Portfolio Management_fiNAL SPURAN

PROJECT REPORTPORTFOLIO MANAGEMENT

Project ReportSubmitted To

SCHOOL OF MANAGEMENT STUDIES

DURING THE ACADAMIC YEAR-2009-2011

UNDER THE GUIDANCE OF PROJECT WORK SUBMITED BY Dr.MARY JESSICA Mr.BODA SPURAN KUMAR 09MBMA61

SCHOOL OF MANAGEMENT STUDIESUNIVERSITY OF HYDERABAD

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Certificate By The Guide

This is to certify that candidate BODA SPURAN KUMAR bearing Roll

No:09MBMA61 is a student of SMS at UNIVERSITY OF HYDERABAD, prepared

this project work entitled “PORTFOLIO MANAGEMENT” under my

supervision.

Dr. Mary Jessica

Place: Hyderabad

Date:

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Declaration

I hereby declare that this final project report titled, “PORTFOLIO

MANAGEMENT” is the result of my own effort in the training which I did as a

part of the curriculum. It has not been duplicated from any other earlier

works and all information provided in this report is genuine. This report is

submitted for the partial fulfillment of MBA program. It has not been

submitted to any other university or for any other degree.

Place: Hyderabad BODA SPURAN KUMAR

Date : (09MBMA61)

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AcknowledgementAcknowledgement

The research on “STOCK MARKET REACTION TO NEW POLICY CHANGE

ANNOUNCEMENTS” has been given to me as part of the curriculum. I have

tried my best to present this information as clearly as possible using basic

terms that I hope will be comprehended by the widest spectrum of

researchers, analyst and students for further studies.

I would like to take the pleasure of this opportunity to express my heartful

gratitude to my guide Professor Dr. MARY JESSICA (Faculty Member, SMS)

who took personal interest and gave valuable suggestions through out my

field work and completion of the project. I thank all my faculty members of

MBA department for their valuable suggestions throughout my course. The

importance of the moral support and good wishes of my parents and friends

is external and I am very much indebted to them. Finally I thank all my

friends who directly or indirectly helped me a lot during my project.

BODA SPURAN KUMAR (09MBMA61)

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SERIAL NO

CONTENTS PAGE NO

CHAPTER 1

Introduction1.1 Efficiency market

1.2 event study methodology

89

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CHAPTER 2

Review Of Literature 13

CHAPTER 3

Methodology3.1 Research Problem

3.2 Purpose of Study

3.3 Objectives of Study

3.4 Data and Sample Size

3.5 Event to be Studied

3.6 Period of Study

3.7 Methodology used

16-19

CHAPTER 4

Data Analysis and Interpretations4.1 Finding of log price

4.2 Regression of market return with stock return.

4.3 Estimation of the residual valves

4.4 Averaging of Residual Valves and findingCumulative Abnormal returns

4.5 Charts of Cumulative Abnormal Returns

4.6 Analysis of Abnormal Returns

20-52

CHAPTER 5

Summary 53

CHAPTER 6

Findings And Conclusions 54

CHAPTER Bibliography 55

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1.1 DEFINITION - PORTFOLIO MANAGEMENT

A portfolio is a collection of assets. The assets may be physical or financial like Shares, Bonds,

Debentures, Preference Shares, etc. The individual investor or a fund manager would not like to

put all his money in the shares of one company, which would amount to great risk. He would

therefore, follow the age-old maxim that “one should not put all the eggs into one basket”. By

doing so, he can achieve objective to maximize portfolio return and at the same time minimizing

the portfolio risk by diversification.

Portfolio management is the management of various financial assets, which comprise the

portfolio.

Portfolio management is a decision – support system that is designed with a view to meet

the multi-faced needs of investors.

According to Securities and Exchange Board of India Portfolio is defined as “portfolio

means the total holdings of securities belonging to any person”.

Portfolio manager is a person who is pursuant to a contract or arrangement with a

client, advises or directs or undertakes on behalf of the client (whether as a discretionary

portfolio manager or otherwise) the management or administration of a portfolio of securities or

the funds of the client.

Discretionary portfolio manager means a portfolio manager who exercises or may,

under a contract relating to portfolio management exercises any degree of discretion as to the

investments or management of the portfolio of securities or the funds of the client.

Portfolio management and investment decision as a concept came to be familiar with the

conclusion of second world war when things in the stock market liberally ruined the fortune of

individual, companies, even government, it was then discovered that investing in various scrips

instead of putting all the money in a single security yielded greater return with low risk

percentage, it goes to the credit of HARRY MARKOWITZ, 1991 noble laurelled to have

pioneered the concept of combining high yielded securities with these slow but steady yielding

securities to achieve optimum correlation coefficient of shares.

Portfolio management refers to the management of portfolio for others by professional

investment managers it refers to the management of an individual investor’s portfolio by

professionally qualified person ranging from merchant banker to specified portfolio company.

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Definition by SEBI

A portfolio is the total holdings of securities belonging to any person. Portfolio is a

combination of securities that have returns and risk characteristics of their own; portfolio may

not take on the aggregate characteristics of their individual parts.

Thus a portfolio is a combination of various assets and /or instruments of investments.

Combination may have different features of risk and return separate from those of the

components. The portfolio is also built up of the wealth or income of the investor over a period

of time with a view to suit return or risk preference to that of the port folio that he holds. The

portfolio analysis is thus an analysis of risk –return characteristics of individual securities in the

portfolio and changes that may take place in combination with other securities due interaction

among them and impact of each on others.

Security analysis is only a tool for efficient portfolio management. Portfolios are

combination of assets held by the investors. These combinations may be various assets classed

like equity and debt or of different issues like Govt. bonds and corporate debts or of various

instruments like discount bonds, debentures and blue chip equity scrips.

Portfolio analysis includes portfolio construction, selection of securities, and revision of

portfolio, evaluation and monitoring of the performance of the portfolio. All these are part of the

portfolio management.

The traditional portfolio theory aims at the selection of such securities that would fit in

well with the asset preferences, needs and choices of the investors. Thus, retired executive

invests in fixed income securities for a regular and fixed return. A business executive or a young

aggressive investor on the other hand invests in growing companies and in risky ventures.

The modern portfolio theory postulates that maximization of returns and minimization of

risk will yield optional returns and the choice and attitudes of investors are only a starting point

for investment decisions and that vigorous risk returns analysis is necessary for optimization of

returns.

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1.2 NEED & IMPORTANCE OF THE STUDY

Portfolio management has emerged as a separate academic discipline in India. Portfolio

theory that deals with the rational investment decision-making process has now become an

integral part of financial literature.

Investing in securities such as share, debentures & bonds is profitable as well as exciting.

It is indeed rewarding but involves a great deal of risk. Investing in financial securities is now

considered to be one of the most risky avenues of investment. It is rare to find investors

investing their entire savings in a single security. Instead they tend to invest in a group of

securities. Such group of securities is called as PORTFOLIO. Creation of portfolio helps to

reduce risk without sacrificing returns. Portfolio management deals with the analysis of

individual securities as well as with the theory and practice of optimally combining securities

into portfolios.

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 perspective of combination of securities under constraints of risk and returns.

1.3 SCOPE OF THE 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.

It includes the calculation of individual Standard Deviation of securities, weights of

individual securities involved in the portfolio. These percentages help in allocating the funds

available for investment based on risky portfolios. It also includes risk and return of

portfolios and their performance evaluation for a limited number of scrips.

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1.4 OBJECTIVES OF THE STUDY

The major objectives of the study are as follows

1. To study the investment pattern and its related risk & returns.

2. To construct an effective portfolio that offers the maximum return for minimum risk.

3. To help the investor choose wisely between alternative investments.

4. To understand, analyze and select the best portfolio.

1.5 RESEARCH METHODOLOGY

The time taken for the completion of the project is 45 days.

Sample Size: 6 COMPANIES

Sampling technique: Random sampling

SOURCES OF DATA COLLECTION: The data collection methods include both the primary

and secondary collection methods.

