Performance of Stocks & Portfolio Construction

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Analysis of Performance of Selected Stocks and Portfolio Construction

M P Birla Institute of Management 1

A DISSERTATION REPORT

ON

AN ANALYSIS OF THE PERFORMANCE OF SHARES OF LISTEDCOMPANIES IN THE INDIAN STOCK MARKET

AND PORTFOLIO CONSTRUCTION

Submitted in partial fulfillment of the requirement for

M.B.A. Degree Course of BANGALORE UNIVERSITY

By

Chandan Raju

(06XQCM6092)

Under the guidance ofProf. Santhanam,

Senior Professor.

2006 - 2008


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Declaration

This is to state that the project titled "AN ANALYSIS OF THE

PERFORMANCE OF SHARES OF LISTED COMPANIES IN THE INDIAN

STOCK MARKET AND PORTFOLIO CONSTRUCTION is best on my work

and bears no resemblance to any project work.

This is submitted in partial fulfillment of the requirements of the MBA

course in Bangalore University.

All the information and data given in my project are authentic to the best of

my knowledge and taken from reliable sources.

Place: Bangalore Chandan Raju

Date: 28-04-2008. (06XQCM6092)


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PRINCIPALS CERTIFICATE

This is to certify that the project titled AN ANALYSIS OF THE


STOCK MARKET AND PORTFOLIO CONSTRUCTION is based on the

original work carried out by Mr. Chandan Raju., bearing Reg. No. 06XQCM6092

under the guidance of Prof. Santhanam.

The work has been satisfactory and is recommended for consideration

towards the partial fulfillment of the requirements of the MBA degree under

Bangalore University.

Place: Bangalore Dr. N. S. Malavalli

Date: 28-04-2008 (Principal)


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GUIDES CERTIFICATE

This is to certify that the project titled AN ANALYSIS OF THE


STOCK MARKET AND PORTFOLIO CONSTRUCTION is based on the

original work carried out by Mr. Chandan Raju., bearing Reg. No. 06XQCM6092

under my guidance and supervision.

The work has been satisfactory and is recommended for consideration

towards the partial fulfillment of the requirements of the MBA degree under

Bangalore University.

Place: Bangalore Prof. Santhanam

Date: 28-04-2008 Guide


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Acknowedgement

Acknowledgement are not the full expression ones gratitude towards the person whose

help is acknowledged. Though language is an inadequate medium to express ones

sentiments, it is the only way one can record ones grateful indebtness to ones guide and

benefactor.

First of all, I want to express my sincere thanks to Dr. N. S. Malavalli, Principal

and Prof. Snathanam, faculty guide and mentor, M P Birla Institute of Management,

Bangalore. for their guidance and encouragement.

I am highly indebted to Dr. N. Mooganagod and Prof. Praveen Bhagawan for

valuable support and guidance for the completion of this project.

Finally, I owe my gratitude to my beloved parents and my dear most friends who have

always stood by me and have been my moral support with sheer zeal and enthusiasm at

the worry and I dedicate my work to them

Chandan Raju


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Table of Contents

CHAPTER NO. CONTENTS PAGE NO.

I Research Extract 1

II Introduction 3

2.1 Theoretical Background

2.2 Performance measurement

2.3 Portfolio construction

2.4 Risk & Return measurement

2.5 Study Design

2.6 Objectives of the study

2.7 Importance of the Study

2.8 Scope of the study

III Review of Literature 24

IV Research Methodology 26

4.1 Type of Research

4.2 Sources of data

4.3 Sampling plan

4.4 Plan of Analysis

4.5 Assumptions

4.6 Limitations of the study

4.7 Operational definition and concepts

V

Presentation and Analysis of Data and

Interpretation 36

5.1 Presentation of Data and Interpretation

5.2 T- Test

5.3 Conclusions

VI Findings and Suggestions 53

Bibliography

Annexure


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List of Tables

Table

No.

Title Page

No.

1 Factors for investment 22

2 List of Companies 38

3 Ranking of securities on excess return to beta 41

4 Determining the cutoff rate 43

5 Selected 14 stocks 45

6 Proportions to be invested in selected 14 stocks 46

7 Consumer durables sector companies 47

8 Cutoff rate for consumer durables 48

9 Investment proportions for consumer durables

sector

49

10 Different combinations 50

11 T - test results 52

List of GraphsGraph

No.

Title Page

No.

1 Risk aversion 14

2 Efficient frontier 15

3 Graph Showing cut off rate 44


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List of Abbreviations Used

ESOP - Employee Stock Option

ERB - Excess Return to Beta

PSU - Public Sector Undertaking

DCF - Discounted Cash Flow

NPV - Net Present Value

CAPM - Capital Asset Pricing Model


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RESEARCH EXTRACT

A stock market is a market for the trading of publicly held company stock and associated

financial instruments.

The stock market in India is very volatile and many investors are in a dilemma to invest in

the securities. Not surprisingly, recent market movements have once more focused

attention on the volatility that has come to characterise Indias stock markets. In volatile

markets, domestic speculators too attempt to manipulate markets in periods of unusually

high prices.

Keeping in view the above observation about the Indian stock market, AN ANALYSIS

OF THE PERFORMANCE OF SHARES OF LISTED COMPANIES IN THE

INDIAN STOCK MARKET AND PORTFOLIO CONSTRUCTION was carried

out, with the problem statement being studying the influence of particular sector on the

performance of the portfolio by taking the share prices from the selected companies in the

Indian stock market.

Ten sectors were picked randomly consisting of five companies in each sector. First, nine

sectors were considered and using various statistical measures and using Sharpes Single

Index Model portfolio was constructed and efficient stocks were selected. Then, efficient

stocks from the tenth sector was selected and combined with the initial portfolio with

various proportions and returns were calculated.

For this reason a hypothesis was created to test, if there was any significant difference in

the portfolio performance, when the consumer durables sector was not included in the

portfolio and after including in the portfolio. T- Test was performed to test the

hypothesis.


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Finally, H1 was accepted, which means to that, there is significant difference in the

portfolios mean return before considering and after considering consumer durables

sector stocks.


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2.1 THEORETICAL BACKGROUND

The study is about analysing the performance of shares of listed companies in the Indian

stock market, constructing the optimum portfolio using the data collected, and calculatingusing various statistical measures.

Generating portfolios is a difficult task at the best of times. It is a task made more

difficult by the present uncertainty surrounding financial markets. What we are really

looking for are investments, which transcend near term gyrations and generate longer

term value. Before examining the nuts and bolts of our portfolios, it is useful to look at

some key definitions and themes.

First of all, the secret of portfolio selection is to diversify and diversify and diversify.

Even with a small number of shares, we must spread our investments in a manner, which

gives protection in uncertain and bad times and captures growth and opportunities in

good times. The second feature of portfolio investing, which we must carry with us at all

times, is that we must operate to a plan. Choose the stocks, which belong in our portfolio

and then buy and sell them as market conditions present opportunities. It is not necessary

to build our portfolio in one hit. We should do it progressively as market conditions

prevail.

The stocks which have been selected are considered taking into account the dividends,

returns, adjusted stock prices and other performance variables. However, there are times

when the price of earnings certainty combined with a growth option requires some

courage when looking at the stock ratios. High quality stocks, with strong growth

characteristics and earnings certainty will often trade at what may initially appear to be

very demanding price ratios. However, if held as part of a larger, well diversified

portfolio, the impact of the holding stocks with above average P/E multiples is

diminished and the investor should be rewarded by above average capital growth from

such stocks.


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2.2 PERFORMANCE MEASUREMENT

Sharpe Ratio

The Sharpe ratio measures the return of a mutual fund compared to the risk-free rate of

return, which is prevailing T-bill rate. This should be similar to money market returns.

Often this ratio is used to determine if a mutual fund is able to beat the money market.

Say a growth fund has a Sharpe ratio over the last five years of 0.57 and the recent range

of Sharpe ratios for global equity funds went from as low a 1.11 to a high of 0.94. A

positive Sharpe ratio means the fund did better on a risk-adjusted basis than the T-bill

rate. In other words, the higher the Sharpe ratio, the better.

The Sharpe ratio tells you about history but it does not tell you anything about the future.

