shifts in interest rates will have an impact on investment value is known as
interest rate risk. This is especially true for bonds, since falling bond values can result from
rising interest rates and vice versa.
vi. Risk of Currency/Exchange Rate
Exchange rate risk, sometimes referred to as currency risk, is caused by changes in the value
of one currency compared to another. Investors and businesses involved in international
commerce or investment are impacted by this risk.
vii. Risk of Inflation
The possibility that prices would rise to the point where money loses buying power is known
as inflation risk. The true return on investments may be impacted by this, especially for fixed-
income instruments like bonds.
1.2.1: Other types of risk
i. Credit risk
Credit risk is the possibility that a borrower would miss payments on their debt, resulting in
losses for the investor or lender. Particularly with regard to bonds, loans, and other credit
instruments, this kind of risk is pertinent.
ii. Risk to Liquidity
When an asset cannot be sold on the market quickly enough to stop or lessen a loss, liquidity
risk results. This may occur as a result of a dearth of market participants or because an asset is
highly specialized and difficult to transfer.
iii. Risk Related to Operations
Operational risk is the chance of suffering a loss as a result of insufficient or unsuccessful
systems, personnel, internal processes, or outside circumstances. Fraud, system malfunctions,
human mistake, and natural disasters are a few examples.
iv. Risk of Regulation and Compliance
The danger of losing money as a result of modifications to laws, rules, or policies that have an
impact on a company or investment is known as regulatory risk. The danger of financial loss
and legal or regulatory repercussions for breaking laws, rules, codes of behavior, or standards
is known as compliance risk.
v. Risk of Interest Rates
The possibility that shifts in interest rates will have an impact on investment value is known as
interest rate risk. This is especially true for bonds, since falling bond values can result from
rising interest rates and vice versa.
vi. Risk of Currency/Exchange Rate
Exchange rate risk, sometimes referred to as currency risk, is caused by changes in the value
of one currency compared to another. Investors and businesses involved in international
commerce or investment are impacted by this risk.
vii. Risk of Inflation
The possibility that prices would rise to the point where money loses buying power is known
as inflation risk. The true return on investments may be impacted by this, especially for fixed-
income instruments like bonds.
5
viii. Political risk
Political risk is the possibility that a political development, like a shift in the government, laws,
or regulations, will have a detrimental effect on an investment or company operations. This is
especially important when making investments in developing or volatile economies.
1.3: Company profile
i. Tata motors
Tata Motors Limited (TML), a $42 billion organization, is India’s largest automobile company
and is a leading global manufacturer of cars, utility vehicles, buses, trucks and defense vehicles.
Incorporated in India in the year 1945, Tata Motors is a part of the over $100 billion Tata Group
founded by Jamshedji Tata in 1868. Recognized for its world-class quality, originality,
engineering and design excellence, the Company is on the path of shaping the future of mobility
in India. Sustainability and the spirit of ‘giving back to society’ is our guiding philosophy and
good corporate citizenship is strongly embedded in our DNA. With a large global footprint, the
Company has consolidated its position as the Tata Motors 0Group through mergers and
acquisitions. It has a network of 76 subsidiaries in India and internationally, which provide a
host of engineering and automotive solutions. Some of the world’s most iconic brands,
including Jaguar Land Rover in the UK and Tata Daewoo in South Korea form part of the
automotive operations of the Group. As of in June, 2024, the share price of Tata Motors was
₹951.80 on the National Stock Exchange (NSE) of India.
ii. Mahindra and Mahindra
Beginning its journey in 1945, Mahindra & Mahindra Ltd. initially launched as a steel trading
enterprise and has since transformed into a global powerhouse, extending its reach to over 100
countries worldwide. Today, it stands proud as the world’s premier tractor company by volume,
reinforcing its significant contribution to strengthening India’s agricultural sector. The
extensive influence of the company spans multiple industries such as automotive, agriculture,
and technology, to name a few.
Mahindra & Mahindra Ltd., part of the esteemed Mahindra Group, is a global giant with an
expansive presence in more than 100 countries and a dedicated team of 260,000. Renowned as
the world’s foremost tractor company by volume, it supports global agriculture, enhancing its
reputation in this critical sector. It also proudly stands as India’s leading SUV manufacturer by
revenue market share, underscoring its significant impact on the automotive industry.
viii. Political risk
Political risk is the possibility that a political development, like a shift in the government, laws,
or regulations, will have a detrimental effect on an investment or company operations. This is
especially important when making investments in developing or volatile economies.
1.3: Company profile
i. Tata motors
Tata Motors Limited (TML), a $42 billion organization, is India’s largest automobile company
and is a leading global manufacturer of cars, utility vehicles, buses, trucks and defense vehicles.
Incorporated in India in the year 1945, Tata Motors is a part of the over $100 billion Tata Group
founded by Jamshedji Tata in 1868. Recognized for its world-class quality, originality,
engineering and design excellence, the Company is on the path of shaping the future of mobility
in India. Sustainability and the spirit of ‘giving back to society’ is our guiding philosophy and
good corporate citizenship is strongly embedded in our DNA. With a large global footprint, the
Company has consolidated its position as the Tata Motors 0Group through mergers and
acquisitions. It has a network of 76 subsidiaries in India and internationally, which provide a
host of engineering and automotive solutions. Some of the world’s most iconic brands,
including Jaguar Land Rover in the UK and Tata Daewoo in South Korea form part of the
automotive operations of the Group. As of in June, 2024, the share price of Tata Motors was
₹951.80 on the National Stock Exchange (NSE) of India.
ii. Mahindra and Mahindra
Beginning its journey in 1945, Mahindra & Mahindra Ltd. initially launched as a steel trading
enterprise and has since transformed into a global powerhouse, extending its reach to over 100
countries worldwide. Today, it stands proud as the world’s premier tractor company by volume,
reinforcing its significant contribution to strengthening India’s agricultural sector. The
extensive influence of the company spans multiple industries such as automotive, agriculture,
and technology, to name a few.
Mahindra & Mahindra Ltd., part of the esteemed Mahindra Group, is a global giant with an
expansive presence in more than 100 countries and a dedicated team of 260,000. Renowned as
the world’s foremost tractor company by volume, it supports global agriculture, enhancing its
reputation in this critical sector. It also proudly stands as India’s leading SUV manufacturer by
revenue market share, underscoring its significant impact on the automotive industry.
6
The company’s achievements stretch beyond these sectors, making substantial progress in the
renewable energy field, and emphasising its dedication to sustainable solutions. This devotion
shines in their groundbreaking automotive creation, the Pininfarina Battista, and their exclusive
Indian presence in the Formula E All-Electric Car Racing Championship.
iii. Maruti Suzuki
Maruti Suzuki India began its journey in 1981, marking a new chapter in India’s automotive
narrative. The following year, 1982, witnessed the strengthening of this relationship through a
significant joint venture agreement between the Government of India and the reputed Suzuki
Motor Corporation (SMC) of Japan. This collaboration set the stage for a series of
achievements and milestones for the Company. Nearly two decades later, by 2002, Maruti
Suzuki India Ltd. transitioned to become a subsidiary of SMC. This alliance highlights the
company’s important role in the automotive sector, not just within India but on a global scale.
