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Optimal Portfolio Construction Using Sharpe Single Index Method

INDUSTRY PROFILE
INTRODUCTION
Stock exchanges to some extent play an important role as indicators, reflecting the
performance of the country’s economic state of health
...
It is exposed to a high degree of volatility, prices fluctuate
within seconds and are determined by the demand and supply of stocks at a given time
...
The securities and exchange board of India (SEBI) is
the authorized body, which regulates the operations of stock exchanges, banks and other
financial institutions
...
It’s history dates back to
nearly 200 years ago India had an active stock market for about 150 years that played a
significant role in developing risk market as also promoting enterprise and supporting the
growth of industry
...
Though the trading list was broader in 1839, there were only half a
dozen brokers recognized by banks and merchants during 1840 and 1850
...
The number of brokers
increased to about 200 to 250
...
In 1887, they formally established in
Bombay, the “Native Share and Stock Brokers Association”
...
Thus, the Stock
Exchange at Bombay was consolidated
...
This
was followed by the formation of associations/exchanges in Ahmadabad (1894), in
Calcutta (1908), and in madras (1937)
...
Under this legislation, it is mandatory on the part of a
stock exchange to seek government recognition
...

They are located at:
1
...
Jaipur,

2
...
Kanpur,

3
...
Ludhiana,

4
...
Mangalore,

5
...
Mumbai (NSE),

6
...
Mumbai(Bombaystock exchange),

7
...
Mumbai(OTC

8
...
Delhi,
10
...
Mumbai (Inter-connected Stock
Exchange of India),

11
...
Patna,

12
...
Pune
23
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

Classification of various financial services
a) Banking services:- The primary operations of banks include:
 Keeping money safe while also allowing withdrawals when needed
...

 Provide personal loans, commercial loans, and mortgage loans
 Issuance of credit cards and processing of credit card transactions and billing
 Issuance of debit cards for use as a substitute for checks
 Allow financial transactions at branches like by using ATMs
...

 Hedge fund management - Hedge funds often employ the services of "prime
brokerage" divisions at major investment banks to execute their trades
...
These
services are designed to cover a number of risks that are related to an individual's
life, property and many more
...

 Reinsurance - Reinsurance is insurance sold to insurers themselves, to protect
them from catastrophic losses
...
Foreign
exchange services include:
 Currency Exchange - where clients can purchase and sell foreign currency
banknotes
...

 Foreign Currency Banking - banking transactions are done in foreign currency

Markets
In tune with the global stock markets that began to recover from the second half
of 2003
...
India’s two leading indices,
the most popular BSE Sensex, and the one most used by the markets the National Stock
Exchanges’ S&P CNX Nifty rose to record levels
...


Market Structure
Indian securities market is fairly large as compared to several other emerging
markets
...

With the abolition of the deferral products and introduction of uniform T+2
settlement cycle, the liquidity in these exchanges flowed to the national level system
consisting of NSE and BSE
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

COMPANY PROFILE
2
...
Background and inception of the Company
Sharekhan ltd, Founded in 1922, SSKI (Shripal Sevantilal Kantilal
Ishwarlal) is one of India’s Oldest Brokerage Houses having eight decades of experience
into Institutional Broking, Investment Banking and Retail Broking
...

Sharekhan ltd, comes under retail arm of SSKI (Shripal Sevantilal Kantilal
Ishwarlal) Investors Services Pvt
...

Sharekhan ltd, is an 90 years old company which started online trading portal in
the year 2000 and is the first company who started online in India
...

Right now Sharekhan Ltd has 1437 share shops across 450 cities all over India serving
around 10,00,000 customers and growing with around 3000 employees
...
It also has an
office in Dubai which has been a new edition to its chain
...
S
...




SSKI Corporate Finance



I dream Productions



Palm spring estates Pvt Ltd
...




I dream Production UK Pvt Ltd
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method



Archfund Properties Pvt Ltd
...


2
...
The company offers a complete range of pre
trade and post trade service on the BSE (Bombay Stock Exchange) and the NSE (National
Stock exchange)
...

 Investment Advisory Service
 Facilitation Services to Retail Investors, Corporate

 Depository Services

2
...
The
Company Vision is:


To be the top most company for providing investment advisory and financial
planning services in India
...


MISSION:
To educate and empower the individual investor to make better investment
decisions through quality advice and superior service
...




Sharekhan has one among the largest network of outlets of the either trading firms

with 180 outlets
...


Milestones of SSKI


1922: The SSKI became the first member in the BSE as institutional broker
...




2000: It has started its retail business with the brand name ‘Sharekhan’
...




2002: The advanced technology in the online business “Speed Trade plus was
launched on October 28th for derivative trading
...


2
...



Online BSE and NSE executions (through BOLT and NEAT terminals)



Free access to investment advice from Sharekhan’s research team
...




Live market information



Derivates trading
...




Internet based online trading-speed trading
...


 Derivatives (Futures and Options)


The company also facilitates the trading system for trading in secondary market

under future and options segment of NSE and BSE
...


 Depositor Services


Sharekhan is a Depository participant of National Securities Depository

and Central Depository and securities Limited
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

 Margin Financing


In the present rolling settlement scenario, Sharekhan understand investor need for

additional capital availability for daily purchaser shares, it offers unique facility avail
finance, for purchasing shares at very competitive interest rates
...


Sharekhan is a distribution house for all mutual funds
...

 Stock lending and Borrowing


One can place an order of shares with Sharekhan
...
These would be sent out the borrows, these earnings
fees for all investor’s idle shares
...
The research team’s inputs will be
available as daily trading calls, quarterly investment picks and long term investment
picks, based on the fundamentals of particular company and the industry as whole
...
The virtual world that Sharekhan offers online trading services
through
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

 Commodity trading


Sharekhan is founder member of two commodity exchanges, the MCX and

NCDEX and offers trading facility for the following commodities and both these
exchanges:


Bullion: Gold and Silver



Oil and Seed: Castor, Soya Rapeseed/Mustard Oil Crude Palm Oil, RBD
palmolein



Soft Commodities: Cotton



Species and Plantation: Pepper and Rubber
...
com in February 2000
...


2
...
It is operating in 28 states across
325 cities in India and having more than 1290 share shops all over country
...
Recently Sharekhan went
one step ahead and opened its new office in Dubai
...
By this Sharekhan has stepped into the way of becoming a
global company from a national one
...
f OWNERSHIP PATTERN
The shareholders of SSKI Investor Pvt Ltd are MR
...
Shreyas
Morkhia, foreign private equity funds and the key employees of the company
...
Shripal Morkhia, who as on march 31, 2005, along with
his family owns 55
...
e
...
5% is HSBC CRLYE and INTEL PACIFIC
...
Ketan Parekh, Chief Technology
Officer at Sharekhan
...
Tarun P
...
Shankar Vailaya – Director Operatins
Mr
...
Ketan Parekh – Chief Technology Officer

2
...
Following are some of the companies that are
its competitors:



Karvy Stock Broking



ICICI Direct



India Infoline



Kotak Securities



Indiabulls



HDFC Securities



Motilal Oswal Securities



UTI Securities



Anand Rathi Securities



Reliance Money



Angel Broking



Religare Securities

2
...
The
book and feel of the offices across India projects an consistent branch image for the
company
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

2
...



Pioneers of online trading in India amongst the top 3 online trading websites from

India
...




Winners of “Best Financial Website” award



India’s most preferred brokers within 5 years
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

2
...
k FUTURE GROWTH AND PROSPECTUS


2,00,000 plus retail customers being serviced through centralized call
centers/web solutions
...




205 independent investment managers/ franchisee servicing 50,000 highly valued
clients
...
Mc KENSY’S 7S FRAMEWORK

While some models of organizational effectiveness go in and out of fashion, one
that has persisted is the McKinsey 7S framework
...
The basic premise of the model is that there are
seven internal aspects of an organization that need to be aligned if it is to be successful
...




Examine the likely effects of future changes within a company
...




Determine how best to implement a proposed strategy
...
The alignment issues apply, regardless of how one decides to define the scope of
the areas he/she studies
...


“Soft” elements, on the other hand, can be more difficult to describe, and are less
tangible and more influenced by culture
...


