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CHAPTER - 1

INTRODUCTION

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INTRODUCTION TO PORTFOLIO MANAGEMENT

A portfolio is a collection of securities since it is really desirable to invest the entire funds of an

individual or an institution or a single security, it is essential that every security be viewed in a

portfolio context. Thus it seems logical that the expected return of the portfolio. Portfolio

analysis considers the determine of future risk and return in holding various blends of individual

securities.

Portfolio expected return is a weighted average of the expected return of the individual securities

but portfolio variance, in short contrast, can be something reduced portfolio risk is because risk

depends greatly on the co-variance among returns of individual securities. Portfolios, which are

combination of securities, may or may not take on the aggregate characteristics of theirindividual parts.

Since portfolio expected return is a weighted average of the expected return of its securities, the

contribution of each security the portfolios expected returns depends on its expected returns and

its proportionate share of the initial portfolios market value. It follows that an investor who

simply wants the greatest possible expected return should hold one security, the one which is

considered to have a greatest expected return. Very few investors do this, and very few

investment advisors would counsel such and extreme policy instead, investors should diversify,

meaning that their portfolio should include

More than one security.

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OBJECTIVES OF PORTFOLIO MANAGEMENT

The main objective of investment portfolio management is to maximize the returns from the

investment and to minimize the risk involved. Moreover, risk in price or inflation erodes the

values of money and hence investment must provide a protection against inflation.

Secondary objectives

Regular return.

Stable income.

Appreciation of capital.

More liquidity.

Safety of investment.

Tax benefits.

Portfolio management services helps investors to make a wise choice between alternative

investment with pit any post trading hassles this service renders optimum returns to the

investors by proper selection of continuous changes of one plan to another plane with in the same

scheme, any portfolio management must specify the objectives like maximum returns, and risk

capital appreciation, safety etc in their offer.

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NEED FOR PORTFOLIO MANAGEMENT

Portfolio management is a process encompassing many activities of investment in assets and

securities. It is a dynamic and flexible concept and involves regular and systematic analysis,

judgment and action. The objective of this service is to help the unknown and investors with theexpertise of professionals in investment portfolio management. It involves construction of a

portfolio based upon the investors objectives, constraints, preferences for risk and returns and

tax liability. The portfolio is reviewed and adjusted from time to time in tune with the marketconditions. The evaluation of portfolio is to be done in terms of targets set for risk and returns.

The changes in the portfolio are to be effected to meet the changing condition.

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 more go towards the

assemble of proper combination of individual securities to form investment portfolio.

A combination of securities held together will give a beneficial result if they grouped in a

manner to secure higher returns after taking into consideration the risk elements.

The modern theory is the view that by diversification risk can be reduced. Diversification can be

made by the investor 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.

PORTFOLIO MANAGEMENT PROCESS

Investment management is a complex activity which may be broken down into the following

steps

Specification of investment objectives and constraints:

The typical objectives sought by investors are currents income, capital appreciation, and safety

of principle. The relative importance of these objectives should be specified further the

constraints arising from liquidity, time horizon, tax and special circumstances must be identified.

Choice of the Asset mix:

The most important decision in portfolio management is the asset mix decision very broadly; this

is concerned with the proportion of stock (equity shares and units/ shares of equity oriented

mutual funds) and bonds in the portfolio.

The appropriate stock-bond mix depends mainly on the risk tolerance and investment horizon

of the investor.

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ELEMENTS OF PORTFOLIO MANAGEMENT

Portfolio management is on-going process involving the following basic tasks:

Identification of the investors objectives, constraints and preferences.

Strategies are to be developed and implemented in tune with investment policy

formulated.

Review and monitoring of the performance of the portfolio.

Finally the evaluation of the portfolio.

RISK

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

risky. The higher the risk taken, the higher is the return. But proper management of risk involves

the rights choices of investments whose risks are compensating. The total risks of two companies

may be different and even lower than the risk of a group of two companies if their companies are

offset by each other.

The two major types of risks are Systematic or market related risk.

Unsystematic or company related risks.

Systematic risks

Systematic risks affected from the entire market are (the problems, raw material availability, tax

policy or government policy, inflation risk, interest risk and financial risk). It is managed by the

use of Beta of different company shares.

Unsystematic risks

Unsystematic risks are mismanagement, increasing inventory, wrong financial policy, defective

marketing etc. this is diversifiable or avoidable because it is possible to eliminate or diversify

away this components of risks to a considerable extents by investing in a large portfolio ofsecurities. The unsystematic risk stems from inefficiency magnitude of those factors different

from one company to another.

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RETURNS ON PORTFOLIO

Each security in a portfolio contributes returns in the proportion of its investments in security.

Thus the portfolio expected return is the weighted average of the expected return, from each ofthe securities, with weights representing the proportions share of the security in the total

investment. Why does an investor have so many securities in his portfolio? If the security ABC

gives the maximum return why not he invests in that security all his funds and thus maximizereturn? The answer to this questions lie in the investors perception of risk attached to

investments, his objectives of income, safety, appreciation, liquidity and hedge against loss of

value of money etc. this pattern of investment in different asset categories, types of investment,etc, would all be described under the caption of diversification, which aims at the reduction or

even elimination of non-systematic risks and achieve the specific objectives of investors.

RISK ON PORTFOLIO

The expected returns from individual securities carry some degree of risk. Risk on the portfoliois different from the risk on individual securities. The risk is reflected in the variability of the

returns from zero to infinity. Risk of the individual assets or a portfolio is measured by the

variance of its returns. The expected return depends on the probability of the returns and their

weighted contribution to the risk of the portfolio. These are two measures of risk in this contextone is the absolute deviation and other standard deviation.

RISK RETURN ANALYSIS

All investment has some risk. Investment in shares of companies has its own risk or uncertainty;these risks arise out of variability of yields and uncertainty of appreciation or depreciation ofshare prices, losses of liquidity etc.

The risk over time can be represented by the variance of the returns. While the return over timeis capital appreciation plus payout, divided by the purchase price of the shar

Y

(SML) Security market line

ExpectedReturn

Variable returns

} Risk Free Return.

o x

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Normally, the higher the risk that the investor takes, the higher is the return. There is, how ever,

a risk less return on capital of about 12% which is the bank rate charged by the R.B.I or long

term, yielded on government securities at around 13% to 14%. This risk less return refers to lack

of variability of return and no uncertainty in the repayment or capital. But other risks such as loss

of liquidity due to parting with money etc. may however remain, but are rewarded by the total

return on the capital. Risk-return is subject to variation and the objectives of the portfolio

manager are to reduce that variability and thus reduce the risky by choosing an appropriate

portfolio.

Traditional approach advocates that one security holds the better, it is according to the modern

approach diversification should not be quantity that should be related to the quality of scripts

which leads to quality of portfolio.

Experience has shown that beyond the certain securities by adding more securities expensive.

Simple diversification reduces

An assets total risk can be divided into systematic plus unsystematic risk, as shown below

Unsystematic risk is that portion of the risk that is unique to the firm (for example, risk due to

strike and management errors). Unsystematic risk can be reduced to zero by simplediversification.

Simple diversification is the random selection of securities that are to be added to a portfolio. As

the number of randomly selected added to a portfolio is increased, the level of unsystematic risk

approaches zero. However market related systematic risk cannot be reduced by simple

diversification. This risk is common to all securities.

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Persons involved in portfolio management

Investor

The peoples who are interested in investing their fund

Portfolio managers

Is a person who is in the wake of a contract agreement with a client, advices or directs or

undertakes on behalf of the clients, the management or distribution or management of the funds

of the clients as the case may be.

Discretionary portfolio manager

Means a manager who exercise under a contract relating to a portfolio management exercise any

degree of discretion as to investment or management of portfolio or securities or funds of clients

as the case may be.

The relationship between an investor and portfolio manager is of a highly interactive nature

The portfolio manger carries out all the transitions pertaining to the investor under the power of

attorney during the last two decades, and increasing complexity was witnessed in the capital

market and its trading procedures in this context a key (uninformed) investor formed investor

found himself in a tricky situation, to keep track of market movement, update his knowledge, yet

stay in the capital market and make money, therefore in looked forward to resuming help from

portfolio manager to do for him.

The portfolio management seeks to strike a balance between risks and return.

The generally rule in that greater risk more of the profits but S.E.B.I in its guidelines prohibits

portfolio managers to promise any return to investor.

Portfolio management is not a substitute to the inherent risks associated with equity investment.

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Who can be a portfolio manager?

Only those who are registered and pay the required license fee are eligible to operate as portfoliomanagers. An applicant for this purpose should have necessary infrastructure with professionally

qualified persons and with a minimum of two persons with experience in this business and a

minimum net worth of Rs.50lacs. The certificate once granted is valid for three years. Fees

payable for registration are Rs.2.5 lacs every for two years and Rs 1 lacs for the third year.From the fourth year onwards, renewal fees per annum are Rs 75000. These are subjected to

change by the SEBI.