Reflecting this prominence, the company today stands proud as the largest subsidiary of SMC
in terms of both production volume and sales. Consolidating its position, SMC currently
possesses a substantial 56.48% equity stake in Maruti Suzuki.
iv. Bajaj Auto
Bajaj Auto Limited is an Indian multinational automotive manufacturing company based
in Pune. It manufactures motorcycles, scooters and auto rickshaws. Bajaj Auto is a part of
the Bajaj Group. It was founded by Jamnalal Bajaj (1889–1942) in Rajasthan in the 1940s.
Bajaj Auto is the world's third-largest manufacturer of motorcycles and the second-largest in
India. It is the world's largest three-wheeler manufacturer. In December 2020, Bajaj Auto
crossed a market capitalization of ₹1 trillion (US$12 billion), making it the world's most
valuable two-wheeler company.
Bajaj Auto was established on 29 November 1945 as M/s Bachraj Trading Corporation Private
Limited. It initially imported and sold two- and three-wheelers in India. In 1959, it obtained a
license from the Government of India to manufacture two-wheelers and three-wheelers and
obtained a licence from Piaggio to manufacture Vespa scooters in India. It became a public
limited company in 1960. With the launch of motorcycles in 1986, the company changed its
branding from a scooter manufacturer to a two-wheeler manufacturer. In 1984, Bajaj Auto
signed a technical assistance agreement with Kawasaki, cooperating to expand production and
sales of motorcycles in the local market.
The company’s achievements stretch beyond these sectors, making substantial progress in the
renewable energy field, and emphasising its dedication to sustainable solutions. This devotion
shines in their groundbreaking automotive creation, the Pininfarina Battista, and their exclusive
Indian presence in the Formula E All-Electric Car Racing Championship.
iii. Maruti Suzuki
Maruti Suzuki India began its journey in 1981, marking a new chapter in India’s automotive
narrative. The following year, 1982, witnessed the strengthening of this relationship through a
significant joint venture agreement between the Government of India and the reputed Suzuki
Motor Corporation (SMC) of Japan. This collaboration set the stage for a series of
achievements and milestones for the Company. Nearly two decades later, by 2002, Maruti
Suzuki India Ltd. transitioned to become a subsidiary of SMC. This alliance highlights the
company’s important role in the automotive sector, not just within India but on a global scale.
Reflecting this prominence, the company today stands proud as the largest subsidiary of SMC
in terms of both production volume and sales. Consolidating its position, SMC currently
possesses a substantial 56.48% equity stake in Maruti Suzuki.
iv. Bajaj Auto
Bajaj Auto Limited is an Indian multinational automotive manufacturing company based
in Pune. It manufactures motorcycles, scooters and auto rickshaws. Bajaj Auto is a part of
the Bajaj Group. It was founded by Jamnalal Bajaj (1889–1942) in Rajasthan in the 1940s.
Bajaj Auto is the world's third-largest manufacturer of motorcycles and the second-largest in
India. It is the world's largest three-wheeler manufacturer. In December 2020, Bajaj Auto
crossed a market capitalization of ₹1 trillion (US$12 billion), making it the world's most
valuable two-wheeler company.
Bajaj Auto was established on 29 November 1945 as M/s Bachraj Trading Corporation Private
Limited. It initially imported and sold two- and three-wheelers in India. In 1959, it obtained a
license from the Government of India to manufacture two-wheelers and three-wheelers and
obtained a licence from Piaggio to manufacture Vespa scooters in India. It became a public
limited company in 1960. With the launch of motorcycles in 1986, the company changed its
branding from a scooter manufacturer to a two-wheeler manufacturer. In 1984, Bajaj Auto
signed a technical assistance agreement with Kawasaki, cooperating to expand production and
sales of motorcycles in the local market.
7
V. Hero MotoCorp
Hero MotoCorp Ltd., headquartered in New Delhi, India, stands as a formidable entity in the
global two-wheeler industry. Established in 1984, it has consistently been the world’s largest
manufacturer of motorcycles and scooters in terms of unit volumes since 2001. With a
commanding 47% share in India’s domestic motorcycle market and a substantial 33.2% in the
overall two-wheeler market, the company solidifies its position as a market leader on its home
turf.
Hero MotoCorp has a vast network of over 10,000 customer touchpoints worldwide, ensuring
a broad and efficient customer reach. With an impressive annual production capacity exceeding
9.50 million units across its 8 manufacturing facilities, the company meets the demand
effectively. Internationally, it extends its presence to 47 countries, offering its products to a
diversified global clientele.
Its commitment to innovation and customer satisfaction is evident through its 110 million-
strong customer bases. The company remains driven by its vision of being ‘The Future of
Mobility,’ and its mission emphasises creating industry-leading mobility solutions,
collaborating for sustainable practices, and inspiring stakeholders through purposeful action.
1.4: Objective of the study
Construct an optimal portfolio empirically using the Sharpe’s Single Index Model.
V. Hero MotoCorp
Hero MotoCorp Ltd., headquartered in New Delhi, India, stands as a formidable entity in the
global two-wheeler industry. Established in 1984, it has consistently been the world’s largest
manufacturer of motorcycles and scooters in terms of unit volumes since 2001. With a
commanding 47% share in India’s domestic motorcycle market and a substantial 33.2% in the
overall two-wheeler market, the company solidifies its position as a market leader on its home
turf.
Hero MotoCorp has a vast network of over 10,000 customer touchpoints worldwide, ensuring
a broad and efficient customer reach. With an impressive annual production capacity exceeding
9.50 million units across its 8 manufacturing facilities, the company meets the demand
effectively. Internationally, it extends its presence to 47 countries, offering its products to a
diversified global clientele.
Its commitment to innovation and customer satisfaction is evident through its 110 million-
strong customer bases. The company remains driven by its vision of being ‘The Future of
Mobility,’ and its mission emphasises creating industry-leading mobility solutions,
collaborating for sustainable practices, and inspiring stakeholders through purposeful action.
1.4: Objective of the study
Construct an optimal portfolio empirically using the Sharpe’s Single Index Model.
8
CHAPTER – 2
LITERATURE REVIEW
1. Gharaibeh (2019): This study applies finance theory to analyze the return behavior and
portfolio characteristics of infrastructure projects in Jordan. From January 2010 to February
2017, it gathered monthly returns and assessed the performance of different infrastructure sub-
indices as well as the qualities of investments. The findings demonstrate that the performance
of the Jordanian infrastructure sub-indices varies, as do the monthly returns and volatilities.
While some sub-indices are preferred, others are not in the best interest of the portfolio
manager. This is a starting point for assessing infrastructure in different nations.
2. Solin et.al (2019, July): A nation's economy depends on investment, yet investors struggle
to find acceptable risk and respectable returns. Artificial Neural Networks (ANN) provide
benefits in terms of data processing speed, accuracy, and future stock value prediction. In order
to lower risk, investment funds are diversified by being split among several benchmark stocks.
The purpose of this research is to use ANN to forecast future stock prices and GA to create
optimal stock portfolios with the goal of maximizing return and minimizing risk. Better
optimization index is shown when GA is used in place of the Single Index Model (SIM)
approach.