Just because a fund has a positive Sharpe ratio for the last five years does not mean it will

outperform money market instruments for the next five years.

It is calculated by subtracting the risk free rate from the rate of return for a portfolio and

dividing the result by the standard deviation of the portfolio returns.

SR = ( )p

RfRp

Where SR = Sharpe Ratio

Rp = Return on portfolio

Rf= Risk free rate of return

p= Standard Deviation of the portfolio


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Sharpes Single Index Model

The Markowitz model is extremely demanding in its data needs for generating the desired

efficient portfolio. It requires N (N+3)/2 estimates (N expected returns + N variances of

returns + N*(N-1)/2 unique covariances of returns). Because of this limitation the singleindex model with less input data requirements has emerged. The Single index model

requires 3N+2 estimates (estimates of alpha for each stock, estimates of beta for each

stock, estimates of variance ei2

for each stock, estimate for expected return on market

index and an estimate of the variance of returns on the market index ( m2)to use the

Markowitz optimization framework. The single index model assumes that co-movement

between stocks is due to movement in the index. The basic equation underlying the single

index model is:

Ri = ai + x Rm

Where, Ri= Return on the ith stock

ai = component of security is that is independent of market performance

= coefficient that measures expected change in Ri given a change in Rm

Rm = rate of return on market index

The term ai in the above equation is usually broken down into two elements ai which is

the expected value of ai and ei which is the random element of ai

The single index model equation therefore, becomes:

Ri= ai + * Rm + ei

Empirical evidence, however, reveal that the more complex models have not been able to

consistently outperform the single index model in terms of their ability to predict ex-ante

co-variances between stock returns.

Jensen's Measure:

A risk-adjusted performance measure that represents the average return on a portfolio

over and above that predicted by the CAPM, given the portfolio's beta and the average


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market return. This is the portfolio's alpha. In fact, the concept is sometimes referred to as

"Jensen's alpha."

Jensens Measure is calculated as:

p = Rp [Rf+ p(Rm-Rf)]

Where p = Jensens Measure (Alpha)

Rp = Expected portfolio Return

p = Fortfolio Beta

Rm = Expected Market return

2.3 PORTFOLIO CONSTRUCTION

Within the context of an ESOP Rollover Portfolio, the two distinct primary strategies for

constructing a portfolio are the Passive/Buy-and-Hold Portfolio and the Active/Managed

Portfolio. To begin constructing a long-term portfolio that will meet an investor's income

requirements and risk tolerance, a three-step process should be followed.

STEP 1: Scenario Modelling

STEP 2: Asset Allocation

STEP 3: Security/Portfolio Manager Selection

Step1: Scenario Modeling

Analyzing a variety of alternatives and scenarios should help the investor understand the

type of portfolio best suited for his or her needs. Evaluating such factors as an investor's

income needs, inflation assumptions, return assumptions, tax bracket and amount of the

investment are an important part of the process.

After the scenario modeling is completed and a decision is made on whether to construct

a Passive/Buy-and-Hold Portfolio or an Active/Managed Portfolio, the next step is to

determine the allocation of stocks, bonds and/or floating-rate notes.


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Step2: Asset allocation

The importance of selecting an appropriate mix of equity or debt securities is well

documented. Modern investment research has shown that asset allocation may be the

most significant factor in investment performance.

For a passive/buy-and-hold portfolio, the choice of asset classes is limited to qualifying

stocks and government bonds.

An investor choosing a passive/buy-and-hold portfolio should first consider the amount

of initial investment. Clearly, the higher the investment, the greater the allocation towards

high-dividend stocks and/or corporate bonds. Once current income returns are examined,

the various asset classes can be evaluated in order to determine an initial asset allocation.

To fine-tune the asset allocation, an investor's tolerance for risk must also be evaluated.

The work of Nobel Laureates Harry Markowitz and William F. Sharpe has helped

investors understand two related aspects of investing - risk and return. (By 'risk' we mean

the fluctuation or variability of returns.) Their work concluded that distinct asset classes

follow different patterns, and historically, these classes have reacted dissimilarly to the

same set of economic data.

This phenomenon is referred to in statistical terms as the correlation between

investments. Investments that are positively correlated move in the same direction, while

negatively correlated investments move in opposite directions.

The key to successful asset allocation is blending investments that are not positively

correlated with one another. Mixing investments that move in dissimilar ways can reduce

the variability/risk of the overall portfolio for a given return. The curve that represents

this statistically optimal combination of assets is called the efficient frontier.

For example, it is often mistakenly assumed that a portfolio comprised of 100% bonds is

very conservative and has very little risk. However a portfolio representing 75% bonds


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and 25% stocks may actually provide an investor with increased returns for slightly less

risk. Further research has shown that similar risk reduction may occur when international

stocks and bonds are added to a portfolio of U.S. stocks and bonds. Returns on

international asset classes are not perfectly correlated with returns on their domestic

counterparts. That is why, when a diversified collection of international stocks and/or

bonds is added to a diversified portfolio, the result can be an even further increase in

return for comparable risk.

Step 3: Security/Portfolio Manager Selection

The Passive/Buy-and-Hold Portfolio Stocks

Once the allocation between stocks and bonds is decided upon, it is usually best to

establish desirable characteristics for portfolio securities. For common and convertible

stocks, there are a number of characteristics to be screened, both quantitative and

qualitative.

Once the desired characteristics are determined, a screening process should be initiated.

The goal is to develop a universe of 100-200 qualifying stocks. The next step involves

researching and ranking these stocks, culminating in a universe of 50-100 stocks. The

third step is to segregate such stocks by index industry groups and again rank them

against their peers. This process of fundamental analysis is then followed by technical

analysis.

While not absolute, technical analysis is used to identify optimal purchase prices.

Technical analysis includes examining a stock's support levels, trading pattern, share

volume and relative strength. This process can be applied not only to specific stocks, but

also to an entire industry group, as similar stocks can trade in sympathy with one another.Historically, there have proven to be specific times when certain groups were abnormally

low priced relative to past patterns. These would include health-care and drugs stocks at

the height of the health-care debate, utility stocks after deregulation and when interest

rates spiked, or consumer stocks when brand loyalty was debated relative to generic

brands. This process of identifying and purchasing stocks should be started at or near the


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beginning of an investor's reinvestment period. If adhered to, the resulting savings can be

significant.

In summary, fundamental stock analysis suggests to an investor what to buy and technical

stock analysis suggests when to buy. A combination of fundamental and technical

analysis provides an investor with suitable portfolio candidates.

Equity Portfolio Construction, Optimization & Management

The portfolio design & construction phase follows research in the investment process.

The research phase has produced buy and sell lists of stocks. The equity portfolio should

be structured with regards to client mandates of: risk, style, quality, safety, tax, social

responsibility, industry / sector concentration, turnover, etc. We need to decide the proper

mix and weightings to use in the construction of the optimal portfolio.

The portfolio construction phase continues to take on more characteristics of portfolio

manufacturing. The manufacturing process follows model portfolios, refines security

selections and weights using optimization tools and techniques.

The portfolio construction process then derives the individual portfolio objectives and

constraints from client databases containing tax, holding, accounting, compliance, and

other rules.

The portfolio must be constructed with the next phase in mind, trading. In order to

minimize slippage and retain alpha, smooth and efficient transition between phases in the

technology-based investment process is critical.

Portfolio Optimization Functions

The portfolio optimization functions assist portfolio managers in constructing risk and

return.


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Capital Allocation

Optimal capital allocation to efficient frontier portfolios

Computes the optimal risky portfolio on the efficient frontier, based on the risk-free rate,

the borrowing rate, and the investor's degree of risk aversion. Also generates the capital

allocation line, which provides the optimal allocation of funds between the risky portfolio

and the risk-free asset.

Efficient Frontier Computation

Mean-variance efficient frontier

Computes portfolios along the efficient frontier for a given group of assets. The

computation is based on sets of constraints representing the maximum and minimum

weights for each asset, and the maximum and minimum total weight for specified groups

of assets.

Portfolios on constrained efficient frontier

Computes portfolios along the efficient frontier for a given group of assets. The

computation is based on a set of user-specified linear constraints. Typically, these

constraints are generated using the constraint specification functions described below.