The SEBI has imposed a number of obligations and a code of conduct on them. The portfolio

manager should have a high standard of integrity, honesty, and should not have been convicted

of any economic offence or moral turpitude. He should not resort to rigging up of prices, insidertrading or creating false markets, etc. their books of accounts are subject to inspection to

inspection and audit by the SEBI. The observance of the code of conduct and guidelines given by

the SEBI are subject to inspection and penalties for violation are imposed. The manager has tosubmit periodical returns and documents as may be required by the SEBI from time-to-time.

Functions of portfolio managers

Advisory role

Conducting market and economic services

Financial analysis

Study of stock market

Study of industry

Decide the type of port folio

Advisory role

Advice new investments, review the existing ones, identification of objectives, recommending

high yield securities etc.

Conducting market and economic service

This is essential for recommending good yielding securities they have to study the current fiscal

policy, budget proposal; individual policy etc. further portfolio manager should take in to

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account the credit policy, industrial growth, foreign exchange possible change in corporate laws

etc.

Financial analysisHe/she should evaluate the financial statement of company in order to understand, their net

worth future earnings, prospectus and strength.

Study of stock market

He/she should observe the trends at various stock exchange and analysis scripts so that he is able

to identify the right securities for investment.

Study of industry

He should study the industry to know its future prospects, technical changes etc. required for

investment proposal he should also see the problems of the industry.

Decide the type of portfolio

Keeping in mind the objectives of portfolio a portfolio manager has to decide weather the

portfolio should comprise equity preference shares, debentures convertibles, non-convertibles or

partly convertibles, money market, securities etc. or a mix of more than one type of proper mix

ensures higher safety yield and liquidity coupled with balanced risk techniques of portfolio

management.

A portfolio manager in the Indian context has been Brokers (Big brokers) who on the basis of

their experience, market trends, Insider trader, helps the limited knowledge persons. The ones

who use to manage the funds of portfolio, now being managed by the portfolio of MerchantBanks professionals like MBAs CAs And many financial institutions have entered the

market in a big way to manage portfolio for their clients.

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According to SEBI rules it is mandatory for portfolio managers to get them selfs registered.

Registered merchant bankers can acts as portfolio managers Investors must look forward, for

qualification and performance and ability and research base of the portfolio managers.

The following points must be considered by portfolio managers while

analyzing the securities

1.Nature of the Industry and its Product:

Long term trends of industries, competition with in, and out side the industry, Technical

changes, labor relations, sensitivity, to Trade cycle.

2.Industrial analysis of prospective earnings cash flows, working capital, dividends, etc.

3. Ratio analysis: Ratio such as Debt Equity Ratio, current ratio, net worth, profit

earnings ratio, return on Investment are worked out to decide the portfolio.

The wise principle of portfolio management suggests that Buy when the market is low or

BEARISH, and sell when the market is rising orBULLISH.

Stock market operation can be analyzed by

1. Fundamental Approach

2. Technical Approach

Fundamental approach

This approach will be worked Based on intrinsic value of shares

Technical approach

This approach will be worked on Dowjones theory, Random walk theory, etc.

Prices are based upon demand and supply of the market.

I. Traditional approach assumes that

II. Objectives are maximization of wealth and minimization of risk.

III. Diversification reduces risk and volatility.

IV. Variable returns, high illiquidity, etc.

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Capital assets pricing approach (CAPM) it pays more weight age, to risk or portfolio

diversification of portfolio.

Diversification of portfolio reduces risk but it should be based on certain

assessment such as

Trend analysis based on past share prices.

Valuation of intrinsic value of company (trend-market moves are known for their uncertainties

they are compared to be high, and low prompts of wave market trends are constituted by these

waves it is a pattern of movement based on past.).

Portfolio Management and Diversification

Combinations of securities that have high risk and return features make up a portfolio.

Portfolios may or may not take on the aggregate characteristics of individual part, portfolio

analysis takes various components of risk and return for each industry and consider the effort of

combined security.

Portfolio selection involves choosing the best portfolio to suit the risk return preferences of

portfolio investor management of portfolio is a dynamic activity of evaluating and revising the

portfolio in terms of portfolios objectives.

It is widely accepted that returns from individual scripts carry certain rate of risk. Portfolio held

in spreading the risk in many securities then the risk is reduced. The basic principle is that of a

portfolio holds several assets or securities.

It may include in cash also, even if one goes bad the other will provide protection from the loss

even cash is subject to inflation the diversification can be either vertical or horizontal the vertical

diversification portfolio can have script of different companys with in the same industry. In

horizontal diversification one can have different scripts chosen from different industries.

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CHAPTER - 2

REVIEW OF LITERATURE

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Portfolio Theories

MARKOWITZ THEORY

Markowitz approach determines for the investor the efficient set of portfolio through 3 important

variables, i.e., Standard Deviation, Covariance and Co-efficient of Correlation. Markowitz model

is called the Full Covariance Model. Through this method, 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 to infinity. According to this theory, the effects of one security

purchase over the effects of the other security purchase are taken into consideration and then the

results are evaluated.

Assumption under Markowitz Theory

Markowitz theory is based on the modern portfolio theory under several assumptions.

The assumptions are:-

1. The market is efficient and all investors have in their knowledge all the facts about thestock market and so on investor can continuously make superior returns either by predicting

past behavior of stocks through technical analysis the intrinsic value of shares. Thus all

investors are in equal category.

2. All investor before making any investment have a common goal. This is the avoidance of

risk because they are risk avers.

3. All investors would like to earn the maximum rate of return that they can achieve from

their investments.

4. The investors base their decisions on he expected rate of return of an investment. The

expected rate of return can be found out by finding out the purchase price of a security

divided by the income per year and by adding annual capital gains. It is also necessary to

know the standard deviation of the rate of return, which is begin offered on the investment.

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The rate of return and standard deviation are important parameters for finding out whether

investment is worthwhile for a person.

5. Markowitz brought out the theory that it was useful insight to find out how the security

returns are correlated to each other. By combining the assets in such way that they give the

lowest risk maximum returns could be brought out by the investor.

6. From the above it is clear that investor assumes that while making an investment he will

combine his investments in such a way that he gets a maximum return and is surrounded by

minimum risk.

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

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

can also be expected to be below.

8. The investor can reduce his risk if he adds investments to his portfolio.

9. An investor should be able to get higher for each level of risk by determining the

efficient set of securities.

THE SHARPE INDEX MODEL

The investor always likes to purchase a combination of stock that provides he highest return and

has lowest risk. He wants to maintain a satisfactory reward to risk ratio. Traditionally analysis

paid more attention to the return aspect of the stocks. Now a days risk has received increased

attention and analysts are providing estimates of risk as well as return.

Sharp has developed a simplified model to analyze the portfolio. He assumed that the return of a

security is linearly related to a single index like the market index. Strictly speaking, the market

index should consist of all the securities trading on the exchange.

In the absence of it, a popular index can be treated as a surrogate for the market index.

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SINGLE INDEX MODELCasual observation of the stock prices over a period of time reveals that most of the stock prices

move with the market index. When sensex increases, stock prices also tend to increase and vice-

versa. This indicates that some underlying factors affect the market index as well as the stock

prices. Stock prices are related to the market index and the relationship could be used to estimate

the return on stock. Towards this purpose, the following equation can be used.

imiij eRaaR ++=

Where R = Expected return on security I

ia = Intercept of the straight line or alpha co-efficient

ia = Slope of straight line or beta co-efficient

Rm = The rate of return on marker index

ei = Error team

Corner Portfolio

The entry or exit of a new stock in the portfolio generates a series of corner portfolio. In a one

stock portfolio, itself is the corner portfolio. In a two stock portfolio, the minimum attainable risk

(variance) and the lowest return would be the corner portfolio. As the member of stocks

increases in a portfolio, the corner portfolio would be the one with lowest return and risk

combination.

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Sharpes Optimal Portfolio

Sharpe has provided a model for the selection of appropriate securities in a portfolio. The

selection of any stock is directly related to its excess return beta ration.

ia/RfRi

Where, Ri = The expected return on stock i

Rf = The return on a risk less asset

ia = The expected change in the rate of return on stock I associated with one unitchanger in the market return.

The excess return is the difference between the expected return on the stock and the risk less rate

of interest such as the rate offered on the government security or Treasury bill. The excess return

to beta ratio measures the additional return on security (excess of the risk less asset return) per

unit of systematic risk or non-diversifiable risk. This ratio provides a relationship between

potential risk and reward.

The steps for finding out the stocks to be included in the optimal portfolio are given below:

1. Finding out the excess return to beta ratio for each stock under consideration.

2. Rank them from the highest to the lowest

3. Proceed to calculate C for all the stocks according to the ranked order using the following

formula.

