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Project Report On
“A STUDY OF THE OPTIMAL PORTFOLIO
CONSTRUCTION USING SHARPE’S SINGLE INDEX
MODEL WITH SPECIAL REFERENCE TO CNX NIFTY
SHARES”
In partial fulfilment of the requirements for the award of post graduate degree of
MASTER OF BUSINESS ADMINISTRATION
Of
UNIVERSITY OF CALICUT
Under taken by
SAID SALIM PALAYI
(ENROLLMENT No. 1292113, REG. No. IHAMDBA 044)
Under the Guidance of
Dr. M.K. RAMAKRISHNAN
Faculty in-charge
DEPARTMENT OF COMMERCE AND MANAGEMENT STUDIES
SCHOOL OF DISTANCE EDUCATION, UNIVERSITY OF CALICUT
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DEPARTMENT OF Phone : 0494-2400297
COMMERCE AND MANAGEMENT STUDIES 2407363
UNIVERSITY OF CALICUT Mobile: 9447123637
Calicut University P.O., PIN 673635
CERTIFICATE
This is to certify that Mr. SAID SALIM PALAYI (Enrolment No. 1292113, Reg.
No. IHAMDBA 044) is a bonafide student of the DCMS MBA Centre of the
School of Distance Education, University of Calicut and this project report
titled “A Study Of The Construction Of Optimal Portfolio Using Sharpe’s
Single Index Model With Special Reference To CNX Nifty Shares” has been
prepared by him and submitted in partial fulfilment of the requirements for
the award of the degree of Master of Business Administration of the
University of Calicut.
Place: University P.O Dr. M.A. Joseph
Date: Co-ordinator
SDE MBA Programme
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DR. M.K. RAMAKRISHNAN
Associate Professor& Head of the Department (Rtd.)
Department of Commerce
Zamorin’s Guruvayurappan College, Calicut
_____________________________________________________________________
CERTIFICATE
This is to certify that Mr. SAID SALIM PALAYI is a bonafide student of the
DCMS MBA Centre of the School of Distance Education, University of Calicut
and this project report titled “A Study Of The Construction Of Optimal
Portfolio Using Sharpe’s Single Index Model With Special Reference To
CNX Nifty Shares” is an authentic record of the project work done by him
under my supervision in partial fulfilment of the requirements for the award
of the degree of Master of Business Administration of the University of
Calicut.
Place: DR. M.K. RAMAKRISHNAN
Date:
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DECLARATION
I, SAID SALIM PALAYI, do hereby declare that the project titled “A Study Of
The Construction Of Optimal Portfolio Using Sharpe’s Single Index Model
With Special Reference To CNX Nifty Shares” is a bonafide record of work
done by me under the guidance of Dr. M.K. RAMAKRISHNAN. I further
declare that the study has not previously formed the basis for the award of
any study, research or the similar title or recognition.
Place: SAID SALIM PALAYI
Date:
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ACKNOWLEDGEMENT
This project would have been complete without acknowledging my sincere
gratitude to all persons who have helped me in carrying out study and in
preparation of this report.
I owe my sincere gratitude to Dr. M.A Joseph, co-ordinator, SDE MBA
Programme, DCMS, University of Calicut for providing me the opportunity to
take up this project work.
I wish to thank Dr. M.K. Ramakrishnan, Project guide who provided expert
guidance through out this project.
I take this opportunity to thank the all staffs and management of M/s. MOTILAL
OSWAL SECURITIES LTD., Manjeri for the valuable help in successfully completing
this project.
I wish to thank all faculty members of DCMS, University of Calicut and who
provided expert guidance through out the project.
I express my sincere thanks to all my friends and colleagues for their support in
completing project on time.
I thank my parents, wife and children for helping me and supporting me a lot in
completion of the project on time.
I thank the God, Almighty and most benevolent for giving me the courage and
wisdom to complete this project as per schedule.
SAID SALIM PALAYI
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CONTENTS
Chapter Title Page No.
1 Introduction 1-4
1.1 Introduction to Problem 1
1.2 Statement of Problem 1
1.3 Scope and Significance of the Study 2
1.4 Objectives of the Study 2
1.5 Research Methodology 2
1.6 Chapter Layout 3
1.7 Limitations of Study 4
2 Industry Profile 5-17
2.1 Introduction 5
2.2 Stock Market 5
2.3 Stock Exchange 6
2.4 History of Indian Stock Market 9
2.5 Major Stock Exchanges In India 10
2.6 Conclusion 16
3 Company Profile 18-26
3.1 Introduction 18
3.2 Overview 18
3.3 Mission 21
3.4 Values 21
3.5 Strengths 21
3.6 Board of Directors 24
3.7 Awards and Recognitions Won 24
3.8 Conclusion 25
4 Theoretical Framework 27-57
4.1 Introduction 27
4.2 Portfolio Construction 27
4.3 Approaches to Portfolio Construction 27
4.4 Traditional Approach 28
4.5 Security Analysis 28
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4.6 Portfolio Analysis 41
4.7 Portfolio Selection 41
4.8 Portfolio Revision 41
4.9 Portfolio Evaluation 42
4.10 Return and Risk Analysis of Portfolio 42
4.11 Modern Approaches to Portfolio Selection 45
4.12 Portfolio Evaluation Methods 53
4.13 Formulae Used For the Study 55
4.14 Conclusion. 57
5 Data Analysis & Interpretations 58-94
5.1 Introduction 58
5.2 List of CNX Nifty Index Shares 58
5.3 Analysis of Securities 60
5.4 Risk Analysis of Securities 62
5.5 Construction of Optimal Portfolio Using
Sharpe’s Single index model 68
5.6 Measuring Return and Risk of Optimal Portfolio 74
5.7 Construction of Portfolio #2 79
5.8 Construction of Portfolio # 3 84
5.9 Portfolio Evaluation. 89
5.10 Conclusion 92
5.11 Chapter Appendix-A 93
6 Conclusion 95-98
6.1 Introduction 95
6.2 Findings 95
6.3 Suggestions 96
6.4 Conclusion 98
Bibliography 99-100
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LIST OF TABLES
Table No. Details of Tables Page No.
2.1 Ranking of Stock Exchanges 8
3.1 Board of Directors of M/s. Motilal Oswal Securities 34
5.1 List of CNX Nifty 50 shares 59
5.2 Summary table showing risk and return of CNX NIFTY shares 61
5.3 Systematic risk of CNX NIFTY shares 63
5.4 Unsystematic risk of CNX NIFTY shares 65
5.5 Total risk of CNX NIFTY shares 67
5.6 Ranking of shares 69
5.7 Calculation of cut-off point 71
5.8 Calculation of optimal portfolio 73
5.9 Calculation of Alpha of optimal portfolio 74
5.10 Beta of optimal portfolio 75
5.11 Calculation of return of optimal portfolio 76
5.12 Calculation of unsystematic risk of optimal portfolio 77
5.13 Calculation of systematic risk of optimal portfolio 78
5.14 Calculation of total risk of optimal portfolio 79
5.15 Calculation of Portfolio #2 79
5.16 Calculation of alpha of portfolio #2 80
5.17 Calculation of beta of portfolio #2 81
5.18 Calculation of return of portfolio #2 81
5.19 Calculation of unsystematic risk of portfolio #2 82
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5.20 Calculation of systematic risk of portfolio #2 83
5.21 Calculation of total risk of portfolio #2 83
5.22 Calculation of Portfolio #3 84
5.23 Calculation of beta of portfolio #3 85
5.24 Calculation of unsystematic risk of portfolio #3 86
5.25 Calculation of systematic risk of portfolio #3 87
5.26 Calculation of total risk of portfolio #3 87
5.27 Calculation of alpha of portfolio #3 88
5.28 Calculation of return of portfolio #3 88
5.29 Calculation of Sharpe’s index of portfolios 89
5.30 Calculation of Treynor’s ratio of portfolios 90
5.31 Calculation of expected return of portfolios 91
5.32 Calculation of Jenson’s measure of portfolios 92
5.33 Calculation of average return and risk of Ambuja Cements 93
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LIST OF FIGURES& CHARTS
Figure No. Details Page No.
2.1 Bombay Stock Exchange 11
2.2 National Stock Exchange 13
2.3 Cochin Stock Exchange 15
4.1 Steps in Fundamental Analysis 29
4.2 Trends in stock market 34
4.3 Moving Averages 35
4.4 Relative Strength Index 36
4.5 Line Chart 38
4.6 Bar Chart 38
4.7 Candlestick Chart 39
4.8 Point and Figure Chart 40
4.9 Efficient Frontier 49
4.10 CAPM Model 51
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Introduction
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CHAPTER 1
INTRODUCTION
1.1 INTRODUCTION TO THE PROBLEM
Due to the volatile nature of capital market the decision making process for an investor is
very difficult. The major factors to be considered while making investment decision are
risk and return. An informed investor has to seek an effective trade-off between these two
factors. Hence, portfolio management is a crucial decision for an investor. An investor
has to use various tools and techniques to find out optimal portfolio.
―A study on the construction of optimal portfolio using Sharpe‘s single index model with
special reference to CNX Nifty Shares‖ is an effort to construct an optimal portfolio from
50 shares which are constituents of CNX Nifty index. Five years historical data is used
analysis. This study is very helpful to get an awareness of various decisions in capital
market.
1.2 STATEMENT OF THE PROBLEM
High inflation rate prevailing in the economy erodes the value of investments in risk free
assets such as bank deposits and debt instruments. Hence, an investor has to allocate
some portion of his savings to high return instruments such as equity for achieving his
long term goals. However, the volatility of stock market makes the decision making a
complex process.
Hence, the problem under study is to construct an optimal portfolio using Sharpe‘s
optimization model and conduct an evaluation of the portfolio with other portfolios of
same return or risk to prove that this optimization model is simple and highly effective
for portfolio construction.
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1.3 SCOPE AND SIGNIFICANCE OF STUDY
The effectiveness of a portfolio is decided the collection of assets under portfolio and
their proportions. There for an investor who want to invest his own shall be thorough
with the methods of security analysis, portfolio analysis, portfolio selection, portfolio
evaluation and revision.
Since this study attempts to touch almost all the points required to reach optimal portfolio
it has very significance for an investor.
1.4 OBJECTIVES OF THE STUDY
1. To perform the risk return analysis of the CNX NIFTY Index shares.
2. To construct an optimal portfolio using Shape‘s optimization model and find out risk
and return of optimal portfolio.
3. Construct two random portfolios. One with same rate of return as optimal portfolio and
another with same risk as optimal portfolio.
4. To evaluate the performance of these three portfolios using Sharpe‘s ratio, Treynor‘s
ratio and Jensen Measure.
1.5 RESEARCH METHODOLOGY
The conceptual structure within which the research is conducted is described below.
Sample Design
The population involved in this project the 50 shares which constitutes in CNX Nifty
index.
Population Size
In this research the sample size constitutes 50 shares which constitute CNX Nifty Index.
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Survey Method
All the 50 Nos. of shares which constitute the CNX Nifty Index is used for the study.
Hence, the survey method used is census method.
Research Design
This project is based on analytical research design.
Area of Research
This research is to be conducted at the Branch of M/s. Motilal Oswal securities Ltd. at
Manjeri.
Sources of Data
The price movements of NSE CNX Nifty index and stock prices are the fundamental data
for the study. The main source of information is web sites, Magazines and journals.
Tools for Data Analysis
The data collected from sources has been analyzed using ratios and formulas .Tools like
Arithmetic mean, standard deviation, Alpha, Beta, Covariance, Sharpe Index, Treynor‘s
ratio and Jensen‘s measure are used.
The Microsoft Excel package is used for performing calculations and analysis.
1.6 CHAPTER LAYOUT
The study is presented in 6 chapters.
Chapter 1: Introduction
Chapter 2: Industry Profile
Chapter 3: Company Profile
Chapter 4: Theoretical Frame Work of study
Chapter 5: Analysis and Interpretations of Data
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Chapter 6: Summary, Findings and Conclusion.
The chapter six is followed by bibliography which contains the details of the books,
journals and web sites referred for this project.
1.7 LIMITATIONS OF THE STUDY
Duration of the study is limited hence extensive and deep study such as fundamental
analysis and technical analysis could not be possible.
The beta value changes from time to time. It may not reflect the future volatility of
returns. Hence the portfolio needs to be revised periodically.
An optimized portfolio cannot reduce systematic risk affecting the entire market. Hence,
the return from the portfolio varies with the general trend in the markets.
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Industry Profile
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CHAPTER 2
INDUSTRY PROFILE
2.1 INTRODUCTION
In the previous chapter brief introduction to the problem, scope and significance of the
problem and research methodology adopted was detailed.
In this chapter the stock market industry profile is described under following headings.
Stock Market, Stock Exchange, History of Indian Stock Market and Major Stock
Exchanges In India. A brief summary of the chapter is given in the Conclusion section.
2.2 STOCK MARKET
Capital market is the financial market for equity instruments and debt instruments with a
maturity greater than one year. The Capital market includes both primary market and
secondary markets.
The primary market is the market that deals with new securities, i.e., the securities that
are offered to the investing public for the first time. So it is a market for new issues.
Because of that, it is also called the new issues market.
The secondary market is the market in which existing securities are traded. This market is
also known as stock market.
2.2.1 History of Stock Market
In 12th century France the courretiers de change were concerned with managing and
regulating the debts of agricultural communities on behalf of the banks. Because these
men also traded with debts, they could be called the first brokers.
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In the middle of the 13th century, Venetian bankers began to trade in government
securities. Bankers in Pisa, Verona, Genoa and Florence also began trading in
government securities during the 14th century. Italian companies were also the first to
issue shares. Companies in England and the Low Countries followed in the 16th century.
The Dutch East India Company (founded in 1602) was the first joint-stock company to
get a fixed capital stock and as a result, continuous trade in company stock occurred on
the Amsterdam Exchange. Soon thereafter, a lively trade in various derivatives, among
which options and repos, emerged on the Amsterdam market. Dutch traders also
pioneered short selling.
There are now stock markets in virtually every developed and most developing
economies, with the world's largest markets being in the United States, United Kingdom,
Japan, India, Pakistan, China, Canada, Germany, France, South Korea and the
Netherlands.
2.3 STOCK EXCHANGE
A stock exchange is a place which aggregates buyers and sellers. In the stock exchanges
buying and selling of long term securities such as stocks and bonds takes place.
Exchanges may also cover other types of security such as derivatives, commodities and
currencies, etc.
2.3.1 Function and the Purpose of Stock Market
The purpose of a stock exchange is to facilitate the exchange of securities between buyers
and sellers, thus providing a marketplace (virtual or real). The exchanges provide real-
time trading information on the listed securities, facilitating price discovery.
The stock market is one of the most important ways for companies to raise money. This
allows businesses to be publicly traded, and raise additional financial capital for
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expansion by selling shares of ownership of the company in a public market. Companies
may want to get their stock listed on a stock exchange for liquidity of shares and increase
share holder value. The liquidity that an exchange affords the investors enables their
holders to quickly and easily sell securities. This is an attractive feature of investing in
stocks, compared to other less liquid investments such as property and other immoveable
assets.
Exchanges also act as the clearinghouse for each transaction, meaning that they collect
and deliver the shares, and guarantee payment to the seller of a security. This eliminates
the risk to an individual buyer or seller that the counterparty could default on the
transaction.
2.3.2 Physical and Electronic Exchanges
Some exchanges are physical locations where transactions are carried out on a trading
floor, by a method known as open outcry. An example of such an exchange is the New
York Stock Exchange. The other type of stock exchange is a virtual kind, composed of a
network of computers where trades are made electronically by traders. An example of
such an exchange is the National Stock Exchange of India (NSE).
The National Stock Exchange of India (NSE) is a virtual listed exchange, where all of the
trading is done over a computer network. The buyers and sellers are electronically
matched. One or more market makers will always provide a bid and ask price at which
they will always purchase or sell 'their' stock. People trading in big exchanges get greater
number of potential counterparties (buyers for a seller, sellers for a buyer), and probably
the best price.
2. 3.4 Size of the Market
At the close of 2012, the size of the world stock market (total market capitalization) was
about US$55 trillion. By country, the largest market was the United States (about 34%),
followed by Japan (about 6%) and the United Kingdom (about 6%).
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The table below represents the list of largest stock exchanges around the world. New
York stock exchange (NYSE) is the biggest stock exchange in the world in terms of
market capitalization. Bombay Stock Exchange (BSE) holds the 10th
place and National
Stock Exchange of India (NSE) holds 11th
place.
Table 2.1: Ranking of Stock Exchanges
based on Market capitalization
Rank Stock Exchange Market Cap
(in US$ trillion)
1 NYSE 19.2
2 NASDAQ 6.84
3 Tokyo Stock Exchange 4.43
4 Euronext 3.37
5 Hong Kong Stock Exchange 3.26
6 Shanghai Stock Exchange 2.96
7 TMX, Canada 2.14
8 Shenzhen Stock Exchange 1.95
9 Deutsche Borse 1.69
10 BSE India 1.58
11 National Stock Exchange India 1.55
12 Swiss Exchange 1.51
13 Australian Stock Exchange 1.41
14 Korea Exchange 1.23
(Source: www.wikipedia.com)
2.3.5 Behaviour of the Stock Market
According to interpretation of the efficient-market hypothesis (EMH), only changes in
fundamental factors, such as the outlook for margins, profits or dividends, ought to affect
share prices beyond the short term, where random 'noise' in the system may prevail.