Constraint Specification

Portfolio constraints

Generates the portfolio constraints matrix for a portfolio of asset investments using linear

inequalities. The inequalities are of the type A*Wts'


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Linear inequalities for asset group comparison constraints

Group-to-group ratio constraint. Generates a constraint set specifying the maximum and

minimum ratios between pairs of groups.

Linear inequalities for asset group minimum and maximum allocation

Asset group minimum and maximum allocation. Generates a constraint set to fix the

minimum and maximum total weight for each defined group of assets.

Linear inequalities for fixing total portfolio value

Total portfolio value. Generates a constraint set to fix the total value of the portfolio.

Constraint Conversion

Convert constraints from absolute format to active format

Transforms a constraint matrix expressed in absolute weight format to an equivalent

matrix expressed in active weight format.

Convert constraints from active format to absolute format

Transforms a constraint matrix expressed in active weight format to an equivalent matrix

expressed in absolute weight format.

Analyzing Portfolios

Portfolio managers concentrate their efforts on achieving the best possible trade-off

between risk and return. For portfolios constructed from a fixed set of assets, the

risk/return profile varies with the portfolio composition. Portfolios that maximize the

return, given the risk, or, conversely, minimize the risk for the given return, are called

optimal. Optimal portfolios define a line in the risk/return plane called the efficient

frontier.


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A portfolio may also have to meet additional requirements to be considered. Different

investors have different levels of risk tolerance. Selecting the adequate portfolio for a

particular investor is a difficult process. The portfolio manager can hedge the risk related

to a particular portfolio along the efficient frontier with partial investment in risk-free

assets.

Portfolio Selection and Risk Aversion

One of the factors to consider when selecting the optimal portfolio for a particular

investor is degree of risk aversion. This level of aversion to risk can be characterized by

defining the investor's indifference curve. This curve consists of the family of risk/return

pairs defining the trade-off between the expected return and the risk. It establishes the

increment in return that a particular investor will require in order to make an increment in

risk worthwhile. Typical risk aversion coefficients range between 2.0 and 4.0, with the

higher number representing lesser tolerance to risk.

GRAPH NO. 1 RISK AVERSION


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Active Returns and Tracking Error Efficient Frontier

To identify an efficient set of portfolios that minimize the variance of the difference in

returns with respect to a given target portfolio, subject to a given expected excess return.

The mean and standard deviation of this excess return are often called the active returnand active risk, respectively. Active risk is sometimes referred to as the tracking error.

Specifically, assume that the target portfolio is expressed as an index weight vector, such

that the index return series may be expressed as a linear combination of the available

assets. This example illustrates how to construct a frontier that minimizes the active risk

(tracking error) subject to attaining a given level of return. That is, it computes the

tracking error efficient frontier.

One way to construct the tracking error efficient frontier is to explicitly form the target

return series and subtract it from the return series of the individual assets. In this manner,

you specify the expected mean and covariance of the active returns, and compute the

efficient frontier subject to the usual portfolio constraints.

GRAPH NO. 2 EFFICIENT FRONTIER


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2.4 RISK AND RETURN MEASUREMENT

The risk/return relationship is a fundamental concept in not only financial analysis, but in

every aspect of life. If decisions are to lead to benefit maximization, it is necessary that

individuals/institutions consider the combined influence on expected (future) return or

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

commensurate with risk/cost is known as the "risk/return trade-off" in finance.

This session discusses the trade-off and, using conventional statistical tools, provides a

method for quantifying risk. Two categories of risk borne by the firm's stockholders,

business risk and financial risk, are discussed and demonstrated, as is the concept of

leverage. The session also examines risk reduction via portfolio diversification and what

requirements need to be met for firms to experience the benefits of diversification. The

Capital Asset Pricing Model (CAPM) is used to demonstrate the risk/return trade-off by

relating the required return on the firm's investments to its beta (or market) risk.

The Risk/Return Trade-off in Financial Analysis

It is widely accepted that the major determinant of the required return on the asset (or the

rate to be applied to a stream of receipts to capitalize its value) is its degree of risk. Risk

refers to the probability that the return and therefore the value of an asset or security may

have alternative outcomes. Risk is the uncertainty (today) surrounding the eventual

outcome of an event which will occur in the future.

Example: when tossing a coin, some one is not sure exactly what will be the outcome.

The outcome may be to have a Tail or the Head, so there is a concept of risk. In a football

match, three outcomes can be experienced: win, lose or draw. In business, the same can

happen regarding the expected return on the investments in various sectors.

In Financial Analysis, the risk/return trade-off states that financial decisions that subject

stockholders to more risk must offer a higher expected return. Risk aversion is the

tendency to try to avoid risky situations unless adequate compensation is offered.


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Example: The risk averse individual faced with two events each having the same

expected outcome will choose the outcome with the lower level of risk.

Measurement of Risk and Return

The expected benefits or returns to be received from an investment come in the form of

the cash flows the investment generates.


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Categories of Risk and Leverage Faced by the Firm and by Stockholders

This type of risk is magnified by the degree to which the firm relies on fixed

operating expenses in producing sales.

In many cases there is not much the firm can do about this type of risk; someindustries have more volatile sales and higher fixed operating expense than others.

Operating leverage results when the firm has fixed operating expenses in its cost

structure.

These expenses do not disappear when sales drop, nor do they increase when sales

increase.

Operating leverage tends to magnify any change in sales on Earnings Before Interest

and Taxes (EBIT).

Stockholders are the ultimate bearers of the risk that results from leverage and they

are the residual recipients of higher EBIT should sales increase.

Financial risk

This type of risk arises primarily because of the fixed interest payments firms must make

to their long-term creditors (debt capital).

This type of risk is reflected in volatile Net Income and Earnings per Share.

Financial leverage results when the firm finances some portion of its assets with

borrowed funds

Financial leverage means that changes in EBIT will magnify changes in net income

and Earnings Per Share

As a firm increases its degree of financial leverage, its expected return (net incomeand Earnings Per Share) increases as does its risk

The financial manager has some discretion in determining the extent of financial

leverage.


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Risk and Diversification

Diversification occurs when different assets make up a portfolio. The benefit of

diversification is risk reduction; the extent of this benefit depends upon how the returns

of various assets behave over time.

The market rewards diversification. We can lower risk without sacrificing expected

return, and/or we can increase expected return without having to assume more risk.

Diversifying among different kinds of assets is called asset allocation. E.g. A telephone

operator with many physical assets such as houses can diversify by acquiring financial

assets which in turn earns return to the company. Compared to diversification within the

different asset classes, the benefits received are far greater through effective asset

allocation e.g. diversifying among different types of financial assets.

Example of diversification in Telecom industry is when a licensed mobile operator who

provides fixed line telephones services also operates the community based telecenters,

teleshops, card phones, etc.

Other ways to reduce risk include the use of the following strategies:

Mass advertising to reduce erratic sales and hence to increased profit

Entering into long-term sales or purchase contracts

Recapitalizing toward more equity and less debt so as to reduce the burden of fixed

financial expenses

The use of temporary labour instead of permanent employees

Risk in a Portfolio Setting

A portfolio is a collection of risky assets. If we view individual assets as one big asset we

have a portfolio. Because of risk reduction, the nature of risk is fundamentally different

when an asset is viewed as part of a portfolio instead of being viewed in isolation.


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Measuring the Expected Return and Standard Deviation of a Portfolio

The expected return on a portfolio is the weighted average of the returns of individual

assets, where each asset's weight is determined by its weight in the portfolio. The formula

is:

E (Rp) = [Wa x E (Ra)] + [Wb x E (Rb)]

Where, E = Expected

Rp = Return on portfolio

Wn = weight of asset n where n may stand for asset a, b. etc

Rn = Return on asset n where n may stand for asset a, b. etc

In MS Excel, the above formula can be computed using the AVERAGE function.

The portfolio standard deviation ( p) measures the risk associated with the expected

return in the portfolio. The formula is:

p =

In MS excel, the above formula can be calculated using SLOPE function.

The term ra,brepresents the correlation between the returns of investment a and b. The

correlation coefficient, r, will always reduce the standard deviation of the portfolio as

long as it is less than +1.00. this is numerical evidence of the benefit of diversification.

This equation gives the theoretically correct required rate of return on a project based

upon its systematic (or beta) risk. The formula is applicable only in situations where all

diversifiable risk has been eliminated.

