A STUDY ON

PORTFOLIO MANAGEMENT USING MARKOWITZ THEORY

AT
INDIA INFOLINE
BY
S.Suresh
H.T.NO: 098-06-0102
PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT
FOR
The Award of
MASTER OF BUSINESS ADMINISTRATION
Under the guidance of
(MR.V.VISHNU PRASAD)

(Affiliated to Osmania University)

IBRAHIMPATNAM, R.R.Dist-501 506,
HYDERABAD, AP.
(2006-2008)

CERTIFICATE

This Is To Certify That The Project Report Titled Portfolio Management Using Markowitz
Theory At Indian Info Line Ltd. Submitted In Partially Fulfillment For The Award Of Master Of
Business Administration Lokamanya Tilak P.G. College Was Carried Out By N.Prasanna Under
My Guidance .This Has Not Been Submitted To Any Other University Or Institution For The
Award Of Any Degree.

Name And Address Of The Supervisor

V.Vishnu Prasad
H.NO 17-1-388/43
Venture 1.
Laxmi nagar ,saidabad colony
Hyderabad.

Signature Of The SuperVisor

ACKNOWLEDEGEMENT

I have received generous help from number of customers to

carry on my research without their co-operation and encouragement I
could not have completed my work pleasure I Acknowledgement by
debt to them.
I profusely thanks to PRINCIPLE Dr. NISAR AHMED Lokamanya
Tilak P.G. College, Sitarampet, Ibramhimpatnam For his and help.
It is not on exaggeration in placing the name of Mrs V. VISHNU
PRASAD Who welcomed me and gave me her guidance whose can
stand works and advice has worked in the development in this project.
I am also thank to other Faculty Members in the department HOD
Dr. Shankar Reddyfor their support completing the work.
I am thankfull to Mr. B.RAMMURTHY (ASST.Manager) for giving
me these opportunities to do the project in this Organization as well as
total support for completing the project work.
I wish to thanks to my parents through whom I got full support
doing the project and my Friends for their kind help assistance in
completing the project successfully.

DECLARATION

I hereby declare that this Project Report titled PORTFOLIO

MANAGEMENT USING MARKOWITZ THEORY .AT INDIAN INFOLINE

LTD.submitted by me to the Department of Business Management,

LOKAMANYATILAK P.G COLLEGE is a bonafide work undertaken by
me and it is not submitted to any other University or Institution for the
award of any degree diploma / certificate or published any time before.

NAME OF THE STUDENT

SIGNATURE OF THE STUDENT

N.PRASANNA,
VANASTHALI PURAM
Hyderabad.

(N.PRASANNA)

CONTENTS

LIST OF TABLES
LIST OF FIGURES
INTRODUCTION
Objectives
Research designing
i)
ii)
iii)
iv)
v)

sample size
methodology
data collections
research tools
scope of study

Limitations
INDUSTRIAL PROFILE:
COMPANY PROFILE
DATA ANALYSY AND INTERPRETATION
FINDINGS
SUGESSIONS
CONCLUSIONS
BIBLIOGRAPHY

INTRODUCTION:

INTRODUCTION:
The financial market is the driver of the economic growth and development of any
country. A sound financial market can take the country to the apex. Financial resources
were by allocating the resources through one of the ways such as portfolios, which are
combinations of various securities. Portfolio analysis includes analyzing the range of
possible portfolios that can be constituted from a given set of securities.
A combination of securities with different risk- return characteristics will constitute the
portfolio of the investor. A portfolio is a combination of various assets and/or instruments
of investments. The portfolio is also built up out of the wealth or income of the investor
over a period of time with a view to suit his risk and return preferences to that of the
portfolio that he holds. The portfolio analysis is an analysis of the risk-return
characteristics of individual securities in the portfolio and changes that may take place in
combination with other securities due to interactions among themselves and impact of
each one of them on others.
As individuals are becoming more and more responsible for ensuring their own
financial future, portfolio or fund management has taken on an increasingly important
role in banks ranges of offerings to their clients. In addition, as interest rates have come
down and the stock market has gone up and come down again, clients have a choice of
leaving their saving in deposit accounts, or putting those savings in unit trusts or
investment portfolios which invest in equities and/or
bonds. Investing in unit trusts or mutual funds is one way for individuals and corporations
alike to potentially enhance the returns on their savings.

Objectives of the study:

To study the investment pattern and its related risks & returns.
To find out optimal portfolio, that give optimal return at a minimized risk to
the investor.
To check whether the selected portfolios are yielding a satisfactory and
constant return to the investor over a period of time.

RESEARCH DESIGN:
SAMPLE SIZE:
I have taken a sampling size 10 companies 5 different sectors the sampling
consists the following .

Company name
CEMENT
GACL,LNT
PHARMACEUTICAL
RANBAXY, CIPLA
TELECOME
MTNL, BHARATH AIRTEL
BANKING ,
INGVYSYA,ICICI
IT

WIPRO, STYAM
RESEARCH METHODOLOGY:
Research design or research methodology is the procedure of collecting, analyzing and
interpreting the data to diagnose the problem and react to the opportunity in such a way
where the costs can be minimized and the desired level of accuracy can be achieved to
arrive at a particular conclusion.
The methodology used in the study for the completion of the project and the fulfillment of
the project objectives, is as follows:

Market prices of the companies have been taken for the years of different dates,
there by dividing the companies into 5 sectors.

A final portfolio is made at the end of the year to know the changes
(increase/decrease) in the portfolio at the end of the year.

DATA COLLECTIONS :
Primary data:
The primary data information is gathered from INDIA INFOLINE by interviewing INDIA
INFOLINE executives.
Secondary data:
The secondary data is collected from various financial books, magazines and from stock
lists of various newspapers and INDIA INFOLINE as part of the training class undertaken
for project
RESEARCH TOOLS
FORMULAS :
Standard deviations :
Variance = 1/n-1 (d2)
Standard Deviation = Variance
Correlation Of co-efficient:
Covariance (COVab) = 1/(n-1) (dx.dy)

Correlation of coefficient = COVab / a* b

WEIGHTS:

Wa =

(b)2 - rab (a) (b)

(a)2 + (b)2 2rab (a) (b)

RISK:
P
=
RETURNS:
Rp = W1R1 + W2R2

a2*(Xa) 2 + b2*(Xb) 2 + 2rab*a*b*Xa*Xb

SCOPE OF STUDY:
The study covers the calculation of correlations between the different securities in order to find
out at what percentage funds should be invested among the companies in the portfolio. Also the study
includes the calculation of individual Standard Deviation of securities and ends at the calculation of
weights of individual securities involved in the portfolio. These percentages help in allocating the funds
available for investment based on risky portfolios.

Limitations of the study:

This study has been conducted purely to understand Portfolio Management for
investors.
Construction of Portfolio is restricted to two companies based on Markowitz
model.
Very few and randomly selected scrips / companies are analyzed from BSE
listings.
Detailed study of the topic was not possible due to limited size of the project.
There was a constraint with regard to time allocation for the research study i.e.
for a period of 45 days.

INDUSTRY PROFILE

INDUSTRY PROFILE:

Bombay Stock Exchange Limited is the oldest stock exchange in Asia with a rich
heritage. Popularly known as "BSE", it was established as "The Native Share &
Stock Brokers Association" in 1875. BSE has played a pioneering role in the
Indian Securities Market - one of the oldest in the world. Much before actual
legislations were enacted, BSE had formulated comprehensive set of Rules and
Regulations for the Indian Capital Markets. It also laid down best practices
adopted by the Indian Capital Markets after India gained its Independence.
BSE is the first stock exchange in the country to obtain permanent recognition in
1956 from the Government of India under the Securities Contracts (Regulation) Act,
1956. The base year of SENSEX is 1978-79. From September 2003, the SENSEX is
calculated on a free-float market capitalization methodology. The "free-float Market
Capitalization-Weighted" methodology is a widely followed index construction
methodology on which majority of global equity benchmarks are based.
The Exchange has a nation-wide reach with a presence in 417 cities and towns of India.
The systems and processes of the Exchange are designed to safeguard market integrity
and enhance transparency in operations. During the year 2004-2005, the trading volumes
on the Exchange showed robust growth.
The Exchange is professionally managed under the overall direction of the Board
of Directors. The Board comprises eminent professionals, representatives of
Trading Members and the Managing Director of the Exchange. The Board is

inclusive and is designed to benefit from the participation of market

intermediaries.