3. Courtois et.al (2019): Kurtosis is employed in the study as an extreme risk indicator, and a
mean variance kurtosis portfolio optimization technique is suggested. It generalizes the Sharpe
ratio and finds efficient portfolios by combining Dirichlet simulations and the Pareto
optimization method. The findings demonstrate that portfolios with mean variance kurtosis
efficiency are always preferable.
4. Mahmud (2020): The research assesses Sharpe's portfolio creation using single-index model
on Chittagong Stock Exchange (CSE) securities. Through the recommendation of a cutoff rate
to gauge security desirability, the model streamlines the procedure. Four industries make up
68% of the total portfolio weight, according to the report. With an overall portfolio risk of just
0.6425 percent, the portfolio had a daily mean return of 0.1095 percent. The model provided
CHAPTER – 2
LITERATURE REVIEW
1. Gharaibeh (2019): This study applies finance theory to analyze the return behavior and
portfolio characteristics of infrastructure projects in Jordan. From January 2010 to February
2017, it gathered monthly returns and assessed the performance of different infrastructure sub-
indices as well as the qualities of investments. The findings demonstrate that the performance
of the Jordanian infrastructure sub-indices varies, as do the monthly returns and volatilities.
While some sub-indices are preferred, others are not in the best interest of the portfolio
manager. This is a starting point for assessing infrastructure in different nations.
2. Solin et.al (2019, July): A nation's economy depends on investment, yet investors struggle
to find acceptable risk and respectable returns. Artificial Neural Networks (ANN) provide
benefits in terms of data processing speed, accuracy, and future stock value prediction. In order
to lower risk, investment funds are diversified by being split among several benchmark stocks.
The purpose of this research is to use ANN to forecast future stock prices and GA to create
optimal stock portfolios with the goal of maximizing return and minimizing risk. Better
optimization index is shown when GA is used in place of the Single Index Model (SIM)
approach.
3. Courtois et.al (2019): Kurtosis is employed in the study as an extreme risk indicator, and a
mean variance kurtosis portfolio optimization technique is suggested. It generalizes the Sharpe
ratio and finds efficient portfolios by combining Dirichlet simulations and the Pareto
optimization method. The findings demonstrate that portfolios with mean variance kurtosis
efficiency are always preferable.
4. Mahmud (2020): The research assesses Sharpe's portfolio creation using single-index model
on Chittagong Stock Exchange (CSE) securities. Through the recommendation of a cutoff rate
to gauge security desirability, the model streamlines the procedure. Four industries make up
68% of the total portfolio weight, according to the report. With an overall portfolio risk of just
0.6425 percent, the portfolio had a daily mean return of 0.1095 percent. The model provided
9
the optimal risk-return combinations, outperforming the market index and all sample securities.
5. Maulana (2020): The study focuses on single index model and Markowitz approach stock
investment portfolio analysis. The study calculates the beta value of an efficient portfolio line
using the market share price index, SBI interest rates, and the share prices of PT Ace Hardware
Indonesia, PT Indocement Tunggal Perkasa, and PT Matahari Putra Prima. The residual
variance in the active ACES portfolio is 0.1054, with values of 0.0041, INTP, 0.0001, and
MPPA.
6. Zhan et.al (2020, October): The study investigates the creation of optimal portfolios using
a variety of graphical models, such as PCA-KMeans, autoencoders, dynamic clustering, and
structural learning. The outcomes demonstrate how well these models are able to identify
temporal connections in time series data, which is helpful for asset management.
7. Rout et.al (2020): The goal of this study is to use Sharp's single index approach to build an
ideal portfolio for the Indian stock market. Market capitalization is used to choose the top 25
Sensex stocks, and a special cut-off rate is set. Based on the beta value, unsystematic risk,
excess return to beta ratio, and cut-off rate, the percentage of investment in each chosen security
is calculated.
8. Pun et.al (2021): This paper presents an optimization problem for minimizing risk in a
portfolio and a novel class of risk measurements. The risk measure is centered on a range of
values rather than assessing the daily return departure from a single goal value. As a result, the
portfolio is more resilient to outliers and has lower turnover rates. The performance of the
portfolio is further assessed by simulation, empirical research, and theoretical results presented
in the article.
9. Aljinovic et.al (2021): In addition to return and risk, the article presents a multicriteria
strategy for cryptocurrency portfolio selection based on PROMETHEE II. Based on daily
return, standard deviation, value-at-risk, volume, market capitalization, and attractiveness of
nine cryptocurrencies from January 2017 to February 2020, the algorithm determines the
optimal cryptocurrency portfolio. With gains ranging from 50% to 94%, the model surpasses
five popular models, highlighting the advantages of using many criteria and a multicriteria
approach when choosing a cryptocurrency portfolio.
the optimal risk-return combinations, outperforming the market index and all sample securities.
5. Maulana (2020): The study focuses on single index model and Markowitz approach stock
investment portfolio analysis. The study calculates the beta value of an efficient portfolio line
using the market share price index, SBI interest rates, and the share prices of PT Ace Hardware
Indonesia, PT Indocement Tunggal Perkasa, and PT Matahari Putra Prima. The residual
variance in the active ACES portfolio is 0.1054, with values of 0.0041, INTP, 0.0001, and
MPPA.
6. Zhan et.al (2020, October): The study investigates the creation of optimal portfolios using
a variety of graphical models, such as PCA-KMeans, autoencoders, dynamic clustering, and
structural learning. The outcomes demonstrate how well these models are able to identify
temporal connections in time series data, which is helpful for asset management.
7. Rout et.al (2020): The goal of this study is to use Sharp's single index approach to build an
ideal portfolio for the Indian stock market. Market capitalization is used to choose the top 25
Sensex stocks, and a special cut-off rate is set. Based on the beta value, unsystematic risk,
excess return to beta ratio, and cut-off rate, the percentage of investment in each chosen security
is calculated.
8. Pun et.al (2021): This paper presents an optimization problem for minimizing risk in a
portfolio and a novel class of risk measurements. The risk measure is centered on a range of
values rather than assessing the daily return departure from a single goal value. As a result, the
portfolio is more resilient to outliers and has lower turnover rates. The performance of the
portfolio is further assessed by simulation, empirical research, and theoretical results presented
in the article.
9. Aljinovic et.al (2021): In addition to return and risk, the article presents a multicriteria
strategy for cryptocurrency portfolio selection based on PROMETHEE II. Based on daily
return, standard deviation, value-at-risk, volume, market capitalization, and attractiveness of
nine cryptocurrencies from January 2017 to February 2020, the algorithm determines the
optimal cryptocurrency portfolio. With gains ranging from 50% to 94%, the model surpasses
five popular models, highlighting the advantages of using many criteria and a multicriteria
approach when choosing a cryptocurrency portfolio.
10
10. Toharudin (2021): The optimization of pension fund investment portfolios and their effect
on financial performance are examined in this study. Using Markowitz and Sharpe models, it
was performed on Employer Pension Fund (DPPK) PT. PLN from 2010 to 2018. The findings
indicate that there is no discernible variation in the financial performance of a portfolio
optimized using the proportions of six different investment instruments, resulting in nearly
identical ideal outcomes. The Fund Adequacy Ratio (FAR) and the Markowitz model exhibit
a robust association when taking investors' risk preferences into account.