The risk-free rate (Rf) is a base rate reflecting the fact that the project should at a

minimum, offer a return equal to what could be earned in the Treasury bill market. Even

risks less investments have a positive required rate of return. The market risk premium,

(Rm - Rf), indicates the premium investors require over the risk-free rate to invest in the


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general market index. The required return on a project is positively related to the project's

beta.

A very risky project (say a new expansion venture) will have a high beta coefficient,

whereas low risk projects (such as a replacement machine) will have a lower beta.

Knowing a project's beta (and thus its minimum required return) is important for good

financial management, because it indicates whether or not the expected rate of return is

above, equal to, or below the required rate of return and whether or not stockholders are

being properly compensated for the non-diversifiable risk they bear due to the project.

Portfolio Diversification

The diversification of portfolios is an important concept in finance management. Both

individuals and firms diversify their investments. Individuals have portfolios of shares

and firms have portfolio of business operation. Remember the aim of an individual or the

firm is to maximize their return at the same time minimizing their risk.

Risk and Return

Because of the volatility of environment, the financial management should consider

investments, which offers better return with optional risk level. A key feature of project

appraisal is its orientation to the future. There are two types of expectations individuals

may have about future: certainty and uncertainty. The risk in an investment, or in a

portfolio of investments, is that the actual return will not be the same as the expected

return. The actual return may be higher, but it may be lower. A prudent investor will want

to avoid too much risk, and will hope the actual returns from his investment are much the

same as what he expected them to be. The risk of a security and the risk of a portfolio is

the standard deviation of the expected return. A portfolio is the collection of different

investments that make up the investors total holding. A portfolio might be the

investments in shares or in the capital project of a company.

Portfolio theory which originates from the work of Markowitz is concerned with

establishing guidelines for building up a portfolio of share or a portfolio of investments.


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Factors in the Choice of an Investment

Table No.1 FACTORS FOR INVESTMENT

Security Maintenance of capital

LiquidityIf made with short-term funds should be convertible into cash

with short notice

Return Obtain highest return compatible with safety

Spreading risksSpread risks over several investments, so losses on some

offset by gains on other

Growth prospects Investment in steadily growing businesses

The risk of an investment might be high or low, depending on the nature of the

investment. Low risk investments usually give low returns. High risk investments might

give high returns, but with more risk of disappointing results.

Correlation of Investments

Portfolio theory states that individual investments cannot be viewed simply by their risk

and return. The relationship between the return from one investment and the return fromthe other investments is just as important. The relationship between investments can be

one of the three types:

1. Negative correlation

Investments in a portfolio with direct opposite in risk and return over time i.e. when

return on one investment is increasing another investment: return will drop. Thus if you

hold shares in one company making umbrellas and another which sells ice cream, the

weather will affect the companies differently. The risk will be reduced through thisdiversification.

2. Positive Correction

Investments in a portfolio having similar trend in rate of return movements. Thus you buy

shares in one company which sells umbrellas and another which makes raincoats you


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would expect both companies to do badly in dry weather. Diversification will not

minimize the risk.

3. Independent investments

A third possibility is that rate if the returns on stocks in two firms are completely

unrelated. If you hold shares in a mining company and in a leisure company, it is likely

that there would be no relationship between the profits and return from each.

Covariance

Measures the extent to which the returns on two investments co-vary or correlate. If

the rate of return tends to go up together or go down together then the covariance will be

positive and if returns move in opposite direction, the covariance will be negative. A

figure close to + 1 indicates high positive correlation, and the figure close to -1 indicates

high negative correlation. A figure of 0 indicates no correlation. If the investments show

high negative correlation, then by combining them in a portfolio overall risk would be

reduced. Risk will also be reduced by combining in portfolio investments which have no

significant correlation.


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2.5 STUDY DESIGN

STATEMENT OF THE PROBLEM

The project deals with studying the influence of particular sector on the performance ofthe portfolio by taking the share prices from the selected companies in the Indian stock

market.

HYPOTHESIS

T test is performed in order to test the hypothesis. The null and alternate hypothesis are

defined as:

H0 : There is no significant difference in the portfolios mean return before

considering and after considering consumer durables sector stocks.

H1 : There is significant difference in the portfolios mean return before


2.6 OBJECTIVES OF THERESEARCH:

To study different companies daily performance for a year.

To study the share price movement of different companies in a given sector.

To construct an optimum portfolio using the Single Index Model.

To calculate the optimum proportion to be invested.

2.7 IMPORTANCE OF THE STUDY:

1. The study concentrates on the select stocks in the Indian stock market.

2. The study shows that diversification has an effect on risk and return of stocks.

3. The study also focuses on the construction of efficient portfolio


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2.8 SCOPE OF THE RESEARCH:

1. The Sectors covered under the study are:

a. Automobiles

b. Banks

c. Cement

d. Oil and gas

e. Textiles

f. Pharmaceuticals

g. Information Technology

h. Steel

i. Consumer durables

2. The share prices of ten sectors, each consisting of five companies have been taken

from 1-04-2007 to 31-03-2008.

3. The share prices are the prices on NSE as in the date.

4. The research is fully based on past data. No fundamental factors are considered

that influence the performance of the share prices.


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LITERATURE REVIEW

The purpose of literature review is to find out the various studies that have been done in

the relative fields of the present study and also to understand the various methodologies

followed by the authors to arrive at the conclusions.

The following are some of the studies:

A STOCHASTIC CONVERGENCE MODEL FOR PORTFOLIO SELECTION

Amy V. Puelz

According to the author, Portfolio selection techniques must provide decision makers

with a dynamic model framework that incorporates realistic assumptions regarding

financial markets, risk preferences, and required portfolio characteristics. Unfortunately,

multistage stochastic programming (SP) models for portfolio selection very quickly

become intractable as assumptions are relaxed and uncertainty is introduced. In this

paper, the author has presented an alternative model framework for portfolio selection,

stochastic convergence (SC) that systematically incorporates uncertainty under a realistic

assumption set. The optimal portfolio is derived through an iterative procedure, where

portfolio plans are evaluated under many possible future scenarios then revised until the

model converges to the optimal plan.

ESTIMATION RISK AND SIMPLE RULES FOR OPTIMAL PORTFOLIO

SELECTION

Son-NanChen and Stephen J. BrownThis paper shows by using the Single Index Model for the return generating process that

the simple decision rules for optimal portfolio selection derived by Elton, Grubber and

Padberg are not identical under the Bayesian and the traditional methods of analysis.

Moreover, in case where short sales are not allowed, the number of component securities

in an optimal portfolio under the Bayesian approach can be considerably smaller than the

traditional method. The result of the study demonstrate that estimation risk must be

properly reflected in the process of optimal portfolio selection.


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HOW MANY STOCKS MAKE A DIVERSIFIED PORTFOLIO?

Stevenson and Jennings

The author writes, a portfolio of approximately eight to sixteen randomly selected stocks

will closely resemble the market portfolio in terms of fluctuations in the rate of return.

Other studies have shown similar results and an unusual consistency using different time

periods, different group of stocks, and different research techniques. Diversification

should be increased as long as the marginal benefits exceed marginal cost.

MEAN-ABSOLUTE DEVIATION PORTFOLIO OPTIMIZATION MODEL AND ITS

APPLICATIONS TO TOKYO

Hiroshi Konno and Hiroaki Yamazaki

The paper demonstrates that a portfolio optimization model using the Li risk (mean

absolute deviation risk) function can remove most of the difficulties associated with the

classical Markowitz's model while maintaining its advantages over equilibrium models.

In particular, the Li risk model leads to a linear program instead of a quadratic program,

so that a large-scale optimization problem consisting of more than 1,000 stocks may be

solved on a real time basis. Numerical experiments using the historical data of NIKKEI

225 stocks show that the Li risk model generates a portfolio quite similar to that of the

Markowitz's model within a fraction of time required to solve the latter.

Conclusion:

From the above articles, it can be seen observed that portfolio construction is of

utmost importance when it comes to investment. There are many models to construct

an efficient portfolio. The research makes an attempt to construct a portfolio using

Single Index Model of the select stocks of Indian stock market.