NATIONAL STOCK EXCHANGE OF INDIA LIMITED

The National Stock Exchange of India Limited has genesis in the report of the High
Powered Study Group on Establishment of New Stock Exchanges, which recommended
promotion of a National Stock Exchange by financial institutions (FIs) to provide access
to investors from all across the country on an equal footing. Based on the
recommendations, NSE was promoted by leading Financial Institutions at the behest of
the Government of India and was incorporated in November 1992 as a tax-paying
company

unlike

other

stock

exchanges

in

the

country.

On its recognition as a stock exchange under the Securities Contracts (Regulation) Act,
1956 in April 1993, NSE commenced operations in the Wholesale Debt Market (WDM)
segment in June 1994. The Capital Market (Equities) segment commenced operations in
November 1994 and operations in Derivatives segment commenced in June 2000.
The national stock exchange of India ltd is the largest stock exchange of the
country. NSE is setting the agenda for change in the securities markets in India.
For last 5 years it has played a major role in bringing investors from 347 cities
and towns online, ensuring complete transparency, introducing financial
guarantee to settlements, ensuring scientifically designed and professionally
managed indices and by nurturing the dematerialization effort across the
country.NSE is a complete capital market prime mover. Its wholly owned
subsidiaries, National securities cleaning corporation ltd (NSCCL) provides
cleaning and settlement of securities, India index services and products ltd (IISL)
provides indices and index services with a consulting and licensing agreement

with Standard & Poors (S&P), and IT ltd forms the technology strength that NSE
works on.

COMPANY PROFILE

COMPANY PROFILEL:
About Us
We are a one-stop financial services shop, most respected for quality of its advice,
personalized service and cutting-edge technology.
India Infoline Group
The India Infoline group, comprising the holding company, India Infoline Limited and its
wholly-owned subsidiaries, straddle the entire financial services space with offerings
ranging from Equity research, Equities and derivatives trading, Commodities trading,
Portfolio Management Services, Mutual Funds, Life Insurance, Fixed deposits, GoI
bonds and other small savings instruments to loan products and Investment banking.
India Infoline also owns and manages the websites www.indiainfoline.com and
www.5paisa.com
The company has a network of 596 branches spread across 345 cities and towns. It has
more than 500,000 customers.
India Infoline Ltd
India Infoline Limited is listed on both the leading stock exchanges in India, viz. the
Stock Exchange, Mumbai (BSE) and the National Stock Exchange (NSE) and is also a
member of both the exchanges. It is engaged in the businesses of Equities broking,
Wealth Advisory Services and Portfolio Management Services. It offers broking services
in the Cash and Derivatives segments of the NSE as well as the Cash segment of the
BSE. It is registered with NSDL as well as CDSL as a depository participant, providing a
one-stop solution for clients trading in the equities market. It has recently launched its
Investment banking and Institutional Broking business.
A SEBI authorized Portfolio Manager; it offers Portfolio Management Services to clients.
These services are offered to clients as different schemes, which are based on differing
investment strategies made to reflect the varied risk-return preferences of clients.

India Info line Media and Research Services Limited.

India Infoline Marketing & Services
India Infoline Marketing and Services Limited is the holding company of India Infoline
Insurance Services Limited and India Infoline Insurance Brokers Limited.
(a) India Infoline Insurance Services Limited is a registered Corporate Agent with the
Insurance Regulatory and Development Authority (IRDA). It is the largest Corporate
Agent for ICICI Prudential Life Insurance Co Limited, which is India's largest private Life
Insurance Company. India Infoline was the first corporate agent to get licensed by IRDA
in early 2001.
(b) India Infoline Insurance Brokers Limited India Infoline Insurance Brokers Limited is a
newly formed subsidiary which will carry out the business of Insurance broking. We have
applied to IRDA for the insurance broking licence and the clearance for the same is
awaited. Post the grant of license, we propose to also commence the general insurance
distribution business.

The Board of Directors

Apart from Nirmal Jain and R Venkataraman, the Board of Directors of India Infoline
comprises:
Mr Sat Pal Khattar (Non Executive Director)
Mr Nilesh Vikamsey (Independent Director)
Mr Kranti Sinha (Independent Director)

DATA ANALYSIS AND INTERPRETATION

INTRODUCTION
A portfolio is a collection of investments held by an institution or a private individual. In
building up an investment portfolio a financial institution will typically conduct its own
investment analysis, whilst a private individual may make use of the services of a
financial advisor or a financial institution which offers portfolio management services.
Holding a portfolio is part of an investment and risk-limiting strategy called diversification.
By owning several assets, certain types of risk (in particular specific risk) can be
reduced. The assets in the portfolio could include stocks, bonds, options, warrants, gold
certificates, real estate, futures contracts, production facilities, or any other item that is
expected to retain its value.
Portfolio management involves deciding what assets to include in the portfolio,
given the goals of the portfolio owner and changing economic conditions. Selection
involves deciding what assets to purchase, how many to purchase, when to purchase
them, and what assets to divest. These decisions always involve some sort of
performance measurement, most typically expected return on the portfolio, and the risk
associated with this return (i.e. the standard deviation of the return). Typically the
expected returns from portfolios, comprised of different asset bundles are compared.
The unique goals and circumstances of the investor must also be considered. Some
investors are more risk averse than others. Mutual funds have developed particular
techniques to optimize their portfolio holdings.

Thus, portfolio management is all about strengths, weaknesses, opportunities and

threats in the choice of debt vs. equity, domestic vs. international, growth vs. safety
and numerous other trade-offs encountered in the attempt to maximize return at a
given appetite for risk.

OBJECTIVES OF PORTFOLIO MANAGEMENT:

The basic objective of Portfolio Management is to maximize yield and minimize risk. The
other ancillary objectives are as per needs of investors, namely:
Regular income or stable return
Appreciation of capital
Marketability and liquidity
Safety of investment
Minimizing of tax liability.

TYPES OF PORTFOLIO MANAGEMENT:

1. DISCRETIONARY PORTFOLIO MANAGEMENT SERVICE (DPMS):

In this type of service, the client parts with his money in favour of the manager, who in return,
handles all the paper work, makes all the decisions and gives a good return on the investment and charges
fees. In the Discretionary Portfolio Management Service, to maximize the yield, almost all portfolio
managers park the funds in the money market securities such as overnight market, 18 days treasury bills
and 90 days commercial bills. Normally, the return of such investment varies from 14 to 18 percent,
depending on the call money rates prevailing at the time of investment.
2. NON-DISCRETIONARY PORTFOLIO MANAGEMENT SERVICE (NDPMS):

The manager function as a counsellor, but the investor is free to accept or reject the managers
advice; manager for a service charge also undertakes the paper work. The manager concentrates on stock
market instruments with a portfolio tailor-made to the risk taking ability of the investor.