3
...
e
...
Market Strategy also takes a longer-term
view on stocks i
...
three to six months
...


3
...
The structure of the company often dictates the way it operates and performs
traditionally, the businesses have been structured in a hierarchical way with several
divisions and departments, each responsible for a specific task such as human resources
management, production or marketing
...

Sharekhan Ltd is one of the premier stock brokers in India
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

Organization structure
CEO
Tarun Shah

Online & Technology
Jaideep A
...

Sr
...

Sr
...
Saravanan
Vice President
Level 3

PDG

IT

Accounts

Operations

Key Accounts

PortfolioManager

Ketan P
...

CFO
Level 3

Amit A
...

AVP
Level4

Customer Service & DNT
Geeta R
...
Manager
Level 5A

Compliance
Anand B
...
Manager
Level 5B

Distribution
Shyam Jajoo
AVP
Level4

Content
Murtuza
Sr
...
Kalyanraman
AVP
Level4

Business Development
Sameer Shah
AVP
Level 4

Regional Managers /

Pomesh M
...

Market Strategist
Level 3

Administration
Ramachandran G
Senior Manager
Level 5B

Commodities

Derivatives

Vacant

PMS
Amit Adesara
Reseacrh Analyst
Level 5A

(Jaideep Arrora)

Head -HNI Elite Guild

Marketing

Sandeep Jain

Bhupendra S
...
Manager
Level 5A

Web Dealing
Anil B / RRaul

Sr
...



Finance department



Administration department



Marketing department



Surveillance department



Legal department



Systems department

3
...

Management information system is identifying the problems in between the departments
and managing the problem with interrelated processes
...
The company is following high
tech system to measure the quality
...

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

The various activities of system department include
...




Maintenance of multex software, providing online trading with NSE and BSE
...
This software’s are developed in house by Sharekhan
...


3
...
But the friendly
approached should not be miss-confused with the lack of professionalism
...
The
firm has open and friendly environment through which it avoids grapevine and informal
communication
...
Transparency in the working of the company also
adds to the positive operating approach of the company
...


3
...
A philosophy that balances personal
lifestyles, perspective and needs is an important part of our culture
...
The talent and passion of their employees is critical to their success
...

They committed to hire, develop, reward, motivate and retain the best people in the
industry and always looking out for fresh talent
...
6 Skills
The actual skills and competencies of the employees working for the company
...
Placing
Super- Ordinate goals in the middle of the model emphasizes that these values are central
to the development of all the other critical elements
...
The original vision of the company was formed from the values of
the creators
...


Skills variable refers to the capabilities of the staff within the organization as a
whole
...


3
...
Super-ordinate goals are the fundamental ideas around which a
business is built
...


All members of the organization share some common fundamental ideas or
guiding concepts around which the business is built
...
These values and common goals keep the
employees working towards a common destination as a coherent team and are important
to keep the team spirit alive
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

Sharekhan Shared Values


Integrity
Sharehan is honest and forthright in their dealings with employees, members
...
Commitment

to excellence: Company is committed to achieve highest level of performance in all
aspects of business activities
...




Diversity
Company encourages diversity of backgrounds and experiences in their
workforce as well as fair treatment based on qualifications and performance
...




They support one another
They believe in one another
...
They push for professional excellence
...
1 Strengths


It is a pioneer in online trading with a turnover of Rs
...




SSKI the parent company of Sharekhan has more than eight decades of trust and
credibility in the Indian Stock Market
...




Sharekhan provides multi-channel access to all its customers through a strong online
presence with www
...
com, 1290 share shops in 640 cities and a call-center
based Dial-n-Trade facility
...
Which
constantly track the pulse of the market and provide timely investment advice free of
cost to its clients which has a strike rate of 70-80%
...
2 Weakness


Localized presence due to insufficient investments for country wide expansion
...




Lesser emphasis on customer retention
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

4
...




It can easily tap the retail investors with small saving through promotional channels
like print media, electronic media, etc
...




Abolition of long term capital gain tax on shares and reduction in short term capital
gain is making stock market as hot destination for investment among small investors
...


4
...




Lack of sufficient branch-offices for speedy delivery of services
...




More and more players are venturing into this domain which can further reduce the
earnings of Sharekhan
...
: Income Statement (in Crores)
Year

2011-12

2010-11

2009-10

30
...
23

21
...
90

2
...
6

Selling Expenses

2
...
18

0
...
50

1
...
92

Cost of Sales

3
...
45

2
...
20

29
...
58

Other Recurring Income

31
...
81

19
...
00

30
...
6

Tax Charges

2
...
38

1
...
5

27
...
47

Reported Net profit

28
...
31

17
...
19

0
...
08

Retained Earning

0
...
14

0
...
Balance Sheet (Crores)
Year

2011-12

2010-11

200910

Sources of Fund
Owners fund
Equity Share Capital

32
...
62

31
...
32

25
...
7

Secured Loans

2
...
91

1
...
87

59
...
89

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

Uses of Fund
Fixed Assets
Gross Block

6
...
96

4
...
50

4
...
76

Net Block

1
...
92

0
...
25

45
...
31

Current assets, loans & Advances

22
...
12

16
...
80

6
...
03

0

0

0

66
...
02

53
...
02

40
...
02

Market value of quoted investments

0
...
16

0
...
5

3
...
5

316
...
2

316
...
25/7
...
83:1

12
...
03 = 2
...
87/4
...
19:1

Current ratio defines the ability of the firm to meet current liabilities
...
In the year 2011-12 the current
ratio was 1
...
19:1 and in the current year
current ratio was 1
...
It is always beneficial to have a considerably high current ratio
...

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

Net Profit Ratio
2011-12

2010-11

2009-10

28
...
65=7
...
31/3
...
48

17
...
64 = 6
...
Thus it depends on the total sales of the company
...
8 in 2011-12, to 7
...
8
...
It shows
marginally shows of better financial position
...
87/32
...
97

59
...
62 = 1
...
89/31
...
13

The Debt Equity Ratio of the Company has gone up from 1
...
87 in year
2010-11 to 1
...
In theory it is not acceptable, because it indicates the firm
is incurring more long term debts
...
20/3
...
64

29
...
45 = 8
...
58/2
...
03

OP is the ratio of profit deducting tax to the total sales of the company
...
It has increased to 9
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

Return on Total Equity
2011-12

2010-11

2009-10

28
...
40=0
...
31/31
...
86

17
...
62 = 0
...
It indicates the actual profit made by the
company excludes the tax which is contributed by the shareholders equity
...
Return on total equity has been
increasing on a regular basis even since the year 2009-10, 2010-11 and 2011-12
...
88
...
20/32
...
64%

29
...
62X100 =93
...
58/31
...
76%

Every company’s profitability depends on the nature it achieves on the total investment it
makes
...
The company’s return on investment has increased drastically form
just more 58
...
26% in 2011 and 93
...
64% in 2012 the company
undoubtedly the avenue for further growth
...
LEARNING EXPERIENCE
Before my summer internship programme, I had very little knowledge about the stock
market and its fundamentals
...
I have gained fair bit of
information about the company – the products, schemes and policies, and also about its
competitors
...
He also taught me how to do
telling calling
...
I was
assigned target to sell demat accounts for 10 days
...


While carrying out the initial part of my project, I met with number of people
...
The employees there helped me in
understanding the impact of sensex and nifty on stock prices, their significance and
various fundamentals and technical aspects that effect stock prices in the short and long
run
...
Working in Sharekhan Ltd was both a pleasure and
challenge because of the prevailing work atmosphere that believes in the maximum work
with joy
...
The
very fact that all the employees are taken special care which automatically motivates me
to constantly learn and also boosts my morale
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

PART-B
A
...
While the procedure was quite capable
of providing perfectly accurate answers to questions such as, “Given a population of
securities, what single combination would have had the lowest volatility in monthly
return over the preceding period?” the computing power of the times limited its
application
...
In essence,
Sharpe’s model replaced the exact, but cumbersome, Markowitz formula for portfolio
volatility with a simplified approximation that assumed all the interrelationships among
security returns could be attributed to the fact that they all respond differentially to the
pull of the single index
...