Primary collection methods: Study was done by personal investigation through observation

and personal discussion with the authorized clerks and members of the exchange.

Secondary collection methods: The secondary collection methods include

Companies Annual Reports

Information from Internet

Publications

COMPANIES SELECTED

Reliance Industries Ltd

Tata steel Ltd

Ultratech Cements Ltd

ICICI Bank

ITC Ltd

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1.6 LIMITATIONS OF THE STUDY

This study has been conducted purely to understand Portfolio Management for investors

while other parameters were given little importance.

Data collection was strictly confined to secondary source. No primary data is associated

with the project.

There is stiff competition that makes it difficult for the investor to choose a good

manager. However, this can be sorted out by taking his previous history and performance into

account. Studying the history of the various companies is time consuming

Construction of portfolio is restricted to two companies based on Markowitz model.

There was a constraint with regard to time allocation for the research study i.e. for a

period of two months. Only 6 companies were selected for the study, which limits the

combination.

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Harry Markowitz opened new vistas to modern portfolio selection by publishing an

article in the Journal of Finance in March 1952. His publication indicated the importance of

correlation among the different stocks’ returns in the construction of a stock portfolio.

Markowitz also showed that for a given level of expected return in a group of securities, one

security dominates the other. To find out this, the knowledge of the correlation coefficients

between all possible securities combinations is required.

After the publication of his paper, numerous investment firms and portfolio managers

developed “Markowitz algorithms” to minimize portfolio variance i.e. risk. Even today the term

Markowitz diversification is used to refer to the portfolio construction accomplished with the

help of security covariance.

2.1 INVESTMENT

Investment is the commitment of funds for a return expected to be realized in the future.

Investment is the employment of funds on assets with the aim of earning income or capital

appreciation. Investment has two attributes namely time and risk. Present consumption is

sacrificed to get a return in the future. Investment can be made in financial assets or physical

assets. In either case there is possibility that the actual return may vary from the expected return,

that possibility is risk involved in it.

Financial investment is the allocation of money to assets that are expected to yield some

gain over a period of time. Investment is an activity that is undertaken by those who have

savings. Savings can be defined as the excess of income over expenditure.

The three important characteristics of any financial asset are:

Return- the potential return possible from an asset.

Risk- the variability in returns of the asset forms the chances of its value going up/down.

Liquidity- the ease with which an asset can be converted into cash.

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Investors tend to look at these three characteristics while deciding on their individual

preference pattern of investments. Each financial asset will have a certain level of each of these

characteristics.

Investment is generally distinguished from speculation in terms of 3 factors namely risk,

capital gain and time period. Speculation means taking up the business risk in the hope of

getting short-term gain. Speculation essentially involves buying and selling activities with the

expectation of getting profit from the price fluctuations. The investor constantly evaluates the

worth of security whereas the speculator evaluates the price movement. Gambling is the

extreme form of speculation. There is no risk and return trade off in gambling and negative

outcomes are expected.

INVESTMENT PROCESS

INVESTMENT AVENUES

There are a large number of investment avenues for savers in India. Some of them are

marketable and liquid, while others are non-marketable. Some of them are highly risky while

some others are almost risk less. Investors may be individual or institutions. Investment avenues

can be broadly categorized as follows.

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CORPORATE SECURITES

PORTFOLIO:

A portfolio is a collection of investments held by an institution or an individual. Holding

a portfolio is a 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 bank accounts, stocks, bonds, options, warrants, gold certificates, real

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Equity Shares

Preference shares

Bonds Warrants Derivatives

Investment

A

Deposits

Tax Shelters

Financial Derivatives

Equity Shares

Mutual Fund

Fixed Income Securities

Life Insurance

Real Estate Precious Objects

RESEARCH (e.g., Security Analysis)

PORTFOLIO MANAGERS

OPERATIONS (e.g. buying and selling of Securities)

CLIENTS

estate, futures contracts, production facilities, or any other item that is expected to retain its

value.

2.2 PORTFOLIO MANAGEMENT

Many times the investors go on acquiring assets in an ad hoc & unplanned manner & the

result is high risk, low return profile that they may face. All such assets of financial nature such

as gold, silver, real-estate, building, insurance policies, post office certificate would constitute

his portfolio & the wise investor not only plans his portfolio as per risk return profile or

preferences but manages his portfolio efficiently so as to secure the highest return for the lowest

risk possible at that level of investment. This is in short the portfolio management.

The basic principle is that the higher the risk, the higher is the return &investor should

have clear perception of elements of risk & return when he makes investments. Risk return

analysis is essential for the investment & portfolio management. An investor considering

investment in securities is faced with the problem of choosing from among a large no. of

securities. His choice depends upon the risk return characteristics of individual securities. He

would attempt to choose the most desirable securities & like to allocate his funds over group of

securities. As the economic and financial environment keep changing the risk return

characteristics of individual securities as well as portfolios also change.

An investor invests his funds in a portfolio expecting to get a good return consistent with

the risk that he has to bear. Portfolio management comprises all the processes involved in the

creation & maintenance of an investment portfolio. It deals specifically with Security Analysis,

Portfolio Analysis, Selection, Revision and Evaluation. Portfolio management is a complex

process, which tries to make investment activity more rewarding and less risky.

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OBJECTIVES OF PORTFOLIOMANAGEMENT:

The main objective of investment portfolio management is to maximize the

returns from the investment and to minimize the risk involved in investment. Moreover, risk in

price or inflation erodes the value of money and hence investment must provide a protection

against inflation.

Secondary objectives:

The following are the other ancillary objectives:

Regular return.

Stable income.

Appreciation of capital.

More liquidity.

Safety of investment.

Tax benefits.

FUNCTIONS OF PORTFOLIO MANAGEMENT:

To frame the investment strategy and select an investment mix to achieve the desired

investment objectives.

To provide a balanced portfolio which not only can hedge against the inflation but also

optimise returns with the associated degree of risk

To maximise the after-tax return by investing in various tax saving investment

instruments.

NEED FOR PORTFOLIO MANAGEMENT:

It is a dynamic and flexible concept and involves regular

and systematic analysis, judgement and action. It involves construction of a portfolio based upon

the investor’s objectives, constraints, preferences for risk and returns and tax liability.

The portfolio is reviewed and adjusted from time to time in

tune with the market conditions.

The evaluation of portfolio is to be done in terms of targets

set for risk and returns.

Portfolio construction refers to the allocation of surplus funds in hand among a variety of

financial assets open for investment. The modern theory is the view that by diversification, risk

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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.

2.3 PHASES IN PORTFOLIO MANAGEMENT

PORTFOLIO MANAGEMENT is a process encompassing many activities aimed at

optimizing investment of funds, each phase is an integral part of the whole process and the

success of portfolio management depends upon the efficiency in carrying out each phase. Five

phases can be identified: -

(1) Security analysis

(2) Portfolio analysis

(3) Portfolio selection

(4) Portfolio revision

(5) Portfolio evaluation

SECURITY ANALYSIS:

It refers to the analysis of trading securities from the point of view of their prices, return,

and risk. All investment is risky and the expected return is related to risk. The securities

available to an investor for investment are numerous and of various types. The shares of over

more than 7000 companies are listed in stock exchanges of the country. Securities classified into

ownership securities such as equity shares and preference shares and debentures and bonds.

Recently, a number of new securities such as convertible debentures and deep discount bonds,

zero coupon bonds, Flexi bonds, Floating rate bonds Global depository receipts, Euro currency

bonds etc…, are issued to raise funds for their projects by companies from which investor has to

choose those securities the is worthwhile to be included in his investment portfolio. This calls

for detailed analysis of the available securities.

Security analysis is the initial phase of the portfolio management process. It examines the

risk return characteristics of individual securities. A basic strategy in securities investment is to

buy under priced securities and sell over priced securities. But the problem is how to identify

such securities in other words mispriced securities. This is what security analysis is all about.