IMPORTANCE OF PORTFOLIO MANAGEMENT:

Emergence of institutional investing on behalf of individuals. A number of financial institutions,

mutual funds and other agencies are undertaking the task of investing money of small investors,
on their behalf.
Growth in the number and size of investible funds a large part of household savings is being
directed towards financial assets.
Increased market volatility risk and return parameters of financial assets are continuously
changing because of frequent changes in governments industrial and fiscal policies, economic
uncertainty and instability.
Greater use of computers for processing mass of data.
Professionalization of the field and increasing use of analytical methods (e.g. quantitative
techniques) in the investment decision making
Larger direct and indirect costs of errors or shortfalls in meeting portfolio objectives increased
competition and greater scrutiny by investors.
STEPS IN PORTFOLIO MANAGEMENT:
Specification and qualification of investor objectives, constraints, and preferences in the form of
an investment policy statement.

Determination and qualification of capital market expectations for the economy, market sectors,
industries and individual securities.

 Allocation of assets and determination of appropriate portfolio strategies for each asset class and
selection of individual securities.
Performance measurement and evaluation to ensure attainment of investor objectives.
Monitoring portfolio factors and responding to changes in investor objectives, constrains and / or
capital market expectations.
Rebalancing the portfolio when necessary by repeating the asset allocation, portfolio strategy and
security selection.
NEED FOR PORTFOLIO MANAGEMENT:
The Portfolio Management deals with the process of selection securities from the
number of opportunities available with different expected returns and carrying different
levels of risk and the selection of securities is made with a view to provide the investors
the maximum yield for a given level of risk or ensure minimum risk for a level of return.
Portfolio Management is a process encompassing many activities of investment in
assets and securities. It is a dynamics and flexible concept and involves regular and
systematic analysis, judgment and actions. The objectives of this service are to help the
unknown investors with the expertise of professionals in investment Portfolio
Management. It involves construction of a portfolio based upon the investors objectives,
constrains, preferences for risk and return and liability. The portfolio is reviewed and
adjusted from time to time with the market conditions. The evaluation of portfolio is to be
done in terms of targets set for risk and return. The changes in portfolio are to be
effected to meet the changing conditions.
Portfolio Construction refers to the allocation of surplus funds in hand among a variety of
financial assets open for investment. Portfolio theory concerns itself with the principles

governing such allocation. The modern view of investment is oriented towards the
assembly of proper combinations held together will give beneficial result if they are
grouped in a manner to secure higher return after taking into consideration the risk
element.
The modern theory is the view that by diversification, risk can be reduced. The investor
can make diversification either by having a large number of shares of companies in
different regions, in different industries or those producing different types of product
lines. Modern theory believes in the perspectives of combination of securities under
constraints of risk and return.

stages in portfolio management:

Specification and
quantification of
investor
objectives,
constraints, and
preferences

Portfolio policies
and strategies

Capital market
expectations

Relevant
economic, social,
political sector
and security
considerations

Monitoring investor
related input factors

Portfolio construction
and revision asset
allocation, portfolio
optimization, security
selection,
implementation and
execution

Monitoring
economic and
market input factors

Attainment of
investor
objectives
Performance
measurement

Process of portfolio management:

The Portfolio Program and Asset Management Program both follow a disciplined
process to establish and monitor an optimal investment mix. This six-stage process
helps ensure that the investments match investors unique needs, both now and in the
future.

1. IDENTIFY GOALS AND OBJECTIVES:

When will you need the money from your investments? What are you saving your
money for? With the assistance of financial advisor, the Investment Profile
Questionnaire will guide through a series of questions to help identify the goals and
objectives for the investments.

2. DETERMINE OPTIMAL INVESTMENT MIX:

Once the Investment Profile Questionnaire is completed, investors optimal
investment mix or asset allocation will be determined. An asset allocation represents

the mix of investments (cash, fixed income and equities) that match individual risk
and return needs.
This step represents one of the most important decisions in your portfolio
construction, as asset allocation has been found to be the major determinant of longterm portfolio performance.
3. CREATE A CUSTOMIZED INVESTMENT POLICY STATEMENT
When the optimal investment mix is determined, the next step is to formalize our
goals and objectives in order to utilize them as a benchmark to monitor progress and
future updates.
4. SELECT INVESTMENTS
The customized portfolio is created using an allocation of select QFM Funds.
Each QFM Fund is designed to satisfy the requirements of a specific asset class,
and is selected in the necessary proportion to match the optimal investment mix.
5 MONITOR PROGRESS
Building an optimal investment mix is only part of the process. It is equally important
to maintain the optimal mix when varying market conditions cause investment mix to
drift away from its target. To ensure that mix of asset classes stays in line with
investors unique needs, the portfolio will be monitored and rebalanced back to the
optimal investment mix

6. REASSESS NEEDS AND GOALS

Just as markets shift, so do the goals and objectives of investors. With the flexibility
of the Portfolio Program and Asset Management Program, when the investors
needs or other life circumstances change, the portfolio has the flexibility to
accommodate such changes.
RISK:

Risk refers to the probability that the return and therefore the value of an asset or
security may have alternative outcomes. Risk is the uncertainty (today) surrounding the
eventual outcome of an event which will occur in the future. Risk is uncertainty of the
income/capital appreciation or loss of both. All investments are risky. The higher the risk
taken, the higher is the return. But proper management of risk involves the right choice
of investments whose risks are compensation.
RETURN:
Return-yield or return differs from the nature of instruments, maturity period and the
creditor or debtor nature of the instrument and a host of other factors. The most
important factor influencing return is risk return is measured by taking the price income
plus the price change.
PORTFOLIO RISK:
Risk on portfolio is different from the risk on individual securities. This risk is reflected by
in the variability of the returns from zero to infinity. The expected return depends on
probability of the returns and their weighted contribution to the risk of the portfolio.

RETURN ON PORTFOLIO:
Each security in a portfolio contributes returns in the proportion of its investment in
security. Thus the portfolio of expected returns, from each of the securities with weights
representing the proportionate share of security in the total investments.

RISK RETURN RELATIONSHIP:

The risk/return relationship is a fundamental concept in not only financial analysis, but in
every aspect of life. If decisions are to lead to benefit maximization, it is necessary that
individuals/institutions consider the combined influence on expected (future) return or

benefit as well as on risk/cost. The requirement that expected return/benefit be

commensurate with risk/cost is known as the "risk/return trade-off" in finance.
All investments have some risks. An investment in shares of companies has its own risks
or uncertainty. These risks arise out of variability of returns or yields and uncertainty of
appreciation or depreciation of share prices, loss of liquidity etc. and the overtime can be
represented by the variance of the returns. Normally, higher the risk that the investors
take, the higher is the return.

.
.

TYPES OF RISKS: risk consists of two components. They are

1.
2.

Systematic Risk
Un-systematic Risk

1. SYSTEMATIC RISK:
Systematic risk refers to that portion of total variability in return caused by factors
affecting the prices of all securities. Economic, Political and sociological changes are
sources of systematic risk. Their effect is to cause prices of nearly all individual common
stocks and/or all individual bonds to move together in the same manner.

i.

Market Risk:

Variability in return on most common stocks that are due to basic sweeping changes in
investor expectations is referred to as market risk. Market risk is caused by investor
reaction to tangible as well as intangible events.
ii.

Interest rate-Risk:
Interest rate risk refers to the uncertainty of future market values and of the size of
future income, caused by fluctuations in the general level of interest rates.

iii.

Purchasing-Power Risk:
Purchasing power risk is the uncertainty of the purchasing power of the amounts to be
received. In more events everyday terms, purchasing power risk refers to the impact of
or deflation on an investment.

2. UNSYSTEMATIC RISK:
Unsystematic risk is the portion of total risk that is unique to a firm or industry.
Factors such as management capability, consumer preferences, and labor strikes Cause
systematic variability of return in a firm. Unsystematic factors are largely independent of
factors affecting securities markets in general. Because these factors affect one firm,
they must be examined for each firm.

Unsystematic risk that portion of risk that is unique or peculiar to a firm or an

industry, above and beyond that affecting securities markets in general. Factors such as
management

capability, consumer

preferences,

and

labor

strikes

can

cause

unsystematic variability of return for a companys stock.

i.