11. Chou et.al (2021): This paper uses the trend ratio to assess portfolio performance in the
stock market, addressing the issue of assessing portfolio risk using the Sharpe ratio. The
Global-best guided Quantum-inspired Tabu Search algorithm with Not-gate (GNQTS) is used
to optimize a portfolio within a limited time. The method can identify a stable uptrend portfolio
in the U.S. stock market, considering all possible combinations. The study also found that the
best single stock may not be contained in a portfolio and negative return stocks cannot be
excluded. The method outperforms other assessment strategies.
12. Tang et.al (2021): In order to achieve superior performance under a range of market and
economic constraints, deep reinforcement learning is utilized to optimize portfolio
management goals. Under a range of circumstances, the multi-sequence, attention-based neural
networks used to construct the AlphaPortfolio models produce reliable results. In addition to
emphasizing "economic distillation" for model interpretation, the paper highlights the
application of deep reinforcement learning in finance.
13. Prakoso et.al (2022): The study uses the Single Index Model to examine the Jakarta
Islamic Index's optimal portfolio from December 2016 to November 2019. The portfolio
consisted of nine equities; the best stocks were ASII, ASRI, ICBP, INCO, INTP, KLBF,
SMGR, UNTR, and UNVR. With a risk of 6.89%, the ideal portfolio has an expected return of
1.1180% and 1.11%.
14. Zhang et.al (2022): In this study, ten stocks from the S&P 500 index are used to evaluate
the Markowitz Model with Sharpe's Single Index Model for optimal and minimal risk
portfolios. The findings demonstrate that while the Single Index Model streamlines processes,
it outperforms other models for assets with associated residual returns. The Markowitz Model
10. Toharudin (2021): The optimization of pension fund investment portfolios and their effect
on financial performance are examined in this study. Using Markowitz and Sharpe models, it
was performed on Employer Pension Fund (DPPK) PT. PLN from 2010 to 2018. The findings
indicate that there is no discernible variation in the financial performance of a portfolio
optimized using the proportions of six different investment instruments, resulting in nearly
identical ideal outcomes. The Fund Adequacy Ratio (FAR) and the Markowitz model exhibit
a robust association when taking investors' risk preferences into account.
11. Chou et.al (2021): This paper uses the trend ratio to assess portfolio performance in the
stock market, addressing the issue of assessing portfolio risk using the Sharpe ratio. The
Global-best guided Quantum-inspired Tabu Search algorithm with Not-gate (GNQTS) is used
to optimize a portfolio within a limited time. The method can identify a stable uptrend portfolio
in the U.S. stock market, considering all possible combinations. The study also found that the
best single stock may not be contained in a portfolio and negative return stocks cannot be
excluded. The method outperforms other assessment strategies.
12. Tang et.al (2021): In order to achieve superior performance under a range of market and
economic constraints, deep reinforcement learning is utilized to optimize portfolio
management goals. Under a range of circumstances, the multi-sequence, attention-based neural
networks used to construct the AlphaPortfolio models produce reliable results. In addition to
emphasizing "economic distillation" for model interpretation, the paper highlights the
application of deep reinforcement learning in finance.
13. Prakoso et.al (2022): The study uses the Single Index Model to examine the Jakarta
Islamic Index's optimal portfolio from December 2016 to November 2019. The portfolio
consisted of nine equities; the best stocks were ASII, ASRI, ICBP, INCO, INTP, KLBF,
SMGR, UNTR, and UNVR. With a risk of 6.89%, the ideal portfolio has an expected return of
1.1180% and 1.11%.
14. Zhang et.al (2022): In this study, ten stocks from the S&P 500 index are used to evaluate
the Markowitz Model with Sharpe's Single Index Model for optimal and minimal risk
portfolios. The findings demonstrate that while the Single Index Model streamlines processes,
it outperforms other models for assets with associated residual returns. The Markowitz Model
11
performs better for low risk, while the Stock Index portfolio has lower systemic risk than the
optimal portfolio, which has a larger return and risk.
15. Riandini et.al (2022): This study uses the Treynor Ratio, Jensen Index, and Sharpe Index
to assess the performance of Indonesian equity mutual funds from 2018 to 2020. Sucorinvest
Equity was the top-performing equity fund among the seven selected funds, even though it
invested at least 80% in equities. Mutual funds that are equity-oriented are riskier than other
kinds. The equity fund with the best performance during the study period is Sucorinvest Equity.
16. Sen et.al (2022): This study creates mean-variance optimized portfolios for six Indian stock
sectors using three measures: the Sortino, Sharpe, and Calmar ratios. Based on cumulative
returns over a test period from January 1, 2021, to December 31, 2021, the portfolios are
assessed. The findings help investors make decisions about their investments based on the risks
and current returns connected to the stocks in the six sectors.
17. Salim et.al (2022): Indonesian stock investments have been greatly damaged by the Covid-
19 pandemic, especially those on the Jakarta Composite Index (JCI). According to the study's
hypothesis, the best portfolio under COVID-19 conditions will be the High Volatility stock
group. Stocks with the highest market capitalization value in JCI are included in the sample.
The findings demonstrate that because high volatility equities can tolerate significant price
swings, they offer better performance and returns. The expectations of investors are met by this
short-term procedure.
18. Reddy et.al (2023): The financial markets have been greatly affected by Covid19, and as
a result, investors have reallocated their portfolios as a result of shifting expectations for risk
and return. There aren't many reliable long-term trends because of the inherent uncertainties
surrounding stock market fluctuations, such as the random walk hypothesis. Consequently,
investors are redistributing their portfolios among alternative stocks; nevertheless, the
circumstances surrounding the transition from high-risk to low-risk investments vary among
investors.
19. Buana: The Single Index Model is used in the study to compare active and passive portfolio
strategies, and Treynor, Jensen's Alpha, and the Sharpe Index are used to quantify return
performance. Three stocks make up the ideal portfolio in the first year and four stocks in the
performs better for low risk, while the Stock Index portfolio has lower systemic risk than the
optimal portfolio, which has a larger return and risk.
15. Riandini et.al (2022): This study uses the Treynor Ratio, Jensen Index, and Sharpe Index
to assess the performance of Indonesian equity mutual funds from 2018 to 2020. Sucorinvest
Equity was the top-performing equity fund among the seven selected funds, even though it
invested at least 80% in equities. Mutual funds that are equity-oriented are riskier than other
kinds. The equity fund with the best performance during the study period is Sucorinvest Equity.
16. Sen et.al (2022): This study creates mean-variance optimized portfolios for six Indian stock
sectors using three measures: the Sortino, Sharpe, and Calmar ratios. Based on cumulative
returns over a test period from January 1, 2021, to December 31, 2021, the portfolios are
assessed. The findings help investors make decisions about their investments based on the risks
and current returns connected to the stocks in the six sectors.
17. Salim et.al (2022): Indonesian stock investments have been greatly damaged by the Covid-
19 pandemic, especially those on the Jakarta Composite Index (JCI). According to the study's
hypothesis, the best portfolio under COVID-19 conditions will be the High Volatility stock
group. Stocks with the highest market capitalization value in JCI are included in the sample.