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Prices of the securities in the stock market fluctuate daily on the account of continuous

buying and selling. Stock prices move in trends and cycles and are never stable. An investor in

the stock market is interested in buying securities at low price and selling them at high price so

as to get a good return on his investment made. He therefore tries to analyse the movement of

share prices in the market. Two approaches are commonly used for this purpose.

Fundamental analysis wherein the analyst tries to determine the intrinsic value of the

share based on the current and future earning capacity of the company.

Technical analysis is an alternative approach to the study of stock price behaviour.

PORTFOLIO ANALYSIS:

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

1. Traditional approach

2. Modern approach

PORTFOLIO SELECTION:

A portfolio that provides the highest returns at a given level of risk is generated. A portfolio

having this characteristic is known as an efficient portfolio. The inputs from portfolio analysis

can be used to identify the set of efficient portfolios. From this set of efficient portfolios, the

optimal portfolio has to be selected for investment. Harry Markowitz portfolio theory provides

both the conceptual framework and analytical tools for determining the optimal portfolio in a

disciplined and objective way.

PORTFOLIO REVISION:

The portfolio that is once selected has to be continuously reviewed over a period of time

and then revised depending on the objectives of the investor. The care taken in construction of

portfolio should be extended to the review and revision of the portfolio. Fluctuations that occur

in the equity prices cause substantial gain or loss to the investors.

The investor should have competence and skill in the revision of the portfolio. The

portfolio management process needs frequent changes in the composition of stocks and bonds.

In securities, the type of securities to be held should be revised according to the portfolio policy.

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PORTFOLIO EVALUATION:

The evaluation of the portfolio (done by portfolio manager) provides a feedback 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.

RETURN:

The term Return from an investment refers to the benefits from that investment. In the field of

finance in general and security analysis in particular, the term return is almost invariably

associated with a percentage (say, return on investment of 12%) and not a mere amount (like,

profit of Rs. 150). In security analysis we are primarily concerned with return forms a particular

investment say, a share or a debenture or other financial instrument.

Single period Returns:

It refers to a situation where an investor is concerned with return from a single period

(say, one day, one week, one month or one year).

Multi period Returns:

It refers to situation where more than single period returns are under consideration.

Investor is concern with computing the return per period, over a longer period.

Ex-Post Returns:

The measurement of return from the historical data can be referred to Ex- Post returns.

This includes the both current income and capital gains (or losses) brought about by gains price

of the security. The income and capital gains are then expressed as .a percentage of the initial

investment.

Ex-Ante Returns:

The majority of investors tend to emphasize the return they expect from a security while

making investment decision and the expected return of a security. This enables the investors to

look into future prospects from an investment and the measurement of returns from expectation

of benefits is known as ex-ante returns.

RISK

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Risk is uncertainty of the income /capital appreciation or loss or both. All investments are risky.

Higher the risk taken, the higher is the return. But proper management of risk involves the right

choice of investments whose risks are compensating.

TYPES OF RISKS

Risk consists of two components. They are

1. Systematic Risk

2. Unsystematic Risk

1. Systematic Risk:

Systematic risk affects the entire market. It is caused by factors external to the particular

company and uncontrollable by the company. The systematic risk affects the market as a whole.

Factors affecting the systematic risk are Economic conditions, Political conditions and

Sociological changes.

The systematic risk is unavoidable. Systematic risk is further sub-divided into three types. They

are

a) Market Risk:

Jack Clark Francis has defined market risk as that portion of total variability of return

caused by the alternating forces of bull and bear markets. The forces that affect the stock market

can be earthquake, war, political uncertainty, etc.

b) Interest Rate Risk:

Interest rate risk is the variation in the single period rates of return caused by the

fluctuations in the market interest rate. It is caused by changes in the government monetary

policy.

c) Purchasing Power Risk:

Variations in the returns are also caused by the loss of purchasing power of currency.

Purchasing power risk is also known as inflation risk.

2. Un-systematic Risk:

Un-systematic risk is unique and peculiar to a firm or an industry. All these factors affect the un-

systematic risk and contribute a portion in the total variability of the return.

Managerial inefficiency

Technological change in the production process

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Availability of raw materials

Changes in the consumer preference

Labour problems

The nature and magnitude of the above-mentioned factors differ from industry to industry and

company to company. They have to be analyzed separately for each industry and firm. Un-

systematic risk can be broadly classified into:

a) Business Risk

b) Financial Risk

Business Risk:

Business risk is that portion of the unsystematic risk caused by the operating

environment of the business. Business risk arises from the inability of a firm to maintain its

competitive edge and growth or stability of the earnings. The volatility in stock prices due to

factors intrinsic to the company itself is known as Business risk. Business risk is concerned with

the difference between revenue and earnings before interest and tax.

Business risk can be divided into

i) Internal Business Risk

Internal business risk is associated with the operational efficiency of the firm. The

efficiency of operation is reflected on the company‘s achievement of its pre-set goals and the

fulfilment of the promises to its investors.

ii) External Business Risk

External business risk is the result of operating conditions imposed on the firm by

circumstances beyond its control. 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.

Financial Risk:

It refers to the variability of the income to the equity capital due to the debt capital.

Financial risk in a company is associated with the capital structure of the company.

RISK AND EXPECTED RETURN:

There is a positive relationship between the amount of risk and the amount of expected

return i.e., the greater the risk, the larger the expected return and larger the chances of substantial

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loss. One of the most difficult problems for an investor is to estimate the highest level of risk he

is able to assume.

Risk is measured along the horizontal axis and increases from the left to right.

Expected rate of return is measured on the vertical axis and rises from bottom to top.

The line from 0 to R (f) is called the rate of return or risk less investments commonly

associated with the yield on government securities.

The diagonal line form R (f) to E(r) illustrates the concept of expected rate of return

increasing as level of risk increases.

PORTFOLIO-AGE RELATIONSHIP

Age Portfolio

Below 30 80% in stocks or mutual funds

10% in cash

10% in fixed income

30 to 40 70% in stocks or mutual funds

10% in cash

20% in fixed income


10% in cash

30% in fixed income


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10% in cash

40% in fixed income

Above 60 40% in stocks or mutual funds

10% in cash

50% in fixed income

These aren't hard and fast allocations, just guidelines to get you thinking about how your

portfolio should look. Your risk profile will give you more equities or more fixed income

depending on your aggressive or conservative bias. However, it's important to always have some

equities in your portfolio no matter what your age.

2.4 PORTFOLIO THEORIES

1. MARKOWITZ MODEL:

Dr. Harry M. Markowitz is credited with developing the first modern portfolio analysis

in order to arrange for the optimum allocation of assets with in portfolio. To reach this objective,

Markowitz generated portfolios within a reward risk context. It used statistical analysis for the

measurement of risk and mathematical programming for selection of assets in a portfolio in an

efficient manner. Markowitz approach determines for the investor the efficient set of portfolio

through three important variables i.e., Return, Standard deviation and Co-efficient of correlation.

Markowitz model is also called as a “Full Covariance Model“. Through this model, the

investor can, with the use of computer, find out the efficient set of portfolio by finding out the

trade off between risk and return, between the limits of zero and infinity. Most people agree that

holding two stocks is less risky than holding one stock. For example, holding stocks from textile,

banking and electronic companies is better than investing all the money on the textile company‘s

stock.

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 adverse

investors would like to join Markowitz rather than keeping a single stock, because

diversification reduces the risk.

ASSUMPTIONS:

All investors are rational and risk-averse.

Investors base their investment decisions on the expected return and standard deviation

of returns from a possible investment.

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The investor assumes that greater or larger the return that he achieves on his investments,

the higher the risk factor surrounds him. On the contrary when risks are low the return can also

be expected to be low.

All investors have access to the same information at the same time.

Investors have an accurate conception of possible returns, i.e., the probability beliefs of

investors match the true distribution of returns.

There are no taxes or transaction costs.

All investors are price takers, i.e., their actions do not influence prices.