The investor always likes to purchase a combination of stocks that
provides the highest return and has lowest risk
...
Traditionally analysts paid more attention to the return aspect of the
stocks
...

Individual securities have risk-return characteristics of their own
...
Portfolio analysis considers the determination of
future risk and return in holding various blends of individual securities
...
The simple fact that securities carry differing degrees of expected risk
leads most investors to the notion of holding more than one security at a time, in an
attempt to spread risks by not putting all their eggs into one basket
...
Most
investors hope that if they hold several assets, even if one goes bad, the other will provide
some protection from an extreme loss
...


PORTFOLIO MANAGEMENT
A portfolio consists of any combination of assets, the outcome of which cannot be
defined with certainty
...
A portfolio is a collection of securities
...

Two basic principles of finance form the basis for portfolio theory
...
A rupee today is worth more than a rupee
tomorrow or a year later, and as parting with money involves the loss of present
consumption, it has to be rewarded by a return commensurate with time of waiting
...
Due to risk
aversion of investors, they feel risk is inconvenient and has to be rewarded by a return
...


Objectives of a Portfolio:
The objective of a portfolio theory is two folded1
...
To optimize return for a given level or risk
...
It is useful here to clarify what an efficient portfolio
...
The same return at a lower risk or
2
...
A higher return and a lower risk
...
Investors prefer higher rate of return to a lower rate of return
...
Investors are risk averse, i
...
, not willing to take risk
...
However this was done on intuition
without really understanding the magnitude of risk reduction
...
This study came to be known as Portfolio Theory
...
Harry M
...
William F
...
It is a dynamic and flexible concept and involves continuous and
systematic analysis, judgment and operations
...
Portfolio Management is the
management of large investible funds with a view to maximizing return and minimizing
risk
...
It is essentially a
systematic method of managing one’s investment efficiently
...
A proper investment decision-making of what to buy and sell
...
Proper money management in terms of investment in a basket of assets so as to satisfy
the asset preferences of investors
...
Reduce the risk and increase returns
...

A portfolio is a basket of investments or assets held by an individual or a corporate body
...
Five phases can be identified in the portfolio management
process1
...

2
...

3
...

4
...

5
...

Each phase is an integral part of the whole process and the success of portfolio
management depends upon the efficiency in carrying out each of these phases
...
Security Analysis:
Security analysis is the initial phase of the portfolio management process
...
A basic
strategy in securities investment is to buy under priced securities and sell overpriced
securities
...
This is what security analysis is all about
...



Fundamental Analysis provides and analytical framework for rational

investment decision-making
...
Fundamental
analysis works out intrinsic value of a security based on its fundamentals; then compares
this intrinsic value with the current market price
...




Technical Analysis believes that share price movements are systematic and

exhibit certain consistent patterns
...

Technical analysis ignores the fundamental of shares
...
Portfolio Analysis:
A portfolio is a group of securities held together as investment
...
The return and risk of each portfolio has to be
calculated mathematically and expressed quantitatively
...


3
...
The main goal of
portfolio selection is to generate a portfolio that provides the highest return and the lowest
risk
...
The portfolio
selection problem is the process of delineating the efficient portfolios and then selection
the best portfolio from the set
...


4
...
The investor has to revise his portfolio in the light
of the developments in the market
...
The mix of securities and
their proportion changes as a result of the revision
...


Portfolio revision has to be done scientifically and objectively so as to ensure the
optimality of the revised portfolio
...


5
...
This involves
quantitative measurement of actual return realized and the risk borne by the portfolio over
the period of investment
...
Portfolio evaluation provides a
mechanism for identifying weaknesses in the investment process and for improving these
deficit areas
...


Role of Portfolio Management:
 Portfolio management is now a familiar term and is widely practiced in India
...

 This reform process has made the Indian capital markets active
...
Large institutional investors with their diversified
portfolios dominate the markets
...
With this development, investment in securities has gained
considerable momentum
...
Professional portfolio management, backed by competent
research, began to be practiced by mutual funds, investment consultants and big brokers
...
Risk is
inherent in any investment
...
While some
securities are almost risk less like Government securities others are more risky
...
The uncertainty associated
with the returns from an investment introduces risk into an investment
...

An investment whose returns are fairly stable is considered as low-risk investment,
whereas an investment whose returns fluctuate significantly is considered to be a highrisk instrument
...
Wrong decision of what to invest in
...
Wrong timings of investments
...
Nature of the instruments invested in
...
Creditworthiness of the issuer
...
Maturity period or the length of investment
...
Amount of investment
...
The difference between purchase price and
sale price is capital appreciation
...
Higher the risk taken, the higher will be the risk
...


The expected return is the uncertain future return that an investor expects to get from his
investment
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

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Optimal Portfolio Construction Using Sharpe Single Index Method

Return on a typical investment consists of two components:
Income or current yield – capital gain/capital losses yield
...
Capital gain/loss is the
charge in the price of asset-the difference between purchase price and the price at which
the asset can be or is sold
...

In symbols

=

∑ Ri
No
...
In other words Beta describes the relationship
between a stock’s return and the market index return
...
The Beta of an asset is the measure of variability of that asset relative to
the variability of the market as a whole
...
The larger the Beta the more volatile is the security
...
If Beta is greater than 1,
the scrip risk is more than the market risk and if the Beta is less than 1, then the scrip risk
is less than the market risk
...
Beta can also be negative, implying that the stock returns move in the
direction opposite to that of the market returns
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 35

Optimal Portfolio Construction Using Sharpe Single Index Method

Calculation of Beta:
1) Calculate Market index return = Closing index – Opening index
Opening index
2) Calculate security return = Closing Price – Closing Price
Opening Price
3) Calculate Beta: n∑xy-∑x∑y
n∑x2-(∑x)2
Where, n=number of years
∑x=sensex (market index)
∑y=security return
 Systematic Risk:
Systematic risk is the variability in the security returns caused by changes in the economy
or market
...
The systematic risk of
a security can be measured by relating that security’s variability with the variability in the
stock market index
...
Systematic risk is
further sub-divided into interest rate risk, market risk and purchasing power risk
...


Interest rate risk: The variation in bond prices caused due to the variations in the
interest rates is known as interest rate risk
...


ii
...
In other words, the variation in
returns caused by the volatility of the stock market is referred to as market risk
...


Purchasing power risk: Purchasing power risk refers to the variation in investor
returns caused by inflation

Calculation of Systematic Risk= βi2*variance of market
 Unsystematic Risk:
Unsystematic risk is the risk that is specific or unique to a company
...
The investor does not seek to measure
the unsystematic risk of a security as it can be reduced through diversification
...
The unsystematic or unique risk affecting specific securities
arises from two sources:
i
...
The financing pattern adopted by the company
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 37

Optimal Portfolio Construction Using Sharpe Single Index Method

TITLE OF THE PROJECT
“A STUDY ON OPTIMAL PORTFOLIO CONSTRUCTION USING SHARPE
SINGLE INDEX METHOD”
...
The investor has to find good
securities among different alternatives
...
Many investor invest in securities
by their emotional forces
...


The study is focused on Risk and Return analysis and Optimal Portfolio Construction
of various Sectors using Single Index Model as formulated by W
...
Sharpe
...
Basically there are 2
methods of portfolio construction namely Markowits Model and Sharpe Index Model
...

Sharpe Index is a simplifactions of the above process which aims at identification of
selected securities to be included in the portfolio from among several
...

 Quantification of necessary ingredients required for single index model namely
residual variance and beta co-efficent and market variance
...
F
...

 Identification of percentage wise investment to be made in each security
...
This study now as taken in to consideration equity shares belonging to
- Banking, Auto, Health care, Infrastructure and IT industries covering the following
companies namely (Axis bank, State Bank of India, YES bank, Bajaj auto, Marut Suzuki,
MRF,Cipla ltd, Glenmark, Ranbaxy, ABB, L&T, Reliance infra, Tech Mahindra, TCS
and Wipro) - Over a period of 2010,2011 & 2012 (3 years)
...


METHODOLOGY
Data Collection Method:
 Primary Data:
Primary

data

is

the

information

collected

through

visiting

the

company,interacting with the manager about the information
...