( )( ) ei/iN1/ei/iRfRiNmCi 2222 +=

4. The calculated values of Ci start declining after a particular Ci and that point is taken as

the cut-off point and that stock ratio is the cut-off ratio.

Capital Asset Price Theory

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We have seen that diversifiable risk can be eliminated by diversification. The remaining risk

portion is the un-diversifiable risk i.e., market risk. As a result, investors are interested in

knowing the systematic risk when they search for efficient portfolios. They would like to have

assets with low beta coefficient i.e., systematic risk. Investors would opt for high beta co-

efficient only if they provide high rate of return. The risk were averse nature of the investors is

the underlying factor for this behavior. The capital asset pricing theory helps the investors top

understand and the risk and return relationship of the securities. It also explains how assets

should be priced in the capital market.

The CAPM Theory

Markowitz, William Sharpe, John Lintner and Jan Mossin provided the basis structure for the

CAPM model. It is a model of linear general equilibrium return. In the CAPM theory, the

required rate of return of an asset is having a linear relationship with assets beta value i.e.,

undiversifiable or systematic risk.

Assumptions

1. An individual seller or buyer cannot affect the price of a stock. This assumption is the

basic assumption of the perfect competitive market.

2. Investors make their decisions only on the basis of the expected returns, standard

deviations and covariances of all pairs of securities.

3. Investors are assumed to have homogenous expectations during the decision making

period.

4. The investor can lend or borrow any amount of funs at the risk less rate of interest. The

risk less rate of interest is the rate of interest offered for the treasury bills or government

securities.

5. Assets are infinitely divisible, according to this assumption, investor could buy and

quantity of share i.e., they can even buy ten rupees worth of Reliance Industry shares.

6. There is no transaction cost i.e., no cost involved in buying and selling of stocks.

7. There is no personal income tax. Hence, the investor is indifferent to the form of return

either gain or dividend.

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8. Unlimited quantum if short sales are allowed. Any amount of shares an individual can

sell short.

Lending and Borrowing

Here, it is assumed that the investor could borrow or lend any amount of money at risk less rate

of interest. When this opportunity is given to the investors, they can mix risk free assets with the

risk assets in a portfolio to obtain in desired rate of risk return combination.

The expected return on the combination of risky and risk free combination

Rp = RfXf + Rm(1 Xf)

Where, Rp = Portfolio return

Xf = The proportion of funds invested in risk free assets

1 Xf = The proportion of funds invested in risk assets.

Rf = Risk free rate of return

Rm = Return on risky assets

This formula can be used to calculate the expected returns for different situation like mixing risk

less assets with risky assets, investing only in the risky asset and mixing the borrowing with risk

assets.

The Concept

According to CAPM, all investors hold only the market portfolio and risk less securities. The

market portfolio is a portfolio comprised of all stocks in the market. Each asset is held in

proportion to its market value to the all risky assets. For example, if Reliance Industry share

represents 20% of all risky assets, then the market portfolio of the individual investor contains

20% of Reliance Industry shares. At this stage, the investor has the ability to borrow or lend any

amount of money at the risk less rate of interest. The efficient frontier of the investor is given in

figure.

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The figure shows the efficient of the investor. The investor prefers any point between B & C

because, with the same level of risk they face on line BA, they are liable to get superior profits.

The ABC lines show the investors portfolio of risky assets. The investors can combine risk less

asset either by lending or borrowing. This is shown in figure,

The line RfS represent all possible combination of risk less and risky asset. The S portfolio does

not represent any risk less asset but the line RfS gives the combination of both. The portfolio

along the path RfS is called lending portfolio i.e., some money is invested in the risk less asset or

may b deposited in the bank for a fixed rate of interest if it crosses the point S, it becomes

borrowing portfolio. Money is borrowed and invested in the risky asset. The straight lines are

called Capital Market Line (CML). It gives the desirable set of investment opportunities between

risk free and risky investments. The CML represents linear relationship between the required

rates of return for efficient portfolio and their standard deviations.

( ) ( ) pm

fmfp

RRRRE

+=

E(Rp) = Portfolios expected rate of return

Rm = Expected return on market portfolio

m = Standard deviation of market portfolio

p = Standard deviation of the portfolio

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For a portfolio on the capital market line, the expected rate of return in excess of the risk free rate

is in proportion to the standard deviation of the market portfolio. The slope of the line gives the

price of the risk. The slope equals the risk premium for the market portfolio Rm Rf divided by

the risk or standard deviation of the market portfolio. Thus, the expected return of an efficient

portfolio is

Expected return = Price of time + (Price of risk X amount of risk)

Price of time is the risk free rate of return. Price of risk is the premium amount higher and above

the risk free return.

Security Market Line

The Capital Market Line measures the risk-return relationship of an efficient portfolio. But, it

does not show the risk- return trade off for other portfolio and individual securities. Inefficient

portfolios lie below the capital market line and the risk-return relationship cannot be established

with the help of his capital market line. Standard deviation includes the systematic and

unsystematic risk. Unsystematic risk can be diversified and it is not related to the market. If the

unsystematic risk is eliminated, then the matter of concern is systematic risk alone. This

systematic risk could be measured by beta. The beta analysis is useful for individual securities

and portfolio whether efficient or inefficient.

When an additional security is added to the market portfolio, an additional risk is also added toit. The variance of a portfolio is equal to the weighted sum of the covariance of the individual

securities in the portfolio. If we add an additional security to the market portfolio, its marginal

contribution to the variance of the market is the covariance between the securitys return and

market portfolios return. If the security is included, the covariance between the security and the

market measures the risk. Dividing it by standard deviation of market portfolio Cov m/lm can

standardize covariance. This shows the systematic risk of the security, and then the expected

return of the security is given by the equation.

mim

m

fmfi /VCov

RRRR

=

This equation can be rewritten as follows:

[ ]fmm

2

imfi RR

CovRR

=

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The first term of the equation is nothing but the beta coefficient of the stock. The beta coefficient

of the equation of SML is same as the beta of the market (Single index) model. In equilibrium,

all efficient and inefficient portfolio lie along the security market line, The SML line helps to

determine the expected return for a given security beta. In other words, when betas are given, we

can generate expected returns for the given securities. This is explained in figure. If we assume

the expected market risk premium to be 8% and the risk free rate of return to be 7%, we can

calculate expected return for A, B, C and D securities using the formula.

( ) ( )[ ]fm1i RRERfRE +=

Market Imperfection and SML

Information regarding the share price and market condition may not be immediately available to

all investors; imperfect information may effect the valuation of securities. In a market with

perfect information, all securities should lie on SML. Market imperfections would lead to a band

to SML rather than a single line. Market imperfections after the width of the SML to a band, if

imperfections were more, the width also would be larger.

Empirical tests of the CAPM

In the CAPM, beta is use to estimate the systematic risk of the security and reflects the future

volatility of the stock in relation to the market. Future volatility of the stock is estimated only

through historical data. Historical data are used to plot the regression line or the characteristics

line and calculate beta. If historical betas are stable over a period of time, they would be good

proxy for their ex-ante or expected risk.

Robert A. levy, Marshall E. Blume and other studied the question of beta stability in-depth. Levy

calculated betas for the both individual securities and portfolios. His study results have provided

the following conclusions.

1. The betas of individuals stocks are unstable; hence the past betas for the individual

securities stocks estimators of future risk.

2. The betas of portfolio of ten or more randomly selected stocks are reasonably stable,

hence he past portfolio betas are good estimators of future portfolio volatility. This is

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because of the errors in the estimate of individual securities betas tending to offset one

another in a portfolio.

Various researchers have attempted to find out the validity of the model by calculating beta and

realized rate of return. They attempted to test (1) whether the intercept is equal to Rf i.e., risk free

rate of interest or the interest for treasury bills (2) whether the line is linear and pass through the

beta = 1 being the required rate of return of the market. In general, the studies have showed the

following results.

1. The studies generally showed a significant positive relationship between the expected

return and the systematic risk. But the slope of the relationship is usually less than that of

predicted by the CAPM.

2. The risk and return relationship appears to be linear. Empirical studies give no evidence

of significant curvature in the risk/return relationship.

3. The attempt of the researchers to access the relative importance of the market and

company risk has yielded results. The CAPM theory implies that unsystematic risk is not

relevant, but unsystematic and systematic risks are positively related to security returns.

Higher returns are needed to compensate both the risks. Most of the observed relationship

reflects statistical problems rather than the true nature of capital market.

4. According to Richard Roll, the ambiguity of the market portfolio leaves the CAPM

untreatable. The practice of using indices, as proxies is loaded with problems. Different

indices yield different betas for the same security.

5. If the CAPM were completely valid, it should apply to all financial assets including

bonds. But, when bonds are introduced into the analysis, they do not all on the security

market line.