The findings demonstrate that because high volatility equities can tolerate significant price
swings, they offer better performance and returns. The expectations of investors are met by this
short-term procedure.
18. Reddy et.al (2023): The financial markets have been greatly affected by Covid19, and as
a result, investors have reallocated their portfolios as a result of shifting expectations for risk
and return. There aren't many reliable long-term trends because of the inherent uncertainties
surrounding stock market fluctuations, such as the random walk hypothesis. Consequently,
investors are redistributing their portfolios among alternative stocks; nevertheless, the
circumstances surrounding the transition from high-risk to low-risk investments vary among
investors.
19. Buana: The Single Index Model is used in the study to compare active and passive portfolio
strategies, and Treynor, Jensen's Alpha, and the Sharpe Index are used to quantify return
performance. Three stocks make up the ideal portfolio in the first year and four stocks in the
12
second, indicating that passive portfolio techniques outperform active portfolio strategies in
terms of returns. Nevertheless, there is no discernible difference in return performance between
the two techniques, according to the Mann Whitney U test results.
20. Rahmawati et.al (2024): The purpose of the study is to use the Single Index Model to
calculate the ideal return, risk, and percentage for every banking stock portfolio in Indonesia
from February to July of 2023. With fund allocations of 21.43% (BNII), 13.52% (BDMN),
35.02% (BBRI), 23.69% (BTPN), and 6.34% (BBCA), the study finds five ideal equities. The
stocks have an estimated return of 0.152% and a daily risk of 0.0011%.
2.1: Research gap
The Sharpe Single Index Method is widely used in various sectors for evaluating investment
performance and risk management, but there is a research gap in its application to the
automobile industry. The William Sharpe Index Method aims to provide deeper insights into
the financial health and investment potential of automobile companies, aiding informed
decision-making.
second, indicating that passive portfolio techniques outperform active portfolio strategies in
terms of returns. Nevertheless, there is no discernible difference in return performance between
the two techniques, according to the Mann Whitney U test results.
20. Rahmawati et.al (2024): The purpose of the study is to use the Single Index Model to
calculate the ideal return, risk, and percentage for every banking stock portfolio in Indonesia
from February to July of 2023. With fund allocations of 21.43% (BNII), 13.52% (BDMN),
35.02% (BBRI), 23.69% (BTPN), and 6.34% (BBCA), the study finds five ideal equities. The
stocks have an estimated return of 0.152% and a daily risk of 0.0011%.
2.1: Research gap
The Sharpe Single Index Method is widely used in various sectors for evaluating investment
performance and risk management, but there is a research gap in its application to the
automobile industry. The William Sharpe Index Method aims to provide deeper insights into
the financial health and investment potential of automobile companies, aiding informed
decision-making.
13
CHAPTER 3
RESEARCH METHODOLOGY
Introduction
Research in common parlance refers to a search for knowledge. One can also define research
as a scientific and systematic search for relevant information on a specific topic Methodology
is the process used to collect information and data for the purpose of making business decisions
which may include publication research, interviews, surveys and other research techniques, and
could include both present and historical information. This chapter explains in detail about the
research process for carrying out the study.
3.1: Design of the Study
The study has been carried out in the following phase:
Phase I: Selecting a topic for the study.
Phase II: Understanding the concepts involved in the topic.
Phase III: Collecting the data.
Phase IV: Making suitable analysis.
Phase V: Interpretation and conclusion.
3.2: Data Collection and Study Period
The data collected for this project is basically from secondary sources such as Economic times,
Yahoo finance, Money control, NSE sites. The data of 5 companies for a period of 1year (2023-
2024) was collected from NSE (Nifty) on weekly basis. Here different companies were selected
(5 Auto companies). To evaluate the return of securities, we also calculate Specific Return.
Market Return, Systematic Risk, Variance of Market Return, Variance of Residual Return by
using MS-Excel.
CHAPTER 3
RESEARCH METHODOLOGY
Introduction
Research in common parlance refers to a search for knowledge. One can also define research
as a scientific and systematic search for relevant information on a specific topic Methodology
is the process used to collect information and data for the purpose of making business decisions
which may include publication research, interviews, surveys and other research techniques, and
could include both present and historical information. This chapter explains in detail about the
research process for carrying out the study.
3.1: Design of the Study
The study has been carried out in the following phase:
Phase I: Selecting a topic for the study.
Phase II: Understanding the concepts involved in the topic.
Phase III: Collecting the data.
Phase IV: Making suitable analysis.
Phase V: Interpretation and conclusion.
3.2: Data Collection and Study Period
The data collected for this project is basically from secondary sources such as Economic times,
Yahoo finance, Money control, NSE sites. The data of 5 companies for a period of 1year (2023-
2024) was collected from NSE (Nifty) on weekly basis. Here different companies were selected
(5 Auto companies). To evaluate the return of securities, we also calculate Specific Return.
Market Return, Systematic Risk, Variance of Market Return, Variance of Residual Return by
using MS-Excel.
14
3.3: Tools Used for Study
3.3.1: Expected Return: The Expected return is the profit or loss an investor anticipates on
an investment.
Alpha: it is a measure of the active return on an investment, the performance of that
investment compared with a suitable market index. An alpha of 1% means the investment's
return on investment over a selected period of time was 1% better than the market during
that same period, a negative alpha means the investment underperformed the market.
Beta: It is a measurement of the volatility or systematic risk of a security or portfolio
compared to the market as a whole.
Cut-Off: The cut-off point is the point at which an investor decides whether or not a
particular security is worth purchasing. The cut-off point is very subjective and will be
based on the personal characteristics of the individual investor.
Unsystematic Risk: It is also known as diversifiable risk or non-systematic risk. It is
associated exclusively with factors related to a particular firm. Unsystematic risk is
measured and managed through the implementation of various risk management tools
including the derivative market.
3.3: Tools Used for Study
3.3.1: Expected Return: The Expected return is the profit or loss an investor anticipates on
an investment.
Alpha: it is a measure of the active return on an investment, the performance of that
investment compared with a suitable market index. An alpha of 1% means the investment's
return on investment over a selected period of time was 1% better than the market during
that same period, a negative alpha means the investment underperformed the market.
Beta: It is a measurement of the volatility or systematic risk of a security or portfolio
compared to the market as a whole.
Cut-Off: The cut-off point is the point at which an investor decides whether or not a
particular security is worth purchasing. The cut-off point is very subjective and will be
based on the personal characteristics of the individual investor.
Unsystematic Risk: It is also known as diversifiable risk or non-systematic risk. It is
associated exclusively with factors related to a particular firm. Unsystematic risk is
measured and managed through the implementation of various risk management tools
including the derivative market.
15
3.3.2: Proportion of Investment (Xi): The percent of investment made in each security can
be know using the below formula
3.3.2: Proportion of Investment (Xi): The percent of investment made in each security can
be know using the below formula
16
CHAPTER – 4
DATA ANALYSIS AND INTERPRETATION
Introduction
This part of the project brings out data analysis and interpretation relating to the present study.