 Secondary Data:
Secondary data is the information that is already collected and analyzed for other
purpose
...
For the purpose of this study secondary data was considered more important
and was collected through www
...
com
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 39

Optimal Portfolio Construction Using Sharpe Single Index Method

 Sampling:
I have mainly concentrated on convenience sampling
...
So selected companies are as follows:
Sl
...

 As the study is depending on the information from the different sources, the
reliability of study is depending on the information
...


 Analysis of data limited to 3 years only
...
DATA ANALYSIS AND INTERPRETATION:
a) Optimum portfolio preparation
 Finding expected return of each stock
...

 Systematic and unsystematic risk of each security
...


SIMPLE SHARPE PORTFOLIO OPTIMIZATION

The construction of an optimal portfolio is simplified if a single number measures the
desirability of including a stock in the optimal portfolio
...
If stocks are ranked by excess return to
beta (from highest to lowest), the ranking represents the desirability of any stock’s
inclusion in a portfolio
...


Step – 1 Ranking Securities:
Excess return to beta ratio = (Ri – Rf) / βi
Ri = Expected return on stock i
Rf = Return on a riskless asset
"i = Expected change in the rate of return on stock i associated with a 1% change in the
market return
Current Risk Free Rate – 7
...

Step – 3 Arriving at the Optimal Portfolio:

Once we know which securities are to be included in the optimum portfolio, we must
calculate the percent invested in each security
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 42

Optimal Portfolio Construction Using Sharpe Single Index Method

ANALYSIS:
Now this companies which I have selected, are they really going to offer the investor a
good return
...
So once it found than the
investor must evaluate such securities by Sharpe optimum portfolio model, which will
say what should be the size of your Portfolio as well as weight of investment for
particular securities
...


Calculation of Sensex(market) returns for the year 2012

Date

Opening price of Market

Closing price of Market

Return on market

02/01/2012

15534
...
55

10
...
64

17752
...
33

01/03/2012

17714
...
2

-1
...
96

17318
...
63

02/05/2012

17370
...
53

-6
...
48

17429
...
47

02/07/2012

17438
...
18

-1
...
44

17380
...
79

03/09/2012

17465
...
74

7
...
64

18505
...
48

01/11/2012

18487
...
9

4
...
83

19426
...
43
∑Ri=23
...
1 Table shows the Bajaj Autos returns, beta (β) and unsystematic risk:
Closing
Price of
Stock

Return
on
Market

Return
on
Stock

X*Y

X2

(R-AR)2
Market

(R-AR)2
Stock

02/01/2012

Openi
ng
Price
of
Stock
1595

1600
...
68

0
...
984

114
...
657

4
...
95

3
...
046

36
...
126

1
...
42

01/03/2012

1820

1677
...
75

-7
...
68

3
...
5094

105
...
1

-0
...
674

2
...
4067

6
...
839

02/05/2012

1623

1513

-6
...
778

44
...
011

73
...
661

01/06/2012

1505

1572

7
...
4518

33
...
898

30
...
897

02/07/2012

1572
...
35

-1
...
8606

-2
...
3484

9
...
3809

01/08/2012

1598

1615
...
79

1
...
861

0
...
28304

1
...
5

7
...
117

97
...
158

30
...
2

01/10/2012

1837

1813
...
48

-1
...
865

2
...
6268

13
...
8

1930
...
60

6
...
48

21
...
21057

17
...
1

2131

0
...
696

4
...
1881

2
...
532

∑Ri=23
...
7

∑X2=309
...
1

σ2=43
...
73,
Market(Sensex) is 23
...
7969, Systematic Risk is 14
...
75 are calculated below based on the above information
...
95 – 1595
...
37
1595
...
55 – 15534
...
68
15534
...
73 = 2
...
2) – (23
...
73) = 0
...
3) – (23
...
7967)2 * 22
...
00

Unsystematic risk: total variance of security return-systematic risk
2012 = 43
...
00 = 29
...
1 Graph Showing 2012 of Bajaj Autos Returns:

Bajaj Auto
100%
50%
0%
-50%
-100%

1

2

3

4

5

6

7

8

9

10

11

12

BAJAJ AUTO (y) 0
...
05 -7
...
67 -6
...
452 1
...
089 13
...
25 6
...
7
SENSEX(x)

10
...
336 -1
...
64 -6
...
477 -1
...
79 7
...
49 4
...
434

INTERPRETATION: From the above graph it can be interpreted that the monthly
returns of a Bajaj autos company selected against the monthly return of sensex
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 45

Optimal Portfolio Construction Using Sharpe Single Index Method

2
...
55

10
...
694

295
...
03

76
...
545

01/02/2012

1195

1256
...
33

5
...
097

11
...
99489

0
...
1

-1
...
3959

-11
...
0707

13
...
87807

02/04/2012

1354

1369
...
63

1
...
749

0
...
55803

9
...
7

1106
...
63

-19
...
29

44
...
2264

553
...
5

1169
...
47

4
...
658

55
...
8395

0
...
15

1133
...
16

-3
...
1601

1
...
51341

60
...
4

1138
...
79

0
...
4995

0
...
28304

12
...
9

7
...
62

138
...
158

30
...
315

01/10/2012

1355
...
25

-1
...
9572

-8
...
2101

11
...
13271

01/11/2012

1440

1473
...
60

2
...
737

21
...
21057

3
...
95

0
...
469

0
...
1881

2
...
8258

∑Ri=23
...
24

∑XY=609
...
3

σm2= 22
...
57

Analysis: From the above table, it can be inferred that Maruti Suzuki’s returns is 50
...
08 and Beta is 1
...
84, Un systematic Risk
is 35
...

Calculations as under:
Return: = Ri = P1-Po
Po
Here:P1 = Closing Price, P0 = Opening Price
Stock
02-01-2012 = 1187
...
00*100 = 27
...
00

Sensex
17193
...
67*100 = 10
...
67

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 46

Optimal Portfolio Construction Using Sharpe Single Index Method

Average return 2012 = 50
...
18
12
Beta (β): = n∑xy-∑x∑y
n∑x2-(∑x)2
2012 = (12) (609
...
08) (-7
...
93
(12) (309
...
08)2

Systematic risk: βi2*variance of market
2012 = (1
...
07 = 82
...
57 – 82
...
72

2
...
68
3
...
75-0
...
637
...
16 0
...
427-1
...
608
0
...
69
5
...
396
1
...
34
...
580
...
62
5
...
330
...
It is evident from the graph that the overall trend of business has
exbhited by sensex closely resembles the returns exbhited by company expecting minor
fluctuations but the prices are low volatility
...
3 Table shows the MRF’ s returns, beta (β) and unsystematic risk:

Date

Opening
Price of
Stock

Return
on
Market

Return
on
Stock

X*Y

X2

(R-AR)2
Market

(R-AR)2
Stock

6964
...
1

02/01/2012

10
...
5471

144
...
03

76
...
178

01/02/2012

7900

9834
...
33

24
...
6921

11
...
99489

359
...
95

9936
...
75

0
...
1209

3
...
5094

29
...
15

11459
...
63

14
...
4599

0
...
55803

86
...
3

-6
...
7556

31
...
011

73
...
92

01/06/2012

10760

10033
...
47

-6
...
501

55
...
8395

151
...
55

-1
...
8028

5
...
3484

9
...
89

01/08/2012

9600

10067
...
79

4
...
85184

0
...
28304

0
...
2

10273
...
42

1
...
68889

55
...
2902

17
...
5

10169
...
48

-1
...
03448

2
...
6268

47
...
2

10915
...
60

7
...
5647

21
...
21057

3
...
8

0
...
4936

7
...
1881

2
...
98

∑Ri=23
...
43

∑XY=261
...
31

σm2=22
...
04

Analysis: From the above table, it can be inferred that MRF’s returns is 66
...
08 and Beta is 0
...
59, Un systematic Risk is
87
...