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RESEARCH METHODOLOGY

4.1 Type of the Research

The research that has been used here is descriptive. Under this type of research, the data

that is collected is used in its original form without any manipulation. This type of

research does not establish causal relationship among the events.

4.2 Sources of Data

As the research is an ex-post analysis, only secondary data is used.

Secondary Data

The various sources of secondary data are:

Internet

Journals

Magazines

Newspaper

Text books

4.3 Sampling Plan

Sample unit: Daily Stock prices of individual securities

Sample size: Ten Sectors and five companies in each sector, i.e., fifty companies.

Sampling Procedure: Non-probabilistic convenient sampling

4.4 Plan of Analysis

Firstly, a portfolio was constructed using the data related to all the nine sectors.

Secondly, another pair of portfolios were constructed, one exclusively in the consumer

durables sector, and the other excluding the consumer durables sector. These two


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portfolios were then combined, and the performance of the combinations was studied to

obtain an optimal combination of the portfolios.

The study further continued to find out if there is any significant difference in the

performance between the optimal portfolio and the portfolio combination obtained from

the second step.

Constructing optimal portfolios using SINGLE INDEX MODEL

This model presents and demonstrates the procedure for selecting stocks to construct an

optimal portfolio when single index model is accepted as the best way to forecast the co-

variance structure of returns.

Steps:

1) Find the excess return to beta ratiofor each stock under consideration and rank

from highest to lowest.

2) The optimal portfolio consists in investing in all stocks fro which excess return

to beta ratio is greater the particular cut-off ratio C*.

The Formation of Optimal Portfolio:

In this model the desirability is directly related to the excess return to beta ratio. Excess

return is difference between the expected return of the stock and the risk less rate of

interest. (T-bill). The excess return to beta measures ratio measures the additional return

on a security for every unit of non-divisible risk.

Excess return to beta =Ri - Rf

i


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Where

Ri = Expected return on stock i,

Rf = Risk free return,

i = The expected change in the return on stock i associated with 1%

change in market return.

If the stocks are ranked according to the excess return to beta ratio, the ranking represents

the desirability of any stocks in the portfolio. If a stock with the particular ratio is

included in the portfolio, all the stocks whose ratio is greater than that of the included

will be included in the portfolio. And if a stock with a particular ratio is excluded all

stocks with the less ratio are excluded from the portfolio. How many stocks are selected

depends on the unique CUT-OFF rate.

SETTING THE CUT-OFF RATE:

The value of C* is computed from the characters of all the securities that belong in the

optimal portfolio. To determine C* it is necessary to calculate its value as if there were

different number of securities in the portfolio. Designate Ci as the candidate for the C*.

We proceed to calculate the values for Ci as if the first ranked security was in the optimal

portfolio (I=1), then again as if security 1st

and 2nd

ranked security were in the optimal

portfolio (I=2).and then the 1st, 2nd, and 3

rdranked security were in the optimal portfolio

(I=3) and so forth. These Cis are the candidates fro the C*.

CALCULATING THE Ci FOR THE C*:

Recall that the stocks ranked by the excess return to Beta from highest to lowest. for a

portfolio ofi stock Ci is given by


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+

=

2

2

2

2

2

1

)(

cj

j

m

cj

i

m

i

RjRi

C

Where :

= Variance of the market index (nifty).

= Un-systematic risk

The un-systematic risk is usually the variance of the stock movement that is not

associated with the movement of the market index.

By using the above formula we calculate the values for Ci with respect to excess return

to Beta ratio ranking. From all the calculated values of Ci we determine the CUT-OFF

rate C* to be 0.213551 as this is the highest value in the column. And all the ranked

securities till Ci value will be selected as an optimal portfolio. As the risk to beta ratio of

all the selected securities are higher then the C* and that satisfies the condition of

selecting.

We are through with selecting the stocks for an optimal portfolio. Now the question

which arises here is:

How much to invest in each stock of the portfolio?

Once the securities that have to comprise the portfolio are determined, it remains to show

the calculation of how much to invest in each stock. The percentage to be invested in

each security is calculated by Zi div sum of Zi

Zi =

2

m

2ej

Zi

Zi


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Where Zi =

The second equation determines the relative investment in each security while the first

equation simply scales the weights on each security. Note that the residual value 2ie

plays an important role in determining how much to invest in each security.

Applying this formula for our table we have the Zi values below stating what percentage

of amount to be invested in each stock in the portfolio.

4.5 ASSUMPTIONS OF THE STUDY

The risk free interest rate was taken to be 7.35% per annum.

The number of trading days was taken to be 252.

No activities taken place that would change the number of outstanding shares.

4.6 LIMITATIONS OF THE STUDY

The data collected are past data, which does not reflect the current situation.

The study tells us how to create an optimum portfolio and not how to manage it.

i

2ie( )Ri - Rf

i

C*


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4.7 OPERATIONAL DEFINITION OF CONCEPTS

Alpha: The expected return of a stock or a portfolio if the market rate of return is zero.

Beta: A statistical measure of the systemic risk of a particular stock (e.g. ACC). It

reflects the historical movement in the stock's share price viz that of a broad market

indicator, such as the NSE/ market index index

Capital Asset Pricing Model (CAPM): CAPM derives the risk appropriate required rate

of return for a given asset in a given market. It was introduced by William Sharpe,

Lintner and Mossin independently, though it is commonly attributed only to the first of

them, who published it earliest (in 1964), and subsequently received (jointly with Harry

Markowitz and Merton Miller) The Bank of Sweden Prize in Economic Sciences in

Memory of Alfred Nobel for his contribution to the field of financial economics.

According to the CAPM the required rate of return for a stock is given by:

rs = ( rm - rf) + rf

Where:

rs = the required rate of return on a stock

rm = the market portfolio (or proxy) rate of return

rf = the risk free interest rate is the beta of the stock - its sensitivity to

the movement of the market portfolio

Descriptive research: Also called as statistical research provides data about the

population or universe being studied. But it can only describe the "who, what, when,

where and how" of a situation, not what caused it. Therefore, descriptive research is used

when the objective is to provide a systematic description that is as factual and accurate aspossible. It provides the number of times something occurs, or frequency,lends itself to

statistical calculations such as determining the average number of occurrences or central

tendencies.


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Diversification: is a measure of the commonality of a population. Greater diversification

denotes a wider variety of elements within that population. Diversification is of central

importance in investments. Diversification reduces the risk of a portfolio. It does not

necessarily reduce the returns. This is why diversification is referred to as the only free

lunch in finance.

Efficient Frontier: Every possible asset combination can be plotted in risk-return space.

For every level of return there exists one portfolio with the lowest risk; conversely, for

every level of risk there is one portfolio with the highest return. The combination of all

such portfolios is called the efficient frontier (sometimes the Markowitz frontier.)

The efficient frontier is illustrated above, with return p on the y axis, and riskp on the x

axis.

Investment Decision: Management must allocate limited resources between competing

opportunities. In general, each will be assessed via a DCF valuation, and the opportunity

with the highest value, as measured by Net present value, NPV, will be selected. In this

approach, project returns are discounted, i.e. "present valued" at the project's hurdle rate.

Investment Portfolio: A set of financial assets chosen by an investor

Mean And Variance: It is further assumed that investor's risk / reward preference can be

described via a quadratic utility function. The effect of this assumption is that only the

expected return, i.e. mean return, and the volatility, i.e. the standard deviation, matter

to the investor. The investor is indifferent to other characteristics of the distribution ofreturns, such as its skew. Note that the theory uses an historical parameter, volatility, as a

proxy for risk while return is an expectation on the future.

Portfolio: is a collection of investments held by an institution or a private individual. In

building up an investment portfolio a financial institution will conduct its own investment


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analysis, whilst a private individual may make use of the services of a merchant bank

which offers portfolio management. Holding a portfolio is part of an investment and risk-

limiting strategy called diversification

Portfolio Leverage: An investor can add leverage to the portfolio by holding the risk

free asset. The addition of the risk free asset allows for a position in the region above the

efficient frontier. Thus, by combining a risk-free asset with risky assets, it is possible to

construct portfolios whose risk-return profiles are superior to those on the efficient

frontier.

Portfolio management: Where assets are combined into a portfolio that fits the

investor's preferences (e.g., level of risk) and needs (e.g., regular dividends and couponpayments).