The data required for this study has been collected from secondary source. Five companies
listed under NSE Nifty have been selected for the study. The chosen companies belong to
Automobile sector. They have been presented below:
4.1: Analysis of Data
The past data of selected companies which we were collected from Nifty index for 1 years on
weekly basis is analyzed as follows-
4.1.1: Calculation of Expected return
The Expected returns of the individual securities are calculated using the following formulae:
Here, three variables are involved in calculation of Expected return (Ri). First of all, we
calculated Alpha and Beta of individual securities by using Regression model in MS- Excel.
Then we evaluate the market return by using the following formula:
CHAPTER – 4
DATA ANALYSIS AND INTERPRETATION
Introduction
This part of the project brings out data analysis and interpretation relating to the present study.
The data required for this study has been collected from secondary source. Five companies
listed under NSE Nifty have been selected for the study. The chosen companies belong to
Automobile sector. They have been presented below:
4.1: Analysis of Data
The past data of selected companies which we were collected from Nifty index for 1 years on
weekly basis is analyzed as follows-
4.1.1: Calculation of Expected return
The Expected returns of the individual securities are calculated using the following formulae:
Here, three variables are involved in calculation of Expected return (Ri). First of all, we
calculated Alpha and Beta of individual securities by using Regression model in MS- Excel.
Then we evaluate the market return by using the following formula:
17
Table 4.1: Expected returns of sample companies
SL.No Company Name Expected Return
1 Tata Motors 0.2741
2 Mahindra & Mahindra 0.2429
3 Maruti Suzuki 0.10417
4 Bajaj Auto Ltd. 0.2060
5 Hero MotoCorp 0.19399
4.1.2: Calculation of Beta values
Table 4.2 represents the beta values which we were calculated by using regression model in
MS-Excel. In this model we used Individual security return as dependent variable and Market
return (or Nifty return) as independent variable. From there we get Nifty return which is
considered as beta of a particular company. Similarly, we calculated all security's beta in this
manner.
Table 4.2: Beta values of sample companies
SL.No Company Name Beta values
1 Tata Motors 1.24057
2 Mahindra & Mahindra 1.098
3 Maruti Suzuki 0.4695
4 Bajaj Auto Ltd. 0.9059
5 Hero MotoCorp 0.8601
4.1.3: Ranking of companies based on Excess return to beta ratio
Table 4.3 depicts the excess return and excess return to beta ratio, Excess return is the
difference between expected return on the stock and the risk-free rate of interest, The excess
return to beta ratio measures the additional return on a security per unit of systematic risk.
Table shows that the Tata Motors, stock has the highest excess return to beta ratio of (-5.42%)
while that of Maruti Suzuki stock has the lowest of (-14.68).
This ratio provides the relationship between potential risk and reward from a company's stock.
Table 4.1: Expected returns of sample companies
SL.No Company Name Expected Return
1 Tata Motors 0.2741
2 Mahindra & Mahindra 0.2429
3 Maruti Suzuki 0.10417
4 Bajaj Auto Ltd. 0.2060
5 Hero MotoCorp 0.19399
4.1.2: Calculation of Beta values
Table 4.2 represents the beta values which we were calculated by using regression model in
MS-Excel. In this model we used Individual security return as dependent variable and Market
return (or Nifty return) as independent variable. From there we get Nifty return which is
considered as beta of a particular company. Similarly, we calculated all security's beta in this
manner.
Table 4.2: Beta values of sample companies
SL.No Company Name Beta values
1 Tata Motors 1.24057
2 Mahindra & Mahindra 1.098
3 Maruti Suzuki 0.4695
4 Bajaj Auto Ltd. 0.9059
5 Hero MotoCorp 0.8601
4.1.3: Ranking of companies based on Excess return to beta ratio
Table 4.3 depicts the excess return and excess return to beta ratio, Excess return is the
difference between expected return on the stock and the risk-free rate of interest, The excess
return to beta ratio measures the additional return on a security per unit of systematic risk.
Table shows that the Tata Motors, stock has the highest excess return to beta ratio of (-5.42%)
while that of Maruti Suzuki stock has the lowest of (-14.68).
This ratio provides the relationship between potential risk and reward from a company's stock.
18
The ranking of stocks done on the basis of excess return to beta ratio reveals that the Tata
motors. stock ranks first, the Maruti Suzuki stock ranks the last. Here, risk-free return is taken
as 7%.
Table 4.3: Ranking of companies based on excess return to beta ratio
SLNo. Company Name Ri βi Ri-Rf
β
Rank
1 Tata Motors 0.2741 1.24057 -5.42 1
2 Mahindra & Mahindra 0.2429 1.098 -6.154 2
3 Maruti Suzuki 0.10417 0.4695 -14.68 5
4 Bajaj Auto Ltd. 0.2060 0.9059 -7.499 3
5 Hero MotoCorp 0.19399 0.8601 -7.91 4
The ranking of stocks done on the basis of excess return to beta ratio reveals that the Tata
motors. stock ranks first, the Maruti Suzuki stock ranks the last. Here, risk-free return is taken
as 7%.
Table 4.3: Ranking of companies based on excess return to beta ratio
SLNo. Company Name Ri βi Ri-Rf
β
Rank
1 Tata Motors 0.2741 1.24057 -5.42 1
2 Mahindra & Mahindra 0.2429 1.098 -6.154 2
3 Maruti Suzuki 0.10417 0.4695 -14.68 5
4 Bajaj Auto Ltd. 0.2060 0.9059 -7.499 3
5 Hero MotoCorp 0.19399 0.8601 -7.91 4
19
4.1.4: Calculation of Unsystematic risk
Table 4.4 reveal that out of 5 companies selected in this study, Hero MotoCorp has highest
unsystematic risk and Maruti Suzuki has the least unsystematic risk. These unsystematic risks
are evaluated by doing variance of the residual return. Residual returns has already ascertain
while calculating the Alpha and Beta in Regression model. These Return to risk ratio values
(Ri-Rf/σ
2
ei)ẞ) and its cumulative (Cumulative of (Ri-Rf/σ
2
ei)ẞ) are very essential to calculate
the Cut-off point.
Table 4.4: Sample companies based on their ranks and unsystematic risk
SL.No
Company Name σ
2
ei Ri-Rf/σ
2
ei) ẞ Cumulative of
Ri-Rf/σ
2
ei) ẞ
1 Tata Motors 0.0009687 -8613.06 -8613.06
2 Mahindra & Mahindra 0.0010547 -7034 -15647.06
3 Bajaj Auto Ltd. 0.0010158 -6058.95 -26620.81
4 Hero MotoCorp 0.001364 -4989.80 -31610.61
5 Maruti Suzuki 0.0006572 -4914.80 -20561.86
4.1.5 Calculation of cut-off point
4.1.4: Calculation of Unsystematic risk
Table 4.4 reveal that out of 5 companies selected in this study, Hero MotoCorp has highest
unsystematic risk and Maruti Suzuki has the least unsystematic risk. These unsystematic risks
are evaluated by doing variance of the residual return. Residual returns has already ascertain
while calculating the Alpha and Beta in Regression model. These Return to risk ratio values
(Ri-Rf/σ
2
ei)ẞ) and its cumulative (Cumulative of (Ri-Rf/σ
2
ei)ẞ) are very essential to calculate
the Cut-off point.