Any investor can lend and borrow an unlimited amount at the risk free rate of interest.

All securities can be divided into parcels of any size.

CONSTRUCTION OF THE PORTFOLIO

The purpose of the study is to find out at what percentage of investment should be invested

between two companies, on the basis of risk and return of each security in comparison. These

percentages help in allocating the funds available for investment based on risky portfolios. In

order to know the risk of the stock or scrip, we use the formula

Standard Deviation = Variance

Variance = (1/n-1) ∑ (R-R) 2

Where,

(R-R) 2 = Square of difference between sample and mean.

n = Number of samples observed.

After that, we need to compare the stocks or scrips of two companies with each other by using

the correlation co-efficient as given below.

Covariance (COV ab) = 1/n (RA-RA) (RB-RB)

nab = Correlation Coefficient = COV ab / σa * σb

Where,

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(RA-RA) (RB-RB) = Combined deviations of A&B

σa * σb = Product of standard deviation of A&B

COV ab = Covariance between A&B

n = Number of observations

The next step would be the construction of the optimal portfolio on the basis of what percentage

of investment should be invested when two securities and stocks are combined i.e. calculation of

two assets portfolio weight by using minimum variance equation, which is given below.

Wa = σb [σb-(nab*σa)]

σa2 + σb2 - 2nab*σa*σb

Wb = 1 – Wa

Where,

Wa = Weight of security A

Wb = Weight of security B

σa = standard deviation of A

σb = standard deviation of B

nab= correlation co-efficient between A&B

The final step is to calculate the portfolio risk (combined risk)

RP = σ a2*Wa2 + σb2*Wb2 + 2nab*σa*σb*Wa*Wb

Where,

Wa = Proportion of investment in security A

Wb = Proportion of investment in security B

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σa = Standard deviation of security A

σb = Standard deviation of security B

nab = Correlation co-efficient between securities A & B

Rp = Portfolio risk

2. THE SHARPE’S INDEX MODEL/SINGLE INDEX MODEL:

William Sharpe has suggested a simplified method of diversification of portfolios. He

has made the estimates of the expected return and variance of indexes, which are related to

economic activity. Sharpe’s Theory assumes that securities returns are related to each other

only through common relationships with basic underlying factor i.e. market return index.

Individual securities return is determined solely by random factors and on its relationship to

this underlying factor with the following formula:

Ri = αi+βi Rm+ei

Where Ri = expected return on security i

αi = intercept of the straight line or alpha co-efficient

βi = slope of straight line or beta co-efficient

Rm = the rate of return on market index

ei = error term with a mean of zero & a std.dev., which is a constant

3. CAPITAL ASSET PRICING MODEL (CAPM):

Markowitz, William Sharpe, John Lintner and Jan Mossin provided the basic structure of

CAPM. William F. Sharpe emphasised the risk factor in portfolio theory is a combination of

two risks i.e., systematic risk and unsystematic risk. The systematic risk attached to each of

the security is same irrespective of any number of securities in the portfolio. The total risk of

portfolio is reduced, with increase in number of stocks, as a result of decrease in the

unsystematic risk distributed over number of stocks in the portfolio. Therefore, the

relationship between an assets return and its systematic risk can be expressed by the CAPM,

which is also called the Security Market Line.

E (Ri) = Rf + β (Rm – Rf)

Where,

25

E (Ri) = Expected return on any individual security (or portfolio)

Rf = Risk free rate of return

β = Market sensitivity index of individual security (or portfolio)

Rm = Expected rate of return on the market portfolio

Rm- Rf = Market premium or risk premium

4. ARBITRAGE PRICING THEORY

According to this theory the returns of the securities are influenced by a number of

macroeconomic factors such as growth rate of industrial production rate of inflation, spread

between low-grade and high-grade bonds.

The foundation for APT is the law of one price. The law of one price states that two

identical goods should sell at the same price. If they sold at different prices anyone could

engage in arbitrage by simultaneously buying at low prices and selling at the high prices and

make a risk less profit.

Arbitrage also applies to financial assets. If two financial assets have the same risk, they

should have the same expected return. If they do not have the same expected return, a

riskless profit could be earned by simultaneously selling the low return asset and buying the

high-return asset. The arbitrage pricing line for one risk factor can be written as:

E (ri) = λ0 + λiβi

Where,

E (ri) = The expected return on the security i

λ0 = The return on the zero beta portfolios

λi = The factor risk premium

βi = The sensitivity of the asset ‘i’ to the risk factor

Two factor Arbitrage pricing model:

E (rp) = λ0 + λ1β1 + λ2β2

Where,

λ2 = The risk premium associated with risk factor2

β2 = The factor beta coefficient for factor 2, and the factors 1 &2 are uncorrelated

26

3.1 INDUSTRY PROFILE:

FINANCIAL SERVICES

Financial services refer to services provided by the finance industry. The finance industry

encompasses a broad range of organizations that deal with the management of money. Among

these organizations are banks, credit card companies, insurance companies, consumer finance

companies, stock brokerages, investment funds and some government sponsored enterprises.

The financial services sector contributed 15 per cent to India's GDP in FY09, and is the

second-largest component after trade, hotels, transport and communication all combined

together, as per the Banking & Finance Journal, released by an industry body in August 2010.

Stock markets: Market capitalization of India as a proportion of world market cap has

risen to a record high. According to data sourced from Bloomberg, the country's market

capitalization as a proportion of the world market cap is currently 3.34 per cent. India's current

market-cap is US$ 1.55 trillion as compared with world market-cap of US$ 46.5 trillion. This is

higher than 3.12 per cent share India enjoyed at the market peak of January 2008.

As analyzed by Venture Intelligence, private equity firms obtained exit routes for their

investments in a record 121 companies during 2010, including 24 via IPOs. (2009 had witnessed

66 liquidity events including 7 via IPOs).

Insurance: The Indian Life Insurance industry is one on the strongest growing sectors in

the country. Currently a US$ 41-billion industry, India is the fifth largest life insurance market

and growing at a rapid pace of 32-34 per cent annually. Currently, there are 22 life insurance

companies operating in India, according to the Life Insurance Council (LIC).

Banking services: Significantly, on a year-on-year basis, bank credit grew by 24.4 per

cent in 2010 as against RBI’s projections of 20 per cent for the entire fiscal 2010-11.

27

Investment management: Investment management is the professional management of

various securities (shares, bonds and other securities) and assets in order to meet specified

investment goals for the benefit of the investors. Investors may be institutions or private investors.

Government-sponsored enterprises (GSEs): The GSEs are group of financial services

corporations created by the United States Congress. Their function is to enhance the flow of credit

to targeted sectors of the economy and to make those segments of the capital market more

efficient and transparent. The desired effect of the GSEs is to enhance the availability and reduce

the cost of credit to the targeted borrowing sectors: agriculture, home finance and education

Scope of financial services:

The scope of financial services in India has grown manifold in recent years, and consumers have

a much wider choice in terms of savings and investments. There is a broad range of brokerage firms,

investment services, financial consulting firms, foreign and private banks, global insurance companies,

taxation service providers, home loan and car equity firms and other banking companies now expanding

their operation in the country. For young candidates there are bright career opportunities in the fields of

financial advisory services, insurance and banking services, investment management, financial analysis,

stock market consultants, brokering agents, financial planners and economists.

History of financial service sector:

The major events that have shaped the modern finance service sector are:

The Great Depression (1929): The Great Depression originated in the US with the Wall Street

crash in October 1929. The effects of the depression spread across the world, especially in the

heavy industries. Capital requirements regulation, financial service industry oversights and the

insurance of deposit accounts sprang out of this tumultuous period.

Black Monday (1987): On October 19, the stock markets across the world witnessed a huge

crash. This was the largest one day decline in the stock market history. The crash started in Hong

Kong, spreading to Europe and the US. Analysts blamed computer trading systems for

magnifying the losses.