Risk: is the potential future harm that may arise from some present action. It is often

combined or confused with the probability of an event which is seen as undesirable.

Usually the probability and some assessment of expected harms must be combined into a

believable scenario combining risk, regret and reward probabilities into expected value.

There are many informal methods which are used to assess (or to "measure" although it is

not usually possible to directly measure) risk, and (for some applications) formal methods

such as value at risk.

Risk Free Asset: The risk free asset is the (hypothetical) asset which pays a risk free rate

- it is usually proxied by an investment in short-dated Government bonds. The risk free

asset has zero variance in returns (hence risk free); it is also uncorrelated with any other

asset. As a result, when it is combined with any other asset, or portfolio of assets, the

change in return and also in risk is linear.

Risk-Free Interest Rate: is the interest rate that it is assumed can be obtained by

investing in financial instruments with no risk.


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Securities: are tradable interests representing financial value. They are often represented

by a certificate. They include shares of corporate stock or mutual funds, bonds issued by

corporations or governmental agencies, stock options or other options, other derivative

securities, limited partnership units, and various other formal "investment instruments."

Banknotes, checks, and some bills of exchange do not fall into this category.

Securities Market Line (SML): The relationship between Beta and required return is

plotted on the Securities Market Line (SML) which shows expected return as a function

of. The intercept is the risk free rate available for the market; the slope is unit of return

per unit of risk.

Stock: also referred to as a share, is commonly a share of ownership in a joint stock

company. The owners and financial backers of a company may desire additional capital

to invest in new projects within the company. If they were to sell the company it would

represent a loss of control over the company.

Standard Deviation: is the most commonly used measure of statistical dispersion.

Standard deviation is defined as the square root of the variance.

Systematic Risk and Specific Risk: Specific risk is the risk associated with individual assets -

within a portfolio these risks can be reduced through diversification (specific risks "cancel out").

Systematic risk, or market risk, refers to the risk common to all securities - systematic risk cannot

be diversified away (within one market). Within the market portfolio, asset specific risk will be

diversified away to the extent possible. Systematic risk is therefore equated with the risk

(standard deviation) of the market portfolio.

Unsystematic Risk: Risk that affects a very small number of assets. Sometimes referred

to as specific risk. For example, news that is specific to a small number of stocks, such as

a sudden strike by the employees of a company you have shares in.


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Volatility: is standard deviation of a financial instrument with a specific time horizon. It

is often used to quantify the risk of the instrument over that time period. Volatility is

typically expressed in annualized terms.

For a financial instrument whose return (finance) follows a Gaussian random walk, or

Wiener process, the volatility increases by the square-root of time as time increases.

Conceptually, this is because there is an increasing probability that the instrument's price

will be farther away from the initial price as time increases. Mathematically, this is a

direct result of applying its lemma to the random process.


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5.1 PRESENTATION OF DATA AND INTERPRETATION:

TABLE NO. 2 LIST OF ALL THE COMPANIES

SLNO LIST OF COMPANIES AVG

RETURNS

VARIANCE

1 ASHOK LEYLAND 0.19000 0.33520 0.00120

2 EICHER MOTORS 0.40000 0.15700 0.00150

3 LML -0.05000 0.31750 0.00110

4 TATA MOTORS 0.05000 0.01690 0.00050

5 TVS MOTORS 0.26000 0.17180 0.00150

6 CANARA BANK -0.01000 0.40390 0.00120

7 CORPBANK 0.02000 0.18830 0.00090

8 HDFC -0.11000 0.10690 0.00070

9 PUNJAB NATIONAL BANK -0.02000 0.27230 0.00090

10 SBI -0.21000 0.02020 0.00070

11 ACC -0.02000 0.12050 0.00080

12 GUJARAT AMBUJA -0.04000 0.05500 0.00030

13 KAKATIYA CEMENT SUGAR AND

INDUSTRIES LTD

-0.01000 0.21300 0.00090

14 MANGALAM 0.04000 0.30450 0.00140

15 PRISM -0.07000 0.05710 0.00130

16 BHARAT PEROLEUM CORPORATION

LTD

-0.10000 0.14930 0.00090

17 ESSAR OIL LTD -0.37000 0.45270 0.00410

18 K S OILS -0.24000 0.07690 0.00220

19 GAIL INDIA LTD 0.24000 0.04270 0.0009020 RELIANCE INDUSTRIES LTD -0.45000 0.55020 0.00330

21 ARVIND MILLS 0.13000 0.38470 0.00190

22 ASHIMA LTD 0.31000 0.53560 0.00230

23 ABHISHEK MILLS 0.29000 0.42220 0.00170


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24 BOMBAY DYEING -0.02000 0.17200 0.00130

25 S KUMAR'S NATIONWIDE LTD 0.02000 0.13030 0.00200

26 AJANTA PHARMA 0.02000 0.12100 0.00130

27 CIPLA 0.04000 0.01840 0.00060

28 Dr. REDDYS 0.09000 0.02820 0.00030

29 GLAXO 0.04000 0.08550 0.00050

30 RANBAXY -0.08000 0.00440 0.00050

31 HCL TECH 0.08000 -0.11010 0.00080

32 I FLEX 0.37000 0.14950 0.00120

33 MPHASIS 0.19000 0.06580 0.00090

34 INFOSYS TECHNOLOGIES LTD 0.15000 0.10250 0.00050

35 PATNI 0.25000 0.08980 0.00120

36 BHARAT GEARS LTD -0.20000 0.74980 0.00530

37 EXIDE -0.19000 0.03090 0.00100

38 INDIA NIPPON -0.26000 0.31870 0.00460

39 RICO 0.29000 0.28410 0.00150

40 AMTEK AUTO 0.15000 0.11280 0.00060

41 ESSAR STEELS -0.13000 0.02910 0.00134

42 JINDAL STEEL& POWER LTD -0.46000 0.28520 0.00267

43 NATIONAL STEEL -0.07000 0.20490 0.00119

44 TATA METALIKS LTD -0.15000 0.26250 0.00129

45 UTTAM GALVA STEELS LTD -0.02000 0.32470 0.00122

46 MIRC ELECTRONICS 0.07000 0.34760 0.00120

47 HITACHI HOME & LIFE SOLUTIONS -0.11000 0.10170 0.00130

48 SAMTEL COLOR LTD 0.22000 0.33220 0.00160

49 VALUE INDUSTRIES 0.09000 0.38990 0.00140

50 KAITHAN 0.35000 0.22340 0.00220


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INTERPRETATION:

From the above table it could be seen that Ashok Leyland, Eicher Motors, Tata Motors,

Tvs Motors, Corpbank, Mangalam, Gail India Ltd, Arvind Mills, Ashima Ltd, Abhishek

Mills, S Kumar's Nationwide Ltd, Ajanta Pharma, Cipla , Dr. Reddys, Glaxo, Hcl Tech, I

Flex, Mphasis, Infosys Technologies Ltd, Patni, Rico, Amtek Auto, Mirc Electronics,

Samtel Color Ltd, Value Industries, Khaithan have positive returns while other stocks

have negative returns. Many of them have negative returns because of the bill fall of nifty

during the year.

Many stocks have positive beta which indicates the riskiness of the stocks. Most of the

stocks are less risky, while HCL Technologies showed a negative beta which indicates

the rise in the price of the stock if the market falls and vice versa.