Table 4.4: Sample companies based on their ranks and unsystematic risk
SL.No
Company Name σ
2
ei Ri-Rf/σ
2
ei) ẞ Cumulative of
Ri-Rf/σ
2
ei) ẞ
1 Tata Motors 0.0009687 -8613.06 -8613.06
2 Mahindra & Mahindra 0.0010547 -7034 -15647.06
3 Bajaj Auto Ltd. 0.0010158 -6058.95 -26620.81
4 Hero MotoCorp 0.001364 -4989.80 -31610.61
5 Maruti Suzuki 0.0006572 -4914.80 -20561.86
4.1.5 Calculation of cut-off point
20
Table 4.5 represents the Ci of sample companies. The β² / σ2ei and its cumulative are necessary
for the calculation of Ci. The Ci value goes on increasing from (-3.99) to (-0.7798) and
thereafter, starts declining. Therefore, the value of -27.94 is considered as the 'cut-off point'.
The securities which come after the cut-off point will not be considered for the optimal
portfolio construction. The Ci is calculated and tabulated as under:
Table 4.5: Ci of sample companies
SL.No Company Name β² / σ
2
ei Cumulative of
β² / σ
2
ei
Ci
1 Tata Motors 1588.72 1588.72 -3.99
2 Mahindra & Mahindra 1443.64 3032.36 -0.7798
3 Bajaj Auto Ltd. 807.83 3840.19 -19.42
4 Hero MotoCorp 541.86 4382.05 -27.94
5 Maruti Suzuki 335.36 4717.41 -22.85
4.1.6 Calculation of proportion of investment
Table represent the proportion investment to be made in each security. Once the companies on
which investment is to be made are known it is essential to know the proportion of investment
to be made in each company’s security. To know the proportion, we calculated Xi by using the
Table 4.5 represents the Ci of sample companies. The β² / σ2ei and its cumulative are necessary
for the calculation of Ci. The Ci value goes on increasing from (-3.99) to (-0.7798) and
thereafter, starts declining. Therefore, the value of -27.94 is considered as the 'cut-off point'.
The securities which come after the cut-off point will not be considered for the optimal
portfolio construction. The Ci is calculated and tabulated as under:
Table 4.5: Ci of sample companies
SL.No Company Name β² / σ
2
ei Cumulative of
β² / σ
2
ei
Ci
1 Tata Motors 1588.72 1588.72 -3.99
2 Mahindra & Mahindra 1443.64 3032.36 -0.7798
3 Bajaj Auto Ltd. 807.83 3840.19 -19.42
4 Hero MotoCorp 541.86 4382.05 -27.94
5 Maruti Suzuki 335.36 4717.41 -22.85
4.1.6 Calculation of proportion of investment
Table represent the proportion investment to be made in each security. Once the companies on
which investment is to be made are known it is essential to know the proportion of investment
to be made in each company’s security. To know the proportion, we calculated Xi by using the
21
above formula. It shows the certain proportion of investment in each security. The figure shows
that 36.1% of investment has to made in the Hero MotoCorp, followed by 34% in Bajaj Auto,
12.9% in Maruti Suzuki, 10.3% in Tata motors, in 6.7% in M&M. A look at the individual
security returns from these stocks as well as their respective proportion of investment is
presented below:
Table 4.6: Proportion of investment proposed
SL.No Company Name Ci Zi Xi
1 Mahindra & Mahindra -0.7798 7772 6.7
2 Tata motors -3.99 3495.18 10.3
3 Bajaj auto ltd. -19.42 10114.03 34
4 Maruti Suzuki -22.85 2749.95 12.9
5 Hero MotoCorp -27.94 14630 36.1
above formula. It shows the certain proportion of investment in each security. The figure shows
that 36.1% of investment has to made in the Hero MotoCorp, followed by 34% in Bajaj Auto,
12.9% in Maruti Suzuki, 10.3% in Tata motors, in 6.7% in M&M. A look at the individual
security returns from these stocks as well as their respective proportion of investment is
presented below:
Table 4.6: Proportion of investment proposed
SL.No Company Name Ci Zi Xi
1 Mahindra & Mahindra -0.7798 7772 6.7
2 Tata motors -3.99 3495.18 10.3
3 Bajaj auto ltd. -19.42 10114.03 34
4 Maruti Suzuki -22.85 2749.95 12.9
5 Hero MotoCorp -27.94 14630 36.1
22
CHAPTER -5
FINDING, CONCLUSION AND LIMITATIONS
Introduction
This chapter discusses the findings of the study after using Sharpe single index model. This
proposed whether Sharpe single index model is useful for security analysis and constructing of
an optimal portfolio or not.
5.1: Findings
The findings of the project are discussed below:
1.The Tata Motors has the highest return of 0.2741% and Maruti Suzuki has the lowest return
of 0.10417% If the investor wants to earn maximum return without considering the risk factor,
then investment can be made on those securities which yield high returns. In these securities,
although the return is higher but the risk involved should be considered while investing.
2. Through diversification we can reduce the risk up to certain extent. The main purpose of
diversification is to achieve expected return without bearing more risk.
3. The return from Tata Motor has the highest beta value of 1.24 which means it is highly
volatile. Mahindra & Mahindra (1.098) have the beta values greater than 1 which means that
they are also volatile. But they are less volatile compared to the Force Motor.
4. The excess return to beta ratio (or Sharpe Ratio) measures the additional return on a security
per systematic risk. The Tata Motor Ltd. return has the highest excess return to beta ratio of(-
5.42) and Maruti Suzuki is the least at (-14.68). This ratio provides the relationship between
risk and return involved in a security's return.
5. Hero MotoCorp return has the highest Unsystematic risk (σ
2
ei) of 0.001364 and Maruti
Suzuki has the lowest Unsystematic risk of 0.0006572. It is the risk affecting the firm due to
certain factors. This risk can be avoidable.
6. Here we have ranked from 1to 8 based on the Ci were selected along with the proportion of
investment. The proportion of investment is made.
CHAPTER -5
FINDING, CONCLUSION AND LIMITATIONS
Introduction
This chapter discusses the findings of the study after using Sharpe single index model. This
proposed whether Sharpe single index model is useful for security analysis and constructing of
an optimal portfolio or not.
5.1: Findings
The findings of the project are discussed below:
1.The Tata Motors has the highest return of 0.2741% and Maruti Suzuki has the lowest return
of 0.10417% If the investor wants to earn maximum return without considering the risk factor,
then investment can be made on those securities which yield high returns. In these securities,
although the return is higher but the risk involved should be considered while investing.
2. Through diversification we can reduce the risk up to certain extent. The main purpose of
diversification is to achieve expected return without bearing more risk.
3. The return from Tata Motor has the highest beta value of 1.24 which means it is highly
volatile. Mahindra & Mahindra (1.098) have the beta values greater than 1 which means that
they are also volatile. But they are less volatile compared to the Force Motor.
4. The excess return to beta ratio (or Sharpe Ratio) measures the additional return on a security
per systematic risk. The Tata Motor Ltd. return has the highest excess return to beta ratio of(-
5.42) and Maruti Suzuki is the least at (-14.68). This ratio provides the relationship between
risk and return involved in a security's return.