Calculations as under:

Return: = Ri = P1-Po
Po
Here: P1 = Closing Price, P0 = Opening Price
Stock
02-01-2012 = 7908
...
60*100 = 13
...
60

Sensex
17193
...
67*100 = 10
...
67

Average return 2012 = 66
...
53
DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 48

Optimal Portfolio Construction Using Sharpe Single Index Method

12
Beta (β): = n∑xy-∑x∑y
n∑x2-(∑x)2
2012 = (12) (261
...
08) (66
...
50
(12) (309
...
08)2

Systematic risk: βi2*variance of market
2012 = (0
...
08 = 5
...
04 – 5
...
45

2
...
7 3
...
8 -0
...
6 7
...
2 0
...
43 -1
...
61 0
...
5 24
...
07 14
...
8 -6
...
8 4
...
3 -1
...
5 17
...
It is evident
from the graph that the overall trend of business has exbhited by sensex closely resembles
the returns exbhited by company expecting major fluctuations but the prices are high
volatility
...
4 Table shows the Axis Bank’ s returns, beta (β) and unsystematic risk:

02/01/2012

812

Closing
Price
of
Stock
1074
...
05

3
...
68808

32
...
126

1
...
901

01/03/2012

1175

1145
...
75

-2
...
33984

3
...
5094

54
...
6

-0
...
438

2
...
4067

6
...
566

02/05/2012

1107

971
...
63

-12
...
173

44
...
2264

293
...
8

7
...
72165

35
...
898

30
...
0327

02/07/2012

1021

1042
...
16

2
...
468

1
...
51341

7
...
9

0
...
4073

-3
...
6248

1
...
673

03/09/2012

1001

1136
...
42

13
...
718

55
...
2902

74
...
65

-1
...
19454

-6
...
2101

11
...
5013

01/11/2012

1184

1316
...
60

11
...
5139

21
...
21057

39
...
5

0
...
62872

1
...
1881

2
...
6227

∑Ri=58
...
758

∑X2=309
...
1

Date

Opening
Price of
Stock

Return
on
Market
10
...
2906

∑Ri=23
...
818

114
...
657

750
...
8

Analysis: From the above table, it can be inferred that Axis Bank’s returns is 58
...
08 and Beta is 1
...
89, Un systematic Risk
is 28
...


Calculations as under:

Return: = Ri = P1-Po
Po
Here: P1 = Closing Price, P0 = Opening Price
Stock
02-01-2012 = 1074
...
00*100 = 32
...
00

Sensex
17193
...
67*100 = 10
...
67

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 50

Optimal Portfolio Construction Using Sharpe Single Index Method

Average return 2012 = 58
...
90
12
Beta (β): = n∑xy-∑x∑y
n∑x2-(∑x)2
2012 = (12) (641
...
08) (58
...
99
(12) (309
...
08)2

Systematic risk: βi2*variance of market
2012 = (1
...
08 = 87
...
80 – 87
...
90

2
...
683
...
75 -0
...
63 7
...
16 0
...
427 -1
...
6080
...
299
...
48 -3
...
2 4
...
125 -4
...
564
...
183
...
It is
evident from the graph that the overall trend of business has exbhited by sensex closely
resembles the returns exbhited by company expecting minor fluctuations but the prices
are low volatility
...
5 Table shows the State Bank of India’s returns, beta (β) and unsystematicrisk:

02/01/2012

1625
...
05

01/02/2012

2054

2243
...
33

9
...
7575

11
...
99489

30
...
75

-6
...
7559

3
...
5094

97
...
5

2137
...
63

1
...
2608

0
...
55803

3
...
5

2055
...
63

-3
...
6231

44
...
2264

52
...
15

7
...
71145

35
...
898

30
...
9947

02/07/2012

2165

2005
...
16

-7
...
57096

1
...
51341

123
...
85

1845

0
...
3844

-6
...
6248

1
...
375

03/09/2012

1850
...
9

7
...
9349

155
...
158

30
...
555

01/10/2012

2240

2109
...
48

-5
...
65437

2
...
6268

90
...
05

4
...
84597

13
...
238

7
...
75365

03/12/2012

2180

2383
...
43

9
...
05303

0
...
21867

31
...
56

∑XY=568
...
31

σm2=22
...
68

26
...
08

Return
on
Stock

X2

(R-AR)2
Market

286
...
03

76
...
801

X*Y

(R-AR)2
Stock

σ2=117
...
56, Market(Sensex) is 23
...
82, Systematic Risk is 73
...
91 are calculated below based on the above information
...
05 – 1625
...
81
1625
...
55 – 15534
...
67
15534
...
56 = 3
...
72) – (23
...
56) = 1
...
31) – (23
...
82)2 * 22
...
38

Unsystematic risk: total variance of security return-systematic risk
2012 = 117
...
38 = 43
...
2 Graph Showing 2012 of State Bank of India Returns:
2012 SBI
30
25
20
15
10
5
0
-5
-10
-15

SENSEX(x)
SBI (y)
1

2

3

4

5

6

7

8

9

10 11 12

INTERPRETATION: From the above graph it can be interpreted that the monthly
returns of a State Bank of India’s company selected against the monthly return of sensex
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 53

Optimal Portfolio Construction Using Sharpe Single Index Method

2
...
6

Closing
Price
of
Stock
329
...
5

01/03/2012

Date

Opening
Price of
Stock

Return
on
Market

Return
on
Stock

X2

X*Y

(R-AR)2
Market

(R-AR)2
Stock

10
...
7087

402
...
03

76
...
715

345
...
33

4
...
3995

11
...
99489

1
...
3

-1
...
46377

-11
...
0707

13
...
09613

02/04/2012

368
...
35

-0
...
8221

3
...
4067

6
...
468

02/05/2012

350
...
1

-6
...
7799

38
...
011

73
...
412

01/06/2012

327
...
15

7
...
63636

27
...
898

30
...
33711

02/07/2012

340
...
25

-1
...
89655

-8
...
3484

9
...
55179

01/08/2012

365

329
...
79

-9
...
6122

0
...
28304

249
...
2

7
...
4683

114
...
158

30
...
7609

01/10/2012

382

411
...
48

7
...
461

2
...
6268

2
...
7

442
...
60

7
...
1645

21
...
21057

1
...
2

0
...
08072

1
...
1881

2
...
29736

∑Ri=73
...
087

∑X2=309
...
1

∑Ri=23
...
23

Analysis: From the above table, it can be inferred that Yes Bank’s returns is 73
...
08 and Beta is 1
...
71, Un systematic Risk
is 68
...


Calculations as under:
Return: = Ri = P1-Po
Po
Here: P1 = Closing Price, P0 = Opening Price
Stock
02-01-2012 = 329
...
6*100 = 37
...
6

Sensex
17193
...
67*100 = 10
...
67

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 54

Optimal Portfolio Construction Using Sharpe Single Index Method

Average return 2012 = 73
...
15
12
Beta (β): = n∑xy-∑x∑y
n∑x2-(∑x)2
2012 = (12) (599
...
08) (73
...
72
(12) (309
...
08)2
Systematic risk: βi2*variance of market
2012 = (1
...
08 = 65
...
20 – 65
...
51

2
...
It is
evident from the graph that the overall trend of business has exbhited by sensex closely
resembles the returns exbhited by company expecting minor fluctuations but the prices
are low volatility
...
7 Table shows the ABB’ s returns, beta (β) and unsystematic risk:

02/01/2012

580

Closing
Price
of
Stock
816
...
25

3
...
3387

-1
...
126

1
...
2171

01/03/2012

815

841
...
75

3
...
7085

3
...
5094

1
...
4

-0
...
3059

2
...
4067

6
...
079

02/05/2012

818

734
...
63

-10
...
8816

44
...
2264

148
...
6

800
...
47

8
...
1631

55
...
8395

45
...
6

-1
...
1721

1
...
3484

9
...
7188

01/08/2012

797
...
35

0
...
346

-8
...
6248

1
...
08

03/09/2012

724

797
...
42

10
...
6531

55
...
2902

67
...
35

-1
...
4843

11
...
2101

11
...
92

01/11/2012

735
...
85

4
...
0795

-14
...
238

7
...
25

03/12/2012

718
...
4

0
...
5802

-1
...
1881

2
...
481

∑Ri=23
...
3452

∑XY=628
...
31

σm2=22
...
68

40
...
876

114
...
657

1503
...
6

Analysis: From the above table, it can be inferred that ABB’s returns is 23
...
08 and Beta is 2
...
12, Un systematic Risk
is 68
...