Business Risk:

Business risk is a function of the operating conditions faced by a firm and the variability
these conditions inject into operating income and expected dividends.
Business risk can be divided into two broad categories
a. Internal Business Risk
b. External Business Risk

a. Internal business risk is associated with the operational efficiency of the firm. The
operational efficiency differs from company to company. The efficiency of operation is
reflected on the companys achievement of its pre-set goals and the fulfillment of the
promises to its investors.
b. External business risk is the result of operating conditions imposed on the firm by
circumstances beyond its control. The external environments in which it operates exert
some pressure on the firm. The external factors are social and regulatory factors,
monetary and fiscal policies of the government, business cycle and the general
economic environment within which a firm or an industry operates.
ii.

Financial Risk:

Financial risk is associated with the way in which a company finances its activities.
Financial risk is avoided risk to the extent that management has the freedom to decide to
borrow or not to borrow funds. A firm with no debit financing has no financial risk

PORTFOLIO ANALYSIS:
Portfolio analysis includes portfolio construction, selection of securities, revision of
portfolio evaluation and monitoring the performance of the portfolio. All these are part of
subject of portfolio management which is a dynamic concept. Individual securities have
risk-return characteristics of their own. Portfolios, which are combinations of securities
may or may not take on the aggregate characteristics of their individuals parts.
Portfolio analysis considers the determination of future risk and return in holding
various blends of individual securities. As we know that expected return from individual
securities carries some degree of risk. Various groups of securities when held together
behave in a different manner and give interest payments and dividends also, which are
different to the analysis of individual securities. A combination of securities held together
will give a beneficial result if they are grouped in a manner to secure higher return after
taking into consideration the risk element.
There are two approaches in construction of the portfolio of securities. They are

Traditional approach
Modern approach

TRADITIONAL APPROACH:
Traditional approach was based on the fact that risk could be measured on each
individual security through the process of finding out the standard deviation and that

security should be chosen where the deviation was the lowest. Traditional approach
believes that the market is inefficient and the fundamental analyst can take
advantage for the situation. Traditional approach is a comprehensive financial plan
for the individual. It takes into account the individual needs such as housing, life
insurance and pension plans.
Traditional approach basically deals with two major decisions. They are
a) Determining the objectives of the portfolio
b) Selection of securities to be included in the portfolio

MODERN APPROACH:
Modern approach theory was brought out by Markowitz and Sharpe. It is the
combination of securities to get the most efficient portfolio. Combination of securities can
be made in many ways. Markowitz developed the theory of diversification through
scientific reasoning and method. Modern portfolio theory believes in the maximization of
return through a combination of securities. The modern approach discusses the
relationship between different securities and then draws inter-relationships of risks
between them. Markowitz gives more attention to the process of selecting the portfolio. It
does not deal with the individual needs.
MARKOWITZ MODEL
THE MEAN VARIANCE CRITERION:
Dr. Harry M. Markowitz is credited with developing the first modern portfolio analysis
model in order to arrange for the optimum allocation of assets with in portfolio. To reach
these objectives, Markowitz generated portfolio with in a reward risk context. In essence,
Markowitz model is a theoretical framework for the analysis of risk return choices.
Decisions are based on the concept of efficient portfolios.

Markowitz model is a theoretical framework for the analysis of risk, return choices
and this approach determines an efficient set of portfolio return through three important
variable that is,
Return
Standard Deviation
Coefficient of correlation
Markowitz model is also called as a Full Covariance Model. Through this model the
investor can find out the efficient set of portfolio by finding out the trade off between risk
and return, between the limits of zero and infinity. According to this theory, the effect of
one security purchase over the effects of the other security purchase is taken into
consideration and then the results are evaluated. Markowitz had given up the single
stock portfolio and introduced diversification.

The single stock portfolio would be

preferable if the investor is perfectly certain that his expectation of highest return would
turn out to be real. In the world of uncertainty, most of the risk averse investors would
like to join Markowitz rather than keeping a single stock, because diversification reduces
the risk.
A portfolio is efficient when it is expected to yield the highest return for the level of risk
accepted or, alternatively the smallest portfolio risk for a specified level of expected
return level chosen, and asset are substituted until the portfolio combination expected
returns, set of efficient portfolio is generated.
Assumptions:
The Markowitz model is based on several assumptions regarding investor behavior:

1. Investors consider each investment alternative as being represented by a

probability distribution of expected returns over some holding period.

2. Investors maximize one period-expected utility and possess utility curve, which
demonstrates diminishing marginal utility of wealth.
3. Individuals estimate risk on the basis of variability of expected return.
4. Investors base decisions solely on expected return and variance of return only.
5. For a given risk level, investors prefer high returns to lower returns. Similarly for a
given level of expected return, investors prefer less risk to more risk.
Under these assumptions, a single asset or portfolio of assets is considered to be
efficient if no other asset or portfolio of assets higher expected return with the same
expected return.
THE SPECIFIC MODEL:
In developing this model, Markowitz first disposed of the investor behavior rule that
the investor should maximize expected return. This rule implies non-diversified single
security analysis portfolio with the highest expected return is the most desirable portfolio.
Only by buying that single security portfolio would obviously be preferable if the investor
were perfectly certain that this highest expected return would turn out to be the actual
return. However, under real world conditions of uncertainty, most risk adverse investors
join with Markowitz in discarding the role of calling for maximizing the expected returns.
As an alternative, Markowitz offers the expected returns/variance rule.

Markowitz has shown the effect of diversification by regarding the risk of securities.
According to him, the security with the covariance, which is either negative or low
amongst them, is the best manner to reduce risk. Markowitz has been able to show that
securities, which have, less than positive correlation will reduce risk with out, in any way,
bringing the return down. According to his research study a low correlation level between
securities in the portfolio will show less risk. According to him, investing in a large

number of securities is not the right method of investment. It is the right kind of security
that brings the maximum results.
Henry Markowitz has given the following formula for a two-security portfolio and three
security portfolios.

= (x1)2 ( 1)2 + (X2)2 ( 2)2 + 2(X1)(X2)(r12)( 1) ( 2)

= (x1)2( 1)2+(X2)2( 2)2 + (X3)2( 3)2 +2(X1)(X2)(r12)( 1) ( 2)+ 2(X1)(X3)(r13)( 1)

( 3)+ 2(X2)(X3)(r23)( 2) ( 3)

Standard deviation of the portfolio return

X1= proportion of the portfolio invested in security 1

X2= proportion of the portfolio invested in security 2
X3= proportion of the portfolio invested in security 3
1= standard deviation of the return on security 1
2= standard deviation of the return on security 2
3= standard deviation of the return on security 3
r12= coefficient of correlation between the returns on securities 1 and 2
r13= coefficient of correlation between the returns on securities 1 and 3
r23= coefficient of correlation between the returns on securities 2 and 3
CAPITAL ASSET PRICING MODEL: (CAPM)
The CAPM is a model for pricing an individual security (asset) or a portfolio. For
individual security perspective, the security market line (SML) is used and its relation to
expected return and systematic risk (beta) to show how the market must price individual

securities in relation to their security risk class. The SML enables us to calculate the
reward-to-risk ratio for any security in relation to that of the overall market. Therefore,
when the expected rate of return for any security is deflated by its beta coefficient, the
reward-to-risk ratio for any individual security in the market is equal to the market
reward-to-risk ratio, thus:
Individual securitys / beta
Reward-to-risk ratio

Markets securities (portfolio)

Reward-to-risk ratio

,
The Security Market Line, seen here in a graph, describes a relation between the beta
and the asset's expected rate of return

The market reward-to-risk ratio is effectively the market risk premium and by rearranging
the above equation and solving for E (Ri), we obtain the Capital Asset Pricing Model
(CAPM).