The excessive optimism may drive prices unduly high or excessive pessimism may drive
prices unduly low. A succession of good news items about a company may lead investors
to overreact positively (unjustifiably driving the price up). A period of good returns also
boosts the investors' self-confidence, reducing their (psychological) risk threshold.
Emotions can drive prices up and down, people are generally not as rational as they think,
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and the reasons for buying and selling are generally obscure. There have been famous
stock market crashes that have ended in the loss of billions of dollars and wealth
destruction on a massive scale. An increasing number of people are involved in the stock
market, especially since the social security and retirement plans are being increasingly
privatized and linked to stocks and bonds and other elements of the market.
2.3.6 Stock Market Index
The movements of the prices in a market or section of a market are captured in price
indices called stock market indices, of which there are many, e.g., the S&P, BSE
SENSEX, CNX NIFTY indices. Such indices are usually market capitalization weighted,
with the weights reflecting the contribution of the stock to the index. The constituents of
the index are reviewed frequently to include/exclude stocks in order to reflect the
changing business environment.
2.3.7 Derivative Instruments
Financial innovation has brought many new financial instruments whose values depend
on the prices of stocks. Some examples are exchange-traded funds (ETFs), stock index
and stock options, single-stock futures, and stock index futures.
2.4 HISTORY OF INDIAN STOCK MARKET
The Indian stock market has a history of about 299 years old. It was in early 18th
Century, the main institution that is dealing in the trading of shares and stocks is the East
India Company. Later by around 1830′s the main dealing in the shares and stocks
(mainly in bank and cotton) was initiated in Bombay. However, the items in which the
trading took place increased tremendously by the end of 1839. There after the concept of
broker business was started which show momentum in the mid 18th century. This
concept has attracted nm\ember of people to indulge in the trading of items. By 1860, the
number of brokers who are dealing in the trading of items goes up to 60 in number.
Further, the number of brokers increased from 60 to 250 in around 1862-1863.
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People who need to trade generally gathered on the street which was popularly known as
the Dalal Street and the trading and the transaction used to take place from the Dalal
Street. It was in year 1875 that the first stock exchange was formulated in the name of
―The Native Share and Stock Brokers Association‖ which is presently known as the
Bombay stock exchange there after it was in year 1908, that the stock exchange in
Calcutta was formulated known as‖ The Calcutta Stock Exchange Association‖. The
formation of the Madras Stock exchange took place in 1920 which was started with
around 100 brokers who are trading in the madras Stock exchange. It was in 1934 when
the Lahore Stock exchange was established. The Uttar Pradesh stock exchange and the
Nagpur stock Exchange were established in year 1940. In year 1944, the Hyderabad stock
exchange was established. It was in year 1947 that the ―Delhi Stock and Share Broker
Association Limited‖ and ―The Delhi stocks and Shares exchange Limited‖ was
established in Delhi.
There was shutdown of various stock exchanges in India due to the depression that took
place after Independence. It was under the Securities Contracts (Regulations) Act, 1956
that various stock exchanges has got a recognition as a recognized stock exchange such
as Bombay, Delhi, Hyderabad, Indore etc. there are several other stock exchanges that
were established post independence.
2.5 MAJOR STOCK EXCHANGES IN INDIA
The Major stock exchanges in India such as Bombay Stock Exchange (BSE), Calcutta
Stock Exchange, National Stock Exchange, Interconnected Stock Exchange (ISE),
OTCEI, Cochin Stock Exchange Ltd. is detailed below.
2.5.1 The Bombay Stock Exchange
The Bombay Stock Exchange is the oldest exchange in Asia. It traces its history to 1855,
when four Gujarati and one Parsi stockbroker would gather under banyan trees in front of
Mumbai's Town Hall. The location of these meetings changed many times as the number
of brokers constantly increased. The group eventually moved to Dalal Street in 1874 and
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in 1875 became an official organization known as "The Native Share & Stock Brokers
Association". Figure below shows Bombay Stock Exchange
Fig 2.1 Bombay Stock Exchange
On 31 August 1957, the BSE became the first stock exchange to be recognized by the
Indian Government under the Securities Contracts Regulation Act. In 1980, the exchange
moved to the Fort area. In 1986, it developed the BSE SENSEX index, giving the BSE a
means to measure overall performance of the exchange. In 2000, the BSE used this index
to open its derivatives market, trading SENSEX futures contracts. The development of
SENSEX options along with equity derivatives followed in 2001 and 2002, expanding
the BSE's trading platform.
Historically an open outcry floor trading exchange, the Bombay Stock Exchange
switched to an electronic trading system in 1995. This automated, screen based trading
platform called BSE On-line trading (BOLT) had a capacity of 8 million orders per day.
The BSE has also introduced a centralized exchange-based internet trading system,
bsewebex.co.in to enable investors anywhere in the world to trade on the BSE platform.
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At present BSE has 5696 listed companies with a market capitalization of Rs.1,03,15,342
crores. It has 2,81,37,285 number of registered investors.
2.5.2 Calcutta Stock Exchange
Calcutta Stock Exchange is located at the Lyons Range, Kolkata is the oldest stock
exchange in South Asia. It was incorporated in 1908 and was the second largest stock
market in India.
In 1830, the bourse activities in Kolkata used to conduct under a neem tree. In 1908, the
stock exchange was incorporated and consisted of 150 members. The present building at
the Lyons Range was constructed in 1928. The Calcutta Stock Exchange Ltd was granted
permanent recognition by the Government of India with effect from April 14, 1980 under
the relevant provisions of the Securities Contracts (Regulation) Act, 1956. The Calcutta
Stock Exchange followed the familiar outcry system for stock trading up until 1997,
when it was replaced by an electronic trading system known as C-STAR (CSE Screen
Based Trading And Reporting).
2.5.3 National Stock Exchange of India (NSE)
The National Stock Exchange of India Limited (NSE) is the leading stock exchange of
India, located in Mumbai. NSE was the first exchange in the country to provide a
modern, fully automated screen-based electronic trading system which offered easy
trading facility to the investors spread across the length and breadth of the country.
NSE was set up by a group of leading Indian financial institutions at the behest of the
government of India to bring transparency to the Indian capital market. Based on the
recommendations laid out by the government committee, NSE has been established with
a diversified shareholding comprising domestic and global investors. The key domestic
investors include Life Insurance Corporation of India, State Bank of India, IFCI Limited
IDFC Limited and Stock Holding Corporation of India Limited. And the key global
investors are Gagil FDI Limited, GS Strategic Investments Limited, SAIF II SE
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Investments Mauritius Limited, Aranda Investments (Mauritius) Pte. Limited and PI
Opportunities Fund I.
The exchange was incorporated in 1992 as a company and was recognized as a stock
exchange in 1993 under the Securities Contracts (Regulation) Act, 1956. NSE
commenced operations in the Wholesale Debt Market (WDM) segment in June 1994.
The capital market (equities) segment of the NSE commenced operations in November
1994, while operations in the derivatives segment commenced in June 2000. The photo of
National Stock Exchange is given below.
Fig 2.2 National Stock Exchange
NSE has a market capitalization of more than US$1.65 trillion, making it the world‘s
12th-largest stock exchange as of 23 January 2015. NSE's flagship index, the CNX
Nifty, the 50 stock index is used extensively by investors in India and around the world
as a barometer of the Indian capital markets.
The National Stock Exchange of India Limited (NSE) commenced trading in derivatives
with the launch of index futures on 12 June 2000. The futures and options segment of
NSE has made a global mark. In the Futures and Options segment, trading in CNX Nifty
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Index, CNX IT index, Bank Nifty Index, Nifty Midcap 50 index and single stock futures
are available. Trading in Mini Nifty Futures & Options and Long term Options on CNX
Nifty are also available. The average daily turnover in the F&O Segment of the Exchange
during the financial year April 2013 to March 2014 stood at Rs 1,52,236 Crores.
NSE‘s trading systems, is a state of-the-art application. It has an up time record of
99.99% and processes more than 450 million messages every day with sub millisecond
response time.
Today NSE can handle 1, 60,000 orders/messages per second, with
infinite ability to scale up at short notice, NSE have continuously worked towards
ensuring that the settlement cycle comes down. Settlements have always been handled
smoothly. The settlement cycle has been reduced from T+5 to T+2/T+1.
2.5.4 Cochin Stock Exchange Ltd.
COCHIN STOCK EXCHANGE LTD. is situated in Cochin in Kerala State, established
in the year 1978. The exchange had a humble beginning with just 5 companies listed in
1978 -79, and had only 14 members. Today the Exchange has more than 508 members
and 240 listed companies. In 1980 the Exchange computerized its offices. In order to
keep pace with the changing scenario in the capital market, CSE took various steps
including trading in dematerialized shares. CSE introduced the facility for computerized
trading - "Cochin Online Trading (COLT)" on March 17, 1997.
CSE was one of the promoters of the "Interconnected Stock Exchange of India (ISE)".
The objective was to consolidate the small, fragmented and less liquid markets into a
national level integrated liquid market. With the enforcement of efficient margin system
and surveillance, CSE has successfully prevented defaults. Introduction of fast track
system made CSE the stock exchange with the shortest settlement cycle in the country at
that time.
To face this challenge CSE promoted a 100% subsidiary called the "Cochin Stock
Brokers Ltd. (CSBL)" and started trading in the National Stock Exchange (NSE) and
Bombay Stock Exchange (BSE). CSBL is the first subsidiary of a stock exchange to get
membership in both NSE & BSE. CSBL also became a depository participant in the
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Central Depository Services Ltd. The CSE has been playing a vital role in the economic
development of Kerala. A photo of Cochin Stock Exchange is given below.
Figure 2.3 Cochin Stock Exchange
The Cochin Stock Exchange is directly under the control and supervision of Securities &
Exchange Board of India (the SEBI), and is today a demutualized entity in accordance
with the Cochin Stock Exchange (Demutualization) Scheme, 2005 approved
and notified by SEBI on 29th
of August 2005. Demutualization essentially means de-
linking and separation of ownership and trading rights and restructuring the Board in
accordance with the provisions of the scheme.
The policy decisions of the CSE are taken by the Board of Directors. The Board is
constituted with 12 members of whom less than one-fourth are elected from amongst the
trading member of CSE, another one fourth are Public Interest Directors selected by
SEBI from the panel submitted by the Exchange and the remaining are Shareholder
Directors. The Board appoints the Executive Director who functions as an ex-
officio member of the Board and takes charge of the administration of the Exchange.
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2.5.5 OTCEI
Started in 1992 with the object of providing market for smaller companies that could not
afford the listing free of larger exchanges and which did not fulfill the minimum capital
requirement for listing. It aimed at creating fully decentralized and transparent market.
OTC means trading across the counter in scripts. The member or dealer of OTCEI
counters are linked to the central OTCEI computer where every counter is treated as
trading floor for the OTCEI where the investor can buy and sell.
The OTCEI is incorporated as a company under section 25 of the companies act 1956
promoted by UTI, ICICI, IDBI, IFCI, LIC, GIC, SBI capital markets and Can Bank
Financial Service. OTCEI have special feature of screen based trading with wide network
coverage rolling settlement and market making. (Market makers in securities quote the
prices at which members are willing to buy and sell the specified number of securities.
NSE is supporting OTCEI in terms of systems and hardware.
2.5.6 Inter Connected Stock Exchange (ISE)
Started in the year 1998with the main objective to interlink the 15 odd regional Stock
Exchanges throughout the country [Bangalore, Bhuvaneswar, Chennai, Kochi,
Coimbatore, Guwahati, Hyderabad, Jaipur, Ludhiana, Indore, Magadh, Mangalore,
Saurashtra (Kutch), Uttar Pradesh (Kanpur) and Vadodara] to ensure liquidity.
The total cost of ISE was 15 crores that were shared equally by participating Stock
Exchanges. The membership fees to ISE costs Rs 16000/- along with the capital
adequacy deposit of Rs 4 lakhs as stipulated by SEBI. Another important objective of ISE
is to minimize the cost of regional exchanges as they are incurring huge costs by
supporting a very illiquid market.
2.6 CONCLUSION
In this chapter the history of world stock market, function and purpose of stock market,
important stock exchanges in the world, and physical and electronic trading systems were
29
detailed. Finally, the history of Indian stock exchanges and important stock exchanges in
India is detailed.
In the next chapter titled company profile, the overview of company, its subsidiaries,
vision, mission, values and strengths of the company will be discussed. Details of the
directors, awards and recognition won by the company are also described.
30
Company Profile
31
CHAPTER 3
COMPANY PROFILE
3.1 INTRODUCTION
In the previous chapter the history of world stock market, function and purpose of stock
market, important stock exchanges in the world, and physical and electronic trading
systems were detailed. Finally, the history of Indian stock exchanges and important stock
exchanges in India was detailed.
In this chapter, the company profile is discussed under following headings. Overview of
the Company, Mission of the Company , Values of the Company. Strengths of the
Company, Board of Directors of the Company, Awards and Recognitions Won By M/S.
MOSL. This chapter ends with a conclusion section in which a brief summary of this
chapter is given.
3.2 OVERVIEW OF THE COMPANY
M/s. Motilal Oswal Securities Limited (MOSL) is a well-diversified financial services
firm offering a range of financial products and services such as retail wealth management
(including securities and commodities broking), portfolio management services,
institutional broking, venture capital management and investment banking services. As a
leading Indian domestic brokerage house, M/s. Motilal Oswal Securities Limited have a
diversified client base that includes retail customers (including high net worth
individuals), mutual funds, foreign institutional investors, financial institutions and
corporate clients. M/s. Motilal Oswal Securities Limited is headquartered in Mumbai and
as of December 31, 2006, had a network spread across 363 cities and towns comprising
1,160 Business Locations operated by the company and Business Associates.
32
Motilal Oswal Financial Services Limited is the holding company and also provides
financing for our retail broking customers. M/s. MOSL operate through the following
four subsidiaries:
• Motilal Oswal Securities Limited (MOSL)
• Motilal Oswal Commodities Brokers Private Limited (MOCB)
• Motilal Oswal Venture Capital Advisors Private Limited (MOVC)
• Motilal Oswal Investment Advisors Private Limited (MOIA).
Since inception, the business has primarily focused on retail wealth management and
institutional broking. In 2006, company diversified into investment banking and venture
capital management.
The principal business activities of the M/s. MOSL are:
Retail wealth management
Institutional broking
Investment banking
Venture capital management and advisory.
Retail wealth management business provides broking and financing services to retail
customers as well as investment advisory, financial planning and portfolio management
services. As at December 31, 2006, M/s. MOSL had 213,624 registered retail equity
broking clients and 3,572 registered commodity broking clients whom M/s. MOSL
classify into three segments, being ―mass retail‖, ―mid-tier millionaire‖ and ―private
client group(PCG)‖. M/s. MOSL offer retail clients investment products across the major
asset classes including equities, derivatives, commodities and the distribution of third-
party products such as mutual fund schemes and primary equity offerings. M/s. MOSL
distribute these products through the Business Locations and online channel.
Institutional broking business offers equity broking services in the cash and derivative
segments to institutional clients in India and overseas. As at December 31, 2014, M/s.
MOSL was empanelled with 2402 institutional clients including 150 FIIs. M/s. MOSL
33
service these clients through dedicated sales teams across different time zones. Retail
wealth management and institutional brokerage businesses are supported by dedicated
research teams. Research teams are focused on cash equities, equity derivatives and
commodities.
Investment banking business offers financial advisory, capital raising and other
investment banking services to corporate clients, financial sponsors and other institutions.
Financial advisory includes advisory assignments with respect to mergers and
acquisitions (domestic and cross-border), divestitures, restructurings and spin-offs.
Capital raising and other investment banking services include management of public
offerings, rights issues, share buybacks, open offers/delisting, private placements
(including qualified institutional placements) and syndication of debt and equity.
The current organization structure of the company is set forth below.
Motilal Oswal Securities Limited (MOSL)
M/s. MOSL was incorporated on July 5, 1994. This subsidiary focuses on the Stock
Broking (Institutional & Retail) business. MOSL also acts as a holding company of other
subsidiaries.
Motilal Oswal Financial Services Limited (MOFSL)
M/s. MOSFL was incorporated on May 18, 2005. This subsidiary focuses in providing
financial services to corporate.
Motilal Oswal Commodities Brokers Private Limited (MOCB)
M/s. MOCB was incorporated on March 26, 1991. This subsidiary provides commodity
broking services to its clients.
Motilal Oswal Venture Capital Advisors Private Limited (MOVC)
M/s. MOVC was incorporated on April 13, 2006. The subsidiary manages Private Equity
Investments.