Calculations as under:
Return: = Ri = P1-Po
Po
Here: P1 = Closing Price, P0 = Opening Price
Stock
02-01-2012 = 816
...
00*100 = 40
...
00

Sensex
17193
...
67*100 = 10
...
67

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 56

Optimal Portfolio Construction Using Sharpe Single Index Method

Average return 2012 = 23
...
94
12
Beta (β): = n∑xy-∑x∑y
n∑x2-(∑x)2
2012 = (12) (628
...
08) (23
...
20
(12) (309
...
08)2

Systematic risk: βi2*variance of market
2012 = (2
...
08 = 107
...
60 – 107
...
48

2
...
It is evident
from the graph that the overall trend of business has exbhited by sensex closely resembles
the returns exbhited by company expecting minor fluctuations but the prices are low
volatility
...
8 Table shows the L&T’ s returns, beta (β) and unsystematic risk:

02/01/2012

1006
...
6

01/02/2012

1303

1308
...
33

0
...
30556

11
...
99489

17
...
85

-1
...
52692

-0
...
0707

13
...
193

02/04/2012

1308
...
3

-0
...
3035

4
...
4067

6
...
82

02/05/2012

1223
...
3

-6
...
1495

27
...
011

73
...
697

01/06/2012

1168

1397
...
47

19
...
81

55
...
8395

227
...
65

-1
...
1679

2
...
3484

9
...
143

01/08/2012

1367
...
4

0
...
9301

-1
...
6248

1
...
004

03/09/2012

1354

1596
...
42

17
...
151

55
...
2902

178
...
75

-1
...
05716

-3
...
2101

11
...
2191

01/11/2012

1630

1667
...
60

2
...
4891

21
...
21057

5
...
85

0
...
8413

-1
...
1881

2
...
43

∑Ri=23
...
6116

∑XY=641
...
31

σm2=22
...
68

30
...
362

114
...
657

657
...
64

Analysis: From the above table, it can be inferred that L&T’s returns is 54
...
08 and Beta is 2
...
36, Un systematic Risk
is 31
...


Calculations as under:
Return: = Ri = P1-Po
Po
Here: P1 = Closing Price, P0 = Opening Price
Stock
02-01-2012 = 1310
...
70*100 = 30
...
70

Sensex
17193
...
67*100 = 10
...
67

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 58

Optimal Portfolio Construction Using Sharpe Single Index Method

Average return 2012 = 54
...
55
12
Beta (β): = n∑xy-∑x∑y
n∑x2-(∑x)2
2012 = (12) (641
...
08) (54
...
02
(12) (309
...
08)2

Systematic risk: βi2*variance of market
2012 = (2
...
08 = 90
...
64 – 90
...
28

2
...
It is evident
from the graph that the overall trend of business has exbhited by sensex closely resembles
the returns exbhited by company expecting major fluctuations but the prices are low
volatility
...
9 Table shows the Reliance Infrastucture’s returns, beta (β) and unsystematic
risk:

02/01/2012

341

Closing
Price
of
Stock
535
...
35

3
...
679702

35
...
126

1
...
903

01/03/2012

596
...
9

-1
...
6753225

2
...
0707

13
...
981

02/04/2012

590

527
...
63

-10
...
78772

0
...
55803

245
...
25

-6
...
238095

94
...
011

73
...
32

01/06/2012

451
...
35

7
...
7203634

177
...
898

30
...
27

02/07/2012

562
...
45

-1
...
275556

14
...
3484

9
...
53

01/08/2012

494
...
65

0
...
1524396

-7
...
6248

1
...
18

03/09/2012

448
...
7

7
...
1114827

149
...
158

30
...
41

01/10/2012

537
...
25

-1
...
681429

18
...
2101

11
...
75

01/11/2012

472
...
35

4
...
68697768

12
...
238

7
...
4966

03/12/2012

488

520
...
43

6
...
90136

0
...
21867

2
...
08

∑Ri=60
...
31

σm2=22
...
68

57
...
338

114
...
657

2716
...
01

(R-AR)2
Stock

σ2=400
...
37, Market(Sensex) is 23
...
78, Systematic Risk is 315
...
11 are calculated below based on the above information
...
9 – 341
...
15
341
...
55 – 15534
...
67
15534
...
37 = 5
...
08) (60
...
78
(12) (309
...
08)2

Systematic risk: βi2*variance of market
2012 = (3
...
08 = 315
...
85 – 315
...
11

2
...
It is evident from the graph that the overall trend of business has exbhited by
sensex closely resembles the returns exbhited by company expecting minor fluctuations
but the prices are low volatility
...
10 Table shows the TCS’ s returns, beta (β) and unsystematic risk:
Date

Opening
Price of
Stock

Return
on
Market

1155
...
5

02/01/2012

Return
on
Stock

10
...
1339

01/02/2012

1130

1221
...
33

01/03/2012

1221
...
85

02/04/2012

1172
...
787

114
...
657

8
...
05752

26
...
126

1
...
677

-1
...
3569

7
...
0707

13
...
59

1244
...
63

6
...
9377

0
...
55803

28
...
8

-6
...
0962

0
...
011

73
...
8025

01/06/2012

1235

1277
...
47

3
...
7591

55
...
8395

6
...
65

-1
...
9225

3
...
3484

9
...
854

01/08/2012

1240

1347
...
79

8
...
84001

0
...
28304

61
...
3

1294

7
...
9561

-29
...
158

30
...
616

01/10/2012

1298

1313
...
48

1
...
7638

2
...
6268

0
...
85

4
...
1635

-0
...
238

7
...
9276

03/12/2012

1315

1258
...
43

-4
...
8616

0
...
21867

25
...
59544

∑XY=10
...
31

σm2=22
...
08

X*Y

(R-AR)2
Stock

σ2=20
...
59,
Market(Sensex) is 23
...
02, Systematic Risk is 0
...
80 are calculated below based on the above information
...
5 – 1155
...
13
1155
...
55 – 15534
...
67
15534
...
59 = 0
...
65) – (23
...
59) = -0
...
31) – (23
...
02)2 * 22
...
01

Unsystematic risk: total variance of security return-systematic risk
2012 = 20
...
01 = 20
...
10 Graph Showing 2012 of TCS Returns:
2012 TCS
15
10
5

SENSEX(x)

0

TCS(y)
1

2

3

4

5

6

7

8

9

10

11

12

-5
-10

INTERPRETATION: From the above graph it can be interpreted that the monthly
returns of a TCS’s company selected against the monthly return of sensex
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 63

Optimal Portfolio Construction Using Sharpe Single Index Method

2
...
7

01/02/2012

655
...
68

13
...
342

114
...
657

78
...
2

3
...
4782

-28
...
126

1
...
46

599
...
65

-1
...
1319

-35
...
0707

13
...
67

02/04/2012

730

700
...
63

-4
...
60321

0
...
55803

69
...
65

-6
...
3295

28
...
011

73
...
914

01/06/2012

666
...
95

7
...
21905

46
...
898

30
...
8074

02/07/2012

709
...
9

-1
...
33827

-0
...
3484

9
...
441

01/08/2012

717

797
...
79

11
...
92435

0
...
28304

49
...
8

7
...
1721

157
...
158

30
...
75

01/10/2012

972

947
...
48

-2
...
7166

2
...
6268

45
...
4

4
...
8143

-31
...
238

7
...
81

03/12/2012

886

931
...
43

5
...
22208

0
...
21867

0
...
21

∑XY=294
...
31

σm2=22
...
08

σ2=96
...
21,
Market(Sensex) is 23
...
74, Systematic Risk is 12
...
55 are calculated below based on the above information
...
7 – 576
...
14
576
...
55 – 15534
...
67
15534
...
21 = 4
...
91) – (23
...
21) = 0
...
31) – (23
...
74)2 * 22
...
13

Unsystematic risk: total variance of security return-systematic risk
2012 = 96
...
13 = 84
...
11 Graph Showing 2012 of Tech Mahindra Returns:

2012 TEC MAHINDRA
25
20
15

SENSEX(x)

10
5

TECH MAHINDRA
(y)