Where:

is the expected return on the capital asset

is the risk-free rate of interest

(the beta coefficient) the sensitivity of the asset returns to market returns, or

also

,
is the expected return of the market

is sometimes known as the market premium or risk premium (the

difference between the expected market rate of return and the risk-free rate of return).
Beta measures the volatility of the security, relative to the asset class. The equation is
saying that investors require higher levels of expected returns to compensate them for
higher expected risk. We can think of the formula as predicting a security's behavior as a
function of beta:
CAPM says that if we know a security's beta then we know the value of r that
investors expect it to have.

Assumptions of CAPM:
All investors have rational expectations.

There are no arbitrage opportunities.

Returns are distributed normally.

Fixed quantity of assets.

Perfectly efficient capital markets.

Investors are solely concerned with level and uncertainty of future wealth

Separation of financial and production sectors. Thus, production plans are fixed.

Risk-free rates exist with limitless borrowing capacity and universal access.

The Risk-free borrowing and lending rates are equal.

No inflation and no change in the level of interest rate exists.

Perfect information, hence all investors have the same expectations about
security returns for any given time period.

Shortcomings Of CAPM:

The model assumes that asset returns are (jointly) normally distributed random
variables. It is however frequently observed that returns in equity and other
markets are not normally distributed.

The model assumes that the variance of returns is an adequate measurement of

risk.

The model does not appear to adequately explain the variation in stock returns.

The model assumes that given a certain expected return investors will prefer
lower risk (lower variance) to higher risk and conversely given a certain level of
risk will prefer higher returns to lower ones.

The model assumes that all investors have access to the same information and
agree about the risk and expected return of all assets. (Homogeneous
expectations assumption)

The model assumes that there are no taxes or transaction costs.

The market portfolio consists of all assets in all markets, where each asset is
weighted by its market capitalization. This assumes no preference between
markets and assets for individual investors, and that investors choose assets
solely as a function of their risk-return profile. It also assumes that all assets are
infinitely divisible as to the amount which may be held or transacted.

The market portfolio should in theory include all types of assets that are held by
anyone as an investment (including works of art, real estate, human capital...)

Unfortunately, it has been shown that this substitution is not innocuous and can
lead to false inferences as to the validity of the CAPM, and it has been said
that due to the in observability of the true market portfolio, the CAPM might
not be empirically testable.

PORTFOLIO PERFORMANCE EVALUATION:

A Portfolio manager evaluates his portfolio performance and identifies the sources of
strengths and weakness. The evaluation of the portfolio provides a feed back about the
performance to evolve better management strategy. Even though evaluation of portfolio
performance is considered to be the last stage of investment process, it is a continuous
process. There are number of situations in which an evaluation becomes necessary and
important.

Evaluation has to take into account:

Rate of returns, or excess return over risk free rate.
Level of risk both systematic (beta) and unsystematic and residual risks through
proper diversification.

Some of the models used to evaluate portfolio performance are:

Sharpes ratio
Treynors ratio
Jensens alpha

Sharpes ratio:
A ratio developed by Nobel Laureate William F. Sharpe to measure risk-adjusted
performance. It is calculated by subtracting the risk-free rate from the rate of return for a
portfolio and dividing the result by the standard deviation of the portfolio returns.

The Sharpe ratio tells us whether the returns of a portfolio are due to smart investment
decisions or a result of excess risk. This measurement is very useful because although
one portfolio or fund can reap higher returns than its peers, it is only a good investment if
those higher returns do not come with too much additional risk. The greater a portfolio's
Sharpe ratio, the better its risk-adjusted performance has been.

Treynors ratio:
The Treynor ratio is a measurement of the returns earned in excess of that which could
have been earned on a risk less investment.
The Treynor ratio is also called reward-to-volatility ratio. It relates excess return over the
risk-free rate to the additional risk taken; however systematic risk instead of total risk is
used. The higher the Treynor ratio, the better is the performance under analysis.
Treynors ratio = (Average Return of the Portfolio - Average Return of the Risk-Free
Rate) / Beta of the Portfolio
Like the Sharpe ratio, the Treynor ratio (T) does not quantify the value added, if any, of
active portfolio management. It is a ranking criterion only. A ranking of portfolios based
on the Treynor Ratio is only useful if the portfolios under consideration are sub-portfolios
of a broader, fully diversified portfolio. If this is not the case, portfolios with identical
systematic risk, but different total risk, will be rated the same.

Jensens alpha:
An alternative method of ranking portfolio management is Jensen's alpha, which
quantifies the added return as the excess return above the security market line in the
capital asset pricing model. Jensen's alpha (or Jensen's Performance Index) is used to
determine the excess return of a stock, other security, or portfolio over the security's
required rate of return as determined by the Capital Asset Pricing Model.
This model is used to adjust for the level of beta risk, so that riskier securities are
expected to have higher returns. The measure was first used in the evaluation of mutual
fund managers by Michael Jensen in the 1970's.
To calculate alpha, the following inputs are needed:

The realized return (on the portfolio),

The market return,

The risk-free rate of return, and

The beta of the portfolio.

Rjt - Rft = j + j (RMt - Rft)

Where
Rjt = average return on portfolio j for period oft
Rft = risk free rate of return for period oft
j = intercept that measures the forecasting ability to the manager
j = systematic risk measure

RMt = average return on the market portfolio for periodt

.
ADVANTAGES:
Basic rules and regulations for the purchase and sale of securities are provided.
The rules and regulations are rigid and help to overcome human emotion.
The investor can earn higher profits by adopting the plans.
A course of action is formulated according to the investors objectives.
It controls the buying and selling of securities by the investor.
It is useful for taking decisions on the timing of investments.
DISADVANTAGES:
The formula plan does not help the selection of the security. The selection of the security has to
be done either on the basis of the fundamental or technical analysis.
It is strict and not flexible with the inherent problem of adjustment.
The formula plans should be applied for long periods, otherwise the transaction cost may be high.
Even if the investor adopts the formula plan, he needs forecasting. Market forecasting helps him
to identify the best stocks.

CALCULATION OF AVERAGE RETURN OF COMPANIES:

Average return = R/N

GUJARAT AMBUJA CEMENT LTD (GACL):

Opening
share price
(P0)

Closing
share price
(P1)

(P1-P0)

(P1-P0)/
P0*100

2002-2003

164.00

303.85

139.85

85.27

2003-2004

306.10

401.55

95.45

31.18

2004-2005

405.00

79.60

-325.40

-80.35

2005-2006

80.00

141.30

61.30

76.63

2006-2007

144.80

119.35

-25.45

-17.58

Year

95.15

TOTAL RETURN
Average return = 95.15/5 = 19.03
LARSEN AND TOUBRO (LNT):
Opening
share price
(P0)

Closing
share price
(P1)

(P1-P0)

(P1-P0)/
P0*100

2002-2003

213.70

527.35

313.65

146.77

2003-2004

530.00

982.00

452.00

85.28

2004-2005

988.70

1844.20

855.50

86.53

2005-2006

1845.00

1442.95

-402.05

-21.79

2006-2007

1400.00

1703.20

303.20

21.66

Year

TOTAL RETURN
Average return = 318.45/5 = 63.69

RANBAXY LABORATORIES:

318.45

Opening
share price
(P0)

Closing
share price
(P1)

(P1-P0)

(P1-P0)/
P0*100

2002-2003

597.80

1098.20

500.40

83.71

2003-2004

1100.10

1251.40

151.30

13.75

2004-2005

1252.00

362.35

-889.65

-71.06

2005-2006

364.40

391.85

27.45

7.53

2006-2007

393.00

349.15

-43.85

11.16

Year

45.09

TOTAL RETURN
Average return = 45.09/5 =9.02

CIPLA:
Opening
share price
(P0)

Closing
share price
(P1)

(P1-P0)