34
Motilal Oswal Investment Advisors Private Limited (MOIA)
M.s MOIA was incorporated on March 20, 2006. This subsidiary focuses on providing
Investment & Merchant Banking services.
3.3 MISSION OF THE COMPANY
The mission of M/s. MOSL is to be a well respected and preferred global financial
services organisation enabling wealth creation for all customers.
3.4 VALUES OF THE COMPANY
Key corporate values of the M/s. MOSL are:
Integrity
Teamwork
Meritocracy
Passion and attitude
Excellence in execution.
3.5 STRENGTHS OF THE COMPANY
The company achieved a prominent place in the Indian financial services company due to
following strengths.
3.5.1 Large and Diverse Distribution Network
Company‘s financial products and services are distributed through a pan-India network.
The business has grown from a single location to a nationwide network spread across
1,160 Business Locations operated by us and Business Associates in 363 cities and
towns. Extensive distribution network provides the company with opportunities to cross-
sell products and services, particularly when diversifying into new business streams. In
35
addition to the geographical spread, M/s. MOSL offer an online channel to service the
customers.
3.5.2 Strong research and sales teams
M/s. MOSL believes that understanding of equity as an asset class and business
fundamentals drives the quality of their research and differentiates them from
competitors. Their research teams are focused on cash equities, equity derivatives and
commodities. As at December 31, 2014, M/s. MOSL had 28 equity research analysts
covering 208 companies in 25 sectors and 5 analysts covering 18 commodities. M/s.
MOSL have 1,964 employees, including 739 on a contract basis.
M/s. MOSL believes that research enables them to identify market trends and stocks with
high growth potential, which facilitates more informed and timely decision making by
their clients. This helps to build and promote their brand image and to acquire and retain
institutional and retail customers. Their research is complemented by a strong sales and
dealing team. Each member of institutional sales team has significant research
experience. M/s. MOSL believe that this experience enables sales team to effectively
market ideas generated by the research team to client base and to build stronger client
relationships.
3.5.3 Experienced top management
Both Promoters of the company, Mr. Motilal Oswal and Mr. Raamdeo Agarwal, are
qualified chartered accountants with over two decades of experience each in the financial
services industry. In addition, the top management team comprises qualified and
experienced professionals with a successful track record. M/s. MOSL We believe that our
management‘s entrepreneurial spirit, strong technical expertise, leadership skills, insight
into the market and customer needs provide with a competitive strength which will help
to implement their business strategies.
36
3.5.4 Well-established brand
―Motilal Oswal‖ is a well established brand among retail and institutional investors in
India. M/s. MOSL believes that this brand is associated with high quality research and
advice as well as good corporate values, like integrity and excellence in execution. M/s.
MOSL have been able to leverage the brand awareness to grow their businesses, build
relationships and attract and retain talented individuals which is important in the financial
services industry.
3.5.6 Wide range of financial products and services
The following products and services are offered by the company;
Equity Broking
PMS (Portfolio Management Service)
Investment
Banking
PE (Private Equity)
Investments
MF (Mutual Funds)
Investments
Commodity
Broking
M/s. MOSL offer a portfolio of products to satisfy the diverse investment and strategic
requirements of retail, institutional and corporate clients. M/s. MOSL believes that wide
range of products and services enables to build stronger relationships with, and increase
business volumes from, their clients. In addition, their diverse portfolio reduces
dependence on any particular product, service or customer and allows exploiting
synergies across their businesses.
37
3.6 BOARD OF DIRECTORS OF THE COMPANY
The list of Board of Directors is given below.
Table 3.1: Board of Directors
CMD & CEO Motilal Oswal
Joint Managing Director Raamdeo Agrawal
Directors
Navin Agarwal ,
Balkumar Agarwal
Vivek Paranjpe ,
Praveen Tripathi
Additional Independent Director Sharda Agarwal
(Source: www.motilaloswal.com)
3.7 AWARDS AND RECOGNITIONS WON BY M/S. MOSL
M/s. Motilal Oswal Securities won the Best Performing Equity Broker (National) Award
at CNBC TV18 Financial Advisor Awards 2013 held in Mumbai.
M/s. Motilal Oswal Financial Services Ltd's Analyst Mr. Jinesh Gandhi won the Best
Market Analyst Award for the categories Equity-Auto at ‗India`s Best Market Analyst
Awards 2013 organized by Zee Business.
M/s. Motilal Oswal Securities was declared "Best Equity Broker" at Bloomberg UTV
Financial Leadership Awards in April 2012.
M/s. Motilal Oswal Securities was awarded with Best Performing National Financial
Advisor Equity Broker Award in 2012, second time in succession.
M/s. Motilal Oswal Financial Services was honoured with an award for Best Use in PR in
Financial Services Category at India PR & Corporate Communications Awards 2012.
M/s. Motilal Oswal Securities received Best Equity Broking House Award by BSE IPF-
D&B Equity Broking Awards 2011.
38
M/s. Motilal Oswal Mutual Fund's MOSt Shares M50 ETF was adjudged Most
Innovative Fund of the Year by CNBC TV18 CRISIL Mutual Fund Award 2011.
CNBC TV18 awarded M/s. Motilal Oswal the Best Performing Equity Broker Award in
2010 at CNBC TV18 Financial Advisor Awards 2010.
Best Capital Markets & Related NBFC Award for FY11 by CNBC TV18 India Best
Banks & Financial Institutions Awards 2011.
M/s. Motilal Oswal IB team won the Asia Pacific Cross Border Deal of the year award in
2010 and the CEO Ashutosh Maheshvari got India M&A Investment Banker of the Year
award.
M/s. Motilal Oswal Securities Ltd. rated as No.1 Broker in ET Now – Starmine Analyst
Awards 2009.
M/s. MOSL was awarded 'The Best Franchisor in Financial Services' by Franchisee
World Magazine 2008 for the second consecutive year.
M/s. Motilal Oswal Securities Ltd. wins the ―Best Research as Research Showcase
Partner‖ at RESEARCHBYTES IC AWARDS 2014. The winners were selected from a
poll of over 1500 Fund Managers/Analysts.
M/s. Motilal Oswal Securities received two awards for its equity research in IT and
commodity (forex) segments at India's Best Market Analyst Awards 2014, India's biggest
Financial Market Awards also called as ZEE Business Awards 2014.
3.8 CONCLUSION
In this chapter, the brief overview of the company, its vision, mission, values and
strengths is detailed. The details of Director Board and awards and recognitions received
by the company are also detailed.
39
In the next chapter titled theoretical framework, traditional approach and modern
approach to portfolio management is described. The portfolio construction by traditional
method is detailed. Tools used for fundamental analysis and Technical analysis are
described. The steps in portfolio construction using Sharpe‘s single index model, the
formula used for portfolio evaluation, Risk and return calculations shall be discussed.
40
Theoretical Framework
41
CHAPTER 4
THEORETICAL FRAMEWORK
4.1 INTRODUCTION
In the previous chapter, the brief overview of the company, its vision, mission, values and
strengths were detailed. The details of Director Board and awards and recognitions
received by the company were also detailed.
In this chapter the theoretical frame work of the study is discussed under following
headings. Portfolio Construction, Traditional Approach, Security Analysis, Portfolio Analysis,
Portfolio Selection, Portfolio Revision, Portfolio Evaluation, Return and Risk Analysis of
Portfolio, Modern Approaches to Portfolio Selection, Portfolio Evaluation Methods,
Formulae Used For the Study. A brief summary of this chapter is given in the Conclusion
section.
4.2 PORTFOLIO CONSTRUCTION
Portfolio is a combination of securities such as stocks bonds and money market
instruments. Diversification of investments over different assets helps to reduce risk
without sacrificing return. When determining a proper asset allocation one aims at
maximizing the expected return and minimizing the risk. The process of blending
together the broad asset classes so as to obtain optimum return with minimum risk is
called portfolio construction.
4.3 APPROACHES TO PORTFOLIO CONSTRUCTION
There are two approaches to portfolio construction of the portfolio of securities viz,
Traditional approach
Modern approach
42
In traditional approach, investor‘s needs in terms of income and capital appreciation are
evaluated and appropriate securities are selected to meet the needs of the investor. The
common practice in the traditional approach is to evaluate the entire financial plan of the
individual.
In modern approach, portfolios are constructed to maximize the expected return for a
given level of risk. It views the portfolio construction in terms of the expected return and
the risk associated with obtaining the expected return.
4.4 TRADITIONAL APPROACH OF PROTFOLIO
CONSTRUCTION
The construction of portfolio by traditional method is carried out in 5 steps.
The five steps are
1. Security analysis
2. Portfolio analysis
3. Portfolio selection
4. Portfolio revision
5. Portfolio evaluation
These steps are detailed below under separate headings.
4.5 SECURITY ANALYSIS
Security analysis is the initial step of portfolio management. Security analysis is a method
which helps to calculate the value of various assets. There are two alternate approaches
to security analysis namely fundamental analysis and technical analysis.
4.5.1 Fundamental Analysis
The fundamental analysis tries to appraise intrinsic value of shares through economic,
industry and company analyses. If the price of share is lower than the intrinsic value, an
investor buys it. If he finds the price of the share higher than the intrinsic value, the
investor sells the share and makes profit.
43
Fig 4.1: Steps in Fundamental Analysis
a. Economic Analysis
Economic Analysis is a systematic approach in which economists and other professionals
will estimate the economic environment and its strengths and weaknesses. The level of
economic activity has an impact on investment in many ways. When the level of
economic activity is low, the stock prices are low, and when the level of economic
activity is high, stock prices are high reflecting the prosperous outlook for sales and
profits of the firm. The commonly analysed macroeconomic factors are as follows;
Gross domestic product (GDP)
Savings and investment
Inflation
Interest rates
Budget
Tax structure
Balance of payment
Monsoon and agriculture
Infrastructure facilities
Demographic factors
Economic forecasts
Economic indicators
Economic Analysis
Industry Analysis
Company Analysis
44
The state of economy determines the growth of GDP and investment opportunities. An
economy with favourable savings, investments, stable prices, balance of payments, and
infrastructure facilities provides a best environment for stock investment. A rising stock
market indicates a strong economy ahead.
b. Industry Analysis
An industry is a group of firms that have similar technological structure of production
and produce similar products. An industry analysis consists of three major elements: the
underlying forces at work in the industry; the overall attractiveness of the industry; and
the critical factors that determine a company's success within the industry.
The first step in performing an industry analysis is to assess the impact of Porter's five
forces. "The collective strength of these forces determines the ultimate profit potential in
the industry, where profit potential is measured in terms of long term return on invested
capital," Porter stated. "The goal of competitive strategy for a business unit in an industry
is to find a position in the industry where the company can best defend itself against these
competitive forces or can influence them in its favor."
Understanding the underlying forces determining the structure of the industry can
highlight the strengths and weaknesses of a business, show where strategic changes can
make the greatest difference, and illuminate areas where industry trends may turn into
opportunities or threats.
i) Ease of Entry
Ease of entry refers to how easy or difficult it is for a new firm to begin competing in the
industry. The ease of entry into an industry is important because it determines the
likelihood that a company will face new competitors. In industries that are easy to enter,
sources of competitive advantage tend to wane quickly. On the other hand, in industries
that are difficult to enter, sources of competitive advantage last longer, and firms also
tend to benefit from having a constant set of competitors.
45
ii) Power of Suppliers
Suppliers can gain bargaining power within an industry through a number of different
situations. For example, suppliers gain power when an industry relies on just a few
suppliers, when there are no substitutes available for the suppliers' product, when there
are switching costs associated with changing suppliers. Supplier power can affect the
relationship between a business and its customers by influencing the quality and price of
the final product.
iii) Power of Buyers
Powerful buyers can exert pressure on small businesses by demanding lower prices,
higher quality, or additional services, or by playing competitors off one another. The
power of buyers tends to increase when single customers account for large volumes of the
business's product, when substitutes are available for the product, when the costs
associated with switching suppliers are low.
iv) Availability of Substitutes
Substitutes limit the potential returns of an industry by placing a ceiling on the prices
firms in the industry can profitably charge. Product substitution occurs when a business's
customer comes to believe that a similar product can perform the same function at a
better price.
v) Competitors
The intensity of competition tends to increase when an industry is characterized by a
number of well-balanced competitors, a slow rate of industry growth, high fixed costs, or
a lack of differentiation between products. Another factor increasing the intensity of
competition is high exit barriers—including specialized assets, emotional ties,
government or social restrictions, strategic interrelationships with other business units,
labor agreements, or other fixed costs which make competitors stay and fight even when
they find the industry unprofitable.
46
vi) Industry attractiveness and industry success factors
Industry attractiveness is the presence or absence of threats exhibited by each of the
industry forces, the greater the threat posed by an industry force, the less attractive the
industry becomes.
Success factors are those elements that determine whether a company succeeds or fails in
a given industry. They vary greatly by industry. Some examples of possible success
factors include quick response to market changes, a complete product line, fair prices,
excellent product quality or performance, knowledgeable sales support, a good record for
deliveries, solid financial standing, or a strong management team.
Industrial growth follows life cycle patterns. Buying shares beyond the pioneering stage
and selling of shares before the stagnation stage are ideal for investors. The cost structure,
R&D and the government policies regarding the industries influence the growth and
profitability of the industries. SWOT analysis reveals the real status of the industry.
c. Company Analysis
Company analysis is a process carried out by investors to evaluate securities, collecting
data related to the company‘s profile, products and services as well as profitability. A
company analysis looks into the goods and services proffered by the company. If the
company is involved in manufacturing activities, the analysis studies the products
produced by the company and also analyzes the demand and quality of these products. If
it is a service business, the investor studies the services put forward.
In the company analysis, the investor analyses information related to the company and
evaluates the present and future values of the stock. The present and future values are
affected by a number of factors and they are given below.
Factors that affect present share values are
Historic stock price
Price/Equity Ratio
47
Economic condition
Stock market condition
Factors that affect future share prices are
Competitive Edge of the company
Earnings of the company
Capital structure of the company
Management quality of the company
Operating efficiency of the company
Financial performance of the company
The competitive edge of the company could be measured with the company‘s market
share, growth and stability of sales.
The financial statement reveals information about the financial state of the company.
Fund flow and cash flow statement is used to analyze the financial health of the
company.
The ratio analysis helps the investor to study the individual parameters like profitability,
liquidity, leverage, and the value of stock.
4.5.2 Technical Analysis
It is the process identifying trend reversals at an earlier stage to formulate the buying and
selling strategy. With the help of several indicators, the analyst analyses the relationship
between price-volume and supply demand for overall market and individual stock.
The generally used technical tools are
Dow theory
Volume of trading
Short selling
Bars and charts
48
Moving averages
Oscillators
4.5.2.1 Dow Theory
The market moves in a general direction called trend. According to ―Dow Theory‖ the
trend is divided in to primary, intermediate and short term trend. The primary trend may
be the broad upward or downward movement that may last for a year or two. The
intermediate trends are corrective movements that may last for three weeks to three
months. The short term trend refers to day-to-day price movement.
Fig 4.2: Trends in stock market
Source: www.fidelity.com
Dow gives special emphasis on volume. Volume expands along with the bull market and
narrows along with the bear market. Large volume with rise in price indicates bull
market. Large volume with fall in price indicates bear market.
4.2.5.2 Breadth of the market
The net difference between the number of stocks advanced and number of stocks
declined is the breadth of the market. A ratio of 0.75 indicates short-term buying
opportunity and there will be an intermediate rally in the beginning of bearish trend. A
rise above 1.25 indicates selling opportunities.
49
4.5.2.3 Short selling
Short selling is a technical indicator referring to selling of shares that are not owned. If the
short selling ratio is less than 1 it indicates that the market is overbought and a decline can be
expected. Value above 1 indicates bullish trend and if it is above 2 the market is oversold.
4.5.2.4 Moving Averages
Moving averages indicates the underlying trend in the scrip. For identifying short term trend
10 to 30 day moving averages are used. In the case of medium term trend, 50 to 125 day are
adopted, 200-day moving average is used to identify long-term trend.
The chart below shows the moving averages for 50 and 200 days.
Fig 4.3: Moving Averages
(Source: www.onlinetradingconcepts.com)
4.5.2.5 Oscillators
Oscillators such as Relative strength index (RSI) and Rate of change (ROC) indicate the
market momentum or scrip momentum. The oscillators indicate overbought and oversold
conditions, possible trend reversal, rise or decline in stock momentum.
50
4.5.2.6 Relative Strength Index
A technical momentum indicator that compares the magnitude of recent gains to recent
losses in an attempt to determine overbought and oversold conditions of an asset. It is
calculated using the following formula:
RSI = 100 - 100/ (1 + RS*)
*Where RS = Average of x days' up closes / Average of x days' down closes.
Fig 4.4: Relative Strength Index
(Source: www.investopedia.com)
From the chart, the RSI ranges from 0 to 100. An asset is deemed to be overbought once
the RSI approaches the 70 level, meaning that it may be getting overvalued and is a good
candidate for a pullback. Likewise, if the RSI approaches 30, it is an indication that the
asset may be getting oversold and therefore likely to become undervalued.