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TABLE NO. 3RANKING OF SECURITIES ON EXCESS RETURN TO BETA

RANKS COMPANIES AVG

RETURNS

ERB

19 GAIL INDIA LTD 0.24000 3.89906

2 EICHER MOTORS 0.40000 2.07955

32 I FLEX 0.37000 1.98321

35 PATNI 0.25000 1.96537

33 MPHASIS 0.19000 1.77036

5 TVS MOTORS 0.26000 1.08551

39 RICO 0.29000 0.76202

34 INFOSYS TECHNOLOGIES LTD 0.15000 0.74624

40 AMTEK AUTO 0.15000 0.6781028 Dr. REDDYS 0.09000 0.58475

23 ABHISHEK MILLS 0.29000 0.51277

22 ASHIMA LTD 0.31000 0.44154

1 ASHOK LEYLAND 0.19000 0.34752

21 ARVIND MILLS 0.13000 0.14684

31 HCL TECH 0.08000 -0.05895

14 MANGALAM 0.04000 -0.11005

6 CANARA BANK -0.01000 -0.20676

7 CORPBANK 0.02000 -0.28417

45 UTTAM GALVA STEELS LTD -0.02000 -0.28799

9 PUNJAB NATIONAL BANK -0.02000 -0.34341

36 BHARAT GEARS LTD -0.20000 -0.36478

3 LML -0.05000 -0.38901

29 GLAXO 0.04000 -0.39193

13 KAKATIYA CEMENT SUGAR AND

INDUSTRIES LTD

-0.01000 -0.39207

25 S KUMAR'S NATIONWIDE LTD 0.02000 -0.41067

26 AJANTA PHARMA 0.02000 -0.44223

24 BOMBAY DYEING -0.02000 -0.54366


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43 NATIONAL STEEL -0.07000 -0.70039

11 ACC -0.02000 -0.77602

44 TATA METALIKS LTD -0.15000 -0.85147

20 RELIANCE INDUSTRIES LTD -0.45000 -0.95149

17 ESSAR OIL LTD -0.37000 -0.97970

38 INDIA NIPPON -0.26000 -1.04647

16 BHARAT PEROLEUM CORPORATION LTD -0.10000 -1.16216

4 TATA MOTORS 0.05000 -1.39112

8 HDFC -0.11000 -1.71665

27 CIPLA 0.04000 -1.82120

42 JINDAL STEEL& POWER LTD -0.46000 -1.87065

12 GUJARAT AMBUJA -0.04000 -2.06382

15 PRISM -0.07000 -2.51331

18 K S OILS -0.24000 -4.07685

41 ESSAR STEELS -0.13000 -6.99347

37 EXIDE -0.19000 -8.52783

10 SBI -0.21000 -14.03515

30 RANBAXY -0.08000 -34.88864

INTERPRETATION:

There are 45 stocks in the table for the readers convenience I have already ranked the

securities on the basis of excess return to beta. The application of the step 2 involves the

comparison of the excess return to beta ratio with the C*(CUT-OFF RATE). The cut off

was C* = 0.213551.

Examining the table shows that the securities RANKED 1-14 (stocks numbered19, 2, 32, 35, 33, 5, 39, 34, 40, 28, 23, 22, 1, 21) have the excess return to beta greater then

the C*(CUT-OFF). Hence the optimal portfolio consists of securities ranked 1-14.

Gail India Lt. and Eicher Motors had an excess return to beta of above 2% and these are

the best stock among the others.

Ranbaxy Ltd had a ve excess return to beta of 34.8864%, which is ranked 45th.


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TABLE NO. 4 DETERMINING THE CUT-OFF RATE.

C* = 0.213551

COLOUMN 1 COLOUMN 2 COLOUMN 3 COLOUMN 4 COLOUMN 5

COLOUMN

6 COLOUMN

(( Ri - Rf ) *)/ ET2

CUMMULATIVE((Ri - Rf ) * )/ ET2

MARKET

VARIANCE*COL 2 2/ ET2 CUM COL 4

1+ MARKET

VARIANCE*COL 5 C*

7.110371581 7.110371581 0.002878989 0.057662555 0.057662555 1.000023348 0.00287

44.8489291 51.95930068 0.021038321 0.658711919 0.716374474 1.00029006 0.02103

46.09853778 98.05783846 0.039703619 0.645215069 1.361589543 1.000551308 0.03968

18.70943095 116.7672694 0.047279067 0.232795612 1.594385155 1.000645567 0.04724

12.50261408 129.2698835 0.052341376 0.136918601 1.731303756 1.000701005 0.05230

31.93399868 161.2038822 0.065271452 0.78917754 2.520481296 1.001020543 0.06520

58.90145557 220.1053377 0.089120651 2.158096524 4.678577821 1.001894356 0.08895

25.63524983 245.7405876 0.099500364 0.429001633 5.107579454 1.002068059 0.0992928.21127981 273.9518674 0.110923111 0.51955247 5.627131924 1.002278426 0.11067

6.345 280.2968674 0.113492202 0.039762 5.666893924 1.002294525 0.11323

81.62463136 361.9214987 0.146542015 4.602448748 10.26934267 1.004158057 0.14593

79.05012257 440.9716213 0.178549409 6.259379446 16.52872212 1.00669248 0.17736

63.69918558 504.6708069 0.20434121 3.553416825 20.08213894 1.008131258 0.20269

27.7791834 532.4499903 0.215589001 3.487958756 23.5700977 1.009543533 0.21355

-9.786666667 522.6633236 0.21162638 0.404067 23.9741647 1.009707139 0.20959

9.366899132 532.0302228 0.215419037 2.571277038 26.54544174 1.010748249 0.21312

-4.039709373 527.9905134 0.213783359 5.159241303 31.70468304 1.012837226 0.21107

4.708922094 532.6994355 0.215690001 1.253779703 32.95846274 1.013344882 0.2128

-5.902300834 526.7971347 0.21330016 3.178477238 36.13693998 1.014631847 0.21022

-7.778537635 519.018597 0.21015063 2.802240741 38.93918072 1.015766474 0.20688

-29.99257526 489.0260218 0.198006636 7.950785462 46.88996618 1.018985747 0.19431

-15.87778814 473.1482336 0.19157772 3.188053447 50.07801963 1.02027659 0.1877

6.840415897 479.9886495 0.194347404 0.326934258 50.40495389 1.020408966 0.1904

-2.663304318 477.3253452 0.193269032 1.604278642 52.00923253 1.021058538 0.18928

1.303079227 478.6284244 0.193796649 0.379653175 52.38888571 1.02121226 0.18977

2.016784985 480.6452094 0.194613245 0.422661663 52.81154737 1.021383396 0.19053

-2.866834854 477.7783746 0.193452464 0.85404157 53.66558894 1.021729197 0.18933

-13.03614119 464.7422334 0.18817413 1.265722339 54.93131128 1.022241688 0.1840

-3.442210007 461.3000234 0.186780379 0.548762283 55.48007356 1.022463882 0.18267

-32.81442511 428.4855983 0.173493819 1.98921045 57.46928401 1.023269313 0.16954

-79.86098209 348.6246162 0.141158107 5.436782328 62.90606634 1.025470666 0.13765

-42.94843401 305.6761822 0.123768286 3.281621938 66.18768828 1.026799395 0.12053

-18.4148974 287.2612848 0.116312094 1.514157573 67.70184585 1.027412477 0.11320


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GRAPH NO. 3 GRAPH SHOWING THE CUT-OFF RATE:

GRAPH SHOWING CUT OFF RATE

0

0.05

0.1

0.15

0.2

0.25

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43

NUMBER OF SCRIPS

Series1

-16.58888889 270.6723959 0.109595253 0.743016333 68.44486218 1.027713325 0.1066

1.684072066 272.3564679 0.110277134 0.012750446 68.45761263 1.027718487 0.10730

-19.60617253 252.7502954 0.102338595 0.46662352 68.92423615 1.027907423 0.0995

1.227157325 253.9774527 0.102835471 0.013824418 68.93806057 1.027913021 0.10004

-50.45884774 203.518605 0.082404683 1.595195921 70.53325649 1.028558916 0.08011

-7.333763581 196.1848414 0.079435242 0.17465358 70.70791007 1.028629633 0.07722-3.073850232 193.1109912 0.07819064 0.090416251 70.79832632 1.028666242 0.07601

-8.78694417 184.324047 0.074632807 0.129033602 70.92735992 1.028718488 0.07254

-2.909275814 181.4147712 0.073454841 0.023483361 70.95084328 1.028727996 0.07140

-5.872031129 175.5427401 0.071077255 0.030196395 70.98103968 1.028740223 0.06909

-6.054283891 169.4884562 0.068625876 0.015415187 70.99645486 1.028746465 0.06670

-0.704042806 168.7844134 0.068340809 0.000865832 70.9973207 1.028746815 0.06643


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INTERPRETATION:

The Y-axis represents the possible values of Ci and the X-axis the number of scrips to be

included in the portfolio. The trend line represents the values of Ci for every additional

scrip included in the portfolio. If we observe the trend properly, after certain no of scrips

the trend starts falling. The vertical line exactly cuts the trend line at the maximum value

ofCi = 0.213551. According to the model all the scrips, which are on the left hand side

of the vertical line, have the excess return to Beta ratio greater then the CUT-OFF rate.