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Present Validity of CAPM

The CAPM is greatly appealing at an intellectual level, logical and rational. The basic

assumptions on which the model is built raise, some doubts in the minds of the investors. Yet,

investment analysis has been more creative in adapting CAPM for their uses.

1. The CAPM focuses on the market risk, makes the investors to think about the risky

ness of the assets in general CAPM provides basic concept, which is truly

fundamental values.

2. The CAPM has been useful in the selection of securities and portfolio. Securities withhigher returns are considered to be undervalued and attractive for buy. The below

normal excepted return yielding securities are considered to be overvalued and

suitable for sale.

3. In the CAPM, it has been assumed that investors consider only the market risk. Given

the estimate of the risk free rate, the beta of the firm, stock and the required market

rate of return, one can find out the expected returns for a firms security. This

expected return could be used as an estimate of the cost of retained earnings.

4. Even through CAPM has been regarded as fuseful tools to financial analysis; it has it

won critics too. They point out, when the model is ex-ante; the inputs also should be

ex-ante, i.e. based on the expecat5ions of the f8re. Empirical test and analysis have

used ex-post i.. Past data only:

5. The historical data regarding the market return, risk free rate of return and betas vary

differently for different periods. The various methods used to estimate these inputs

also affect the beta value. Since the inputs cannot be estimated precisely, the expected

return found out through the CAPM model is also subjected to criticism.

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Arbitrage pricing theory

Arbitrage pricing theory is one of the tools used by the investors and portfolio mangers. The

capital asset pricing theory explains the returns of the securities on the basis of their respective

bets. According to the previous model, the investor chooses the investment on the basis of

expected return and variance. The alternative model deployed in asset pricing by Stephen Ross is

known as Arbitrage Pricing Theory. The APT explains the nature of equilibrium in the asset

pricing in a less complicated manner with fewer assumptions compare to CAPM.

The Assumptions1. The investors have homogeneous expectations.

2. The investor are risk averse and utility maxi misers

3. Perfect competition prevails in the market and there is no transaction cost.

The APT theory does not assume:

a) Single period investment horizon

b) No taxes

c) Investors can borrow and lend at risk free rate of interest and

d) The selection of the portfolio is based on the mean and variance analysis.

These assumptions are present in CAPM theory.

Arbitrage portfolio

According to the APT theory an investor tries to find out the possibility to increase returns form

his portfolio without increasing the funds in the portfolio. He also likes to keep the risk at the

same level.

For example, the investor holds A, B and C securities and he wants to change in proportion of

securities can be denoted by X, bX

and CX . The increase in the investment in security A could be

carried out only if he reduces the proportion of investment either in B or C because it has already

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stated that the investor tries to earn more income without increasing his financial commitment.

Thus, arbitrage portfolio. If X indicates the change in proportion,

0XXX CBA =++

The factor sensitivity indicates the responsiveness of a securitys return to a particular factor.

The sensitiveness of securities to any factor is the weighted average of the sensitivities of the

securities, weighted being the changes made in the proportion. For example, bA, bB and bC are

sensitive in an arbitrage portfolio the sensitive become zero.

0XbXbXb CCBBAA =++

APT and CAPM

The simplest form of APT model is consistent with the simple form of the CAPM model, when

only one factor is taken into consideration, the APT can be stated as.

Ii0i bR +

It is similar to the capital market line equation:

)RR(RR Fmifi += , Which is similar to CAPM model

APT is more general and less restrictive than CAPM, in APT, the investor has no need to hold

the market portfolio because it does not make use of the market portfolio concept. The portfolios

are constructed on the basis of the factors eliminate arbitraged profits. APT is based on the law

of one price to hold for all possible portfolio combinations.

The APT model takes on to account of the impact of numerous factors on the security. The |

Macro economic factors are taken into consideration and it is closer to reality then CAPM.

The market portfolio is well defined conceptually. In APT model, factors are not well specified.

Hence, the investor finds it difficult to establish equilibrium relationship. The well defined

market portfolio is a significant advantage of the CAPM leading to the wide usage of the model

in the stock market.

The factors that have impact on one group of securities may not affect other group securities.

There is a lack of constituency in the measurement of the APT model. Further, the influences of

the factors are not independent of each other. It may be difficult to identify the influence

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corresponds exactly to each factor. Apart from this, not all variable that exerts influence on

factor measurable.

CHAPTER 3Company profile

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CHAPTER 4

ABOUT STOCK MARKET

HISTORY OF STOCK EXCHANGE

The only stock exchanges operating in the 19 the century were those of Bombay set up in 1875and Ahmadabad set up in 1894. These were organized as voluntary non-profit-making

association of brokers to regulate and protect their interests. Before the control on securities

trading become a central subject and the Bombay securities contracts (control) Act of 1925 used

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to regulate trading in securities. Under this Act, the Bombay stock exchange was recognized in

1927 and Ahmadabad in 1937

During the war boom, a number of stock exchanges were organized even in Bombay,

Ahmadabad and other centers, but they were not recognized. Soon after it became a central

subject, central legislation was proposed and a committees and public discussion, the securitiescontracts (regulation) Act became law in 1956.

DEFINITION OF STOCK EXCHANGE

Stock exchange means anybody or individuals whether incorporated or not, constituted for the

purpose of assisting, regulating or controlling the business of buying, selling or dealing in

securities.

It is an association of member brokers for the purpose of self-regulation and protecting the

interests of its members.

It can operate only if it is recognized by the Government under the securities contracts

(regulation) Act, 1956. The recognition is granted under section 3 of the act by the centralgovernment, Ministry of Finance.

NATURE & FUNCTIONS OF STOCK EXCHANGE

There is an extraordinary amount of ignorance and of prejudice born out of ignorance with

regard to nature and functions of Stock Exchange. As economic development proceeds, thescope for acquisition and ownership of capital by private individuals also grow. Along with it,

the opportunity for Stock Exchange to render the service of stimulating private savings and

challenging such savings into productive investment exists on a vastly great scale. These are

services, which the Stock Exchange alone can render efficiently.

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The Stock Exchanges in India have an important role to play in the building of a real

shareholders democracy. To protect the interest of the investing public, the authorities of the

Stock Exchanges have been increasingly subjecting not only its members to a high degree of

discipline, but also those who use its facilities-Joint Stock Companies and other bodies in whose

stocks and shares it deals.

The activities of the Stock Exchange are governed by a recognized code of conduct apart from

statutory regulations. Investors both actual and potential are provided, through the daily Stock

Exchange quotations. The job of the Stock Exchange and its members is to satisfy the need of

market for investments to bring the buyers and sellers of investments together, and to make the

Exchange of Stock between them as simple and fair a process as possible.

CHARACTERISTICS OF STOCK EXCHANGES IN INDIA

Traditionally, a stock exchange has been as association of individual members called brokers,

formed for the express purpose of regulating and facilitating the buying and selling of securities

by the public and institutions at large. A stock exchange in India operates with the recognition

from the government under the securities and contracts (Regulation Act, 1956). The member

brokers are essentially the middlemen, who transact in securities on behalf of the public for a

communism or on their behalf. There are at present 24 stock exchanges in India. The largest

among them, being the Bombay Stock Exchange (BSE), which alone accounts for over 80% of

due total volume of transactions in shares in the country.

Securities and Exchange Board of India (SEBI) has been setup in Bombay by the Government to

oversee the orderly development of Stock Exchange in the country. All companies wishing to

raise capital from the public are required to list their securities on at least one Stock Exchange.

Thus, all ordinary shares, Preference Shares and Debentures of publicly held companies are

listed in one or more Stock Exchanges. Stock Exchanges also facilitate trading in the securities

of the public sector companies as well as Government Securities.

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NEED FOR A STOCK EXCHANGE

As the business and industry expanded and economy became more complex in nature, a need for

permanent finance arose. Entrepreneurs require money for long-term needs, were as investors

demand liquidity. The solution to this problem gave way for the origin of Stock Exchange,

which is a ready market for investment and liquidity.

As per the Securities Contract Act, 1956, Stock Exchange means any body of individuals

whether incorporated or not, constituted for the purpose of regulating or controlling the business

of buying, selling or dealing in securities.

Securities include:

Shares, Scrips, Stocks, Bonds, Debentures and other Marketable Securities.

Government Securities.

Rights or Interests in Securities.

SECURITIES AND EXCHANGE BOARD OF INDIA (SEBI)

Securities and Exchange Board of India (SEBI) set up as an autonomous regulatory authority by

the government of India in 1988 to protect the interests of investors in securities and to promote

the development of, and to regulate the securities market and for matters connected therewith or

incidental thereto. It is empowered by two acts namely the SEBI Act, 1992 and the securities

contract (regulation) Act, 1956 to perform the function of protecting investors rights and

regulating the capital markets.