(P1-P0)/
P0*100

2002-2003

904.00

1317.25

413.25

45.71

2003-2004

1339.00

317.25

-1021.75

-76.31

2004-2005

320.00

443.40

123.40

38.56

2005-2006

445.00

250.70

-194.30

-43.66

2006-2007

253.40

239.30

-14.10

-5.56

Year

-41.26

TOTAL RETURN

Average return = -41.26/5 = -8.25

MTNL:

Year
2002-2003

Opening
share price
(P0)

Closing
share price
(P1)

(P1-P0)

(P1-P0)/
P0*100

95.15

137.70

42.55

44.72

2003-2004

139.10

154.90

15.80

11.36

2004-2005

156.00

144.20

11.80

7.56

2005-2006

145.20

142.85

-2.35

-1.62

2006-2007

143.00

152.35

9.35

6.54
68.56

TOTAL RETURN
Average return = 68.56/5 = 13.71
BHARTI AIRTEL:
Opening
share price
(P0)

Closing
share price
(P1)

(P1-P0)

(P1-P0)/
P0*100

2002-2003

23.50

105.10

81.60

347.23

2003-2004

106.25

215.60

109.35

102.92

2004-2005

218.90

345.70

126.80

57.93

2005-2006

348.90

628.85

279.95

80.24

2006-2007

635.00

862.80

227.80

35.87

Year

624.19

TOTAL RETURN

Average return = 624.19/5 = 125.18

ING VYSYA:
Opening
share price
(P0)

Closing
share price
(P1)

(P1-P0)

(P1-P0)/
P0*100

2002-2003

252.05

549.00

296.95

117.81

2003-2004

560.00

585.75

25.75

4.60

2004-2005

585.00

162.25

-422.75

-72.26

Year

2005-2006

164.50

157.45

-7.05

-4.29

2006-2007

159.00

185.15

26.15

16.45
62.31

TOTAL RETURN
Average return = 62.31/5 = 12.46

ICICI:
Opening
share price
(P0)

Closing
share price
(P1)

(P1-P0)

(P1-P0)/
P0*100

2002-2003

141.70

295.70

154.00

108.68

2003-2004

299.70

370.75

71.05

23.71

2004-2005

374.85

584.70

209.85

55.98

2005-2006

586.25

890.40

304.15

51.88

2006-2007

889.00

950.25

61.25

6.89

Year

247.14

TOTAL RETURN

Average return = 247.14/5 = 49.43

WIPRO:

Opening
share price
(P0)

Closing
share price
(P1)

(P1-P0)

(P1-P0)/
P0*100

2002-2003

1644.40

1737.60

93.2

5.67

2003-2004

1744.40

748.00

-996.40

-57.12

2004-2005

753.00

463.45

-289.55

-38.45

2005-2006

464.00

604.55

140.55

30.29

2006-2007

607.90

554.35

-53.55

-8.81

Year

-68.42

TOTAL RETURN
Average return = -68.42/5 = -13.68
SATYAM COMP:
Opening
share price
(P0)

Closing
share price
(P1)

(P1-P0)

(P1-P0)/
P0*100

2002-2003

280.10

367.35

87.25

31.15

2003-2004

370.00

409.90

39.90

10.78

2004-2005

412.00

737.80

325.80

79.08

2005-2006

740.70

483.95

-256.75

-34.66

2006-2007

486.00

474.95

-11.05

-2.27

Year

84.08

TOTAL RETURN

Average return = 84.08/5 = 16.82

CALCULATION OF STANDARD DEVIATION:
Standard Deviation = Variance
Variance

1/n-1 (d2)

GUJARAT AMBUJA CEMENT LTD:

Year

Return (R)

Avg. Return
(R )

d=
(R-R)

d2

2002-2003

85.27

19.03

66.24

4387.74

2003-2004

31.18

19.03

12.15

147.62

2004-2005

-80.35

19.03

-61.32

3760.14

2005-2006

76.63

19.03

57.60

3317.76

2006-2007

-17.58

19.03

-36.66

1343.96

TOTAL
Variance = 1/n-1 (d2) = 1/5-1 (12957.22) = 56.91

d2=12957.22

Standard Deviation =

Variance

= 3239.305 = 56.91

LARSEN & TOUBRO:

Year

Return (R)

Avg. Return
(R )

d=
(R-R)

D2

2002-2003

146.77

63.69

83.08

6902.29

2003-2004

85.28

63.69

21.59

466.13

2004-2005

86.53

63.69

22.84

521.67

2005-2006

-21.79

63.69

-85.48

7306.83

2006-2007

21.66

63.69

-42.03

1766.52
d2=16963.44

TOTAL
Variance = 1/n-1 (d2) = 1/5-1 (16963.44) = 4240.86
Standard Deviation = Variance = 4240.86 = 65.12

RANBAXY LABORATORIES:

Year

Return (R)

Avg. Return
(R )

d=
(R-R)

D2

2002-2003

83.71

9.02

74.69

5578.60

2003-2004

13.75

9.02

4.73

22.37

2004-2005

-71.06

9.02

80.08

6412.81

2005-2006

7.53

9.02

-1.49

2.22

2006-2007

11.16

9.02

2.14

4.58
d2=12020.58

TOTAL
Variance = 1/n-1 (d2) = 1/5-1 (12020.58) = 3005.145
Standard Deviation =

Variance

= 3005.145 = 54.82

CIPLA:

Year

Return (R)

Avg. Return
(R )

d=
(R-R)

D2

2002-2003

45.17

-8.25

53.96

2911.68

2003-2004

-76.31

-8.25

-68.06

4632.16

2004-2005

38.56

-8.25

46.81

2191.18

2005-2006

-43.66

-8.25

-35.41

1253.87

2006-2007

-5.56

-8.25

-2.69

7.24
d2=10996.13

TOTAL

Variance = 1/n-1 (d2) = 1/5-1 (10996.13) = 2749.0325

Standard Deviation =

Variance

= 2749.0325 = 52.43

MTNL:

Year

Return (R)

Avg. Return
(R )

d=
(R-R)

d2

2002-2003

44.72

13.72

31

961

2003-2004

11.36

13.72

-2.36

5.57

2004-2005

7.56

13.72

-6.16

37.95

2005-2006

-1.62

13.72

-15.34

235.32

2006-2007

6.54

13.72

-7.18

51.55
d2=1291.39

TOTAL
Variance = 1/n-1 (d2) = 1/5-1 (1291.39) = 322.8475
Standard Deviation =

Variance

= 322.8475 = 17.97

BHARTI AIRTEL:
Year

Return (R)

Avg. Return
(R )

d=
(R-R)

D2

2002-2003

347.23

125.18

222.05

49306.20

2003-2004

102.92

125.18

-22.26

495.51

2004-2005

57.93

125.18

-67.25

4522.56

2005-2006

80.24

125.18

-44.94

2019.60

2006-2007

37.59

125.18

-87.59

7672.01
d2=64015.88

TOTAL
Variance = 1/n-1 (d2) = 1/5-1 (64015.88) = 16003.97
Standard Deviation =

Variance

= 16003.97 = 126.51

ING VYSYA:

Year

Return (R)

Avg. Return
(R )

d=
(R-R)

D2

2002-2003

117.81

12.46

105.35

11098.62

2003-2004

4.60

12.46

-7.86

61.78

2004-2005

-72.26

12.46

-84.72

7177.48

2005-2006

-4.29

12.46

-16.75

280.56

2006-2007

16.45

12.46

3.99

15.92
d2=18634.36

TOTAL
Variance = 1/n-1 (d2) = 1/5-1 (18634.36) = 4658.59
Standard Deviation =

Variance

= 4658.59 = 68.25

ICICI:

Year

Return (R)