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4.5.2.7 Rate- Of-Change (ROC) Indicator
The Rate-of-Change (ROC) indicator, which is also referred to as simply Momentum, is a
pure momentum oscillator that measures the percent change in price from one period to
the next. The ROC calculation compares the current price with the price ―n‖ periods ago.
The plot forms an oscillator that fluctuates above and below the zero line as the Rate-of-
Change moves from positive to negative. As a momentum oscillator, ROC signals
overbought-oversold conditions.
4.5.2.8 Charts
Charts are valuable and easiest tools in the technical analysis. The graphic presentation of
the data helps the investor to find out the trend of the price without the difficulty. The
charts indicate past historic price movement, current trend, important support and
resistance, and probable future action of the market by projection.
There are four main types of charts that are used by investors and traders depending on
the information that they are seeking and their individual skill levels. The chart types are:
the line chart, the bar chart, the candlestick chart and the point and figure chart. In the
following sections, we will focus on the S&P 500 Index during the period of January
2006 through May 2006. Notice how the data used to create the charts is the same, but
the way the data is plotted and shown in the charts is different.
a. Line Chart
The most basic of the four charts is the line chart because it represents only the closing
prices over a set period of time. The line is formed by connecting the closing prices over
the time frame. Line charts do not provide visual information of the trading range for the
individual points such as the high, low and opening prices. However, the closing price is
often considered to be the most important price in stock data compared to the high and
low for the day and this is why it is the only value used in line charts. A line chart is
shown in the figure below.
52
Fig 4.5: Line Chart
(Source: www.investopedia.com)
b. Bar Charts
The bar chart expands on the line chart by adding several more key pieces of information
to each data point. A bar chart is shown in the figure below.
Fig 4.6: Bar Chart
(Source: www.investopedia.com)
The chart is made up of a series of vertical lines that represent each data point. This
vertical line represents the high and low for the trading period, along with the closing
53
price. The close and open are represented on the vertical line by a horizontal dash. The
opening price on a bar chart is illustrated by the dash that is located on the left side of the
vertical bar. Conversely, the close is represented by the dash on the right. Generally, if
the left dash (open) is lower than the right dash (close) then the bar will be shaded black,
representing an up period for the stock, which means it has gained value. A bar that is
colored red signals that the stock has gone down in value over that period. When this is
the case, the dash on the right (close) is lower than the dash on the left (open).
c. Candlestick Charts
The candlestick chart is similar to a bar chart, but it differs in the way that it is visually
constructed. Similar to the bar chart, the candlestick also has a thin vertical line showing
the period's trading range. A candlestick chart is shown below.
Fig 4.7: Candlestick Chart
(Source: www.investopedia.com)
The difference comes in the formation of a wide bar on the vertical line, which illustrates
the difference between the open and close. And, like bar charts, candlesticks also rely
heavily on the use of colors to explain what has happened during the trading period. A
54
major problem with the candlestick color configuration, however, is that different sites
use different standards; therefore, it is important to understand the candlestick
configuration used at the chart site you are working with. There are two color constructs
for days up and one for days that the price falls. When the price of the stock is up and
closes above the opening trade, the candlestick will usually be white or clear. If the stock
has traded down for the period, then the candlestick will usually be red or black,
depending on the site. If the stock's price has closed above the previous day's close but
below the day's open, the candlestick will be black or filled with the color that is used to
indicate an up day.
d. Point and Figure Charts
The point and figure chart has a long history of use dating back to the first technical
traders. This type of chart reflects price movements and is not as concerned about time
and volume in the formulation of the points. The point and figure chart removes the
noise, or insignificant price movements, in the stock, which can distort traders' views of
the price trends. These types of charts also try to neutralize the skewing effect that time
has on chart analysis.
Fig 4.8: Point and figure Chart
( Source:www.investopedia.com)
55
The Xs represent upward price trends and the Os represent downward price trends. There
are also numbers and letters in the chart; these represent months, and give investors an
idea of the date. Each box on the chart represents the price scale, which adjusts
depending on the price of the stock: the higher the stock's price the more each box
represents. On most charts where the price is between $20 and $100, a box represents $1,
or 1 point for the stock. The other critical point of a point and figure chart is the reversal
criteria. This is usually set at three but it can also be set according to the chartist's
discretion. The reversal criteria set how much the price has to move away from the high
or low in the price trend to create a new trend or, in other words, how much the price has
to move in order for a column of Xs to become a column of Os, or vice versa. When the
price trend has moved from one trend to another, it shifts to the right, signaling a trend
change.
4.6 PORTFOLIO ANALYSIS
Security analysis provides a set of securities suitable for investment. From these
securities a large number of portfolios can be constructed by choosing different set of
securities and also by varying weight of securities. The diversification has the effect of
reducing the portfolio risk by minimizing the unsystematic risk which affects individual
security or industry. Whereas over diversification reduces the return from portfolio. A
rational investor has to find out the most efficient portfolio by choosing appropriate
trade-off between risk and return.
4.7 PORTFOLIO SELECTION
Portfolio analysis gives different portfolios available for investment. From these
portfolios an optimal portfolio is selected for investment.
4.8 PORTFOLIO REVISION
As the economy and business environment changes the return from securities also
changes. The portfolio has to include new securities which promises high return and
56
exclude securities which has become underperformer. Hence, after constructing an
optimal portfolio the investor has to periodically monitor the portfolio to ensure that it
remains optimal.
4.9 PORTFOLIO EVALUATION
The evaluation of portfolio provides feedback about performance to evolve better
management strategy. The return and risk of portfolio over a period of time is evaluated.
These values are compared with standard values such as market index to assess the
relative performance of the portfolio.
4.10 RETURN AND RISK ANALYSIS OF PORTFOLIO
Portfolio‘s performance analysis consists of examining the risk-return characteristics of
the portfolio.
4.10.1 Return
The return of a portfolio is measured by its average total return over a standard holding
period, usually one year. The total return consists of investment income such as dividends
plus capital gain/loss. The rate of return earned by the portfolio is calculated compared
with the bench mark like market index.
The return of a portfolio is given by
n
Rp = Σ Xi Ri i=1
Where
Rp = Portfolio average return
Xi = Weight or proportion of security ‗i‘ in portfolio
Ri = Expected return of Security i
57
4.10.2 Risk
Risk is the possibility of not realizing return or realizing return less than expected. The
risk is broadly classified into two types;
1. Systematic Risk
2. Unsystematic Risk
4.10.2.1 Systematic Risk
Systematic risk refers to that portion of variation in return caused by factors that affect
the price of all securities. The effect of systematic risk is to move prices of all individual
securities in same direction. The systematic risk arises due to following reasons.
a. Market Risk: Variation in prices arises out of changes in demand and supply
pressures in the market following the changing flow of news and expectations.
b. Interest Rate risk: The market perception is influenced by changes in interest rates
which in-turn affects the riskiness of investments due to their effects on returns
expectations and the total principal amount due to be refunded.
c. Purchasing Power Risk: Purchasing power risk is the uncertainty of the purchasing
power of the amounts to be received due to both inflation and deflation.
4.10.2.2 Unsystematic Risk
Unsystematic risk refers to that portion of risk which is caused due to factors unique or
related to a firm or industry. This type of risk can be divided further in to the following
types.
a. Business Risk: Business risk may be due to internal factors or external factors.
Internal risk is caused by factors such as improper product mix, non availability of
raw material, incompetence to face competence, absence of strategic management,
etc. External risks arise due to factors which are beyond the control of the firm e.g.
58
business cycles, government controls, changes in laws, international market
conditions.
b. Financial Risk: Financial risk is associated with the capital structure of the company.
The extent of risk depends on the leverage of the firm‘s capital structure.
c. Credit of Default Risk: Credit risk is associated with probability of a buyer will
default. The borrower‘s credit rating might have fallen suddenly and he may become
default prone. Proper management of credit risk reduces the chances of non- payment
and reduces credit risk.
d. Other Risks: In addition to above risk there are many more risks particularly
associated with foreign securities. These are monetary value risk, political risk, and
foreign government indebtedness risk.
4.10.3 Calculation of Risk on a Portfolio
Risk on a portfolio is not same as risk on individual securities. Portfolios standard
deviation is a good indicator of the risk of the portfolio. The portfolio risk of a portfolio
of 2 securities can be calculated using the following formula:
σp = √W12 σ1
2 + W22 σ2
2 + 2 W1 W2 (r 12
σ1 σ2)
Where
σp= Standard deviation of portfolio
W1 = Weight or proportion of security 1 in portfolio
W2 = Weight or proportion of security 2 in portfolio
σ1= Standard deviation of security 1
σ2= Standard deviation of security 2
r12 = Correlation co-efficient of returns of security 1 and security 2
59
4.11 MODERN APPROACHES TO PORTFOLIO SELECTION
In modern approach of portfolio selection the stocks are not selected based on the need
for income or appreciation. The selection is based on the risk and return analysis. Modern
Portfolio Theory (MPT) approaches investing by examining the entire market and the
whole economy. The theory is an alternative to the older method of analyzing each
investment‘s individual merits. MPT places a large emphasis on the correlation between
investments. Correlation is the amount we can expect various investments – and various
asset classes – to change in value compared with each other. The commonly used models
are given below.
Sharpe‘s single index model
Markowitz mean-variance optimization model
Capital Asset Pricing Model (CAPM)
Arbitrage Pricing Theory
4.11.1 Sharpe’s Single Index Model
Sharpe‘s single index model was developed by William Sharpe for the construction of
optimal portfolio using less number of inputs. The simplicity is the most important
feature of the Sharpes‘s single index model over Markowit‘z model. Markowitz‘s model
uses large number of covariance. Taking idea from the Markowit‘z, suggested that index
to which securities are related can be used for covariance generation, William Sharpe
formulated single index model.
The regression equation is
Ri =αi +βi*Rm+ei
Where,
Ri = Return on security i
αi = Constant term (Securities return when market excess return is zero)
βi = Beta of security
60
ei = error term.
The key assumptions are
1. The error term ei is zero mean and had finite variance.
2. The securities are related through common response to return of market index.
Meaning the error term of one security is not correlated with error term of any other
security. COV (ei, ej) = 0
3.There is no correlation between error term and return on market index.
COV (ei, Rm)=0
The expected return of security is
Ri =αi +βi*Rm+ei
As ei zero in value so,
Ri =αi +βi*Rm
The variance of the return of the security is
σi2
= σei2+ βi2 *
σm2
The major assumption of Sharpe‘s single model is that the co-variation of the security can
be explained by one single factor known as index.
COV (i, j) = βi *
βj*σm2
Where,
COV (i, j) = Covariance between security i and j.
βi = Beta of security i
βj = Beta of security j.
σm2
= Variance of the return of market index.
61
Steps in Construction of Optimal Portfolio Using Single Index Model
This model firstly ranks the securities based on their excess return to beta ratio. After that
all securities are arranged according to their ranks. Then cutoff rate is calculated and it is
compared with excess return to beta for deciding whether to select the security for
investment or not. The model explains the weight that should be allocated to each
security to obtain optimal portfolio.
Step 1: Calculate excess return to beta ratio for each security under consideration
Excess return to beta ratio = (Ri-Rf)/βi
Where
Ri = Expected return of Security i
Rf = Risk free rate of return
Present MIBOR rate is taken as risk free rate Rf
βi = the Beta co-efficient of the security or excess return of the security over
market index
Step 2: Rank the securities based on the excess return to beta ratio.
Step 3: Calculate the cut of rate using the formulae. Highest cut off rate will be regarded
as C*
Where
σm2 = Market variance
Ri - Rf = Market risk premium
σei2 = Unsystematic risk of the security
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Step 4: Selection of securities for investment. If (Ri- Rf)/βi is greater than cut off rate then
the security will be included in the portfolio.
Step 5: Calculate the proportion to be invested in each security is calculated.
Where
C* is the cut off rate
4.11.2 Markowitz Mean-Variance Optimization Model (Tangency
Model)
Harry Markowitz developed algorithms to minimize portfolio risk. His study was first
published in Journal of Finance in March 1952. Markowitz indicated the importance of
correlation among the returns of different stocks in construction of a stock portfolio.
Markowitz Model
The theory assumes that investors prefer to minimize risk. The theory assumes that given
the choice of two portfolios with equal returns, investors will choose the one with the
least risk. If investors take on additional risk, they will expect to be compensated with
additional return. According to MPT, risk comes in two major categories:
Systematic Risk – the possibility that the entire market and economy will show
losses negatively affecting nearly every investment; also called market risk.
Unsystematic Risk – the possibility that an investment or a category of investments
will decline in value without having a major impact upon the entire market
Diversification generally does not protect against systematic risk because a drop in the
entire market and economy typically affects all investments. However, diversification is
63
designed to decrease unsystematic risk. Since unsystematic risk is the possibility that one
single thing will decline in value, having a portfolio invested in a variety of stocks, a
variety of asset classes and a variety of sectors will lower the risk of losing much money
when one investment type declines in value.
The Efficient Frontier
In order to compare investment options, Markowitz developed a system to describe each
investment or each asset class with math, using unsystematic risk statistics. Then he
further applied that to the portfolios that contain the investment options. He looked at the
expected rate-of-return and the expected volatility for each investment. He named his
risk-reward equation The Efficient Frontier. The graph below is an example of what the
Efficient Frontier equation looks like when plotted. The purpose of The Efficient Frontier
is to maximize returns while minimizing volatility.
Fig 4.9: Efficient Frontier
(Source: www.investopedia.com)
64
Portfolios along The Efficient Frontier should have higher returns than is typical, on
average, for the level of risk the portfolio assumes.
The Efficient Frontier line starts with lower expected risks and returns, and it moves
upward to higher expected risks and returns. So people with different Investor Profiles
(tolerance for risk and personal preferences) can find an appropriate portfolio anywhere
along the Efficient Frontier line. The optimal portfolio is the Tangent Portfolio that is the
mix found where the straight line is tangent to the Efficient Frontier portfolio.
4.11.3 Capital Asset Pricing Model (CAPM)
William F. Sharpe developed CAPM. He emphasized that the risk factor in portfolio
theory is a combination of two risks, the systematic risk and unsystematic risk. The total
risk of the portfolio is reduced with increase in number of securities in a portfolio. This is
due in the unsystematic risk distributed over a number of securities.
Beta Coefficient
CAPM calculates a required return based on a risk measurement. To do this, the model
relies on a risk multiplier called the beta coefficient. Beta coefficient is a measure of the
volatility or systematic risk, of a security or a portfolio in comparison to the market as a
whole. Beta is the tendency of a security's returns to respond to swings in the market.
A beta of 1 indicates that the security's price will move with the market. A security with
beta of less than 1 will be less volatile than the market. A beta of greater than 1 indicates
that the security's price will be more volatile than the market. For example, if a stock's
beta is 1.2, it's theoretically 20% more volatile than the market.
Assumptions of CAPM
The CAPM depends on certain assumptions. The original assumptions were:
1. Investors are wealth maximizers who select investments based on expected return and
standard deviation.
65
2. Investors can borrow or lend unlimited amounts at a risk-free (or zero risk) rate.
3. There are no restrictions on short sales (selling securities that you don't yet own) of
any financial asset.
4. All investors have the same expectations related to the market.
5. All financial assets are fully divisible (you can buy and sell as much or as little as you
like) and can be sold at any time at the market price.
6. There are no transaction costs.
7. There are no taxes.
8. No investor's activities can influence market prices.
9. The quantities of all financial assets are given and fixed.
CAPM Formula
The CAPM formula is sometimes called the Security Market Line formula and consists
of the following equation:
r* = Rf + β(Rm - Rf)
It is basically the equation of a line, where:
r* = required return , Rf = the risk-free rate , Rm = the average market return
β = the beta coefficient of the security
Fig 4.10: CAPM Model
(Source: www.investopedia.com)
66
The Rm – Rf term is called the market risk premium.
The risk-free rate (Rf) is the return that an investment with no risks should earn,
commonly returns on Treasury securities is used as risk-free rate.
Limitations of CAPM
1. The CAPM is based on the expectations about the future.
2. The beta coefficient is unstable. It may not reflect the future volatility of returns.
3. CAPM focuses attention only to systematic (market related) risk. However, total risk is
more relevant and related to returns.
4. Investors do not follow postulation of CAPM and do not diversify in a planned
manner.
5. SML is not applicable to bond analysis, although bonds are a part of portfolio of
investors.
4.11.4 Arbitrage Pricing Theory (APT)
Arbitrage pricing theory (APT) was developed by Stephen Ross in 1976. It is a method of
estimating the price of an asset. The theory assumes an asset's return is dependent on
various macroeconomic, market and security-specific factors.
The APT formula is:
E (rj) = rf + bj1RP1 + bj2RP2 + bj3RP3 + bj4RP4 + ... + bjnRPn
Where:
E (rj) = the asset's expected rate of return
rf = the risk-free rate
bj = the sensitivity of the asset's return to the particular factor
RP = the risk premium associated with the particular factor
There are an infinite number of security-specific influences for any given security
including inflation, production measures, investor confidence, exchange rates,
67
market indices or changes in interest rates. It is up to the analyst to decide which
influences are relevant to the asset being analyzed.