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Securities and Exchange Board of India (SEBI) regulatory reach has been extended to more areas

and there is a considerable change in the capital market. SEBI's annual report for 1997-98 has

stated that through out its six-year existence as a statutory body, it has sought to balance the twin

objectives of investor protection and market development. It has formulated new rules and

crafted regulations to foster development. Monitoring and surveillance was put in place in the

Stock Exchanges in 1996-97 and strengthened in 1997-98.

SEBI was set up as an autonomous regulatory authority by the government of India in 1988 to

protect the interests of investors in securities and to promote the development of, and to regulate

the securities market and for matters connected therewith or incidental thereto. It is empowered

by two acts namely the SEBI Act, 1992 and the securities contract (regulation) Act, 1956 to

perform the function of protecting investors rights and regulating the capital markets.

OBJECTIVES OF SEBI

The promulgation of the SEBI ordinance in the parliament gave statutory status to SEBI in 1992.

According to the preamble of the SEBI, the three main objectives are: -

To protect the interests of the investors in securities.

To promote the development of securities market.

To regulate the securities market.

FUNCTIONS OF SEBI

Regulating the business in Stock Exchange and any other securities market.

Registering and regulating the working of Stock Brokers, Sub-Brokers, Share Transfer

Agents, Bankers to the issue, Trustees to trust deeds, Registrars to an issue, Merchant

Bankers, Underwriters, Portfolio Managers, Investment Advisers and such other

Intermediaries who may be associated with securities market in any manner.

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Registering and regulating the working of collective investment schemes including

Mutual Funds.

Promoting and regulating self-regulatory organizations.

Prohibiting fraudulent and unfair trade practices in the securities market.

Promoting investor's education and training of intermediaries in securities market.

Prohibiting Insiders Trading in securities.

Regulating substantial acquisition of shares and take-over of companies.

Calling for information, understanding inspection, conducting enquiries and audits of the

Stock Exchanges, Intermediaries and Self-Regulatory organizations in the securities

market.

BOMBAY STOCK EXCHANGE

The Stock Exchange, Mumbai, Popularly known as "Bombay Stock Exchange" (BSE) wasestablished in 1875 as "The Native Share and Stock Brokers Association", as a voluntary non-

profit making association. It has evolved over the years into its present status as the premier

Stock Exchange in the country. It may be noted that the Bombay Stock Exchange is the oldest

one in Asia, even older than the Tokyo Stock Exchange, which was founded in 1878.

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The Bombay Stock Exchange, while providing an efficient and transparent market for trading in

securities, upholds the interests of the investors and ensures redressal of their grievances,

whether against the companies or its own member-brokers. It also strives to educate andenlighten the investors by making available necessary informative inputs and conducting

investor education programmes

A Governing Board comprising of 9 elected Directors (one third of them retire every year byrotation), Two SEBI Nominees, Seven Public representatives and an Executive Director is theApex Body, which decides the policies and regulates the affairs of the Bombay Stock Exchange

The Executive Director as the Chief Executive Officer is responsible for the day-to-day

administration of the Bombay Stock Exchange.

SECURITIES TRADEDThe securities traded in the BSE are classified into three groups namely, specified shares of 'A'

group and non-specified securities. The latter is sub-divided into 'B1' and 'B' groups. 'A' group

contains the companies with large outstanding shares, good track record and large volumes ofbusiness in the

secondary market. Settlements of all the shares are carried out through the Clearing House.

Year Number of Listed

Companies

Market

Capitalization

(In Crores)

Annual Turnover

(In Crores)

Average Daily

Turnover

(Rs. In Billion)

1994-95 4702 4355 677 1.8

1995-96 5602 5365 501 2.2

1996-97 5832 4639 1243 5.2

1997-98 5853 5630 2706 8.5

2000-04 6000 5479 2449 11.5

NATIONAL STOCK EXCHANGE

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The National Stock Exchange was incorporated in November, 1992 with an equity capital of Rs.

25crores. The International Securities Consultancy (ISC) of Hong Kong has helped in

setting up National Stock Exchange. ISC has prepared the detailed business plans and

installation of hardware and software systems. The promotions for National Stock

Exchange were Financial Institutions, Insurances Companies, Banks and SEBI Capital

Market Limited, Infrastructure Leasing and Financial Services Limited and Stock

Holding Corporation Limited. It has been set up to strengthen the move towards

professionalisation of the capital market as well as provide nation wide securities

trading facilities to investors.

National Stock Exchange is not an exchange in the traditional sense where brokers own and

manage the exchange. A two tier administrative set up involving a company board and a

governing board of the exchange is envisaged.

National Stock Exchange is a national market for shares Public Sector Units Bonds, Debentures

and Government

The National Stock Exchange (NSE) of India became operational in the capital market segment

on 3rd, November 1994 in Mumbai. The genesis of the NSE lies in the recommendations

of the Pherwani Committee (1991). Apart from NSE, it had recommended for the

establishment of National Stock Market System also. Committee pointed out six major

defects in the Indian Stock Market.

OBJECITVES OF NATIONAL STOCK EXCHANGE

To establish a nation wide trading facility fro equities, debt instruments and hybrids.

To ensure equal access to investors all over the country through appropriate

communication network.

To provide a fair, efficient and transparent securities market to investors using an

electronic communication network.

To enable shorter settlement cycle and book entry settlement system.

To meet current international standards of securities market.

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PROMOTERS OF NATIONAL STOCK EXCHANGE

IDBI, ICICI, IFCI, LIC, GIC, SBI, Bank of Baroda, Canara Bank, CorporationBank, Indian Bank, Oriental Bank of Commerce, Union Bank ofIndia, Punjab National Bank, Infrastructure Leasing and Financial

Services, StockHolding Corporation of India and SBI Capital Market are the promoters of

NATIONAL STOCK EXCHANGE.

NSE-NIFTY

The National Stock Exchange on April 22, 1996 launched a new Equity Index. The NSE-50.

The new Index which replaces the existing NSE-100 Index, is expected to serve as anappropriate Index for the new segment of futures and options.

"Nifty" means National Index for Fifty Stock.

The NSE-50 comprises 50 companies that represent 20 broad Industry groups with an aggregate

market capitalization of around Rs.1,70,000 crores. All companies included in the Index have amarket capitalization in excess of Rs.500crores each and should have traded for 85% of trading

days at an impact cost of less than 1.5%.

The base period for the index is the close of prices on Nov 3, 1995, which makes one year of

completion of operation of NSE's capital market segment. The base value of the Index has been

set at 1000.

NSE-MIDCAP INDEX

The National Stock Exchange Midcap Index or the Junior Nifty comprises 50 stocks that

represents 21 board Industry groups and will provide proper representation of the madcap

segment of the Indian Capital Market. All stocks in the Index should to establish a nation

wide trading facility fro equities, debt instruments and hybrids.

To ensure equal access to investors all over the country through appropriate

communication network.

To provide a fair, efficient and transparent securities market to investors using an

electronic communication network.

To enable shorter settlement cycle and book entry settlement system.

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To meet current international standards of securities market.

STOCK EXCHANGES IN INDIA

S.No NAME OF THE STOCK EXCHANGE YEAR

1. Bombay Stock Exchange 1875

2. Hyderabad Stock Exchange. 1943

3. Ahmadabad Share and Stock Brokers Association. 1957

4. Calcutta Stock Exchange Association Limited. 1957

5. Delhi Stock Exchange Association Limited. 1957

6. Madras Stock Exchange Association Limited. 1957

7. Indoor Stock Brokers Association. 1958

8. Bangalore Stock Exchange. 1963

9. Cochin Stock Exchange. 1978

10. Pune Stock Exchange Limited. 1982

11. U.P Stock Exchange Association Limited. 1982

12. Ludhiana Stock Exchange Association Limited. 1983

13. Jaipur Stock Exchange Limited. 1984

14. Gauhathi Stock Exchange Limited. 1984

15. Mangalore Stock Exchange Limited. 1985

16. Maghad Stock Exchange Limited, Patna. 1986

17. Bhubaneswar Stock Exchange Association Limited. 1989

18. Over the Counter Exchange of India, Bombay. 1989

19. Saurasthra Kutch Stock Exchange Limited. 199020. Vadodara Stock Exchange Limited. 1991

21. Coimbatore Stock Exchange Limited. 1991

22. Meerut Stock Exchange Limited. 1991

23. National Stock Exchange Limited. 1992

24. Integrated Stock Exchange. 1999

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CHAPTER 5

DATA ANALYSIS

PORTFOLIO MANAGEMENT CONCEPTUAL FRAME WORK

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Portfolio analysis believes in the maximization of return through a combination of securities. The

modern portfolio theory discusses the relationship between different securities and then draws

inter-relationship of risks between them. It is not necessary to achieve success only by trying to

get all securities of minimum risk. The theory states that by combining a security of low risk

with another security of high risk, success can be achieved by an investor in making a choice of

investment outlets.