Avg. Return
(R )

d=
(R-R)

d2

2002-2003

108.68

49.43

59.25

3410.56

2003-2004

23.71

49.43

-25.72

661.52

2004-2005

55.98

49.43

6.55

42.90

2005-2006

51.88

49.43

2.45

6.00

2006-2007

6.89

49.43

-42.54

1809.65
d2=6030.63

TOTAL
Variance = 1/n-1 (d2) = 1/5-1 (6030.63) = 1507.6575
Standard Deviation =

Variance

= 1507.6575 = 38.83

WIPRO:

Year

Return (R)

Avg. Return
(R )

d=
(R-R)

d2

2002-2003

5.67

-13.68

19.35

374.42

2003-2004

-57.12

-13.68

-43.44

1887.03

2004-2005

-38.45

-13.68

-24.77

613.55

2005-2006

30.29

-13.68

43.97

1933.36

2006-2007

-8.81

-13.68

-4.87

23.72
d2=4832.08

TOTAL
Variance = 1/n-1 (d2) = 1/5-1 (4832.08) = 1208.02
Standard Deviation =

Variance

= 1208.02 = 34.76

SATYAM:

Year

Return (R)

Avg. Return
(R )

d=
(R-R)

d2

2002-2003

31.15

16.82

14.33

205.55

2003-2004

10.78

16.82

-6.04

36.48

2004-2005

79.08

16.82

62.26

3876.31

Company name

expected returns

standard dev

Cement

2005-2006

-34.66

16.82

51.48

2050.19

2006-2007

-2.27

16.82

19.09

364.43
d2=6532.76

TOTAL
GACL

19.03
Variance = 1/n-1 (d2) = 1/5-1 (6532.76) =
1633.19

56.91

Standard Deviation =

Variance

1633.19 = 40.41
PHARMACEUTICAL
CALCULATED EXPECTED RETURNS AND
STANDARD DEVIATIONS
RANBAXY

9.02

54.82

TELECOM

MTNL

13.71

17.97

BANKING

ING VYSYA

12.46

68.25

IT

WIPRO
34.76

- 13.68

Company name

expected returns

standard dev

Cement

LNT

63.69

65.12

PHARMACEUTICAL

CIPLA

-8.25

52.43

TELECOM

BHARTHI AIRTEL

125.18

127.51

CALCULATION OF CORRELATION

BANKING

BETWEEN TWO COMPANIES:

Covariance (COVab) = 1/(n-1) (dx.dy)

Correlation of coefficient = COVab / a*

ICICI

49.43

38.83

IT
GACL & LNT:

SATYAM
40.41

16.82

YEAR

Dev. Of
GACL
(dx)

Dev. Of LNT
(dy)

Product of dev.
(dx)(dy)

2002-2003

66.24

83.08

5503.2192

2003-2004

12.15

21.59

262.3185

2004-2005

-61.32

22.84

-1400.5488

2005-2006

57.6

-85.48

-4923.648

2006-2007

-36.66

-42.03

1540.8198
dx. dy = 982.1607

TOTAL

COVab =1/(5-1)(982.1607) =245.54

Correlation of coefficient = 245.54/(56.91)(65.12) = 0.066

RANBAXY & CIPLA:

YEAR

Dev. Of
GACL
(dx)

Dev. Of LNT
(dy)

Product of dev.
(dx)(dy)

2002-2003

74.69

53.96

4030.2724

2003-2004

4.73

-68.06

-321.9238

2004-2005

80.08

46.81

3748.5448

2005-2006

-1.49

-35.41

52.7609

2006-2007

2.14

2.69

-5.7566

dx. dy =
7503.8977

TOTAL

COVab =1/(5-1)(7503.8977) = 1875.97

Correlation of coefficient = 1875.97/(54.82)(52.43) = 0.65

MTNL & BHARTI AIRTEL:

YEAR

Dev. Of
GACL
(dx)

Dev. Of LNT
(dy)

Product of dev.
(dx)(dy)

2002-2003

31

222.05

6883.55

2003-2004

-2.36

-22.06

52.0616

2004-2005

-6016

-67.25

414.26

2005-2006

-15.34

-44.94

689.3796

2006-2007

-7.18

-87.59

628.8962
dx. dy =
8668.1474

TOTAL

COVab =1/(5-1)(8668.1474) = 2167.04

Correlation of coefficient = 2167.04/(17.97)(126.51)
ING VYSYA & ICICI:

YEAR

Dev. Of
GACL
(dx)

Dev. Of LNT
(dy)

2002-2003

105.35

59.25

6241.9875

2003-2004

-7.86

-25.72

202.1592

2004-2005

-84.72

6.55

-554.916

2005-2006

-16.75

2.45

-41.0375

2006-2007

3.99

-42.54

-169.7346

TOTAL

Product of dev.
(dx)(dy)

dx. dy =
5678.4586

COVab =1/(5-1)(5678.4586) =1419.61

Correlation of coefficient = 1419.61/(68.25)(38.83) = 0.54
WIPRO & SATYAM:

YEAR

Dev. Of
GACL
(dx)

Dev. Of LNT
(dy)

2002-2003

19.35

14.33

277.2855

2003-2004

-43.44

-6.04

262.3376

2004-2005

-24.77

62.26

-1542.1802

2005-2006

43.97

51.48

2263.5756

2006-2007

-4.87

19.09

-92.9683

TOTAL

Product of dev.
(dx)(dy)

dx. dy =
1168.0802

COVab =1/(5-1)(1168.0802) = 233.62

Correlation of coefficient = 233.62/(34.76)(40.41) = 0.17
CORRELATION COEFFICIENT BETWEEN THE COMPANIES
Company name

Correlation coefficient (r)

CEMENT
GACL
LNT

0.66

PHARMACEUTICAL
RANBAXY
CIPLA

0.65

TELECOM
MTNL
BHARTI AIRTEL
BANKING

0.95

ING VYSYA
ICICI

0.54

I.T.
WIPRO
SATYAM

0.17

CALCULATION OF PORTFOLIO WEIGHTS:

Deriving the minimum risk portfolio, the following formula is used:
(b)2 - rab (a) (b)

Wa =

(a)2 + (b)2 2rab (a) (b)

Where,
Xa is the proportion of security A
Xb is the proportion of security B
a = standard deviation of security A
b = standard deviation of security B
rab = correlation co-efficient between A&B
GACL & LNT:
(65.12)2- 0.066(56.91) (65.12)
Xa =
(56.91)2 + (65.12)2-2 (0.066) (56.91) (65.12)
= 0.57
Xb = 1- Xa
=1- 0.57

= 0.43
RANBAXY & CIPLA:
(52.43)2- 0.65(54.82) (52.43)
Xa =
(54.82)2 + (52.43)2 -2 (0.65) (54.82) (52.43)
= 0.44
Xb = 1-Xa
= 1-0.44
= 0.56

MTNL & BHARTI AIRTEL:

(126.51)2 0.95 (17.97) (126.51)
Xa =
(17.97)2 + (126.51)2 2(0.95) (17.97) (126.51)
= -1.15
Xb = 1 Xa
= 1- (-1.15)
= 2.15
ING VYSYA & ICICI:
(38.83)2 0.54(68.25) (38.83)
Xa =
(68.25)2 + (38.83)2 2 (0.54) (68.25) (38.83)
= 0.03
Xb = 1 Xa
= 1 0.03
= 0.97
WIPRO & SATYAM:

(40.41)2 0.17(34.76) (40.41)

Xa =
(34.76)2 + (40.41)2 2 (0.17) (34.76) (40.41)
= 0.59
Xb = 1 Xb
= 1 0.59
= 0.41
CALCULATION OF PORTFOLIO RISK:
For two securities:
P

a2*(Xa) 2 + b2*(Xb) 2 + 2rab*a*b*Xa*Xb

Where,
P = portfolio risk
Xa = proportion of investment in security A
Xb = proportion of investment in security B
R12 = correlation co-efficient between security 1 & 2
a = standard deviation of security 1
b = standard deviation of security 2
For Two securities:
P

a2*(Xa) 2 + b2*(Xb) 2 + 2rab*a*b*Xa*Xb

GACL & LNT:

p = (0.57)2 *(56.91)2 +(0.43)2 *(65.12)2 +2(0.57)(0.43)(0.066)(56.91)(65.12)
= 1956.259145
= 44.23