Once the analyst derives the asset's expected rate of return from the APT model, he or she
can determine what the "correct" price of the asset by using discounted cash flow model. .
The APT allows the user to adapt the model to the security being analyzed. And as with
other pricing models, it helps the user decide whether a security is undervalued or
overvalued and so he or she can profit from this information. APT is also very useful for
building portfolios because it allows managers to test whether their portfolios are exposed
to certain factors.
4.12 PORTFOLIO EVALUATION METHODS
The different evaluation methods commonly used for portfolio evaluation are
1. Sharpe‘s Ratio
2. Treynor‘s Ratio
3. Jenson‘s Performance Index
4.12.1 Sharpe’s Ratio
Sharpe‘s performance index or Sharpe‘s ratio was developed by William Sharpe and
gives a single value to be used for the performance ranking of various portfolios. The
index assigns highest value to the portfolio which has best risk-adjusted average rate of
return.
Sharpe‘s ratio measures risk premium of the portfolio relative to the total amount of risk
in the portfolio. The risk premium is the difference between the portfolio‘s average rate
of return and riskless rate of return. The standard deviation of the portfolio indicates the
risk.
Sharpe Ratio = Rp-Rf
σp
68
Where;
Rp = Portfolio average return
Rf = Risk free rate of return
σp = Standard deviation of the portfolio return
4.12.2 Treynor’s Ratio
Treynor‘s ratio was developed by Jack Treynor. It is the ratio of risk premium to the
volatility of return. The risk premium is the difference between average return of the
portfolio riskless rate of return. Volatility of portfolio is measured by the portfolio beta.
Treynor‘s Ratio = Rp-Rf
βp
Where;
Rp = Portfolio average return
Rf = Risk free rate of return
βp = the Beta co-efficient of the portfolio
4.12.3 Jensen’s Measure
This absolute risk adjusted return measure was developed by Michael Jensen. This ratio
attempts to measure the differential between actual return of the portfolio and the
expected return of the portfolio.
Jensen‘s Measure = Rp - E(Rp)
E (Rp) = α + βp (Rm - Rf)
Where;
Rp = Portfolio average return
E (Rp) = Expected return of portfolio
Rm = Average market return
Rf = Risk free rate of return
βp = Beta co-efficient of the portfolio
69
4.13 FORMULAE USED FOR THE STUDY
The formulas used for the study are detailed below.
4.13.1 Portfolio Construction
Return = (Today‘s price- Last year‘s price)*100
Last year‘s price
Alpha = Stock return- (Beta * Market return)
αi = Ri – (βi*Rm)
βi = nΣxy- ΣxΣy
n Σx2- (Σx)
2
n
Portfolio Alpha (αp) = Σ wi αi
i=1
Where wi = the proportion of security in the portfolio
n
Portfolio Beta (βp) = Σ wi βi
i=1
Portfolio return = Portfolio Alpha + (Portfolio Beta * Market return)
Rp = αp+ (βp* Rm)
Portfolio Systematic Risk= βp2
σm 2
n
Portfolio Beta (βp) = Σ wi σei2
i=1
n
Total risk of Portfolio = βp2 σm 2 +
Σ wi σei2
i=1
4.13.2 Portfolio Evaluation 1. Sharpe’s Ratio Sharpe‘s ratio = Portfolio Return- Risk free rate Portfolio standard deviation
70
Sharpe Ratio = Rp-Rf
σp
Where;
Rp = Portfolio average return
Rf = Risk free rate of return
σp = Standard deviation of the portfolio return
2. Treynor’s Ratio
Treynor‘s Ratio = Portfolio Return – Risk free rate of return
Portfolio Beta
Treynor‘s Ratio = Rp-Rf
βp
Where;
Rp = Portfolio average return
Rf = Risk free rate of return
βp = the Beta co-efficient of the portfolio
3. Jensen’s Measure
Jensen‘s Measure = Rp - E(Rp)
E (Rp) = α + βp (Rm - Rf)
Where;
Rp = Portfolio average return
E (Rp) = Expected return of portfolio
Rm = Average market return
Rf = Risk free rate of return
βp = Beta co-efficient of the portfolio
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4.14 CONCLUSION
In this chapter the traditional approaches and modern approaches to portfolio
management is described. The portfolio construction by traditional method is detailed.
Tools of fundamental analysis and Technical analysis are described.
The steps in portfolio construction using Sharpe‘s single index model, the formula used
for portfolio evaluation, risk and return calculations are detailed. Finally, an abstract of
formulae used for this study is given.
In the next chapter titled Analysis and Interpretation, the data collected will be analyzed
and optimal portfolio using Sharpe‘s single index model is constructed. Along with, a
portfolio having same return as optimal portfolio and another portfolio with same risk as
optimal portfolio is constructed. The portfolios are evaluated using Sharpe‘s ratio,
Treynor‘s ratio and Jensen Measure.
72
Data Analysis & Interpretations
73
CHAPTER 5
ANALYSIS AND INTERPRETATIONS
5.1 INTRODUCTION
In the previous chapter the traditional approaches and modern approaches to portfolio
management is described. The portfolio construction by traditional method is detailed.
Tools of fundamental analysis and Technical analysis are described. The steps in
portfolio construction using Sharpe‘s single index model, the formula used for portfolio
evaluation, risk and return calculations are detailed. Finally, an abstract of formulae used
for this study is given.
The data for study, mainly stock prices for the last five years were collected from the
Motilal Oswal Securities, Manjeri. The analysis done using those data and its
interpretations are discussed under following headings. CNX Nifty Index Shares,
Analysis of Securities, Analysis of Risk of Securities, Construction of Optimal Portfolio
Using Sharpe‘s Single Index model, Measuring Return and Risk of Optimal Portfolio,
Construction of Portfolio #2 with Same Return as Optimal Portfolio, Construction of
Portfolio # 3 with Same Risk as Optimal Portfolio. The three portfolios are evaluated in
the section called portfolio evaluation using three ratios viz, Sharpe‘s index, Treynor‘s
ratio and Jensen Measure. A brief summary of this chapter is provided in the conclusion
section.
5.2 CNX NIFTY INDEX SHARES
The CNX NIFTY 50 Index comprises of 50 companies from various sectors, which ranks
high in market capitalization. The weight of stocks in the index is determined by the
market capitalization of free floating shares of the respective companies.
CNX Nifty index is used as a barometer of Indian stock market and economy. The list of
50 shares which constitutes the index is shown the table 5.1given in the next page.
74
Table 5.1: List of CNX Nifty 50 shares
SLNo Security SLNo. Security
1 ACC 26 Infosys
2 Ambuja Cements 27 ITC
3 Asian Paints 28 Jindal Steel& Power (JSP)
4 Axis Bank 29 Kotak Bank
5 Bajaj Auto 30 L&T
6 Bharti Airtel 31 Lupin
7 BHEL 32 Mahindra &Mahindra
(M&M)
8 BoB 33 Maruti Suzuki
9 BPCL 34 NMDC
10 Cairn Energy 35 NTPC
11 Cipla 36 ONGC
12 Coal India 37 Power Grid
13 DLF 38 PNB
14 Dr. Reddy's Laboratories
(DRL) 39 Reliance Industries
15 GAIL 40 SBI
16 Grasim 41 Sesa Sterlite
17 HCL Tech 42 Sun pharma
18 HDFC 43 Tata Motors
19 HDFC Bank 44 Tata Power
20 Hero Motor Corporation 45 Tata Steel
21 Hindalco 46 TCS
22 Hindustan Unilever Ltd.
(HUL) 47 Tech Mahindra
23 ICICI Bank 48 Ultratech Cements
24 IDFC 49 Wipro
75
25 IndusInd bank 50 Zee Entertainment.
(Source: www.nse.com)
5.3 ANALYSIS OF SECURITES
Here all of the 50 CNX NIFTY index stocks are used for study. Security analysis
involves calculation of average return, variance, alpha and beta of the securities. These
values form the basic secondary data for the formation of optimal portfolio.
Security analysis on all the CNX Nifty shares were conducted and average return,
variance, alpha and beta of the security of the shares were calculated using Microsoft
Excel
Return = (Today‘s price- Last year‘s price)*100
Last year‘s price
Average return of security Ri‘= Σ Ri/n
Average return of the market Rm = Σ Rm/n
Variance of security σi2
= Σ
(Ri-Ri‘)
2/(n-1)
Variance of market σm2 = Σ
(Rm-Rm‘)2/(n-1)
Covariance of Security & Market COV R,M = Σ(Ri-Ri‘)*(Rm-Rm‘)/ (n-1)
Beta of security β = COV R, M / σm2
Alpha of security α = Ri‘- β Rm‘
A Microsoft Excel work sheet was prepared with above formulae and calculations were
done using computers. A sample calculation of Ambuja Cements is shown in the
Chapter Appendix –A (Page.93). The table below shows the summary of calculation of
all shares.
5.3.1 Summary Table Showing Return and Risk
76
The table 5.2 given in the next page shows the return, alpha, beta and variance of CNX
Nifty shares.
77
Table 5.2: Summary table showing risk and return of CNX NIFTY shares
Name of Security Return
Ri %) Alpha
α
Beta
β
Variance σi
2 (%)2 Name of Security
Return
Ri (%) Alpha
α
Beta
β
Variance σi
2 (%)2
ACC 11.29 17.04 -0.56 186.92 ITC 24.69 32.71 -0.79 409.81 Ambuja Cements 17.82 10.79 0.21 211.34 Jindal Steel 24.44 -19.75 -0.45 346.71 Asian Paints 42.05 39.90 1.65 3723.36 Kotak Bank 15.35 -0.96 1.59 748.70 Axis Bank 27.00 0.81 0.55 1342.00 L&T 13.06 -4.81 1.744 552.70 Bajaj Auto 14.65 18.47 -0.37 230.48 Lupin 41.66 27.7 1.36 458.18 Airtel 7.68 -3.60 1.10 331.74 M&M 27.95 45.39 -1.70 774.93 BHEL -7.99 -26.53 1.80 331.74 Maruti 25.77 4.63 2.06 1060.17 BoB 22.83 10.60 0.66 1175.07 NMDC 19.78 20.88 -0.107 849.63 BPCL 31.74 13.60 1.07 779.79 NTPC 10.39 10.10 0.03 148.28 Cairn -3.59 4.06 -0.74 245.22 ONGC 8.42 4.76 0.35 193.62 Cipla 17.33 -0.33 1.72 935.17 Power Grid 9.59 1.39 0.799 368.82 Coal India 9.64 -0.24 0.965 329.21 PNB 11.52 2.29 0.90 675.25 DLF -10.99 -16.14 0.502 715.38 Reliance -1.23 -8.86 0.745 262.39 Dr. Reddy's 23.24 14.76 0.82 202.80 SBI 24.48 6.54 1.75 500.94 Gail 1.05 -9.91 1.06 292.50 Sesa Sterlite -24.44 -19.75 -0.457 346.71 Grasim 6.11 -1.13 0.706 253.11 Sun Pharma 39.38 33.79 0.645 219.51 HCL Tech 41.93 28.98 1.26 1297.79 Tata Motors 18.41 17.72 0.07 335.99 HDFC 21.65 8.86 1.24 358.71 Tata Power -5.22 -7.43 0.215 65.75 HDFC Bank 22.89 18.77 0.402 151.07 Tata Steel -5.92 -10.71 0.466 726.16 Hero Motor 9.52 14.56 -0.49 547.74 TCS 29.92 27.36 0.249 673.14 Hindalco -1.667 -15.35 1.33 1707.17 Tech Mahindra 35.29 18.80 1.60 1762.50 HUL 32.17 32.06 0.011 130.87
Ultratech Cements 24.32 23.71 0.06 179.75 ICICI Bank 24.24 4.83 1.89 666.45 IDFC 5.19 -13.69 1.84 1126.94 Wipro 10.59 2.59 0.78 681.72 IndusInd bank 40.77 27.37 1.30 701.68 Zee Ent. 22.03 9.15 1.25 1519.34
Infosys 15.35 -9.66 1.59 748.70 CNX NIFTY 10.2746 0 1 149.25
(Source: Summarized from the secondary data)
78
Inferences:
Form the above table following inferences are made.
Asian Paints has highest return (42.05 %) and Sesa Sterlite has lowest return
(-24.44 %).
Mahindra & Mahindra has highest Alpha (45.39) and BHEL has lowest Alpha
(-26.53).
Maruti Suzuki has highest Beta (2.06) and Mahindra and Mahindra has lowest
Beta (-1.70).
Asian Paints has highest Variance (3723.36 %2) and Tata Power has lowest
variance (65.75%2).
The return of CNX Nifty index was 10.2476 % for the period and market risk was
149.25 % 2.
5.4 RISK ANALYSIS OF SECURITIES
The total risk of securities is divided in to two; the systematic risk which cannot be
diversified and unsystematic or security specific risk which can be reduced by
diversification. Systematic and unsystematic risks are measured by using Sharpe‘s index
model.
5.4.1 Systematic Risk of Securities
The systematic risk indicates non diversifiable part of the risk of a security. It is
calculated using the following formulae.
Systematic risk = βi2 σm
2
Where σm2 = Variance of Market
Market is represented by CNX NIFTY, from table No. 5.2 = 149.25 %2.
The calculations are performed using Microsoft excel software. The result of calculation
of systematic risk of securities is given in the table below.
79
Table 5.3: Systematic Risk of CNX NIFTY Shares
Security βi σm2
Systematic
Risk
(βi2 σm
2)
Security βi σm2
Systematic Risk
(βi2 σm
2)
ACC -0.56 149.25 46.80 Infosys 1.59 149.25 377.32
Ambuja Cements 0.21 149.25 6.58 ITC -0.79 149.25 93.15
Asian Paints 1.65 149.25 406.33 JSP -0.45 149.25 30.22
Axis Bank 0.55 149.25 45.15 Kotak Bank 1.59 149.25 377.32
Bajaj Auto -0.37 149.25 20.77 L&T 1.74 149.25 453.95
Bharti Airtel 1.10 149.25 180.59 Lupin 1.36 149.25 276.05
BHEL 1.80 149.25 483.57 M&M -1.70 149.25 431.33
BoB 0.66 149.25 65.01 Maruti 2.06 149.25 633.36
BPCL 1.07 149.25 170.88 NMDC -0.11 149.25 1.71
Cairn Energy -0.75 149.25 83.28 NTPC 0.03 149.25 0.13
Cipla 1.72 149.25 441.54 ONGC 0.35 149.25 18.28
Coal India 0.97 149.25 139.92 Power Grid 0.80 149.25 95.28
DLF 0.50 149.25 37.61 PNB 0.90 149.25 120.89
Dr. Reddy's 0.82 149.25 100.36 Reliance 0.75 149.25 82.84
Gail 1.06 149.25 167.70 SBI 1.75 149.25 457.08
Grasim 0.71 149.25 74.39 Sesa Sterlite -0.46 149.25 31.17
HCL Tech 1.26 149.25 236.95 Sun Pharma 0.65 149.25 62.09
HDFC 1.24 149.25 229.49 Tata Motors 0.07 149.25 0.73
HDFC Bank 0.40 149.25 24.28 Tata Power 0.22 149.25 6.90
Hero Mot -0.49 149.25 35.83 Tata Steel 0.47 149.25 32.41
Hindalco 1.33 149.25 264.01 TCS 0.25 149.25 9.25
HUL 0.01 149.25 0.02 Tech Mahindra 1.60 149.25 382.08
ICICI Bank 1.89 149.25 533.14 Ultra tech 0.06 149.25 0.54
IDFC 1.84 149.25 505.30 Wipro 0.78 149.25 90.80
IndusInd bank 1.30 149.25 252.23 Zee Ent. 1.25 149.25 233.20
(Source: Summarized from the secondary data in the Table 5.2)
80
Inference:
From the above table it is inferred that Hindustan Unilever has minimum systematic risk
(0.02 %2) and Axis bank has highest systematic risk (975.06 %
2).
It means Hindustan Unilever is less affected by ups and downs in market and Axis Bank
share price is highly influenced by volatility in the market.
5.4.2 Unsystematic Risk of the Securities
Unsystematic risk refers to that portion of risk which is caused due to factors unique or
related to a firm or industry.
The total Risk of the security is the sum of systematic risk and non-systematic risk, the
unsystematic risk is fond out by deducting systematic risk from total risk. i.e.
Unsystematic risk = Variance of security- Systematic risk.
The unsystematic risk is calculated using the formula,
Unsystematic risk = σi2- βi
2 σm
2.
Where
σi2 = Variance of security
βi = Beta of Security
σm
2 = The variance of market index
Market is represented by CNX NIFTY INDEX
From Summary table 5.2, σm 2= 149.25(%2)
The table 5.4 given in the next page shows the calculation of unsystematic risk of
securities.