Average Returns of The Company: Table No 1

S. No. Security Average

1 WIPRO 1.84

2 ICICI 8.48

3 RELIANCE 11.76

4 RANBAXY 23.06

5 ITC -1.76

Average Return = N/RiR =

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Where

R = Average Return

Ri = Return of the Security I for the year T

N = Number of Years

Based on above average return of securities of Ranbaxy is earning higher return and ITC isearning lowest return. Other securities are earning medium rage returns such are Wipro, ICICI

and Reliance.

FIGURE NO 1

Standard Deviation of the Companies: Table No 2

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S. No. Security Std dev

1 WIPRO 65.49

2 ICICI 72.11

3 RELIANCE 86.304 RANBAXY 96.62

5 ITC 33.59

2)RR(1n/1D.S =

T = 1

Based on above calculations Standard deviations like that Ranbaxy is highest and ITC is lower,where other securities are having medium standard deviation.

FIGURE NO 2

CORRELATION CO-EFFICIENT BETWEEN THE SECURITIES

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Security Wipro ICICI Reliance Ranbaxy ITC

Wipro 1 0.3787 0.2774 0.9333 0.6444

ICICI 1 0.3093 0.8050 0.3911

Reliance 1 0.4326 0.7980

Ranbaxy 1 0.7445

ITC 1

Formula

Correlation Co-efficient b.a/)ab(COV)abn( =

Where COV (ab) = RBRB)(RARA(1n/1

PORTFOLIO WEIGHTS: Table No 3

S.NO PORTFOLIO CORRELATION WEIGHT

OF A

WEIGHT OF

B

1 Wipro & ITC 0.6444 -0.1120 1.1120

2 Wipro & Ranbaxy 0.9333 1.89 -0.89

3 Wipro & ICICI 0.3787 0.5770 0.423

4 Wipro & Reliance 0.2774 0.683 0.317

5 ITC & Ranbaxy 0.7445 1.228 -0.228

6 ITC & ICICI 0.3911 0.959 0.041

7 ITC & Reliance 0.7980 1.300 -0.30

8 Ranbaxy & ICICI 0.8050 -0.123 1.123

9 Ranbaxy & Reliance 0.4326 0.401 0.59910 ICICI & Reliance 0.3093 0.627 0.373

Formula

Weight of a (Wa) = )b.a.nab2()ba/()anabb(b 22 +

Weight of b (Wb) = 1 Wa

Portfolio Risk: Table No 4

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S.NO COMBINATION PORTFOLIO

RISK

1 Wipro & ITC 33.10

2 Wipro & Ranbaxy 109.27

3 Wipro & ICICI 56.84

4 Wipro & Reliance 58.54

5 ITC & Ranbaxy 11.69

6 ITC & ICICI 33.47

7 ITC & Reliance 23.82

8 Ranbaxy & ICICI 69.76

9 Ranbaxy & Reliance 23.62

10 ICICI & Reliance 63.09

Formula:

WaWb.b.a.nab.2WbbWaap 2222 ++=

Where:

RiskPortfoliop

b&aSecutirybetweenCoeffientnCorrelationab

bSecurityofWeightWb

aSecurityofWeightWa

bSecurityofdeviationdradtanSb

aSecuritiyofdeviationdrardtanSa

=

=

=

=

=

=

Portfolio Return: Table No 5

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RETURN

1 Wipro & ITC -2.1632

2 Wipro & Ranbaxy -17.045

3 Wipro & ICICI 4.648

4 Wipro & Reliance 4.984

5 ITC & Ranbaxy -7.418

6 ITC & ICICI -1.340

7 ITC & Reliance -5.816

8 Ranbaxy & ICICI 6.686

9 Ranbaxy & Reliance 16.291

10 ICICI & Reliance 9.703

Formula:

Rp = (Ra X Wa) + (Rb X Wb)Where:

Ra = Average Return of Security a

Rb = Average Return of Security b

Wa = Weight of Security a

Wb = Weight of Security b

Rp = Portfolio Return

Portfolio Risk & Return: Table No 6

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RISK

Portfolio

Return

1 Wipro & ITC 33.10 -2.1632

2 Wipro & Ranbaxy 109.27 -17.045

3 Wipro & ICICI 56.84 4.648

4 Wipro & Reliance 58.54 4.984

5 ITC & Ranbaxy 11.69 -7.418

6 ITC & ICICI 33.47 -1.340

7 ITC & Reliance 23.82 -5.816

8 Ranbaxy & ICICI 69.76 6.686

9 Ranbaxy & Reliance 23.62 16.291

10 ICICI & Reliance 63.09 9.703

FIGURE NO 3

PORTFOLIO SELECTION, REVISION & EVALUATION

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Portfolio Section

Portfolio analysis provides the input for next phase in portfolio management, which is portfolio

selection. The proper goal of portfolio construction is to generate a portfolio that provides the

highest returns at a given level of risk. The inputs from portfolio analysis can be used to identify

the set of efficient portfolios. From this the optimal portfolio must 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.

So, out of the various combinations (related to five companies), the optimal portfolio is Ranbaxy

& Reliance, as this portfolio has minimum risk of 23.62% with maximum return of 16.291%.

Hence, I can say that it is better to invest in these portfolios.

Portfolio revision

Economy and financial markets are dynamic, change take place almost daily. As time passes

securities which were once attractive may lease to be so. New securities with promise of high

return and low risk may emerge. The investor now has to revise his portfolio in the light of

developments in the market. This leads to purchase of some new securities and sale of some of

the existing securities and their proportion in the portfolio changes as a result of the revision.

The revision has to be scientifically and objectively so as to ensure the optimality of the revised

portfolio, it important as portfolio analysis and selection.

Portfolio Evaluation

The objective of constructing a portfolio and revising I t periodically is to earn maximum returns

with minimum risk. Portfolio evaluation is the process, which is concerned with assessing the

performance of the portfolio over a selected period of time in terms of returns and risk. This

involves quantities measurement of actual return realized. Alternative measures of performance

evaluation have been developed by investor and portfolio managers for their use.

It provides a mechanism for identifying weakness in the investment process and improving them.

The portfolio management process is an on going process to portfolio construction, continues

with portfolio revision and evaluation. The evaluation provides the necessary feedback for better

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designing of portfolio the next time and around. Superior performance is achieved thorough

continual refinement of portfolio management skills.

CALCULATION OF AVERAGE RETURNS OF COMPANIES

WIPRO

Year Opening

Share price

(P0)

Closing

Share price

(P1)

(P1 P0) (P1 P0)/

P0*100

2006-07

2007-08

2008-092009-10

2010-11

538.55

571.60

488.75330.85

671.50

559.40

432.10

245.90706.95

441.40

20.85

-139.50

-242.85376.10

-230.10

3.87

-24.40

-49.69113.67

-34.27

Total Return 9.18

Returns are calculated as below

Return of 06-07

= (P1-P0)/P0*100 = (559.40-538.55)/538.55*100 = 3.87

Return of 07-08

= (P1-P0)/P0*100 = (432.10-571.60)/571.60*100 = -24.40

Return of 08-09

= (P1-P0)/P0*100 = (245.90-488.75)/488.75*100 = -49.69

Return of 09-10

= (P1-P0)/P0*100 = (706.95-330.85)/330.85*100 = 113.67

Return of 10-11

= (P1-P0)/P0*100 = (441.40-671.50)/671.50*100 = -34.27

Average Return = 9.18/5 = 1.84

ICICI

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Year OpeningShare price

(P0)

ClosingShare price

(P1)

(P1 P0) (P1-P0)/P0*100

2006-07

2007-082008-092009-10

2010-11

591.75

865.85879.60479.20

951.95

853.35

769.40332.80952.50

1016.35

261.60

-96.42-546.80473.75

64.40

44.20

-11.13-96.2798.86

6.76

Total Return 42.42


Return of 06-07

= (P1-P0)/P0*100 = (853.35-591.75)/591.75*100 = 44.20

Return of 07-08

= (P1-P0)/P0*100 = (769.40-865.85)/865.85*100 = -11.13

Return of 08-09

= (P1-P0)/P0*100 = (332.80-879.60)/879.60*100 = -96.27

Return of 09-10

= (P1-P0)/P0*100 = (952.50-479.20)/479.20*100 = 98.86

Return of 10-11

= (P1-P0)/P0*100 = (1016.35-951.95)/951.95*100 = 6.76


RELIANCE

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(P0)

ClosingShare price

(P1)