Asian Financial Crisis (1990): The Asian Financial Crisis was triggered by the collapse of Thai

baht as the government of Thailand decided to float the national currency. The nation had a huge

foreign debt at that point, driving it to the verge of bankruptcy. The crisis rippled across the

whole of Southeast Asia and has led to many emerging market countries to reduce debts and

build up foreign currency reserves.

28

Stock Market Downturn (2002): Stock exchanges around the world witnessed a significant

decline in March 2002. It was attributed to the bursting of the “Dot-com Bubble”, which saw

major Internet companies going bankrupt.

Sub-prime Crisis (2007): Credit markets faced major crunch due to large scale default on loans.

It led to the Financial Crisis of 2008 – 2009 and resulted in the bankruptcy, fire-sale acquisition

and government bailouts of finance service industry giants such as Lehman Brothers, Bear

Stearns, AIG, Fannie Mae, Freddie Mac, Merrill Lynch, Wachovia, Northern Rock, Lloyds TSB,

HBOS, RBS and the entire banking system of Iceland. The world economy can expect reduced

growth rates and tighter regulations as a result of this crisis.

Growth of financial services sector:

In the post-economic reform and liberalization era, the banking and financial services sector has

witnessed rapid growth in India. As of 2007, the value of banking assets in India was growing at a

compounded annual growth rate of 24%. A large number of mutual funds, venture capital funds and

private equity funds have mushroomed in India with substantial foreign investments in this sector.

Almost all of the world class financial services institutions and foreign banks have established their

presence in India.

The growth of financial sector in India at present is nearly 8.5% per year. The rise in the growth rate

suggests the growth of the economy. The financial policies and the monetary policies are able to sustain

a stable growth rate. The reforms pertaining to the monetary policies and the macroeconomic policies

over the last few years have influenced the Indian economy to the core. The development of the system

pertaining to the financial sector was the key to the growth of the same. With the opening of the

financial market variety of products and services were introduced to suit the need of the customer. The

Reserve Bank of India played a dynamic role in the growth of the financial sector of India.

The financial services sector contributed 15% to India’s GDP in FY09, and is the second-largest

component after trade, hotels, transport and communication all combined together, as per the Banking &

Finance Journal, released by an industry body in August 2010.

29

CALCULATION OF AVERAGE RETURN OF COMPANIES:

Return(R) = Dividend + (Closing Price-Opening price) * 100

Opening Price

Average Return = R/N

1. RELIANCE INDUSTRIES LTD.

Year Dividend

(D) (Rs)

Open

Price

(P0)

(Rs)

Closing

Price (P1)

(Rs)

(P1-P0) (D+(P1-

P0))/

P0*100

2006-2007 11 1252.55 2881.05 1628.5 130.893

2007-2008 13 2950 1230.25 -1719.8 -57.8559

2008-2009 13 1240.05 1089.4 -150.65 -11.1004

2009-2010 7 1094 1058.25 -35.75 -2.62797

30

2010-2011 - 1062 1018.4 -43.6 -4.10546

TOTAL RETURNS 55.20326

Average Return = 55.20326/5 = 11.04

2. TATA STEEL LTD:

Year Dividend

(D) (Rs)

Open

Price

(P0)

(Rs)

Closing

Price (P1)

(Rs)

(P1-P0) (D+(P1-

P0))/

P0*100

2006-2007 15.5 484 934.8 450.8 96.34298

2007-2008 16 938 216.85 -721.15 -75.1759

2008-2009 16 218.4 617.6 399.2 190.1099

2009-2010 8 622.7 678.95 56.25 10.31797

2010-2011 - 684.2 630.35 -53.85 -7.87051


Average Return = 213.7244/5 = 42.74

3. ULTRATECH CEMENT LTD:

31

Year

Dividend

(D) (Rs)

Opening

Price

(P0)

(Rs)

Closing

Price (P1)

(Rs) (P1-P0)

(D+(P1-

P0))/

P0*100

2006-2007 4 1108 1014.5 -93.5 -8.07762

2007-2008 5 1040 383.1 -656.9 -62.6827

2008-2009 5 389.25 915.1 525.85 136.3776

2009-2010 6 915 1082.15 167.15 18.9235

2010-2011 - 1086 1073.6 -12.4 -1.1418


Average Return = 83.39903/5 = 16.68

4. ICICI BANK:

Year

Dividend

(D) (Rs)

Opening

Price

(P0)

(Rs)

Closing

Price (P1)

(Rs) (P1-P0)

(D+(P1-

P0))/

P0*100

2006-2007 10 889 1232.4 343.4 39.75253

2007-2008 11 1235 448.35 -786.65 -62.8057

2008-2009 11 455 875.7 420.7 94.87912

2009-2010 12 888 1144.65 256.65 30.25338

2010-2011 - 1153 1101.3 -51.7 -4.48395


Average Return = 97.59541/5 = 19.52

5. ITC LTD:

32

Year

Dividend

(D) (Rs)

Opening

Price

(P0)

(Rs)

Closing

Price (P1)

(Rs) (P1-P0)

(D+(P1-

P0))/

P0*100

2006-2007 3.1 177.9 210.3 32.4 19.95503

2007-2008 3.5 212 171.45 -40.55 -17.4764

2008-2009 3.7 172.5 250.85 78.35 47.56522

2009-2010 10 251 174.5 -76.5 -26.494

2010-2011 - 175.8 191.4 15.6 8.87372


Average Return = 32.42353/5 = 6.48

AVERAGE RETURNS

COMPANY AVERAGE RETURN

RELIANCE INDUSTRIES (REFINARIES) 11.04

TATA STEEL (STEEL) 42.74

ULTRATECH (CEMENTS) 16.68

ICICI (BANKING) 19.52

ITC (Cigarettes, tobacco products) 6.48

33

INTERPRETATION:

From the above graph, we understand that by investing in diversified securities, we can diversify

the risk of losses. Tata Steel (42.74) is earning higher returns, and other securities are earning

medium or low returns.

CALCULATION OF STANDARD DEVIATION:

Variance = 1/n-1 (R-R) 2

Standard Deviation = Variance

1. RELIANCE INDIA LTD:

Year Return (R) Avg. Return

34

(R) (R-R) (R-R)2

2006-2007 130.893 11.04 119.853 14364.7

2007-2008 -57.8559 11.04 -68.896 4746.65

2008-2009 -11.1004 11.04 -22.14 490.197

2009-2010 -2.62797 11.04 -13.668 186.813

2010-2011 -4.10546 11.04 -15.145 229.385

TOTAL = ∑(R-R)2 20017.78

Variance = 1/n-1 (R-R) 2 = 1/4 (20017.78) = 5004.45

Standard Deviation = Variance = 5004.45 = 70.74

2. TATA STEEL:

Year Return (R)

Avg. Return

(R) (R-R) (R-R) 2

2006-2007 96.34298 42.74 53.603 2873.28

2007-2008 -75.1759 42.74 -117.92 13904.2

2008-2009 190.1099 42.74 147.37 21717.9

2009-2010 10.31797 42.74 -32.422 1051.19

2010-2011 -7.87051 42.74 -50.611 2561.42

TOTAL = ∑ (R-R) 2 42107.94

35

Variance = 1/n-1 (R-R) 2 = 1/4 (42107.94) = 10526.98

Standard Deviation = Variance = 10526.98= 102.60

3. ULTRATECH CEMENT:

Year Return (R)

Avg. Return

(R) (R-R) (R-R) 2

2006-2007 -8.0776 16.68 -24.758 612.939

2007-2008 -62.683 16.68 -79.363 6298.49

2008-2009 136.378 16.68 119.698 14327.6

2009-2010 18.9235 16.68 2.2435 5.03329

2010-2011 -1.1418 16.68 -17.822 317.617

TOTAL = ∑ (R-R) 2 21561.69

Variance = 1/n-1 (R-R) 2 = 1/4 (21561.69) = 5390.42


4. ICICI BANK:

Year Return (R)