81
Table 5.4: Unsystematic risk of CNX NIFTY shares
Security σi2 βi Unsystematic
Risk
σei2=σi
2-(βi
2 σm
2)
Security σi2 βi Unsystematic
Risk
σei2=σi
2-(βi
2 σm
2)
ACC 186.92 -0.56 140.11 Infosys 748.7 1.59 371.38 Ambuja Cements 211.34 0.21 204.76 ITC 409.81 -0.79 316.66 Asian Paints 3723.36 1.65 3317.03 Jindal
SteelPPPPPPower
346.71 -0.45 316.49 Axis Bank 1342 0.55 1296.85 Kotak Bank 748.7 1.59 371.38 Bajaj Auto 230.48 -0.37 209.72 L&T 552.7 1.74 98.75 Bharti Airtel 331.74 1.10 151.15 Lupin 458.18 1.36 182.13 BHEL 331.74 1.80 -151.83 M&M 774.93 -1.70 343.60 BoB 1175.07 0.66 1110.06 Maruti Suzuki 1060.17 2.06 426.81 BPCL 779.79 1.07 608.91 NMDC 849.63 -0.11 847.92 Cairn Energy 245.22 -0.75 161.94 NTPC 148.28 0.03 148.15 Cipla 935.17 1.72 493.63 ONGC 193.62 0.35 175.34 Coal India 329.21 0.97 189.30 Power Grid 368.82 0.80 273.54 DLF 715.38 0.50 677.77 PNB 675.25 0.90 554.36 Dr. Reddy's 202.80 0.82 102.44 Reliance Ind. 262.39 0.75 179.55 Gail 292.50 1.06 124.80 SBI 500.94 1.75 43.86 Grasim 253.11 0.71 178.72 Sesa Sterlite 346.71 -0.46 315.54 HCL Tech 1297.79 1.26 1060.84 Sun Pharma 219.51 0.65 157.42 HDFC 358.71 1.24 129.22 Tata Motors 335.99 0.07 335.26 HDFC Bank 151.07 0.40 126.79 Tata Power 65.75 0.22 58.85 Hero Mot 547.74 -0.49 511.91 Tata Steel 726.16 0.47 693.75 Hindalco 1707.17 1.33 1443.16 TCS 673.14 0.25 663.89 HUL 130.87 0.01 130.85 Tech Mahindra 1762.5 1.60 1380.42 ICICI Bank 666.45 1.89 133.31 Ultratech Cements 179.75 0.06 179.21 IDFC 1126.94 1.84 621.64 Wipro 681.72 0.78 590.92 IndusInd bank 701.68 1.30 449.45 Zee Entertainment 1519.34 1.25 1286.14
(Source: Secondary data from Table 5.2)
82
Inference:
From the table it is inferred that the Asian Paints has highest unsystematic risk (3317.02
%2) and Dr. Reddy‘s lab has lowest unsystematic risk (100.77 %
2).
5.4.3 Total Risk of Securities
Total risk of a security is the sum of systematic and unsystematic risks.
Total Risk = Systematic Risk + Unsystematic Risk.
The table 5.5 given in the next page shows the total risk of securities.
83
Table 5.5: Total risk of CNX NIFTY shares
Security Systematic
Risk
Unsystematic
Risk
Total
Risk Security
Systematic
Risk
Unsystematic
Risk
Total
Risk
ACC 46.80 140.11 186.92 Infosys 377.32 371.38 748.70
Ambuja Cements 6.58 204.76 211.34 ITC 93.15 316.66 409.81
Asian Paints 406.33 3317.03 3723.36 JSP 30.22 316.49 346.71
Axis Bank 45.15 1296.85 1342.00 Kotak Bank 377.32 371.38 748.70
Bajaj Auto 20.77 209.72 230.48 L&T 453.95 98.75 552.70
Bharti Airtel 180.59 151.15 331.74 Lupin 276.05 182.13 458.18
BHEL 483.57 -151.83 331.74 M&M 431.33 343.60 774.93
BoB 65.01 1110.06 1175.07 Maruti 633.36 426.81 1060.17
BPCL 170.88 608.91 779.79 NMDC 1.71 847.92 849.63
Cairn Energy 83.28 161.94 245.22 NTPC 0.13 148.15 148.28
Cipla 441.54 493.63 935.17 ONGC 18.28 175.34 193.62
Coal India 139.92 189.30 329.21 Power Grid 95.28 273.54 368.82
DLF 37.61 677.77 715.38 PNB 120.89 554.36 675.25
Dr. Reddy's 100.36 102.44 202.80 Reliance 82.84 179.55 262.39
Gail 167.70 124.80 292.50 SBI 457.08 43.86 500.94
Grasim 74.39 178.72 253.11 Sesa Sterlite 31.17 315.54 346.71
HCL Tech 236.95 1060.84 1297.79 Sun Pharma 62.09 157.42 219.51
HDFC 229.49 129.22 358.71 Tata Motors 0.73 335.26 335.99
HDFC Bank 24.28 126.79 151.07 Tata Power 6.90 58.85 65.75
Hero Motor 35.83 511.91 547.74 Tata Steel 32.41 693.75 726.16
Hindalco 264.01 1443.16 1707.17 TCS 9.25 663.89 673.14
HUL 0.02 130.85 130.87 Tech Mahindra 382.08 1380.42 1762.50
ICICI Bank 533.14 133.31 666.45 Ultra tech 0.54 179.21 179.75
IDFC 505.30 621.64 1126.94 Wipro 90.80 590.92 681.72
IndusInd bank 252.23 449.45 701.68 Zee Entertainment 233.20 1286.14 1519.34
(Source: Secondary data from Tables 5.2 to 5.4)
84
Inference:
From the above table it is inferred that, the Asian Paints has highest total risk (3723.36
%2) and Hindustan Uniliver Ltd (130.88 %
2) has lowest total risk.
5.5 CONSTRUCTION OF OPTIMAL PORTFOLIO USING
SHARPE’S OPTIMIZATION MODEL
The construction of optimal portfolio using Sharpe‘s single index model involves
following steps.
1. Ranking of the securities based on excess return over risk i.e. (Ri - Rf)/ β ratio.
2. Calculation of Cut-off point
3. Selection of securities based on the cut-off point
4. Calculation of Weight of each security in the portfolio.
5.5.1 Ranking of Securities
The CNX NIFTY securities are ranked based on (Ri - Rf)/ β ratio.
Where;
Ri= Return of the security
Rf = the risk free rate.
The latest MIBOR (Mumbai Inter Bank Offer Rate) is taken as risk free rate Rf. The
present rate is 7.21 %. Hence, 7.21% is taken as risk free rate for calculation.
The table 5.6 given in the next page shows the rank of securities based on (Ri - Rf)/ β
ratio.
85
Table 5.6: Ranking of CNX NIFTY shares
Security Ri Rf β (Ri - Rf)/ β Rank Security Ri Rf β (Ri - Rf)/ β Rank
ACC 11.29 7.21 -0.56 -7.29 41 Infosys 15.35 7.21 1.59 5.12 28
Ambuja
Cements 17.82 7.21 0.21 50.52 7 ITC 24.69 7.21 -0.79 -22.13 45
Asian Paints 42.05 7.21 1.65 21.16 16 Jindal Steel&
Power 24.44 7.21 -0.45 -38.29 48
Axis Bank 27.00 7.21 0.55 35.98 10 Kotak Bank 15.35 7.21 1.59 5.12 29
Bajaj Auto 14.65 7.21 -0.37 -19.94 44 L&T 13.06 7.21 1.74 3.35 32
Bharti Airtel 7.68 7.21 1.10 0.42 34 Lupin 41.66 7.21 1.36 25.33 13
BHEL -7.99 7.21 1.80 -8.44 40 M&M 27.95 7.21 -1.70 -12.20 43
BoB 22.83 7.21 0.66 23.67 14 Maruti 25.77 7.21 2.06 9.01 24
BPCL 31.74 7.21 1.07 22.93 15 NMDC 19.78 7.21 -0.11 -117.48 50
Cairn -3.59 7.21 -0.75 14.46 19 NTPC 10.39 7.21 0.03 106.00 4
Cipla 17.33 7.21 1.72 5.88 26 ONGC 8.42 7.21 0.35 3.46 25
Coal India 9.64 7.21 0.97 2.52 33 Power Grid 9.59 7.21 0.80 2.98 31
DLF -10.99 7.21 0.50 -36.26 47 PNB 11.52 7.21 0.90 4.79 27
Dr. Reddy's 23.24 7.21 0.82 19.55 17 Reliance -1.23 7.21 0.75 -11.32 42
GAIL 1.05 7.21 1.06 -5.81 38 SBI 24.48 7.21 1.75 9.87 22
Grasim 6.11 7.21 0.71 -1.56 35 Sesa Sterlite -24.44 7.21 -0.46 69.26 6
HCL Tech 41.93 7.21 1.26 27.56 11 Sun Pharma 39.38 7.21 0.65 49.88 8
HDFC 21.65 7.21 1.24 11.65 21 Tata Motors 18.41 7.21 0.07 160.00 3
HDFC Bank 22.89 7.21 0.40 39.01 9 Tata Power -5.22 7.21 0.22 -57.82 49
Hero Motor
Corp 9.52 7.21 -0.49 -4.71 39 Tata Steel -5.92 7.21 0.47 -28.18 46
Hindalco -1.667 7.21 1.33 -6.67 37 TCS 29.92 7.21 0.25 91.20 5
HUL 32.17 7.21 0.01 2269.09 1 Tech
Mahindra 35.29 7.21 1.60 17.55 18
ICICI Bank 24.24 7.21 1.89 9.01 23 Ultratech 24.32 7.21 0.06 285.17 2
IDFC 5.19 7.21 1.84 -1.10 36 Wipro 10.59 7.21 0.78 4.33 30
IndusInd
Bank 40.77 7.21 1.30 25.82 12 Zee Ent. 22.03 7.21 1.25 11.86 20
(Source: Summarized from the secondary data of Table 5.2)
86
5.5.2 Calculation of Cut-Off Point
The securities are rearranged based on the rank of (Ri - Rf)/ β ratio.
Then the he cut of rate is calculated using the formulae.
Where
σm2 = Market variance
Ri - Rf = Market risk premium
σei2 = Unsystematic risk of the security
The calculation of cut-off point is shown in the table 5.7 given in the next page.
From the table it seen that the cut- off point Ci shows a character of increasing gradually and
after reaching a peak value it i starts decreasing gradually. This point is highest cut off rate and it
will be denoted as C*.
The cut-off point determines which securities are to be included in the portfolio. The Securities
with (Ri-Rf)/ β values up to cut off point C* (25.1394) are included in the portfolio. Securities
with (Ri-Rf)/ β values beyond cut off point are excluded from the portfolio.
87
Table 5.7: Calculation of cut-off point
RANK SECURITY Ri - Rf β σei2 (Ri - Rf)* β/
σei2
Σ (( (Ri - Rf)*
β/σei2 )
σm2 β
2/ σei
2 Σβ
2/ σei
2 CUT
OFF
(Ci)
STATUS
1 Hindustan Uniliver 4.08 -0.56 130.85 0.0022 0.0022 149.25 0.000001
0.000001 0.3282 IN
2 Ultratech Cements 10.61 0.21 179.21 0.0061 0.0083 149.25 0.000020
0.000021 1.2393 IN
3 Tata Motors 34.84 1.65 335.26 0.0026 0.0109 149.25 0.000015
0.000036 1.6209 IN
4 NTPC 19.79 0.55 148.15 0.0009 0.0118 149.25 0.000006
0.000042 1.7510 IN
5 TCS 7.44 -0.37 663.89 0.0090 0.0208 149.25 0.000093
0.000135 3.0391 IN
6 Sesa Sterlite 0.47 1.10 315.54 0.0441 0.0649 149.25 0.000662
0.000797 8.6532 IN
7 Ambuja Cements -15.2 1.80 204.76 0.0121 0.0770 149.25 0.000215
0.001012 9.9820 IN
8 Sun pharma 15.62 0.66 157.42 0.1367 0.2137 149.25 0.002643
0.003655 20.6382 IN
9 HDFC Bank 24.53 1.07 126.79 0.0535 0.2672 149.25 0.001275
0.004930 22.9783 IN
10 Axis Bank -10.8 -0.75 1296.9 0.0089 0.2761 149.25 0.000233
0.005163 23.2769 IN
11 HCL Tech 10.12 1.72 1060.8 0.0427 0.3188 149.25 0.001497
0.006660 23.8629 IN
12 IndusInd bank 2.43 0.97 449.45 0.1005 0.4193 149.25 0.003760
0.010420 24.4945 IN
13 Lupin -18.2 0.50 182.13 0.2662 0.6856 149.25 0.010156
0.020575 25.1344 IN
14 BoB 16.03 0.82 1110.1 0.0100 0.6956 149.25 0.000392
0.020968 25.1394 IN
15 BPCL -6.16 1.06 608.91 0.0452 0.7408 149.25 0.001880
0.022848 25.0699 OUT
16 Asian Paints -1.1 0.71 3317 0.0179 0.7587 149.25 0.000821
0.023669 24.9826 OUT
17 Dr. Reddy's 34.72 1.26 102.44 0.1379 0.8966 149.25 0.006564
0.030232 24.2770 OUT
18 Tech Mahindra 14.44 1.24 1380.4 0.0339 0.9305 149.25 0.001855
0.032087 23.9912 OUT
19 Cairn 15.68 0.40 161.94 0.0443 0.9748 149.25 0.003446
0.035533 23.0823 OUT
20 Zee Ent. 2.31 -0.49 1286.1 0.0156 0.9904 149.25 0.001215
0.036747 22.7953 OUT
21 HDFC -8.877 1.33 129.22 0.1501 1.1405 149.25 0.011899
0.048646 20.6062 OUT
22 SBI 24.96 0.01 43.862 0.7369 1.8774 149.25 0.069821
0.118468 14.9990 OUT
23 ICICI Bank 17.03 1.89 133.31 0.2584 2.1358 149.25 0.026795
0.145262 14.0551 OUT
24 Maruti -2.02 1.84 426.81 0.0954 2.2312 149.25 0.009943
0.155205 13.7810 OUT
25 ONGC 33.56 1.30 175.34 0.0048 2.2360 149.25 0.000699
0.155904 13.7514 OUT
26 Cipla 8.14 1.59 493.63 0.0394 2.2755 149.25 0.005993
0.161897 13.4965 OUT
27 PNB 17.48 -0.79 554.36 0.0089 2.2844 149.25 0.001461
0.163358 13.4331 OUT
28 Infosys 17.23 -0.45 371.38 0.0400 2.3244 149.25 0.006807
0.170165 13.1422 OUT
29 Kotak Bank 8.14 1.59 371.38 0.0400 2.3644 149.25 0.006807
0.176972 12.8728 OUT
88
30 Wipro 5.85 1.74 590.92 0.0060 2.3704 149.25 0.001030
0.178002 12.8338 OUT
31 Power Grid 34.45 1.36 273.54 0.0105 2.3809 149.25 0.002334
0.180336 12.7296 OUT
32 L&T 20.74 -1.70 98.751 0.1245 2.5054 149.25 0.030800
0.211136 11.5013 OUT
33 Coal India 18.56 2.06 189.29 0.0185 2.5239 149.25 0.004919
0.216055 11.3304 OUT
34 Bharthi Airtel 12.57 -0.11 151.15 0.0122 2.5361 149.25 0.008005
0.224061 10.9900 OUT
35 Grasim 3.18 0.03 178.72 0.0004 2.5365 149.25 0.002789
0.226850 10.8604 OUT
36 IDFC 1.21 0.35 621.64 -0.0024 2.5340 149.25 0.005446
0.232296 10.6028 OUT
37 Hindalco 2.38 0.80 425.91 -0.0051 2.5307 149.25 0.000469
0.232765 10.5680 OUT
38 Gail 4.31 0.90 124.8 -0.0421 2.4694 149.25 0.009003
0.241768 9.9384 OUT
39 Hero Motor Corp. -8.44 0.75 511.91 -0.0034 2.5115 149.25 0.002739
0.244507 9.9978 OUT
40 BHEL 17.27 1.75 -151.8 0.1660 2.6966 149.25 -0.02134
0
0.223167 11.7313 OUT
41 ACC -31.65 -0.46 140.12 -0.0211 2.4483 149.25 0.002238
0.225405 10.5482 OUT
42 Reliance Industries 32.17 0.65 179.55 -0.0300 2.4815 149.25 0.003091
0.228496 10.5506 OUT
43 M&M 11.2 0.07 343.6 -0.1086 2.5881 149.25 0.008411
0.236907 10.6240 OUT
44 Bajaj Auto -12.43 0.22 209.71 -0.0154 2.4329 149.25 0.000663
0.237571 9.9599 OUT
45 ITC -13.13 0.47 316.66 -0.0466 2.4349 149.25 0.001971
0.239542 9.8881 OUT
46 Tata Steel 22.71 0.25 693.75 -0.0080 2.5801 149.25 0.000313
0.239855 10.4645 OUT
47 DLF 28.08 1.60 677.77 -0.0126 2.4203 149.25 0.000372
0.240226 9.8018 OUT
48 Jindal Steel&
Power
17.11 0.06 316.49 -0.0262 2.4087 149.25 0.000640
0.240866 9.7294 OUT
49 Tata Power 3.38 0.78 58.851 -0.0410 2.5390 149.25 0.000785
0.241652 10.2236 OUT
50 NMDC 14.82 1.25 847.92 -0.0017 2.4186 149.25 0.000014
0.241665 9.7380 OUT
Note: C = 25.1394 is taken as cut off point C*.