And only those scrips, which are on the left hand side of the vertical line, are taken as

potential stocks to construct a portfolio.


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TABLE NO. 5 SELECTED 14 STOCKS

C*= 0.21355097

RANKS COMPANIES C* PROPORTIONS

19 GAIL INDIA LTD 0.002878922 0.08324422

2 EICHER MOTORS 0.02103222 0.123341526

32 I FLEX 0.039681742 0.130707733

35 PATNI 0.047248565 0.077805686

33 MPHASIS 0.05230471 0.061625006

5 TVS MOTORS 0.065204907 0.070527639

39 RICO 0.088952144 0.081873175

34 INFOSYS TECHNOLOGIES LTD 0.099295016 0.067464311

40 AMTEK AUTO 0.110670956 0.067464311

28 Dr. REDDYS 0.113232387 0.021807589

23 ABHISHEK MILLS 0.145935208 0.076346625

22 ASHIMA LTD 0.177362415 0.059560737

1 ASHOK LEYLAND 0.20269306 0.061632802

21 ARVIND MILLS 0.21355097 0.01659864

INTERPRETATION:

As we keep including number of stocks to the portfolio, simultaneously we keep track of

the cumulative excess return to beta

As the cumulative excess return to beta starts declining it implies that the last stock

included is not potential enough to give the maximum returns.

So C* will tell us that those stocks which should be included in the portfolio that are

above the C*. The below ones are not potential enough to be included in the portfolio.

By using this C*, 14 stocks were selected, and with these14 stocks, a portfolio was

constructed, the table shows what proportion should be invested in each securities


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TABLE NO. 6 PROPORTIONS TO BE INVESTED IN SELECTED 14 STOCKS

RANKS COMPANIES PROPORTIONS

19 GAIL INDIA LTD 0.08324422

2 EICHER MOTORS 0.123341526

32 I FLEX 0.130707733

35 PATNI 0.077805686

33 MPHASIS 0.061625006

5 TVS MOTORS 0.070527639

39 RICO 0.081873175

34 INFOSYS TECHNOLOGIES LTD 0.067464311

40 AMTEK AUTO 0.067464311

28 Dr. REDDYS 0.021807589

23 ABHISHEK MILLS 0.076346625

22 ASHIMA LTD 0.059560737

1 ASHOK LEYLAND 0.061632802

21 ARVIND MILLS 0.01659864

INTERPRETATION:

After determining the cut off rate, the various values of Z i are calculated and proportions

to be invested in each scrips are determined to make it an efficient portfolio.

In the above table, I flex investment proportion was around 13%, which is highest in the

set of stocks.


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TABLE NO. 7 CONSUMER DURABLES SECTOR COMPANIES

SL.

NO.

COMPANIES AVG

RETURNS

BETA ERB

46 MIRC ELECTRONICS 0.07000 0.34760 -0.01010

47 HITACHI HOME & LIFE SOLUTIONS -0.11000 0.10170 -1.80442

48 SAMTEL COLOR LTD 0.22000 0.33220 0.44097

49 VALUE INDUSTRIES 0.09000 0.38990 0.04229

50 KAITHAN 0.35000 0.22340 1.23765

INTERPRETATION:

These are the 5 companies in the consumer durables sector selected to combine with the

stocks of other nine sectors efficient stocks. Excess return to beta is calculated for these

five stocks and ranked accordingly.


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TABLE NO. 8 CUT-OFF RATE FOR CONCUMER DURABLES SECTOR

C* = 0.025697

RANKS SL.NO. COMPANIES AVG.

RETURNS

ERB BETA C*

1 50 KAITHAN 0.35000 1.23765 0.22340 0.011794

2 48 SAMTEL COLOR LTD 0.22000 0.44097 0.33220 0.024943

3 49 VALUE INDUSTRIES 0.09000 0.04229 0.38990 0.025697

4 46 MIRC ELECTRONICS 0.07000 -0.01010 0.34760 0.024158

5 47 HITACHI HOME & LIFE

SOLUTIONS

-0.11000 -1.80442 0.10170 0.018997

INTERPRETATION:

This above table shows the five stocks of the consumer durables sector. Excess return to

beta was calculated for the stocks ranked accordingly. Cut off rate was calculated at

0.025697. Three out five stocks i.e Khaitan, Samtel Color and Value Industries were

selected and proportions were calculated.

The beta of Khaitan was 1.23765 which indicates the risk level of the stock to be highest.


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TABLE NO. 9 INVESTMENT PROPORTIONS FOR CONSUMER DURABLES

SECTOR

COMPANIES PROPORTIONS TO BE

INVESTED

KAITHAN 0.554664126

SAMTEL COLOR LTD 0.423923494

VALUE INDUSTRIES 0.02141238

INTERPRETATION:

The above table shows the various proportions to be invested in each stock to make it an

efficient portfolio. Zi values are calculated for the purpose and proportions are

determined.

As per the above table, around 55 % of the investment should be invested in Kaithan,

around 42 % in Samtel Colour Ltd and around 2 % in Value industries.


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TABLE NO.10 DIFFERENT COMBINATIONS

Consumer

Durables

Portfolio

14

Companies

Portfolio

Expected Returns

(Daily Basis )

Expected Returns (

Annual Basis)

Portfolio

Exp Beta

0.1 0.9 0.269765 67.980809 0.202987

0.15 0.85 0.270852 68.254615 0.206881

0.2 0.8 0.271938 68.528422 0.210776

0.25 0.75 0.273025 68.802228 0.214670

0.3 0.7 0.274111 69.076035 0.218565

0.35 0.65 0.275198 69.349842 0.222459

0.4 0.6 0.276284 69.623648 0.226354

0.45 0.55 0.277371 69.897455 0.230248

0.5 0.5 0.278457 70.171261 0.234143

0.55 0.45 0.279544 70.445068 0.238037

0.6 0.4 0.280630 70.718874 0.241932

0.65 0.35 0.281717 70.992681 0.245826

0.7 0.3 0.282804 71.266488 0.249721

0.75 0.25 0.283890 71.540294 0.253615

0.8 0.2 0.284977 71.814101 0.257510

0.85 0.15 0.286063 72.087907 0.261404

0.9 0.1 0.287150 72.361714 0.265299

0.95 0.05 0.288236 72.635521 0.269194

INTERPRETATION:

Assuming that these 2 portfolios to be different, another portfolio of the two portfolios

was constructed, taking the different combinations from them. The result showed that

consumer sector outperformed. If the investor invests 95% in consumer sector durables,


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5.2 Test for Equality (T test)

Test for equality /difference of mean portfolio returns.

H0 : There is no significant difference in the portfolios mean return before


H1 : There is significant difference in the portfolios mean return before


The test statistics is

)( yxSEyxtcal

=

The standard error (S E) in the difference in the portfolios mean return is found to be

n

Covyxyxsiyx

yxSE

k

i

jjjiiii =

= 1

22 ))()(()(

)(

Using this for formula for standard error (SE), a test of equality /difference of portfolio

mean returns is constructed.

TABLE NO.11 T-TEST RESULTS

Mean 1 = 0.236 Mean 2 = 0.234

Standard deviation 1= .091 Standard Deviation 2 = 0.095

N = 14 N = 17

t cal = 0.9319


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Difference between means = 0.0029

At 95% CI: -0.0628


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FINDINGS:

Gail India ltd. Ranked 1 in the selected set of stocks on the basis of excess return to

beta of 3.89906. This is because of its return of 24% with a beta of 0.3352.

When the portfolio was constructed using 45 stocks, portfolio of 14 companies was

formed with an annualised return of 67. 43 % with a beta of 0.195.

Out of 5 stocks of consumer durables sector, three stocks were found to be efficient

and a portfolio was constructed using the three stocks.

The consumer durables portfolio generated an annual return of 72.90% with a beta of

0.2731.

The combined portfolio of 17 stocks showed an annual return of 58.48%.

Both these portfolios were combined and returns were calculated at various

combinations which showed that the return was

Documents

Performance of Stocks & Portfolio Construction