0
-5

1

2

3

4

5

6

7

8

9 10 11 12

-10

INTERPRETATION: From the above graph it can be interpreted that the monthly
returns of a Tech Mahindra’s company selected against the monthly return of sensex
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 65

Optimal Portfolio Construction Using Sharpe Single Index Method

2
...
25

01/02/2012

412
...
75

3
...
65398

15
...
126

1
...
5388

01/03/2012

425

439

-1
...
29412

-5
...
0707

13
...
0623

02/04/2012

439
...
1

-0
...
9109

5
...
4067

6
...
5274

02/05/2012

406

409
...
63

0
...
8007

44
...
2264

0
...
3

7
...
6098

-19
...
898

30
...
46251

02/07/2012

401
...
9

-1
...
427

17
...
3484

9
...
763

01/08/2012

343
...
6

0
...
04718

5
...
6248

1
...
958

03/09/2012

368

381
...
42

3
...
8415

55
...
2902

12
...
8

-1
...
6842

11
...
2101

11
...
937

01/11/2012

351

392
...
60

11
...
0778

21
...
21057

139
...
35

0
...
08883

0
...
1881

2
...
0011

∑Ri=1
...
48

∑X2=309
...
1

Date

Opening
Price of
Stock

Return
on
Market
10
...
57143

∑Ri=23
...
1378

114
...
657

11
...
48

Analysis: From the above table, it can be inferred that Wipro’s returns is 1
...
08 and Beta is 0
...
31, Un systematic Risk is
45
...


Calculations as under:
Return: = Ri = P1-Po
Po
Here: P1 = Closing Price, P0 = Opening Price
Stock
02-01-2012 = 413
...
00*100 = 3
...
00

Sensex
17193
...
67*100 = 10
...
67

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 66

Optimal Portfolio Construction Using Sharpe Single Index Method

Average return 2012 = 1
...
12
12
Beta (β): = n∑xy-∑x∑y
n∑x2-(∑x)2
2012 = (12) (144
...
08) (1
...
53
(12) (309
...
08)2
Systematic risk: βi2*variance of market
2012 = (0
...
08 = 6
...
48 – 6
...
17

2
...
It is evident
from the graph that the overall trend of business has exbhited by sensex closely resembles
the returns exbhited by company expecting major fluctuations but the prices are low
volatility
...
13 Table shows the Cipla’ s returns, beta (β) and unsystematic risk:

02/01/2012

320
...
15

01/02/2012

351

01/03/2012

Date

Opening
Price of
Stock

Return
on
Market

Return
on
Stock

X2

X*Y

(R-AR)2
Market

(R-AR)2
Stock

10
...
0242

96
...
03

76
...
929

316
...
33

-9
...
5

11
...
99489

130
...
55

-1
...
2296

7
...
0707

13
...
93

02/04/2012

305

311
...
63

2
...
4322

0
...
55803

0
...
65

-6
...
7532

4
...
011

73
...
9233

01/06/2012

310
...
4

7
...
0316

15
...
898

30
...
1232

02/07/2012

316

338
...
16

7
...
2865

1
...
51341

29
...
15

0
...
04167

3
...
6248

1
...
297

03/09/2012

378

380
...
42

0
...
1084

55
...
2902

0
...
4

363
...
48

-4
...
23025

2
...
6268

34
...
9

414

4
...
1457

60
...
238

7
...
45

03/12/2012

415
...
1

0
...
2289

-0
...
1881

2
...
646

∑Ri=20
...
549

∑X2=309
...
1

∑Ri=23
...
45

Analysis: From the above table, it can be inferred that Cipla’s Ltd returns is 20
...
08 and Beta is 0
...
43, Un systematic Risk is
32
...


Calculations as under:

Return: = Ri = P1-Po
Po
Here: P1 = Closing Price, P0 = Opening Price
Stock
02-01-2012 = 349
...
25*100 = 9
...
25

Sensex
17193
...
67*100 = 10
...
67

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 68

Optimal Portfolio Construction Using Sharpe Single Index Method

Average return 2012 = 20
...
68
12
Beta (β): = n∑xy-∑x∑y
n∑x2-(∑x)2
2012 = (12) (157
...
08) (20
...
44
(12) (309
...
08)2

Systematic risk: βi2*variance of market
2012 = (0
...
08 = 4
...
44 – 4
...
00

2
...
It is evident
from the graph that the overall trend of business has exbhited by sensex closely resembles
the returns exbhited by company expecting major fluctuations but the prices are low
volatility
...
14 Table shows the Glenmark’ s returns, beta (β) and unsystematic risk:
Date

Opening
Price of
Stock

Closing
Price of
Stock

Return
on
Market

Return
on
Stock

X*Y

X2

(R-AR)2
Market

(R-AR)2
Stock

02/01/2012

292
...
8

10
...
284

13
...
03

76
...
726

01/02/2012

300

308
...
33

2
...
117

11
...
99489

4
...
65

-1
...
758

1
...
0707

13
...
466

02/04/2012

309
...
15

-0
...
5983

-2
...
4067

6
...
0641

02/05/2012

325

356
...
63

9
...
71

44
...
2264

24
...
1

362
...
47

2
...
69

55
...
8395

7
...
4

384
...
16

5
...
149

1
...
51341

0
...
95

441
...
79

14
...
43

0
...
28304

92
...
9

7
...
404

-40
...
158

30
...
16

01/10/2012

422

426
...
48

1
...
726

2
...
6268

13
...
60

2
...
713

21
...
21057

7
...
6

527
...
43

20
...
058

0
...
21867

257
...
08

∑Ri=58
...
6

∑X2=309
...
1

σ2=46
...
21,
Market(Sensex) is 23
...
59, Systematic Risk is 7
...
56 are calculated below based on the above information
...
8 – 292
...
28
292
...
55 – 15534
...
67
15534
...
21 = 4
...
6) – (23
...
21) = -0
...
31) – (23
...
59)2 * 22
...
80

Unsystematic risk: total variance of security return-systematic risk
2012 = 46
...
80 = 38
...
12 Graph Showing 2012 of Glenmark Returns:

2012 GLENMARK
25
20
15
10

SENSEX(x)

5

GLENMARK (y)

0
-5

1

2

3

4

5

6

7

8

9 10 11 12

-10

INTERPRETATION: From the above graph it can be interpreted that the monthly
returns of a Glenmark’s company selected against the monthly return of sensex
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 71

Optimal Portfolio Construction Using Sharpe Single Index Method

2
...
45

453
...
68

10
...
8

467
...
33

01/03/2012

475

474
...
649

114
...
657

82
...
375

-14
...
126

1
...
585

-1
...
60505

-16
...
0707

13
...
348

443
...
63

7
...
6267

0
...
55803

29
...
25

429
...
63

1
...
821

44
...
2264

0
...
9

460
...
47

-5
...
882

55
...
8395

49
...
6

449
...
16

0
...
7045

1
...
51341

1
...
4

490
...
79

10
...
63619

0
...
28304

82
...
15

7
...
5856

-34
...
158

30
...
245

01/10/2012

563

579
...
48

-0
...
67575

2
...
6268

5
...
45

4
...
1429

-19
...
238

7
...
755

03/12/2012

579

598
...
43

-0
...
0646

0
...
21867

3
...
04

∑Ri=-13
...
3

σm2=22
...
08

X*Y

(R-AR)2
Stock

σ2=35
...
04,
Market(Sensex) is 23
...
21, Systematic Risk is 0
...
89 are calculated below based on the above information
...
15 – 517
...
92
517
...
55 – 15534
...
67
15534
...
03 = 1
...
71) – (23
...
03) = -0
...
31) – (23
...
21)2 * 22
...
98

Unsystematic risk: total variance of security return-systematic risk
2012 = 35
...
98 = 34
...
15 Graph Showing 2012 of Ranbaxy Returns:

2012 RANBAXY
15
10
5

SENSEX(x)

0

RANBAXY(y)
1

2

3

4

5

6

7

8

9 10 11 12

-5
-10

INTERPRETATION: From the above graph it can be interpreted that the monthly
returns of a Ranbaxy’s company selected against the monthly return of sensex
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 73

Optimal Portfolio Construction Using Sharpe Single Index Method

 2012

Ri

βi

Var
...
7329

0
...
7593

14
...
7527

Maruti Suzuki

50
...
9372

118
...
8481

35
...
4315

0
...
0458

5
...
451

Axis Bank

58
...
9953

116
...
8966

28
...
5692

1
...
2969

73
...
9116

Yes Bank

73
...
7252

134
...
7141

68
...
3451

2
...
6084

107
...
482

L&T

54
...
0231

121
...
3629

31
...
3776

3
...
8519

315
...
11

TCS

9
...
0294

20
...
0191

20
...
2136

0
...
6824

12
...
5465

Wipro

1
...
5347

51
...
3132

45
...