(Source: Summarized from the secondary data of Tables 5.2 and 5.6)
89
Inference :
14 shares up to cut point rank 14 corresponding to highest cut-off point of 25.139 are
included in the port folio.
5.5.3 Calculation of Optimal Portfolio
The proportion to be invested in each security (weight) is calculated using the following
equation.
C* is the cut off rate.
The calculation of optimal portfolio is shown in the table below.
Table 5.8: Calculation of optimal portfolio
SECURITY β σei2 (Ri - Rf)/ β C* Zi ΣZi Weight
Xi=Zi/ ΣZi
HUL 0.01 130.85 2378.18 25.1394 0.0022 0.1684 0.013 Ultratech
Cements 0.06 179.21 305.17 25.1394
0.0056 0.1684
0.033 Tata Motors 0.07 335.26 177.14 25.1394 0.0022 0.1684 0.013 NTPC 0.03 148.15 146.00 25.1394 0.0007 0.1684 0.004 TCS 0.25 663.89 96.02 25.1394 0.0066 0.1684 0.039 Sesa Sterlite 0.46 315.54 66.63 25.1394 0.0275 0.1684 0.163 Ambuja Cements 0.21 204.76 56.24 25.1394 0.0067 0.1684 0.040 Sun Pharma 0.65 157.42 51.74 25.1394 0.0703 0.1684 0.417 HDFC Bank 0.40 126.79 41.99 25.1394 0.0215 0.1684 0.128 Axis Bank 0.55 1296.9 38.16 25.1394 0.0030 0.1684 0.018 HCL Tech 1.26 1060.8 28.51 25.1394 0.0050 0.1684 0.030 IndusInd bank 1.30 449.45 26.74 25.1394 0.0060 0.1684 0.036 Lupin 1.36 182.13 26.21 25.1394 0.0109 0.1684 0.065 BoB 0.66 1110.1 25.48 25.1394 0.0001 0.1684 0.001
Total Σ Zi= 0.1684 Σ Wi= 1.00
(Source: Secondary data in the table 5.7)
90
Inference:
The Sun pharma has highest weight in the portfolio (41.7 %) and Bank of Baroda has
lowest weight in the optimal portfolio (0.1%).
5.6 MEASURING RETURN AND RISK OF OPTIMAL PORTFOLIO
The return and risk of optimal portfolio is required for evaluation of portfolio with other
portfolios.
5.6.1 Calculation of Portfolio Alpha in Optimal Portfolio
The portfolio alpha is the weighted average of the specific returns (alpha) of the
individual securities. The Portfolio alpha is calculated using the equation
n
Portfolio Alpha (αp) = Σ wi αi,
i=1
Where Wi= weight of security, αi = Alpha of security
Table 5.9: Calculation of alpha of optimal portfolio
Security Alpha (αi) Weight (wi) Alpha * Weight
(wi* αi)
Ambuja Cements 39.90 0.040 1.5960
Axis Bank 0.81 0.018 0.0146
BoB 10.60 0.001 0.0106
HCL Tech 28.98 0.030 0.8694
HDFC Bank 18.77 0.128 2.4026
Hindustan Uniliver 32.06 0.013 0.4168
IndusInd bank 27.37 0.036 0.9853
Lupin 27.70 0.065 1.8005
NTPC 10.10 0.004 0.0404
Sesa Sterlite -19.75 0.163 -3.2193
Sun Pharma 33.79 0.417 14.0904
Tata Motors 17.72 0.013 0.2304
TCS 27.36 0.039 1.0670
Ultratech Cements 23.71 0.033 0.7824
Total 21.0872
(Source: Secondary data from the table 5.2 and table 5.7)
91
Inference:
From the above table, it is inferred that the alpha (excess return over the market) of
optimal portfolio is 21.09%.
5.6.2 Calculation of Portfolio Beta in Optimal Portfolio
The portfolio beta is the weighted average of the beta coefficient of the individual
securities. The portfolio beta is calculated using the equation.
n
Portfolio Beta (βp) = Σ wi βi
i=1
Where
wi = Proportion of investment in security i.
βi = beta of individual securities.
The table below shows the calculation of beta of optimal portfolio.
Table 5.10: Calculation of beta of optimal portfolio
Security Beta
(βi)
Weight
(wi)
Beta * Weight
(wi βi)
Ambuja Cements 0.21 0.040 0.00840
Axis Bank 0.55 0.018 0.00990
BoB 0.66 0.001 0.00066
HCL Tech 1.26 0.030 0.03780
HDFC Bank 0.40 0.128 0.05120
Hindustan
Uniliver 0.01 0.013
0.00013
IndusInd bank 1.30 0.036 0.04680
Lupin 1.36 0.065 0.08840
NTPC 0.03 0.004 0.00012
Sesa Sterlite -0.46 0.163 -0.07500
Sun Pharma 0.65 0.417 0.27105
Tata Motors 0.07 0.013 0.00091
TCS 0.25 0.039 0.00975
Ultratech Cements 0.06 0.033 0.00198
Total 0.45212
(Source: Secondary data from the table 5.2 and table 5.7)
92
Inference:
From the above table it is inferred that beta of the portfolio is 0.4512, i.e. for 1%
variation in value of market index, the risk in portfolio will be only 0.45 %.
5.6.3 Calculation of Return of the Optimal Portfolio
The expected return of a portfolio is calculated using the formulae
Rp= αp + βp*Rm
Where,
αp = Portfolio alpha
βp = Portfolio beta
Rm = Market Return
The table below shows the calculation of return of optimal portfolio.
Table 5.11: Calculation of return of optimal portfolio
Portfolio Portfolio
Alpha
(αp)
Portfolio
Beta
(βp)
Market
Return
(Rm)
Portfolio Return
Rp= αp + βp*Rm
(%)
OPTIMAL
PORTFOLIO 21.09 0.45 10.25 25.72
(Source: Secondary data from the table 5.2, table 5.9 and table 5.10)
Inference:
From the above table it is inferred that, the average return of the optimal portfolio for the
five years from 2010-2015 is 25.72 %.
93
5.6.4 Calculation of Residual Variance (Unsystematic Risk) In Optimal
Portfolio
Unsystematic risk or Residual variance of a portfolio is given by the equation
n
Unsystematic risk = Σ wi2
σei2
i = 1
Where
wi = Weight of Security in portfolio
σei2 = Residual variance of individual securities.
The table given below shows the calculation of unsystematic risk of optimal portfolio.
Table 5.12: Calculation of unsystematic risk of optimal portfolio
Security
Residual
Variance
(σei2)
Weight
(wi) wi
2
wi2* σei
2
(%2)
Ambuja Cements 204.76 0.040 0.001600 0.3276
Axis Bank 1296.90 0.018 0.000324 0.4202
BoB 1110.10 0.001 0.000001 0.0011
HCL Tech 1060.80 0.030 0.000900 0.9547
HDFC Bank 126.79 0.128 0.016384 2.0773
Hindustan Uniliver 130.85 0.013 0.000169 0.0221
IndusInd bank 449.45 0.036 0.001296 0.5825
Lupin 182.13 0.065 0.004225 0.7695
NTPC 148.15 0.004 0.000016 0.0024
Sesa Sterlite 315.54 0.163 0.026569 8.3836
Sun Pharma 157.42 0.417 0.173889 27.3736
Tata Motors 335.26 0.013 0.000169 0.0567
TCS 663.89 0.039 0.001521 1.0098
Ultratech Cements 179.21 0.033 0.001089 0.1952
Total 42.1762
(Source: Secondary data from the table 5.2 and table 5.9)
Inference:
From the above table it is inferred that the residual variance of the optimal portfolio is
42.176 %2.
94
5.6.5 Calculation of Systematic Risk of Optimal Portfolio
Systematic risk of a portfolio is calculated using the equation given below.
Systematic risk of Portfolio = βp2 σm
2
Where,
βp= Beta of Portfolio
σm 2
= Variance of market index.
The table below shows the calculation of systematic risk of optimal portfolio.
Table 5.13: Calculation of systematic risk of optimal portfolio
Portfolio βp βp2 σm
2
Systematic Risk
βp2 σm
2 (%
2)
OPTIMAL PORTFOLIO 0.4521 0.2044 149.26 30.51
(Source: Secondary data from the table 5.2 and table 5.10)
Inference:
From the above table it is inferred that the systematic risk of optimal portfolio is
30.51%2.
5.6.6 Calculation of Total Risk of Portfolio
The total risk of a portfolio is sum of systematic risk and unsystematic risk of a portfolio.
This may be expressed as:
n
σp2 =
βp2
σm2
+Σ wi2
σei2
i = 1
Where,
σp2
= Total risk
βp2 σm
2 = Systematic risk
n
Σ wi2
σei2 = Unsystematic risk
i = 1
The table below shows the calculation of total risk of optimal portfolio.
95
Table 5.14: Calculation of systematic risk of optimal portfolio
Portfolio Unsystematic
Risk
Systematic
Risk
Total Risk
(%2)
OPTIMAL PORTFOLIO 42.18 30.51 72.69
(Source: Secondary data from the table 5.12 and table 5.13)
Inference:
From the above table it is inferred that the total risk of optimal portfolio is 72.69 %2.
5.7 CONSTRUCTION OF PORTFOLIO #2. (A portfolio with same
return as optimal portfolio)
A portfolio is constructed selecting 14 securities is selected in random from remaining
NIFTY 50 shares. Their weight is selected in such a way that portfolio return is same as
that of optimal portfolio (25.72%). Microsoft excel solver was used to find out the weight
of securities.
The table below represents the securities selected and their proportion (weight) in the
portfolio#2.
Table 5.15: Portfolio #2
SL No. Security Weight (Wi)
1 Asian Paints 0.04
2 Bajaj Auto 0.03
3 BHEL 0.03
4 Cairn Energy 0.01
5 Coal India 0.01
6 Dr. Reddy's Lab 0.25
7 Grasim 0.03
8 Hero motor corp. 0.02
9 ICICI Bank 0.04
10 Jindal Steel & Power 0.01
11 Maruti Suzuki 0.02
12 SBI 0.02
13 Tech Mahindra 0.38
14 Zee Entertainment 0.11
Total 1.00
(Source: Summarized from the table 5.2)
96
Inference:
From the above table it is inferred that the Tech Mahindra has highest weight (0.38) and
Jindal Steel, Coal India, and Cairn Energy have lowest weight of 0.01 each.
5.7.1 Calculation of Alpha of Portfolio #2
The table below shows the calculation of alpha of portfolio#2.
Table 5.16: Calculation of alpha of portfolio #2
SL No. Security Weight (Wi) Alpha (αi) αi * wi (%)
1 Asian Paints 0.04 39.90 1.5960
2 Bajaj Auto 0.03 18.47 0.5541
3 BHEL 0.03 -26.53 -0.7959
4 Cairn Energy 0.01 4.06 0.0406
5 Coal India 0.01 -0.24 -0.0024
6 Dr. Reddy's Lab 0.25 14.76 3.6900
7 Grasim 0.03 -1.13 -0.0339
8 Hero motor corp. 0.02 14.56 0.2912
9 ICICI Bank 0.04 4.83 0.1932
10
Jindal Steel &
Power 0.01 -19.75 -0.1975
11 Maruti Suzuki 0.02 4.63 0.0926
12 SBI 0.02 6.54 0.1308
13 Tech Mahindra 0.38 18.80 7.1440
14 Zee Entertainment 0.11 9.15 1.0065
Total 1.00 13.7093
(Source: Secondary data from the table 5.2 and table 5.15)
Inference:
From the above table it is inferred that the alpha of portfolio#2 is 13.7093 %.
97
5.7.2 Calculation of Portfolio Beta of Portfolio #2
The table below shows the calculation of beta of portfolio#2.
Table 5.17: Calculation of beta of portfolio #2
Sl No. Security Beta (βi) Weight (wi) βi * wi
1 Asian Paints 0.21 0.04 0.008
2 Bajaj Auto -0.373 0.03 -0.011
3 BHEL 1.8 0.03 0.054
4 Cairn Energy -0.747 0.01 -0.007
5 Coal India 0.965 0.01 0.010
6 Dr. Reddy's Lab 0.82 0.25 0.205
7 Grasim 0.706 0.03 0.021
8 Hero motor corp. -0.49 0.02 -0.010
9 ICICI Bank 1.89 0.04 0.076
10 Jindal Steel &Power 0.45 0.01 0.005
11 Maruti Suzuki Ltd 2.06 0.02 0.041
12 SBI 1.75 0.02 0.035
13 Tech Mahindra 1.6 0.38 0.608
14 Zee Entertainment 1.25 0.11 0.138
Total 1.00 1.172
(Source: Secondary data from the table 5.2 and table 5.15)
Inference:
From the above table it is inferred that the beta of portfolio#2 is 1.172.
5.7.3 Calculation of Return of the Portfolio #2
The table below shows the calculation of return of portfolio#2.
Table 5.18: Calculation of Return of portfolio #2
Portfolio
Portfolio
Alpha
(αp)
Portfolio
Beta
(βp)
Market
Return
(Rm)
Portfolio Return
Rp= αp + βp*Rm
(%)
PORTFOLIO #2 13.7093 1.172 10.2476 25.72
(Source: Secondary data from the tables 5.2, 5.16 and 5.17)
98
Inference:
From the above table it is inferred that the return of portfolio#2 is 25.72%.
5.7.4 Calculation of Unsystematic Risk in Portfolio #2
The table below shows the calculation of unsystematic risk of portfolio#2.
Table 5.19 Calculation of unsystematic risk of portfolio #2
Security
Residual
Variance
(σei2)
Weight
(wi) wi
2 wi
2* σei
2
Asian Paints 3317.03 0.04 0.0016 5.3072
Bajaj Auto 209.71 0.03 0.0009 0.1887
BHEL -151.83 0.03 0.0009 -0.1366
Cairn Energy 161.94 0.01 0.0001 0.0162
Coal India 189.29 0.01 0.0001 0.0189
Dr. Reddy's Lab 102.44 0.25 0.0625 6.4025
Grasim 178.72 0.03 0.0009 0.1608
Hero motor corp. 511.91 0.02 0.0004 0.2048
ICICI Bank 133.31 0.04 0.0016 0.2133
Jindal Steel &Power 316.49 0.01 0.0001 0.0316
Maruti Suzuki 426.81 0.02 0.0004 0.1707
SBI 43.86 0.02 0.0004 0.0175
Tech Mahindra 1380.42 0.38 0.1444 199.3326
Zee Entertainment 1286.14 0.11 0.0121 15.5623
Total 1.00 227.4907
(Source: Secondary data from the table 5.2 and table 5.15)
Inference:
From the above table it is inferred that the unsystematic risk of portfolio#2 is 227.49 %2.
99
5.7.5 Calculation of Systematic Risk in Portfolio #2
The table below shows the calculation of systematic risk of portfolio#2.
Table 5.20: Calculation of systematic risk of portfolio #2
Portfolio βp σm2
Systematic
Risk
(βp2 σm
2)
PORTFOLIO #2 1.172 149.25 205.01
(Source: Secondary data from the table 5.2 and table 5.17)
Inference:
From the above table it is inferred that the systematic risk of portfolio#2 is 205.01 %2.
5.7.6 Calculation of Total Risk of Portfolio #2
The table below shows the calculation of total risk of portfolio#2.
Table 5.21: Calculation of total risk of portfolio #2
Portfolio Unsystematic risk Systematic risk Total
risk
PORTFOLIO #2 227.4907 205.01 432.50
(Source: Secondary data from the table 5.19 and table 5.20)
Inference:
From the above table it is inferred that the total risk of portfolio#2 is 432.50 %2.
100
5.8 CONSTRUCTION OF PORTFOLIO # 3.
(A portfolio with same risk as optimal portfolio)
A portfolio was constructed selecting 14 securities in random from remaining NIFTY 50
shares. Their weight is selected in such a way that portfolio risk is same as that of optimal
portfolio (72.69 %2). Microsoft Excel solver was used to find out the weight of securities
in the portfolio.
The table below shows securities selected and their proportion (weight) in the portfolio
#3.
Table 5.22: Portfolio #3
Sl No. Security Weight (wi)
1 Barati Airtel 0.080
2 BPCL 0.030
3 Cipla 0.050
4 HDFC 0.100
5 Infosys 0.018
6 ITC 0.050
7 Kotak Bank 0.030
8 L&T 0.050
9 Mahindra Mahindra 0.147
10 NMDC 0.111
11 ONGC 0.264
12 PNB 0.020
13 Power Grid 0.010
14 Wipro 0.040
Total 1.00
(Source: Secondary data from table 5.2)
Inference:
From the above table it is inferred that the ONGC has highest weight (26.4 %) and Power
Grid has lowest weight (1%) in the portfolio#3.