RANBAXY & CIPLA:

p = (0.44)2 *(54.82)2 +(0.56)2 *(52.43)2 +2(0.44)(0.56)(0.65)(54.82)(52.43)
= 2364.537348
= 48.63

MTNL & BHARTI AIRTEL:

p =(-1.15)2 *(17.97)2+(2.15)2*(126.51)2+2(-1.15)(2.15)(0.95)(17.97)(126.51)
= 63729.36593
= 252.45

ING VYSYA & ICICI:

p = (0.03)2 *(68.25)2 + (0.97)2 *(38.83)2 +2(0.03)(0.97)(0.54)(68.25)(38.83)
= 1506.140849
= 38.81

WIPRO & SATYAM:

p = (0.59)2 *(34.76)2 + (0.41)2 *(40.41)2 +2(0.59)(0.41)(0.17)(34.76)(40.41)
= 810.6233835
= 28.47

CALCULATION OF PORTFOLIO RETURN:

Rp = W1R1 + W2R2 (for two securities)

Where,
W1, W2, W3 are the weights of the securities
R1, R2, R3 are the Expected returns
GACL & LNT:
Rp = (0.57)(19.03) + (0.43)(63.69)
= 38.2338
RANBAXY & CIPLA:
Rp = (0.44)(9.02) + (0.56)(-8.25)
= -0.6512
MTNL & BHARTI AIRTEL:
Rp = (-1.15)(13.17) + (2.15)(125.18)
= 253.99
ING VYSYA & ICICI:
Rp = (0.03)(12.46) + (0.97)(49.43)
= 48.3209
WIPRO & SATYAM:
Rp = (0.59)(-13.68) + (0.41)(16.82)
= - 1.175

Portfolio Returns and Risks of Companies

Company name

Returns (%)

Risks (%)

38.2338

44.23

CEMENT
GACL
LNT

PHARMACEUTICAL
RANBAXY
CIPLA

-0.6512

48.63

253.99

252.45

48.3209

38.81

-1.175

28.47

TELECOM
MTNL
BHARTI AIRTEL
BANKING
ING VYSYA
ICICI
I.T.
WIPRO
SATYAM

PORTFOLIO A
Companies

Returns

GACL
RANBAXY
MTNL
ING VYSYA
WIPRO

19.03
09.02
13.71
12.46
-13.68

(R8.11
8.11
8.11
8.11
8.11

10.92
0.91
5.6
4.35
-21.79

)
119.25
0.82
31.36
18.923
474.80

R 40.54

644.15

R/n
Variance

40.54/5 = 8.18
=

645.158/5-1

161.29

S.D = (Variance)
(161.29) = 12.69 %

PORTFOLIO B
Companies

Returns

LNT
CIPLA
BHARATHI
ICICI
SATYAM

63.69
-8.25
125.89
49.43
16.82

(R49.37
49.37
49.37
49.37
49.37

14.32
-57.62
75.81
0.06
-32.55

R 246.87

)
205.06
3320.06
5747.16
3.6
1059.50
10335.38

R/n = 246.87/5 = 49.374

Variance = 10335.58/4
S.D = (Variance) (2548.845) = 50.83
INTERPRETATION:
By Comparing portfolio A and portfolio B, portfolio A having 8.18 % of returns, risk
12.69 , portfolioB having 49.374 % of returns, risk 50.83.we can easily justify that
portfolio B is giving good results .

Interpretation
When we form the optimum of two securities by using minimum variance equation, then
the return of the portfolio may decrease in order to reduce the portfolio risk.
GACL & LNT
The prime objective of this combination is to reduce risk of portfolio. Least preference is
given to the portfolio returns. As per the calculations GACL, bears a proportion of 0.57
whereas LNT bears a proportion of 0.43. The standard deviations of the companies are
56.91 for GACL and 65.12 for LNT.
This combination yields a return of a return of 38.2338 and a risk of 44.23
respectively.
RANBAXY & CIPLA
As per the calculations RANBAXY, bears a proportion of 0.44 whereas CIPLA bears a
proportion of 0.56. The standard deviations of the companies are 54.82 for RANBAXY
and 52.43 for CIPLA.
This combination yields a return of a return of -.6512 and a risk of 48.63
respectively. The investors shall not invest in this combination as there is negative return
and there is not much difference in their standard deviation.
MTNL & BHARTI AIRTEL
The proportion of investment for MTNL is -1.15 and for BHARTI ARTL 2.15. BHARTI
ARTL bears a major proportion which is dominating one. The standard deviations of the
two companies are 67.97 and 126.51 respectively.
This combination yields a return of 253.99 and a risk of 252.45. hence investor
should invest his major proportion in BHARTI ARTL in order to minimize risk.
ING VYSYA & ICICI
In this situation optimum weights of ING VYSYA and ICICI are 0.03 and 0.97
respectively. The portfolio risk is 38.81, which is lesser than the individual risks of two
companies. Hence, it is recommended to invest the major proportion of the funds in
ICICI, in order to reduce the portfolio risk.

WIPRO & SATYAM

The proportion of investments for WIPRO is 0.59 and for SATYAM it is 0.41. The
standard deviations of the companies are 34.76 and 40.41 respectively.
This combination yields a return of -1.175 with a risk of 28.47.

SUGGESTIONS:

SUGGESTIONS:
Select your investments on economic grounds.
Public knowledge is no advantage.
Buy stock with a disparity and discrepancy between the situation of the firm - and
the expectations and appraisal of the public (Contrarian approach vs. Consensus
approach).
Buy stocks in companies with potential for surprises.
Take advantage of volatility before reaching a new equilibrium.
Listen to rumors and tips, check for yourself.

Dont put your trust in only one investment. It is like putting all the eggs in one
basket . This will help lesson the risk in the long term.

The investor must select the right advisory body which is has sound knowledge
about the product which they are offering.
Professionalized advisory is the most important feature to the investors.
Professionalized research, analysis which will be helpful for reducing any kind of
risk to overcome.

FINDINGS & CONCLUSIONS

FINDINGS & CONCLUSIONS

1. Cement sector has got the returns was 38.23 and risk was 44.23 thus we can
say the risk is very high level compare to returns.
2. Pharmaceutical sector has got negative values of returns and the risk was very
high 48.63 thus we can say the risk factors is very high level compare to returns .
3. The telecom industry has got stable result where the risk and returns is same
level and the returns were 253.99 risk was 252.45.
4. Banking sector has got very significant and good result; where the returns was
48.32 and risk was 38.81 in this sector thus we can say the risk is very low when
compare to returns.
5. it sector has got negative value of returns and risk was 28.47 in thus we can say
the risk is very high when compare to returns .
6. As market is not doing well, investor should wait for sometimes, in order to get positive returns.
7. In order to enjoy more returns, he should invest in more; investor should invest in more risky
securities as a risk taker.
8. If he is a risk-averse investor, then he should invest in less risky securities and enjoy normal
returns.
1.The portfolio A has got the returns was 8.81 and risk was 12.69 and the
portfolio B

has got returns was 49.374 risk was 58.3

2. portfolio B was given very significant result when compare to portfolio those we can say
under this portfolio management .

BIBLIOGRAPHY

Books referred:

 Security analysis and portfolio management by V.A. Avadhani

Security analysis and portfolio management by Fischer & Jordan
Investment decisions by V.K. Bhalla
Security analysis & portfolio management by Robbins
Websites:
www.investopedia.com
www.capitalmarket.com
www.icicidirect.com
www.bse.com
www.nse.com