20
...
4482

36
...
4367

32
...
2167

-0
...
3619

7
...
5527

Ranbaxy

22
...
2117

35
...
9898

34
...

β = Expected change in the rate of return on stock i associated with a 1% change
in the market return
...
Above all data are calculated on the basis of prices of each security from
1st January 2012 to 31st December 2012
...
Cov
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 74

Optimal Portfolio Construction Using Sharpe Single Index Method

Step-1 Ranking the securities:

Company

Ri

βi

Unsys
...
7329

0
...
7527

28
...
2471

1
...
7234

22
...
4315

0
...
451

118
...
8309

1
...
9076

25
...
5692

1
...
9116

20
...
8447

1
...
5198

38
...
3451

2
...
482

7
...
6115

2
...
2823

23
...
3776

3
...
11

14
...
5954

-0
...
7915

-88
...
2136

0
...
5465

59
...
464

0
...
174

-10
...


20
...
4482

32
...
3771

4

Glenmark

58
...
5947

38
...
122

14

Ranbaxy

22
...
2117

34
...
043

13

As seen above table here Excess returns to beta ratio are already ranked from highest to
lowest
...

Here we have to find out cut-off rate, which helps in selecting securities in our optimum
portfolio
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 75

Optimal Portfolio Construction Using Sharpe Single Index Method

Step – 2 Establishing Cutoff Rate:

Company

RRR=

(Ri - Rf)*βi)/

Σ((Ri -

σ 2

(Ri – Rf)/βi

e

(βi2 / σ2)

σ 2

Rf)*βi)/ e

Σ (βi2 /

C

2

σ)

MRF

118
...
3421

0
...
0029

0
...
0987

Tec Mahindra

59
...
3877

0
...
0065

0
...
344

Yes Bank

38
...
683

2
...
0434

0
...
588

Cipla Ltd
...
377

0
...
5972

0
...
0591

24
...
5409

0
...
2058

0
...
0804

25
...
9764

3
...
7833

0
...
2182

25
...
5339

3
...
8625

0
...
349

25
...
3245

2
...
208

0
...
454

24
...
6073

1
...
767

0
...
5297

23
...
1147

2
...
139

0
...
6978

21
...
4204

0
...
665

0
...
7686

20
...
3534

-0
...
599

0
...
7749

20
...
0429

-0
...
508

0
...
7762

20
...
1219

-0
...
718

0
...
7854

18
...
2789

-0
...
714

4E-05

0
...
916

All securities, whose excess return-to-beta ratio is above the cut-off rate, are selected and
all whose ratios are below are rejected
...
So here first 5
companies are those whose excess returns to beta ratio are more than Ci
...
e
...
So the cut-off rate will be (C*) =
25
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 76

Optimal Portfolio Construction Using Sharpe Single Index Method

Calculations for Weights using cut – off rate:

Company

Z = (rrr – scl)β

Weights

σe2
MRF

(118
...
7478)0
...
5313

0
...
2971

0
...
3272

0
...
0507

0
...
0749

0
...
016

0
...
2972

1

87
...
6352-25
...
7414
84
...
746-25
...
725
68
...


(29
...
748)0
...
451

Bajaj Auto

(28
...
748)0
...
451

Axis Bank

(25
...
748)1
...
9

2
...
43

0
...
203

Tec Mahindra

51
...
229

11
...
845

0
...
624

Cipla Ltd
...
167

Bajaj Auto

29
...
831

0
...
0577
0
...
7865
1
...
7236
Erp= 60
...
14 Graph Shows the Investment Criteria in the year 2012:

Percentage of returns
1%
4%

6%
MRF
41%

TEC MAHINDRA
YES BANK

25%

CIPLA LTD
...
Further we invest 41% in MRF, 25% in YES Bank, 23% in Tec Mahindra, 6% in
Bajaj auto,4% in cipla Ltd and 1% in Axis Bank
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 78

Optimal Portfolio Construction Using Sharpe Single Index Method

C
...

 Along with the Sharpe’s Single index model it is wise for investors to make a
technical and fundamental analysis of the companies before investing in the
particular company during the period 2010,2011 & 2012
...


 Auto, IT and Banking segment though contineous to be major contributors during
the period 2011 and 2012, but in 2010 Bajaj auto’s only the major contributor
during the period
...


 In 2010- Bajaj auto, Glenmark and TCS’s having less risk( Beta’s 0
...
49 and
0
...
23,0
...
34,0
...
41 respectivly) and in the year 2012Cipla Ltd, MRF and Wipro having less risk(0
...
5 and 0
...


 The most volatility stock is Reliance infra in(3
...
38) and Tech Mahindra in the year 2010(1
...


 In the year 2012 TCS, Glenmark and Ranbaxy having a negative beta(β) compare
to any other stocks
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 79

Optimal Portfolio Construction Using Sharpe Single Index Method

D
...

 MRF having less risk in 2011 & 2012, but TCS having less risk in 2010 while the
investor can invest in these stocks, he can expect much return with the less risk
...
In 2011 only a Bajaj auto giving much return but its not
a porfolio and In 2010 the portfolio is to Bajaj auto,TCS and Axis bank
...

 By the portfolio construction the investor can minimizing the risk and get the high
returns and if the risk is heavy he can manage among them by using these
portfolio construction
...

 Sharpe single index model will helps the investor to construct the portfolio which
will give the optimal return for the given level of risk
...
CONCLUSIONS:
Each individual stock will have its own risk and return characters when combined
in a portfolio overall return from the portfolio will be weighted average returns were as
risk from the portfolio will not weighted average risk because when we consider a pair
off securities one security in a pair may act against another security and this reduce the
risk content
...
However, even now despite the fact
that Markowits Model is vert employed
...

In other words, a portfolio may be give better returns for the same return
...
F
...
Sharpe’s Single Index
portfolio optimization is a considerable improvement over Markowits Model, is these
may give the weighted average return but of selected stocks at desired combination
levels
...
These project as try to apply Sharpe Index Model of portfolio
construction and optimization for randomly picked companies 5 sectors 3 companies
each
...
Annexure

Sharekhan Ltd
...
10

28
...
22

Personal Expenses

2
...
04

1
...
00

0
...
12

Administrative Expenses

1
...
24

0
...
65

3
...
64

Operating Profit

35
...
49

18
...
00

30
...
6

Adjust PBDIT

31
...
81

19
...
50

2
...
54

Adjusted PAT

28
...
31

17
...
5

27
...
47

Earning Before Appreciation

0
...
17

0
...
17

0
...
06

Income
Operating Income
Expenses

Sharekhan Ltd
...
40

31
...
62

Reserves and Surplus

29
...
49

20
...
15

1
...
37

Total

63
...
02

53
...
12

5
...
47

Less: Accumulated Depreciation

4
...
04

3
...
62

1
...
71

Investments

50
...
01

40
...
05

18
...
91

Less: Current Liabilities & Provisions

7
...
03

4
...
12

59
...
89

Book value of unquoted investment

40
...
02

40
...
16

0
...
16

Contingent liabilities

3
...
5

3
...
2

316
...
22

Net Current Assets

Miscellaneous Expenses not written
Total

Note:

Number of equity shares outstanding lakhs

DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 83

Optimal Portfolio Construction Using Sharpe Single Index Method

G
...

Prasanna Chandra, Investment Analysis and Portfolio Management,5th edition
...
yahoofinance
...
economics
...
sharekhan
...
bse
...


DEPARTMENT OF MANAGEMENT STUDIES, SVIT

Page 84



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