101
5.8.1 Calculation of Beta of Portfolio #3
The table below shows the calculation of beta of portfolio#3.
Table 5.23: Calculation of beta of portfolio #3
Sl No. Security Weight (wi) Beta (βi) βi * wi
1 Airtel 0.080 1.10 0.09
2 BPCL 0.030 1.77 0.05
3 Cipla 0.050 1.72 0.09
4 HDFC 0.100 1.24 0.12
5 Infosys 0.018 1.59 0.03
6 ITC 0.050 -0.79 -0.04
7 Kotak Bank 0.030 1.59 0.05
8 L&T 0.050 1.74 0.09
9 Mahindra& Mahindra 0.147 -0.56 -0.08
10 NMDC 0.111 -0.11 -0.01
11 ONGC 0.264 0.35 0.09
12 PNB 0.020 0.90 0.02
13 Power Grid 0.010 0.80 0.01
14 Wipro 0.040 0.78 0.03
Total 1.00 0.53
(Source: Secondary data from the tables 5.2 and 5.22)
Inference:
From the above table it is inferred that the beta of portfolio#3 is 0.53.
102
5.8.2 Calculation of Unsystematic Risk in Portfolio #3
The table below shows the calculation of beta of portfolio#3.
Table 5.24: Calculation of unsystematic risk of portfolio #3
Security Residual Variance (σei2) Weight (wi) wi
2* σei
2
Airtel 151.15 0.080 0.97
BPCL 608.91 0.030 0.55
Cipla 493.63 0.050 1.23
HDFC 129.22 0.100 1.29
Infosys 371.38 0.018 0.12
ITC 316.66 0.050 0.79
Kotak Bank 748.70 0.030 0.67
L&T 98.75 0.050 0.25
M&M 46.80 0.147 1.01
NMDC 847.92 0.111 10.45
ONGC 175.34 0.264 12.22
PNB 554.36 0.020 0.22
Power Grid 273.54 0.010 0.03
Wipro 590.92 0.040 0.95
Total 1.00 30.74
(Source: Secondary data from the table 5.2 and table 5.22)
Inference:
From the above table it is inferred that the unsystematic risk of portfolio #3 is 30.74 %2.
103
5.8.3 Calculation of Systematic Risk in Portfolio #3
The table shown below calculates the systematic risk of portfolio #3.
Table 5.25: Calculation of systematic risk of portfolio #3
Portfolio βp βp2 σm
2
Systematic Risk
βp2 σm
2
PORTFOLIO #3
(Portfolio with same risk
as optimal portfolio)
0.53 0.281 149.25 41.95
(Source: Secondary data from the tables 5.2 and 5.23)
Inference:
From the above table it is inferred that the systematic risk of portfolio #3 is 41.95 %2
5.8.4 Calculation of Total Risk of Portfolio #3
The table below shows the calculation of total risk of portfolio#3.
Table 5.26: Calculation of total risk of portfolio #3
Portfolio Unsystematic Risk Systematic Risk Total
Risk
PORTFOLIO #3
(Portfolio with
same risk as
optimal portfolio)
30.74 41.95 72.69
(Source: Secondary data from the tables 5.24 and 5.25)
Inference:
From the above table it is inferred that the total risk of portfolio #3 is 72.69 %2.
104
5.8.5 Calculation of Alpha of Portfolio #3
The table below shows the calculation of alpha of portfolio#3.
Table 5.27: Calculation of alpha of portfolio #3
SL No. Security Alpha (αi) Weight (wi) αi * wi
1 Airtel -3.60 0.080 -0.29
2 BPCL 13.60 0.030 0.41
3 Cipla -0.33 0.050 -0.02
4 HDFC 8.86 0.100 0.89
5 Infosys -0.97 0.018 -0.02
6 ITC 32.71 0.050 1.64
7 Kotak Bank -0.96 0.030 -0.03
8 L&T -4.81 0.050 -0.24
9 M&M 4.80 0.147 0.71
10 NMDC 20.88 0.111 2.32
11 ONGC 4.76 0.264 1.26
12 PNB 2.29 0.020 0.05
13 Power Grid 1.39 0.010 0.01
14 Wipro 2.59 0.040 0.10
Total 1.00 6.78
(Source: Secondary data from the tables 5.2 and 5.22)
5.8.6 Calculation of Return of the Portfolio #3
The table below shows the calculation of return of portfolio#3.
Table 5.28: Calculation of return of portfolio #3
Portfolio Portfolio
Alpha
(αp)
Portfolio
Beta
(βp)
Market
Return
(Rm)
Portfolio Return
Rp= αp + βp*Rm
PORTFOLIO #3 6.78 0.53 10.2476 12.21
(Source: Secondary data from the tables5.2, 5.23 and 5.27)
Inference:
From the above table it is inferred that the return of portfolio #3 is 12.21 %.
105
5.9 PORTFOLIO EVALUATION
For evaluating the performance a portfolio it is necessary to consider both risk and return.
The following three evaluation methods are used.
Sharpe‘s Ratio
Treynor‘s Ratio
Jensen Measure
5.9.1. Portfolio Evaluation Using Sharpe’s Index
Sharpe‘s ratio is the ratio of excess return to risk. The risk is taken as total risk of
portfolio indicated by standard deviation of portfolio.
Sharpe’s Ratio = (Rp-Rf)/ σp
The table below shows the calculation of Sharpe‘s index.
Table 5.29: Calculation of Sharpe’s index of portfolios
PORTFOLIO Rp
(%)
Rf
(%)
σp
(%)
(Rp-Rf)/
σp Rank
Optimal Portfolio 25.72 7.21 72.69 0.255 1
Portfolio#2
(Portfolio with same return as
optimal portfolio)
25.72 7.21 432.50 0.043 3
Portfolio #3
(Portfolio with same risk as
optimal portfolio)
12.21 7.21 72.69 0.069 2
(Source: Secondary data from the tables 5.11, 5.14, 5.18, 5.21, 5.26 and 5.28)
Inference:
106
Sharpe‘s ratio is highest for optimal portfolio indicating that the performance of Sharpe‘s
optimal portfolio is superior to that of other portfolios.
5.9.2 Portfolio Evaluation by Using Treynor’s Ratio
Treynor‘s ratio also indication of excess returns to risk. Here risk is defined as systematic
risk or market risk.
Treynor’s Ratio = (Rp-Rf)/ βp
Table below shows the calculation of Treynor‘s ratio.
Table 5.30: Calculation of Treynor’s ratio of portfolios
Portfolio Rp
(%)
Rf
(%)
βp (%) (Rp-Rf)/ βp Rank
OPTIMAL
PORTFOLIO 25.72 7.21 0.452 40.95 1
PORTFOLIO#2
(Portfolio with same return as
optimal portfolio)
25.72 7.21 1.172 15.79 2
PORTFOLIO #3
(Portfolio with same risk as
optimal portfolio)
12.21 7.21 0.53 9.43 3
(Source: Secondary data from the tables 5.10, 5.11, 5.17, 5.18, 5.23 and 5.28)
Inference:
Treynor‘s ratio is highest for Sharpe‘s optimal portfolio indicating that the performance
of Sharpe‘s optimal portfolio is superior to that of other portfolios.
107
5.9.3 Portfolio Evaluation by Using Jensen Measure
Jensen Measure gives return earned by the portfolio above the expected return as
mandated by the Capital Asset Pricing Model (CAPM). A positive value indicates
superior performance of the port folio.
Jensen’s Measure = Rp - E(Rp)
E(Rp) = Rf + βp (Rm - Rf)
Where
Rp = Portfolio average return
E(Rp) = Expected return of portfolio
Rm = Average market return
Rf = Risk free rate of return = (Latest MIBOR rate =7.21)
βp = Beta co-efficient of the portfolio.
The table below shows the calculation of expected return of portfolios.
Table 5.31: Calculation of expected return of portfolios
Portfolio Rf βp Rm Rm - Rf E(Rp)
Optimal Portfolio 7.21 0.452 10.2476 3.0376 8.58
Portfolio#2
(Portfolio with same
return as optimal
portfolio)
7.21 1.172 10.2476 3.0376 10.77
Portfolio #3
(Portfolio with same risk
as optimal portfolio)
7.21 0.53 10.2476 3.0376 8.82
(Source: Secondary data from the tables 5.2, 5.10, 5.17, and 5.23)
108
The table below shows the calculation of Jensen Measure of portfolios.
Table 5.32: Calculation of Jenson’s measure of portfolios
(Source: Secondary data from the tables 5.2, 5.11, 5.18, 5.28 and 5.31)
Inference:
Jensen Measure is highest for Sharpe‘s optimal portfolio indicating that the performance
of Sharpe‘s optimal portfolio is superior to that of other portfolios.
5.10 CONCLUSION
In this chapter the data collected was analyzed and an optimal portfolio using Sharpe‘s
single index model was constructed. Along with, a portfolio having same return as
optimal portfolio and another portfolio with same risk as optimal portfolio is constructed.
The portfolios were evaluated using Sharpe‘s ratio, Treynor‘s ratio and Jensen Measure.
In the next chapter the finding, Suggestion and conclusion of the study is detailed.
Portfolio Ri E(Rp) Rp - E(Rp) Rank
PORTFOLIO#1
Optimal Portfolio 25.72 8.58 17.14 1
PORTFOLIO#2
(Portfolio with same return
as optimal portfolio)
25.72 10.77 14.95 2
PORTFOLIO #3
(Portfolio with same risk as
optimal portfolio)
12.21 8.82 3.39 3
109
APPENDIX-A
RISK AND RETURN ANALYSIS OF SECURITES
Sample Calculation of Ambuja Cements
The 5 years average return, risk, Beta and alpha of Ambuja Cements for the years 2011-
15 are calculated below.
Table: 5.33: Risk & Return calculations of Ambuja Cements
Yea
r
Pri
ce
Nif
ty
Ri
Rm
Ri-
Ri‘
Rm
-Rm
‘
(Ri-
Ri‘
)*
(Rm
-Rm
‘)
(Ri-
Ri‘
)2
(Rm
-Rm
‘)2
2010 108.86 5278
2011 145.47 5749 33.63 8.93 15.81 -1.31 -20.78 249.97 1.73
2012 141.64 5248 -2.63 -8.72 -20.45 -18.97 387.93 418.31 359.77
2013 178.74 5930 26.193 12.97 8.37 2.75 23.01 70.11 7.55
2014 199.64 6696 11.693 12.92 -6.13 2.67 -16.38 37.54 7.14
2015 240.00 8377 20.216 25.11 2.40 14.86 35.61 5.74 220.84
Total 89.1 51.24 409.41 781.68 597.03
(Source: Summarized from secondary data from www.finance.yahoo.com)
Average return of security Ri‘= Σ Ri/n
= 89.1/5 = 17.82 %
Average return of the market Rm = Σ Rm/n
=51.238/5 =10.2476
Variance of security σi2
= Σ
(Ri-Ri‘)
2/(n-1)
= 781.679/4 = 195.4197 (%)2
Variance of market σm2 = Σ
(Rm-Rm‘)2/(n-1)
= 597.03/ (5-1) =149.25 (%)2
Covariance of Security & Market COV R,M = Σ(Ri-Ri‘)*(Rm-Rm‘)/ (n-1)
= 409.4087/4 = 102.352
110
Beta of security β = COV R, M / σm2
=102.352/149.25 = 0.6857
Alpha of security α = Ri‘- β Rm‘
= 17.82-0.6857*10.247 = 10.79 %
Inference:
From the calculation it was found that the 5 average return (Ri‘) of the Ambuja Cements
is 17.82 %, Variance (σi2 )
of the Ambuja Cements is 195.4197 (%)2
, The variance of the
market (σm2)
is 149.25 (%)2, The covariance between the prices of Ambuja cement and
CNX Nifty index is 102.352, The Beta (β) of Ambuja Cements is 0.68 and the Alpha(α )
of the Ambuja Cements is 10.79 %.
111
Conclusion
112
CHAPTER 6
CONCLUSION
6.1 INTRODUCTION
In the previous chapter the data collected were analyzed and optimal portfolio using
Sharpe‘s single index model was constructed. Along with, a portfolio having same return
as optimal portfolio and another portfolio with same risk as optimal portfolio was
constructed.
The portfolios were evaluated using Sharpe‘s ratio, Treynor‘s ratio and Jensen Measure
and they were ranked based on those ratios.
In this chapter the finding, Suggestion and conclusion of study is detailed.
6.2 FINDINGS
The study titled ―A study on construction of optimal portfolio of CNX Nifty shares using
Sharpe‘s portfolio single index model‖ has following findings.
6.2.1 Security Analysis
Risk & Return of Securities
Risk
Tech Mahindra has highest risk (1762.49)
Hindustan Uniliver (130.88) has lowest risk.
Return
Asian Paints has highest return (42.05 %).
113
Sesa Sterlite has lowest return (-24.44 %).
Alpha
Mahindra & Mahindra has highest Alpha (45.39).
BHEL has lowest Alpha (-26.53).
Beta
Maruti Suzuki has highest Beta (2.06).
Mahindra &Mahindra has lowest Beta (-1.70).
Systematic & Unsystematic Risk of Securities
Systematic Risk
Axis bank has highest systematic risk (975.06 %).
Hindustan Uniliver has minimum systematic risk (0.02 %).
Unsystematic Risk
Asian Paints has highest unsystematic risk (3317.02).
Dr. Reddy‘s Lab has lowest unsystematic risk (100.77)
6.2.2 Portfolio Construction & Optimization
An optimal portfolio and two other portfolios with different criteria were constructed and
their risk and return has been evaluated. The optimal portfolio had 14 shares with a cut
of point of 25.1394. Two other Portfolios were constructed by using 14 nos. of randomly
selected Nifty Shares each such a way that Portfoilo#2 has same return as that of Optimal
Portfolio (25.72 %) and Portfolio #3 had same risk as that of Optimal Portfolio (72.69%).
Return & Risk
Optimal portfolio has a return of 25.72 % and a risk of 72.69 %.
Portfoilo#2 has same return of 25.72 % but its risk was very high (432.50%).
114
Portfolio #3 has a risk of 72.69% (same as optimal portfolio) but its return is very
low (12.21%).
6.2.3 Portfolio Evaluation
Three methods were employed for evaluation of portfolios, i.e., Sharpe‘s Ratio, Treynor‘s
ratio and Jensen Measure.
Sharpe‘s ratio indicated that optimal port folio has highest rank (0.255).
Treynor‘s ratio indicated that the optimal portfolio is the best portfolio (40.95%)
Jenson‘s measure indicated that optimal portfolio is the best portfolio with
maximum extra return (17.14%).
All those evaluation methods proved that optimal portfolio is the best portfolio.
6.3 SUGGESTIONS
Since the equity markets are highly volatile, the investors must strive to maximize return
with minimum risk.
This study has revealed that the Sharpe‘s single index model of portfolio optimization is
very simple and most effective tool for delivering highest risk adjusted return. Hence,
investors are advised to use this financial model to improve the performance of their
portfolio and achieve the investment objective of maximizing return and minimizing risk.
The study can be also extended to include a midcap and small cap stock which offers
higher return than large cap stocks.
Statistical tools such as ‗t- test‘ can be used for proving the superiority of optimal
portfolio constructed using Sharpe‘s single index model.
115
6.4 CONCLUSION
Since there are thousands of companies listed in the stock market, the equity selection
and portfolio construction is a highly complex task. The study titled “A study on
construction of optimal portfolio of CNX Nifty shares using Sharpe’s portfolio
single index model” was a successful attempt to simplify the task of equity selection,
portfolio construction and portfolio evaluation.
This study gives a practical knowledge of construction of portfolio by considering risk
and reward factors of security market.
116
BIBLIOGRAPHY
BOOKS
1. Kothari C.R, Research Methodology: Methods and Techniques, New Age International
Pvt.Ltd., New Delhi, 2004.
2. Gupta K Shashi, Gupta Neeti, Financial Management, Kalyani Publishers, Ludhiana,
2013.
3. Dr. Chandra Prasanna, Investment Analysis and Portfolio Management, Tata
McGraw- Hill Publishing Company Limited, 2004.
4. Pandian Punithavathy, Meera E, Machiraju H.R, Investment Management, Vikas
Publishing House PVT LTD, New Delhi, 2011.
5. Kevin.S, Portfolio Management, Printice Hall of India Pvt. Ltd, New Delhi, 2003
MAGAZINES, JOURNALS & NEWS PAPERS
JOURNALS
1. Chauhan . A. Apurva, A study on usage of Sharpe’s single index model in Portfolio
Construction, Global Journal for Research Analysis, 2014
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1. http://www.nseindia.com
2. http://www.bse.com
3. http://www.investopedia.com
4. http:// www.cochinstockexchange.com
5. http://www.fidelity.com
6. http://www.finance.yahoo.com
117
7. http://www.motilaloswal.com
8. http:// www.onlinetradingconcepts.com
9. http:// www.capitalmarket.com