Avg. Return

(R) (R-R) (R-R)2

2006-2007 39.7525 19.52 20.2325 409.354

2007-2008 -62.806 19.52 -82.326 6777.57

2008-2009 94.8791 19.52 75.3591 5678.99

2009-2010 30.2534 19.52 10.7334 115.206

2010-2011 -4.484 19.52 -24.004 576.192

TOTAL = ∑ (R-R) 2 13557.32

36

Variance = 1/n-1 (R-R) 2 = 1/4 (13557.32) = 3389.33


5. ITC LTD:

Year Return (R)

Avg. Return (R)

(R-R) (R-R) 2

2006-2007 19.955 6.48 13.475 181.576

2007-2008 -17.476 6.48 -23.956 573.89

2008-2009 47.5652 6.48 41.0852 1687.99

2009-2010 -26.494 6.48 -32.974 1087.28

2010-2011 8.87372 6.48 2.39372 5.7299

TOTAL = ∑ (R-R) 2 3536.474

Variance = 1/n-1 (R-R) 2 = 1/4 (3536.474) = 884.12

Standard Deviation = Variance = 884.12 = 29.73

AVERAGE RISK

COMPANY RISK

RELIANCE INDUSTRIES 70.74

TATA STEEL 102.60

ULTRATECH 73.42

ICICI BANK 58.22

ITC LTD 29.73

37

INTERPRETATION:

From the above graph, we can understand that Tata Steel & Ultratech Cement has highest

standard deviation and hence high risk; where as other securities have average risk. By investing

in diversified portfolio, we can diversify the risk.

CALCULATION OF CORRELATION:

Covariance (COV ab) = 1/n (RA-RA) (RB-RB)

Correlation Coefficient = COV ab / σa * σb

1. RELIANCE INDUSTRIES AND OTHER COMPANIES :

(i) RELIANCE (RA) & TATA STEEL (RB):

YEAR

38

(RA-RA) (RB-RB) (RA-RA) (RB-RB)

2006-2007 119.853 53.603 6424.48

2007-2008 -68.896 -117.92 8124.216

2008-2009 -22.14 147.37 -3262.77

2009-2010 -13.668 -32.422 443.1439

2010-2011 -15.145 -50.611 766.5036

TOTAL 12495.57

Covariance (COV ab) = 1/5 (7692.5) = 2449.11

σa = 70.74 ; σb = 102.6

Correlation Coefficient = COV ab / σa * σb = 2449.11/(70.74)(102.6)= 0.34

(ii) RIL (RA) & ULTRATECH CEMENT (RB):

YEAR (RA-RA) (RB-RB) (RA-RA) (RB-RB)

2006-2007 119.853 -24.758 -2967.3

2007-2008 -68.896 -79.363 5467.79

2008-2009 -22.14 119.698 -2650.1

2009-2010 -13.668 2.2435 -30.664

39

2010-2011 -15.145 -17.822 269.914

TOTAL 89.609


σa = 70.74 ; σb = 73.42

Correlation Coefficient = COV ab / σa * σb = 17.92/(70.74)(73.42) = 0.003

(iii) RIL (RA) & ICICI BANK (RB):


2006-2007 119.853 20.2325 2424.93

2007-2008 -68.896 -82.326 5671.93

2008-2009 -22.14 75.3591 -1668.5

2009-2010 -13.668 10.7334 -146.7

2010-2011 -15.145 -24.004 363.541

TOTAL 6645.24

Covariance (COV ab) = 1/5(6645.24) = 1329.05

σa = 70.74 ; σb = 58.22


(iv) RIL (RA) & ITC LTD (RB):


2006-2007 119.853 13.475 1615.02

2007-2008 -68.896 -23.956 1650.47

2008-2009 -22.14 41.0852 -909.63

2009-2010 -13.668 -32.974 450.689

40

2010-2011 -15.145 2.39372 -36.253

TOTAL 2770.3


σa = 70.74 ; σb = 29.73


2. TATA STEEL & OTHER COMPANIES:

(i) TATA STEEL (RA) & ULTRATECH (RB):


2006-2007 53.603 -24.758 -1327.1

2007-2008 -117.92 -79.363 9358.48

2008-2009 147.37 119.698 17639.9

2009-2010 -32.422 2.2435 -72.739

2010-2011 -50.611 -17.822 901.989

TOTAL 26500.5


σa = 102.6 ; σb = 73.42


(ii) TATA STEEL (RA) & ICICI BANK (RB):


2006-2007 53.603 20.2325 1084.52

2007-2008 -117.92 -82.326 9707.88

2008-2009 147.37 75.3591 11105.7

2009-2010 -32.422 10.7334 -348

41

2010-2011 -50.611 -24.004 1214.87

TOTAL 22764.9


σa = 102.6; σb = 58.22


(iii) TATA STEEL (RA) & ITC LTD (RB):


2006-2007 53.603 13.475 722.3

2007-2008 -117.92 -23.956 2824.89

2008-2009 147.37 41.0852 6054.73

2009-2010 -32.422 -32.974 1069.08

2010-2011 -50.611 2.39372 -121.15

TOTAL 10549.9


σa = 102.6; σb = 29.73


3. ULTRATECH CEMENT & OTHER COMPANIES:

(i) ULTRATECH (RA) & ICICI BANK (RB):


2006-2007 -24.758 20.2325 -500.92

2007-2008 -79.363 -82.326 6533.64

42

2008-2009 119.698 75.3591 9020.33

2009-2010 2.2435 10.7334 24.0804

2010-2011 -17.822 -24.004 427.799

TOTAL 15504.94


σa = 73.42 ; σb = 58.22


(ii) ULTRATECH (RA) & ITC LTD (RB):


2006-2007 -24.758 13.475 -333.61

2007-2008 -79.363 -23.956 1901.22

2008-2009 119.698 41.0852 4917.82

2009-2010 2.2435 -32.974 -73.977

2010-2011 -17.822 2.39372 -42.661

TOTAL 6368.784


σa = 73.42 ; σb = 29.73


4. ICICI BANK & OTHER COMPANIES:

(i) ICICI BANK (RA) & ITC LTD (RB):


2006-2007 20.2325 13.475 272.633

2007-2008 -82.326 -23.956 1972.2

2008-2009 75.3591 41.0852 3096.14

43

2009-2010 10.7334 -32.974 -353.92

2010-2011 -24.004 2.39372 -57.459

TOTAL 4929.596


σa = 58.22 ; σb = 29.73


CALCULATION OF PORTFOLIO WEIGHTS:

Wa = σb [σb-(nab*σa)]

σa2 + σb2 - 2nab*σa*σb

Wb = 1 – Wa

44

1. CALCULATION OF WEIGHTS OF RIL & OTHER COMPANIES:

(i) RIL (a) & TATA STEEL (b)

σa = 70.74

σb = 102.6

nab = 0.34

Wa = 102.6[102.6-(0.34*70.74)]

(70.74)2 + (102.6)2 – 2(0.34*70.74*102.6)

Wa = 8059.06

10595.52

Wa = 0.76

Wb = 1 – Wa

Wb = 1- 0.76 = 0.14

(ii) RIL (a) & ULTRATECH (b)

σa = 70.74

σb = 73.42

nab = 0.003

Wa = 73.42 [73.42-(0.003*70.74)]

(70.74)2 + (73.42)2 – 2(0.003*73.42*70.74)

45

Wa = 5374.92

10363.35

Wa = 0.52

Wb = 1 – Wa

Wb = 1- 0.52 = 0.48

(iii) RIL (a) & ICICI BANK (b)

σa = 70.74

σb = 58.22

nab = 0.32

Wa = 58.22 [58.22-(0.32*70.74)]

(70.74)2 + (58.22)2 – 2(0.32*70.74*58.22)

Wa = 2071.65

5757.89

Wa = 0.36

Wb = 1 – Wa

Wb = 1- 0.36 = 0.64

(iv) RIL (a) & ITC LTD (b)