5. Hero MotoCorp return has the highest Unsystematic risk (σ
2
ei) of 0.001364 and Maruti
Suzuki has the lowest Unsystematic risk of 0.0006572. It is the risk affecting the firm due to
certain factors. This risk can be avoidable.
6. Here we have ranked from 1to 8 based on the Ci were selected along with the proportion of
investment. The proportion of investment is made.
23
5.2: Conclusion
This study aims at analyzing the opportunity that are available for investors as per as returns
are concerned and the investment of risk thereof while investing in equity of firms listed in the
National stock exchange.
Securities analysis is an extremely difficult process to complete. When analysing the movement
of assets and creating the ideal investment portfolio, even the largest financial institutions and
advisors become confused. The goal of this project is to use the Sharpe single index model to
analyse the list of securities and determine which ones are the best for building an efficient
portfolio. This research is predicated on risk-return analysis and historical price movement. In
addition to these, there are a plethora of other factors, such as macroeconomic and economic
ones, that influence the ultimate decision. Given that India is an emerging market, there is a
greater likelihood of discovering inexpensive stocks there. These factors have piqued the
attention of numerous foreign investors in making investments in India.
From this empirical analysis, to some extent one can able to forecast individual security’s return
through the market movement and can make use of it. More micro level studies is required to
conduct different types of samples. This technique will lead to portfolio has best trade –off
between Risk and Return from any other portfolio under concern.
5.3 Managerial Applications:
i. Utilize the Sharpe Single Index Method to evaluate the performance of companies listed on
NSE and BSE. Higher Sharpe ratios indicate better risk-adjusted returns, reflecting strong
financial health and effective management practices.
ii. Compare individual company performance against a market index to identify outperformers
and underperformers.
iii. Focus on sectors or industries with higher average Sharpe ratios to foster balanced industrial
growth and economic stability.
iv. Assist policymakers in understanding the impact of market dynamics on economic growth
and industrial production, guiding the formulation of supportive economic policies.
v. Increased investor participation in high Sharpe ratio stocks improves market liquidity,
facilitating efficient capital flow and industrial expansion.
5.2: Conclusion
This study aims at analyzing the opportunity that are available for investors as per as returns
are concerned and the investment of risk thereof while investing in equity of firms listed in the
National stock exchange.
Securities analysis is an extremely difficult process to complete. When analysing the movement
of assets and creating the ideal investment portfolio, even the largest financial institutions and
advisors become confused. The goal of this project is to use the Sharpe single index model to
analyse the list of securities and determine which ones are the best for building an efficient
portfolio. This research is predicated on risk-return analysis and historical price movement. In
addition to these, there are a plethora of other factors, such as macroeconomic and economic
ones, that influence the ultimate decision. Given that India is an emerging market, there is a
greater likelihood of discovering inexpensive stocks there. These factors have piqued the
attention of numerous foreign investors in making investments in India.
From this empirical analysis, to some extent one can able to forecast individual security’s return
through the market movement and can make use of it. More micro level studies is required to
conduct different types of samples. This technique will lead to portfolio has best trade –off
between Risk and Return from any other portfolio under concern.
5.3 Managerial Applications:
i. Utilize the Sharpe Single Index Method to evaluate the performance of companies listed on
NSE and BSE. Higher Sharpe ratios indicate better risk-adjusted returns, reflecting strong
financial health and effective management practices.
ii. Compare individual company performance against a market index to identify outperformers
and underperformers.
iii. Focus on sectors or industries with higher average Sharpe ratios to foster balanced industrial
growth and economic stability.
iv. Assist policymakers in understanding the impact of market dynamics on economic growth
and industrial production, guiding the formulation of supportive economic policies.
v. Increased investor participation in high Sharpe ratio stocks improves market liquidity,
facilitating efficient capital flow and industrial expansion.
24
5.4: Future Research Directions
i. Integrate real-time data analytics to continuously update and refine risk measures, improving
decision-making processes.
ii. Leverage big data technologies to enhance the model's ability to process and analyze large
datasets, improving its accuracy and relevance.
iii. Study the impact of investor behavior on the Sharpe ratio, incorporating behavioral finance
theories to better understand market anomalies and irrational behaviors.
iv. Extend the research to include comparisons across different global markets, understanding
the method's applicability and effectiveness in various economic environments.
5.5: Limitations of the study
i. With the only 5 companies, the portfolio may not be well-diversified, which increases
specific risk that could have been mitigated with a larger number of securities.
ii. The Sharpe single method assumes that returns are linearly related to the market index. This
simplification may not capture all the complexities and nuances of the real-world market
behavior, particularly with a small and non-diverse set of companies.
iii. The selected companies may not represent the entire market or different sectors, leading to
biased portfolio performance.
5.4: Future Research Directions
i. Integrate real-time data analytics to continuously update and refine risk measures, improving
decision-making processes.
ii. Leverage big data technologies to enhance the model's ability to process and analyze large
datasets, improving its accuracy and relevance.
iii. Study the impact of investor behavior on the Sharpe ratio, incorporating behavioral finance
theories to better understand market anomalies and irrational behaviors.
iv. Extend the research to include comparisons across different global markets, understanding
the method's applicability and effectiveness in various economic environments.
5.5: Limitations of the study
i. With the only 5 companies, the portfolio may not be well-diversified, which increases
specific risk that could have been mitigated with a larger number of securities.
ii. The Sharpe single method assumes that returns are linearly related to the market index. This
simplification may not capture all the complexities and nuances of the real-world market
behavior, particularly with a small and non-diverse set of companies.
iii. The selected companies may not represent the entire market or different sectors, leading to
biased portfolio performance.
25
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Aljinović, Z., Marasović, B., & Šestanović, T. (2021). Cryptocurrency portfolio selection—A
multicriteria approach. Mathematics, 9(14), 1677.
Chou, Y. H., Lai, Y. T., Jiang, Y. C., & Kuo, S. Y. (2021). Using trend ratio and GNQTS to
assess portfolio performance in the us stock market. IEEE Access, 9, 88348-88363.
Cong, L. W., Tang, K., Wang, J., & Zhang, Y. (2021). AlphaPortfolio: Direct construction
through deep reinforcement learning and interpretable AI. Available at SSRN 3554486.
Gharaibeh, O. K. (2019). Optimal portfolio selection based on Jordanian infrastructure sub-
index returns. International Journal of Scientific & Technology Research, 8(12), 2560-2566.
Le Courtois, O., & Xu, X. (2019). Portfolio Optimization in the Presence of Extreme Risks: A
Pareto-Dirichlet Approach (Vol. 3376921). SSRN Working Paper.
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WEBSITES:
Moneycontrol.com
Yahoofinance.com
Economictimes.com
NSE.com
Zhan, N., Sun, Y., Jakhar, A., & Liu, H. (2020, October). Graphical models for financial time
series and portfolio selection. In Proceedings of the first acm international conference on ai in
finance (pp. 1-6).
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on Social Sciences and Economic Development (ICSSED 2022) (pp. 1930-1938). Atlantis
Press.
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