(P1 P0) (P1- P0) /P0*100

2006-07

2007-082008-092009-10

2010-11

615.45

509.751430.55695.20

1137.40

494.20

1250.85515.55999.05

606.75

-121.25

741.10-915.00303.85

-530.65

-19.70

145.38-68.9643.71

-46.65

Total Return 58.78


Return of 06-07

= (P1-P0)/P0*100 = (494.20-615.45)/615.45*100 =-19.70

Return of 07-08

= (P1-P0)/P0*100 = (1250.85-509.75)/ 509.75*100 = 145.38

Return of 08-09

= (P1-P0)/P0*100 = (515.55-1430.55)/ 1430.55*100 = -68.96

Return of 09-10

= (P1-P0)/P0*100 = (999.05-695.20)/ 695.20*100 = 43.71

Return of 10-11

= (P1-P0)/P0*100 = (606.75-1137.40)/ 1137.40*100 = -46.65


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RANBAXY

Year Opening

Share price(P0)

Closing

Share price(P1)

(P1 P0) (P1-P0)/

P0*100

2006-072007-08

2008-09

2009-102010-11

472.50371.95

479.75

166.00443.30

351.90438.45

165.70

475.40452.20

-120.6066.50

-314.05

309.408.90

-25.5217.88

-65.46

186.382.01

Total Return 115.29


Return of 06-07

= (P1-P0)/P0*100 = (351.90-472.50)/ 472.50*100 = -25.52

Return of 07-08

= (P1-P0)/P0*100 = (438.45-371.95)/ 371.95*100 = 17.88

Return of 08-09

= (P1-P0)/P0*100 = (165.70-479.75)/ 479.75*100 = --65.46

Return of 09-10

= (P1-P0)/P0*100 = (475.40-166.00)/ 166.00*100 = 186.38

Return of 10-11= (P1-P0)/P0*100 = (452.20-443.30)/ 443.30*100 = 2.01

Average Return = 115.29/5 = 23.06

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ITC (Indian Tobacco Corporation)


(P0)

ClosingShare price

(P1)

(P1 P0) (P1-P0)/P0*100

2006-07

2007-08

2008-092009-10

2010-11

203.75

160.05

219.90188.90

265.85

151.15

206.25

184.85263.05

172.40

-52.60

46.20

-35.0574.15

-93.45

-25.81

28.86

-15.9439.25

-35.15

Total Return -8.79


Return of 06-07

= (P1-P0)/P0*100 = (151.15-203.75)/ 203.75*100 = -25.81

Return of 07-08

= (P1-P0)/P0*100 = (206.25-160.05)/ 160.05*100 = 28.86

Return of 08-09

= (P1-P0)/P0*100 = (184.85-219.90)/ 219.90*100 = -15.94

Return of 09-10

= (P1-P0)/P0*100 = (263.05-188.90)/ 188.90*100 = 39.25

Return of 10-11

= (P1-P0)/P0*100 = (172.40-265.85)/ 265.85*100 = -35.15

Average Return = -8.79/5 = -1.76

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CALCULATION OF STANDARD DEVIATIONS

WIPRO

Year Return (R) Avg. Rtn. ( )R RR ( RR )2

2006-072007-

08

2008-09

2009-

102010-

11

3.87

-24.40-49.69

113.67

-34.27

1.841.841.84

1.84

1.84

2.03-26.24-51.53

111.83

-36.11

4.12688.542655.34

12505.95

1303.93

(R) = 9.18 ( RR )2 17157.88

Average Return = (R)/N = 9.18/5 = 1.84

Variance = 1/N 1 ( RR )2 = 1/5 1 (17157.88) = 4289.47

Standard Deviation = 47.4289 = 65.49

ICICI


2006-

07

2007-08

2008-

092009-

10

2010-

11

44.20-11.13

-96.27

98.866.76

8.48

8.48

8.488.48

8.48

35.72

-19.61

-104.7590.38

-1.72

1275.92

384.55

10972.568168.54

-2.96

(R) = 42.42 ( RR )2 20798.61


Variance = 1/N 1 ( RR )2

= 1/5 1 (20798.61) = 5199.65


RELIANCE


2006- -19.70 11.76 -31.46 989.73

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07

2007-08

2008-

09

2009-10

2010-11

145.38

-68.9643.71

-46.65

11.76

11.7611.76

11.76

133.62

-80.7231.95

-58.41

17854.30

6515.721020.80

3411.73

(R) = 58.78 ( RR )2 29792.28


Variance = 1/N 1 ( RR )2 = 1/5 1 (29792.28) = 7448.07


RANBAXY


2006-

072007-

08

2008-09

2009-

10

2010-

11

-25.52

17.88

-65.46186.38

2.01

23.06

23.0623.06

23.06

23.06

-48.58

-5.18-88.52

163.32

-21.05

2360.02

26.837835.79

26673.42

443.10

(R) = 115.29 ( RR )2 37339.16


Variance = 1/N 1 ( RR )2 = 1/5 1 (37339.16) = 9334.79


ITC


2006-07

2007-

082008-

-25.8128.86

-15.94

39.25-35.15

-1.76-1.76

-1.76

-1.76-1.76

-24.0530.62

-14.18

41.01-33.39

578.40937.58

201.07

1681.821114.89

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09

2009-10

2010-

11

(R) = -8.79 ( RR )2

4513.76

Average Return = (R)/N = -8.79/5 = -1.76

Variance = 1/N 1 ( RR )2 = 1/5 1 (4513.76) = 1128.44


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CALCULATION OF CORRELATIONS

1. CORRELATION BETWEEN WIPRO & ITC

Year RARA RBRB ( )( )RBRBRARA 2006-07

2007-

08

2008-09

2009-

102010-

11

2.03

-26.24-51.53

111.83

-36.11

-24.05

30.62-14.18

41.01

-33.39

-48.82

-803.47730.69

4586.15

1205.71

( )( )RBRBRARA 5670.26

COVARIANCE (COVab) = 1/n-1 ( )( )RBRBRARA

= 1/5-1(5670.26) = 1417.56

59.3349.65 == ba

Correlation Coefficient (n ~ab) = COVab/ b.a

= 1417.56/65.49*33.59 = 0.6444

2. CORRELATION BETWEEN WIPRO & RANBAXY

Year RARA RBRB ( )( )RBRBRARA 2006-

07

2007-08

2008-

09

2009-10

2010-11

2.03

-26.24

-51.53111.83

-36.11

-48.58

-5.18

-88.52163.32

-21.05

-98.62

135.92

4561.4318264.07

760.12

( )( )RBRBRARA 23622.92


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= 1/5-1(23622.92) = 5905.73

62.9649.65 == ba


= 5905.73/65.49*96.62 = 0.9333

3. CORRELATION BETWEEN WIPRO & ICICI


07

2007-08

2008-09

2009-

102010-

11

2.03-26.24

-51.53111.83

-36.11

35.72-19.61

-104.7590.38

-1.72

72.51514.56

5397.761107.19

62.11

( )( )RBRBRARA 7154.13


= 1/5-1(7154.13) = 1788.53

11.7249.65 == ba


= 1788.53/65.49*72.11 = 0.3787

4. CORRELATION BETWEEN WIPRO & RELIANCE


072007-

08

2008-

2.03

-26.24-51.53

111.83

-36.11

-31.46

133.62-80.72

31.95

-58.41

-63.86

-3506.194159.50

3572.97

2109.18

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09

2009-10

2010-

11

( )( )RBRBRARA 6271.60


= 1/5-1(6271.60) = 1567.90

30.8649.65 == ba


= 1567.90/65.49*86.30 = 0.2774

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5. CORRELATION BETWEEN ITC & RANBAXY


07

2007-

082008-

09

2009-10

2010-

11

-24.0530.62

-14.18

41.01-33.39

-48.58-5.18

-88.52

163.32-21.05

1168.35-158.61

1255.21

6697.75702.86

( )( )RBRBRARA 9665.56

COVARIANCE (COVab) = 1/n-1 ( )( )RBRBRARA = 1/5-1(9665.56) = 2416.39

62.9659.33 == ba


= 2416.39/33.59*96.62= 0.7445

6. CORRELATION BETWEEN ITC & ICICI


2007-

082008-

09

2009-

102010-

11

-24.0

530.62

-14.18

41.01

-33.3

9

35.72-19.61

-104.75

90.38

-1.72

-859.07-600.46

1485.35

3706.48

57.43

( )( )RBRBRARA 3789.73


= 1/5-1(3789.73) = 947.43

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11.7259.33 == ba


= 947.43/33.59*72.11= 0.3911

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7. CORRELATION BETWEEN ITC & RELIANCE


07

2007-082008-

09

2009-10

2010-

11

-24.05

30.62

-14.18

41.01

-33.39

-31.46133.62

-80.72

31.95

-58.41

756.614091.44

1144.61

1310.27

1950.31

( )( )RBRBRARA 9253.24


30.8659.33 == ba


= 2313.31/33.59*86.30= 0.7980

8. CORRELATION BETWEEN RANBAXY & ICICI


2007-

082008-

09

2009-10

2010-

11

-48.58

-5.18-88.52

163.32

-21.05

35.72

-19.61-104.75

90.38

-1.72

-1735.28

101.579272.47

14760.86

36.21

( )( )RBRBRARA 22435.83


= 1/5-1(22435.83) = 5608.96

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11.7262.96 == ba


= 5608.96/96.62*72.11= 0.8050

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9. CORRELATION BETWEEN RANBAXY & RELIANCE