σa = 70.74

σb = 29.73

nab = 0.2

Wa = 29.73 [29.73-(0.2*70.74)]

(70.74)2 + (29.73)2 – 2(0.2*70.74*29.73)

46

Wa = 463.25

5046.78

Wa = 0.09

Wb = 1 – Wa

Wb = 1- 0.09 = 0.91

2. CALCULATION OF WEIGHTS OF TATA STEEL & OTHER COMPANIES:

(i) TATA STEEL (a) & ULTRATECH (b)

σa = 102.6

σb = 73.42

nab = 0.7

Wa = 73.42 [73.42-(0.7*102.6)]

(102.6)2 + (73.42)2 – 2(0.7*102.6*73.42)

Wa = 117.47

5371.21

Wa = 0.02

Wb = 1 – Wa

Wb = 1- 0.02 = 0.98

(ii) TATA STEEL (a) & ICICI BANK (b)

σa = 102.6

σb = 58.22

nab = 0.76

Wa = 58.22 [58.22-(0.76*102.6)]

(102.6)2 + (58.22)2 – 2(0.76*102.6*58.22)

Wa = -1150.19

47

4836.8

Wa = -0.24

Wb = 1 – Wa

Wb = 1+0.24 = 1.24

(iii) TATA STEEL (a) & ITC LTD (b)

σa = 102.6

σb = 29.73

nab = 0.69

Wa = 29.73 [29.73-(0.69*102.6)]

(102.6)2 + (29.73)2 – 2(0.69*102.6*29.73)

Wa = -1220.83

4209.41

Wa = -0.29

Wb = 1 – Wa

Wb = 1+0.29 = 1.29

3. CALCULATION OF WEIGHTS OF ULTRATECH & OTHER COMPANIES:

(i) ULTRATECH (a) & ICICI BANK (b)

σa = 73.42

σb = 58.22

nab = 0.72

Wa = 58.22 [58.22-(0.72*73.42)]

(73.42)2 + (58.22)2 – 2(0.72*73.42*58.22)

48

Wa = 311.92

6155.3

Wa = 0.05

Wb = 1 – Wa

Wb = 1- 0.05 = 0.95

(ii) ULTRATECH (a) & ITC LTD (b)

σa = 73.42

σb = 29.73

nab = 0.58

Wa = 29.73 [29.73-(0.58*73.42)]

(73.42)2 + (29.73)2 – 2(0.58*73.42*29.73)

Wa = -382.14

3742.35

Wa = -0.1

Wb = 1 – Wa

Wb = 1+0.1 = 1.1

4. CALCULATION OF WEIGHTS OF ICICI BANK & OTHER COMPANIES:

(i) ICICI BANK (a) & ITC LTD (b)

σa = 58.22

σb = 29.73

nab = 0.57

Wa = 29.73 [29.73-(0.57*58.22)]

(58.22)2 + (29.73)2 – 2(0.57*58.22*29.73)

49

Wa = -102.73

2300.24

Wa = -0.04

Wb = 1 – Wa

Wb = 1+ 0.04 = 1.04

CALCULATION OF PORTFOLIO RISK:

σP = σa2*Wa2 + σb2*Wb2 + 2nab*σa*σb*Wa*Wb

1. CALCULATION OF PORTFOLIO RISK OF RIL & OTHER COMPANIES:

50

(i) RIL (a) & TATA STEEL (b)

σa = 70.74

σb = 102.6

Wa = 0.76

Wb = 0.14

nab = 0.34

σP = (70.74)2(0.76)2+(102.6)2(0.14)2+2(0.34)(70.74*102.6)(0.76*0.14)

= 3621.85 = 60.18

(ii) RIL (a) & ULTRATECH (b)

σa = 70.74

σb = 73.42

Wa = 0.52

Wb = 0.48

nab = 0.003

σP = (70.74)2(0.52)2+(73.42)2(0.48)2+2(0.003)(70.74*73.42)(0.52*0.48)

51

= 2602.87 = 51.02

(iii) RIL (a) & ICICI BANK (b)

σa = 70.74

σb = 58.22

Wa = 0.36

Wb = 0.64

nab = 0.32

σP = (70.74)2(0.36)2+(58.22)2(0.64)2+2(0.32)(70.74*58.22)(0.36*0.64)

= 2644.2 = 51.42

(iv) RIL (a) & ITC LTD (b)

σa = 70.74

σb = 29.73

Wa = 0.09

Wb = 0.91

nab = 0.2

σP = (70.74)2(0.09)2+(29.73)2(0.91)2+2(0.2)(70.74*29.73)(0.09*0.91)

52

= 841.37 = 29.01

2. CALCULATION OF PORTFOLIO RISK OF TATA STEEL & OTHER COMPANIES:

(i) TATA STEEL (a) & ULTRATECH (b)

σa = 102.6

σb = 73.42

Wa = 0.02

Wb = 0.98

nab = 0.49

σP = (102.6)2(0.02)2+(73.42)2(0.98)2+2(0.49)(102.6*73.42)(0.02*0.98)

= 5325.93 = 72.98

(ii) TATA STEEL (a) & ICICI BANK (b)

σa = 102.6

σb = 58.22

Wa = -0.24

Wb = 1.24

nab = 0.76

σP = (102.6)2(-0.24)2+(58.22)2(1.24)2+2(0.76)(102.6*58.22)(-0.24*1.24)

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= 3116.08 = 55.82

(iii) TATA STEEL (a) & ITC LTD (b)

σa = 102.6

σb = 29.73

Wa = -0.29

Wb = 1.29

nab = 0.69

σP= (102.6)2(-0.29)2+(29.73)2(1.29)2+2(0.69)(102.6*29.73) (-0.29*1.29)

= 781.41 = 27.95

3. CALCULATION OF PORTFOLIO RISK OF ULTRATECH & OTHER COMPANIES:

(i) ULTRATECH (a) & ICICI BANK (b)

σa = 73.42

σb = 58.22

Wa = 0.05

Wb = 0.95

nab = 0.72

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σP = (73.42)2(0.05)2+(58.22)2(0.95)2+2(0.72)(73.42*58.22)(0.05*0.95)

= 3364.94 = 58.01

(ii) ULTRATECH (a) & ITC LTD (b)

σa = 73.42

σb = 29.73

Wa = -0.1

Wb = 1.1

nab = 0.58

σP = (73.42)2(-0.1)2+(29.73)2(1.1)2+2(0.58)(73.42*29.73)(-0.1*1.1)

= 844.87 = 29.07

4. CALCULATION OF PORTFOLIO RISK OF ICICI BANK & OTHER COMPANIES:

(i) ICICI BANK (a) & ITC LTD (b)

σa = 58.22

σb = 29.73

Wa = -0.04

Wb = 1.04

nab = 0.57

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σP = (58.22)2(-0.04)2+(29.73)2(1.04)2+2(0.57)(58.22*29.73)(-0.04*1.04)

= 878.23 = 29.63

CALCULATION OF PORTFOLIO RETURNS

Rp = Ra*Wa + Rb*Wb

PORTFOLIO Ra Wa Rb Wb Rp

RIL & Tata Steel 11.04 0.76 42.74 0.14 14.374

RIL & Ultratech 11.04 0.52 16.68 0.48 13.7472

RIL & ICICI Bank 11.04 0.36 19.52 0.64 16.4672

RIL & ITC Ltd 11.04 0.09 6.48 0.91 6.8904

56

Tata Steel &

Ultratech

42.74 0.02 16.68 0.98 17.2012

Tata Steel & ICICI

Bank

42.74 -0.24 19.52 1.24 13.9472

Tata Steel & ITC

Ltd

42.74 -0.29 6.48 1.29 -4.0354

Ultratech & ICICI

Bank

16.68 0.05 19.52 0.95 19.378

Ultratech & ITC

Ltd

16.68 -0.1 6.48 1.1 5.46

ICICI Bank & ITC

Ltd

19.52 -0.04 6.48 1.04 5.9584

PORTFOLIO WEIGHTS, RETURN & RISK:

PORTFOLIO

(A & B)

WEIGHT

OF A

WEIGHT

OF B

PORTFOLIO

RETURN

PORTFOLIO

RISK

INFOSYS & RIL 0.76 0.14 14.374 60.18

INFOSYS & TATA

STEEL

0.52 0.48 13.7472 51.02

INFOSYS &

ULTRATECH CEMENT

0.36 0.64 16.4672 51.42

57

INFOSYS & ICICI BANK 0.09 0.91 6.8904 29.01

INFOSYS & ITC LTD 0.02 0.98 17.2012 72.98

RIL & TATA STEEL -0.24 1.24 13.9472 55.82

RIL & ULTRATECH

CEMENT

-0.29 1.29 -4.0354 27.95

RIL & ICICI BANK 0.05 0.95 19.378 58.01

RIL & ITC LTD -0.1 1.1 5.46 29.07

TATA STEEL &

ULTRATECH CEMENT

-0.04 1.04 5.9584 29.63

TATA STEEL & ICICI

BANK

0.76 0.14 14.374 60.18

TATA STEEL & ITC LTD 0.52 0.48 13.7472 51.02

ULTRATECH CEMENT

& ICICI BANK

0.36 0.64 16.4672 51.42

ULTRATECH CEMENT

& ITC LTD

0.09 0.91 6.8904 29.01

ICICI BANK & ITC 0.02 0.98 17.2012 72.98

5.1 FINDINGS:

RIL & TATA STEEL:

The portfolio weights suggest that more investment should be made in RIL than TATA STEEL.

Portfolio weights for RIL & TATA STEEL are 0.68 & 0.32 respectively. This is a high risk high

return portfolio. Standard deviation for RIL is 73.37 and for TATA STEEL it is 99.06.

Combined portfolio risk is 64.24. Individual returns are 35.6 and 48.29 respectively for RIL and

TATA STEEL. It is suggested that an investor should invest more in RIL compared to TATA

STEEL as it provides better returns for lower risk than the returns provided by TATA STEEL.

58

RIL & ULTRATECH:

This is one of the best combinations. The portfolio weights suggest that more investment should

be made in RIL than ULTRATECH. Portfolio weights for RIL & ULTRATECH are 0.68 & 0.32

respectively. This is a high risk-high return portfolio. Standard deviation for RIL is 73.37 and

93.39 for ULTRATECH. Combined portfolio risk is 58.25, which is less compared to individual

risk of RIL. Individual returns are 35.6 and 48.29 respectively for RIL and ULTRATECH.

It is suggested that an investor should invest more in RIL, as it provides better returns (35.6) for

lower risk (73.37) when compared to ULTRATECH that provides a return of 48.98 at a risk of

93.39.

RIL & ICICI BANK:

The investor has another alternative bearing the investment proportion of 0.24 & 0.76 for RIL &

ICICI. The standard deviation of RIL is 73.37 and for ICICI it is 59.49. Hence the investor

should invest their funds more in ICICI, as the risk involved is low. It gives higher return at

lower risk when compared to RIL.

The combined portfolio risk is 57.67, which is less compared to individual risk of ICICI.

RIL & ITC:

This combination has investment proportion of 0.37 & 0.63 for RIL & ITC respectively. The

standard deviation of RIL is 73.37 and ITC’s standard deviation is 54.56, it means ITC has less

risk compared to RIL. It is suggested to invest more in ITC though it has negative returns

because investing in RIL could be more risky.

TATA STEEL & ULTRATECH:

This is of the best combinations for a risk taker. It involves the highest risk and gives the highest

return. An investor should be careful while investing in this portfolio.

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The portfolio weights are 0.44 & 0.56 respectively. The standard deviation of TATA STEEL &

ULTRATECH is 99.06 & 93.39 respectively. And the returns are 48.29 & 48.98.

The risk associated with these companies has been diversified and reduced to 82.88 and portfolio

return is 48.68.

TATA STEEL & ICICI BANK:

The portfolio weights suggest that more investment should be made in ICICI than TATA

STEEL.

Portfolio weights for TATA STEEL & ICICI are -0.05 & 1.05 respectively. The standard

deviation is 99.06 & 59.49 respectively which has been reduced to 59.36. Optimum investment

decision from the investor’s point of view is to invest all in funds in ICICI, which will give him

better returns with less risk.

TATA STEEL & ITC LTD:

The combination of TATA STEEL & ITC gives the proportion 0.0006 & 0.9994. The standard

deviation of TATA STEEL is 99.06 and ITC is 54.56. Hence the investor should invest their

funds more in ITC as the risk involved in ITC is less than that of TATA STEEL. Investing more

in TATA STEEL is highly risky.

The combined portfolio risk is 54.56 which is less than the individual risk of TATA STEEL.

ULTRATECH & ICICI BANK:

According to this combination the portfolio weights are 0.02 (ULTRATECH) & 0.98 (ICICI).

The standard deviation of ULTRATECH is more than that of ICICI i.e., 93.39 > 59.49.

If the investor wants to take low risk then ICICI is a better option as it provides better return

with less risk.

ULTRATECH & ITC LTD:

The combination of ULTRATECH & ITC gives the proportion 0.12 & 0.88. The standard

deviation of ULTRATECH is 93.39 and ITC is 54.56. Hence the investor should invest their

60

funds more in ITC as the risk involved in ITC is less than that of TATA STEEL. Investing more

in TATA STEEL is highly risky.

The combined portfolio risk is 53.49 which is less than the individual risk of ULTRATECH.

ICICI BANK & ITC LTD:

According to this combination the portfolio weights are 0.45 (ICICI) & 0.55 (ITC). The standard

deviation of ICICI is more than that of ITC i.e., 59.49 > 54.56. The combined portfolio risk is

44.03 which is less than the individual risk of ICICI & ITC.

5.2 SUGGESTIONS:

1. The combination of TATA STEEL & ULTRATECH gives highest returns but is highly

risky. It is the best portfolio for a risk seeker. It is suggested to be careful while investing in

this portfolio.

2. It is suggested to invest in RIL & ULTRATECH. This is the best combination available to an

investor among the selected portfolios, since it gives a high return for a lower risk.

3. Investing in the combinations, RIL & ICICI, TATA STEEL & ICICI and ULTRATECH &

ICICI is suggested because they compensate for the risk taken.

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4. The combination of TATA STEEL & ITC is very risky and provides negative return. Hence

it is advised not to invest in this combination.

5. The combination of ULTRATECH & ITC has a moderate risk but gives very low return

compared to other combinations. I suggest that an investor should not invest in this portfolio.

5.3 CONCLUSION:

Portfolio management helps the investors to make wise choice between alternate investments

and render optimum returns to the investors. When different assets are added to the portfolio, the

total risk tends to decrease. Simple random diversification reduces the unsystematic risk or

unique risk and hence reduces the total risk. Investor decision is solely dependent on the

expected return & variance of return only. For a given level of risk investor prefers higher return

to lower return. Likewise for a given level of return investor prefers lower risk than higher risk.

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Keeping a portfolio of single security may lead to a greater likelihood of the actual return

somewhat different from that of the expected return. Hence, it is a common practice to diversify

securities in the portfolio.

TEXT BOOKS:

1. Donald.E.Fisher, Ronald.J.Jordan, (2009) Security Analysis and Portfolio Management, 5th

Edition, Pearson Education.

2. Alexander.G.J, Sharpe.W.F, and Bailey.J.V, (2007) Fundamentals of Investments, 5th Edition,

Pearson Education, PHI.

3. Punivathy Pandian, (2005), Security Analysis and Portfolio Management, Vikas Publishing

House Pvt Ltd.

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4. Prasanna Chandra, (2006), Investment Analysis and Portfolio Management, 3rd Edition, TMH.

5. S. Kevin (2006), Security Analysis & Portfolio Management, 2nd Edition, PHI.

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http://www.investopedia.com/

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