07

2007-

082008-

09

2009-10

2010-

11

-48.58-5.18

-88.52

163.32-21.05

-31.46133.62

-80.72

31.95-58.41

1528.33-692.15

7145.33

5218.071229.53

( )( )RBRBRARA 14429.11


30.8662.96 == ba


= 3607.28/96.62*86.30 = 0.4326

10. CORRELATION BETWEEN ICICI & RELIANCE


2007-

08

2008-09

2009-

10

2010-11

35.72

-19.61-104.75

90.38

-1.72

-31.46

133.62-80.72

31.95

-58.41

-1123.75

-2620.298455.42

2887.64

100.46

( )( )RBRBRARA 7699.48


= 1/5-1(7699.48) = 1924.87

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30.8611.72 == ba


= 1924.87/72.11*86.30 = 0.3093

CALCULATION OF PORTFOLIO WEIGHTS

FORMULA

( ) b.a.nab2ba/a.nabbbXa 22 +=

Xb = 1 Xa

1. CALCULATION OF WEIGHT OF WIPRO & ITC

Where, Xa = WIPRO, Xb = ITC

Xa = 33.59(33.59 (0.6444)65.49)/65.492+33.592-(2*0.6444*65.49*33.59)

= -289.26/2582.11 = -0.1120

Xb = 1 Xa = 1 (-0.1120) = 1.1120

Xa = -11.20%, Xb = 111.20%

2. CALCULATION OF WEIGHT OF WIPRO & RANBAXY

Where, Xa = WIPRO, Xb = RANBAXY

Xa = 96.62(96.62 (0.9333)65.49)/65.492+96.622-(2*0.9333*65.49*96.62)

= 3429.83/1813.18 = 1.89

Xb = 1 Xa = 1 1.89 = -0.89

Xa = 189%, Xb = -89%

3. CALCULATION OF WEIGHT OF WIPRO & ICICI

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Where, Xa = WIPRO, Xb = ICICI

Xa = 72.11(72.11 (0.3787)65.49)/65.492+72.112-(2*0.3787*65.49*72.11)

= 3411.44/5911.98 = 0.5770

Xb = 1 Xa = 1 0.5770 = 0.423

Xa = 57.7%, Xb = 42.3%

4. CALCULATION OF WEIGHT OF WIPRO & RELIANCE

Where, Xa = WIPRO, Xb = RELIANCE

Xa = 86.30(86.30(0.2774)65.49)/65.492+86.302 (2*0.2774*65.49*86.30)

= 5879.88/8601.02 = 0.683

Xb = 1 Xa = 1 0.683 = 0.317

Xa = 68.3%, Xb = 31.7%

5. CALCULATION OF WEIGHT OF ITC & RANBAXY

Where, Xa = ITC, Xb = RANBAXY

Xa = 96.62(96.62(0.7445)33.59)/33.592+96.622 (2*0.7445*33.59*96.62)

= 6919.17/5631.21 = 1.228

Xb = 1 Xa = 1 1.228 = -0.228

Xa = 122.8%, Xb = -22.8%

6. CALCULATION OF WEIGHT OF ITC & ICICIWhere, Xa = ITC, Xb = ICICI

Xa = 72.11(72.11(0.3911)33.59)/33.592+72.112 (2*0.3911*33.59*72.11)

= 4252.54/4433.51= 0.959

Xb = 1 Xa = 1 0.959= 0.041

Xa = 95.9%, Xb = 4.1%

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7. CALCULATION OF WEIGHT OF ITC & RELIANCEWhere, Xa = ITC, Xb = RELIANCE

Xa = 86.30(86.30(0.7980)33.59)/33.592+86.302 (2*0.7980*33.59*86.30)

= 5134.43/3949.47 = 1.300

Xb = 1 Xa = 1 1.300 = -0.3

Xa = 130%, Xb = -30%

8. CALCULATION OF WEIGHT OF RANBAXY & ICICIWhere, Xa = RANBAXY, Xb = ICICI

Xa = 72.11(72.11(0.8050)96.62)/96.622+72.112 (2*0.8050*96.62*72.11)

= -408.86/3317.97 = -0.123

Xb = 1 Xa = 1 (-0.123) = 1.123

Xa = -12.3%, Xb = 112.3%

9. CALCULATION OF WEIGHT OF RANBAXY & RELIANCEWhere, Xa = RANBAXY, Xb = RELIANCE

Xa = 86.30(86.30(0.4326)96.62)/96.622+86.302 (2*0.4326*96.62*86.30)

= 3840.54/9568.81 = 0.401

Xb = 1 Xa = 1 0.401 = 0.599

Xa = 40.1%, Xb = 59.9%

10. CALCULATION OF WEIGHT OF ICICI & RELIANCEWhere, Xa = ICICI, Xb = RELIANCE

Xa = 86.30(86.30(0.3093)72.11)/72.112+86.302 (2*0.3093*72.11*86.30)

= 5522.88/8797.94= 0.627

Xb = 1 Xa = 1 0.627 = 0.373

Xa = 62.7%, Xb = 37.3%

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CALCULATION OF PORTFOLIO RISK

FORMULA

WaWbbanabWbbWaap ..22222 ++=

Wherea = Standard Deviation of Security a

b = Standard Deviation of Security b



nab = Correlation Coefficient between Security a & b

p = Portfolio Risk

1. WIPRO & ITC59.3349.65 == ba , Wa = -0.1120, Wb = 1.1120, nab = 0.6444

p = 65.492*-0.11202+33.592*1.11202 + 2(0.6444*65.49*33.59*-0.1120*1.1120)

10.3388.1095 ==

2. WIPRO & RANBAXY62.96,49.65 == ba , Wa = 1.89, Wb = -0.89, nab = 0.9333

p = 65.492 * 1.892 + 96.622 * -0.892 + 2(0.9333*65.49*96.62*1.89*-0.89)

27.10965.11941 ==

3. WIPRO & ICICI11.72,49.65 == ba , Wa = 0.577, Wb = 0.423, nab = 0.3787

p = 65.492 * 0.5772 + 72.112 * 0.4232 + 2(0.3787*65.49*72.11*0.577*0.423)

84.5631.3231 ==

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4. WIPRO & RELIANCE30.86,49.65 == ba , Wa = 0.683, Wb = 0.317, nab = 0.2774

p = 65.492*0.6832+86.302*0.3172+2(0.2774*65.49*86.30*0.683*0.317)

54.5804.3428 ==

5. ITC & RANBAXY62.96,59.33 == ba , Wa = 1.228, Wb = -0.228, nab = 0.7445

p = 33.592*1.2282+96.622*-0.2282+2(0.7445*33.59*96.62*1.228*-0.228)

69.1187.136 ==

6. ITC & ICICI

11.72,59.33 == ba , Wa = 0.959, Wb = 0.041, nab = 0.3911

p = 33.592*0.9592+72.112*0.0412+2(0.3911*33.59*72.11*0.959*0.041)

47.3390.1120 ==

7. ITC & RELIANCE30.86,59.33 == ba , Wa = 1.300, Wb = -0.3, nab = 0.7980

p = 33.592*1.3002+86.302*-0.32+2(0.7980*33.59*86.30*1.300*-0.3)

82.2382.567 ==

8. RANBAXY & ICICI11.72,62.96 == ba , Wa = -0.123, Wb = 1.123, nab = 0.8050

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p = 96.622*-0.1232+72.112*1.1232+2(0.8050*96.62*72.11*-0.123*1.123)

76.6901.4867 ==

9. RANBAXY & RELIANCE30.86,62.96 == ba , Wa = 0.401, Wb = 0.599, nab = 0.4326

p = 96.622*0.4012+86.302*0.5992+2(0.4326*96.62*86.30*0.401*0.599)

62.2390.557 ==

10.ICICI & RELIANCE30.86,11.72 == ba , Wa = 0.627, Wb = 0.373, nab = 0.3093

p = 72.112*0.6272+86.302*0.3732+2(0.3093*72.11*86.30*0.627*0.373)

09.6371.3980 ==

Calculation of Portfolio Return

Rp = (Ra * Wa) + (Rb * Wb)

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Where,Ra = Average Return of Security a

Rb = Average Return of Security b



Rp = Portfolio Return

Portfolios Ra Wa Rb Wb Rp= (Ra*Wa)+(Rb*Wb)

WIPRO & ITCWIPRO & RANBAXY

WIPRO & ICICI

WIPRO & RELIANCE

portfolio 20-03-2011

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