Description
This is to certify that the project work entitled “A Case Study on Portfolio Management” with reference to Inter-Connected Stock Exchange of India Limited [ISE]; Hyderabad has been carried out by Krishna under my guidance in partial fulfillment of the Requirements for the award of Master of Business Administration.
PROJECT REPORT ON “A CASE STUDY ON PORT FOLIO MANAGEMENT ”
CERTIFICATE
This is to certify that the project work entitled “A Case Study on Portfolio Management” with reference to Inter-Connected Stock Exchange of India Limited [ISE]; Hyderabad has been carried out by XXXXX under my guidance in partial fulfillment of the Requirements for the award of –
MASTER OF BUSINESS ADMINISTRATION
(Faculty – Finance) (Director)
(Course Co-ordinator)
CONTENTS
1. 2. 3.
4.
COMPANY PROFILE INTRODUCTION PORTFOLIO ANALYSIS ANALYSIS & INTERPRETION CALCULATION OF AVERAGE RETURN OF COMPANIES CALCULATION OF PORTFOLIO RISK CALCULATION OF PORTFOLIO WEIGHTS CONCLUSION BIBILOGRAPHY
5. 6. 7. 8. 9.
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COMPANY PROFILE
Inter-connected stock exchange of India limited [ISE] has been promoted by 14 Regional stock exchanges to provide cost-effective trading linkage/connectivity to all the members of the participating Exchanges, with the objective of widening the market for the securities listed on these Exchanges. ISE aims to address the needs of small companies and retail investors with the guiding principle of optimizing the existing infrastructure and harnessing the potential of regional markets, so as to transform these into a liquid and vibrant market through the use of state-of-the-art technology and networking. The participating Exchanges of ISE in all about 4500 stock brokers, out of which more than 200 have been currently registered as traders on ISE. In order to leverage its infrastructure and to expand its nationwide reach, ISE has also appointed around 450 Dealers across 70 cities other than the participating Exchange centers. These dealers are administratively supported through the regional offices of ISE at Delhi [north], kolkata [east], Coimbatore, Hyderabad [south] and Nagpur [central], besides Mumbai.
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ISE has also floated a wholly-owned subsidiary, ISE securities and services limited [ISS], which has taken up corporate membership of the National Stock Exchange of India Ltd. [NSE] in both the Capital Market and Futures and Options segments and The Stock Exchange, Mumbai In the Equities segment, so that the traders and dealers of ISE can access other markets in addition to the ISE markets and their local market. ISE thus provides the investors in smaller cities a one-stop solution for cost-effective and efficient trading and settlement in securities. With the objective of broad basing the range of its services, ISE has started offering the full suite of DP facilities to its Traders, Dealers and their clients.
OBJECTIVES OF THE COMPANY:
1. Create a single integrated national level solution with access to multiple markets for providing high cost-effective service to millions of investors across the country. 2. Create a liquid and vibrant national level market for all listed companies in general and small capital companies in particular. 3. Optimally utilize the existing infrastructure and other resources of participating Stock Exchanges, which are under-utilized now. 4. Provide a level playing field to small Traders and Dealers by offering an opportunity to participate in a national markets having investment-oriented business. 5. Reduce transaction cost. 6. Provide clearing and settlement facilities to the Traders and Dealers across the Country at their doorstep in a decentralized mode. 7. Spread demat trading across the country
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SAILENT FEATURES Network of intermediaries:
As at the beginning of the financial year 2003-04, 548 intermediaries (207 Traders and 341 Dealers) are registered on ISE. A broad of members forms the bedrock for any Exchange, and in this respect, ISE has a large pool of registered intermediaries who can be tapped for any new line of business.
Robust Operational Systems:
The trading, settlement and funds transfer operations of ISE and ISS are completely automated and state-of-the-art systems have been deployed. The communication network of ISE, which has connectivity with over 400 trading members and is spread across46 cities, is also used for supporting the operations of ISS. The trading software and settlement software, as well as the electronic funds transfer arrangement established with HDFC Bank and ICICI Bank, gives ISE and ISS the required operational efficiency and flexibility to not only handle the secondary market functions effectively, but also by leveraging them for new ventures.
Skilled and experienced manpower:
ISE and ISS have experienced and professional staff, who have wide experience in Stock Exchanges/ capital market institutions, with in some cases, the experience going up to nearly twenty years in this industry. The staff has the skillset required to perform a wide range of functions, depending upon the requirements from time to time.
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Aggressive pricing policy:
The philosophy of ISE is to have an aggressive pricing policy for the various products and services offered by it. The aim is to penetrate the retail market and strengthen the position, so that a wide variety of products and services having appeal for the retail market can be offered using a common distribution channel. The aggressive pricing policy also ensures that the intermediaries have sufficient financial incentives for offering these products and services to the endclients.
Trading, Risk Management and Settlement Software Systems:
The ORBIT (Online Regional Bourses Inter-connected Trading) and AXIS (Automated Exchange Integrated Settlement) software developed on the Microsoft NT platform, with consultancy assistance from Microsoft, are the most contemporary of the trading and settlement software introduced in the country. The applications have been built on a technology platform, which offers low cost of ownership, facilitates simple maintenance and supports easy up gradation and enhancement. The soft wares are so designed that the transaction processing capacity depends on the hardware used; capacity can be added by just adding inexpensive hardware, without any additional software work. Vibrant Subsidiary Operations: ISS, the wholly owned subsidiary of ISE, is one of the biggest Exchange subsidiaries in the country. On any given day, more than 250 registered intermediaries of ISS traded from 46 cities across the length and breadth of the country.
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Name of the Board of directors
1. Prof. P. V. Narasimham 2. Shri V. Shankar 3. Dr. S. D. Israni 4. Dr. M. Y. Khan 5. Mr. P. J. Mathew 6. M. C. Rodrigues 7. Mr. M. K. Ananda Kumar 8. Mr. T.N.T Nayar 9. Mr. K. D. Gupta 10. Mr. V. R. Bhaskar Reddy 11. Mr. Jambu Kumar Jain Public Interest Director Managing Director Public Interest Director Public Interest Director Shareholder Director Shareholder Director Shareholder Director Shareholder Director Shareholder Director Shareholder Director Trading Member Director
INTRODUCTION
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Investment may be defined as an activity that commits funds in any financial form in the present with an expectation of receiving additional return in the future. The expectations bring with it a probability that the quantum of return may vary from a minimum to a maximum. This possibility of variation in the actual return is known as investment risk. Thus every investment involves a return and risk. Investment is an activity that is undertaken by those who have savings. Savings can be defined as the excess of income over expenditure. An investor earns/expects to earn additional monetary value from the mode of investment that could be in the form of financial assets. • The three important characteristics of any financial asset are:
Return-the potential return possible from an asset. • Risk-the variability in returns of the asset form the chances of its value
going down/up. • Liquidity-the ease with which an asset can be converted into cash. Investors tend to look at these three characteristics while deciding on their individual preference pattern of investments. Each financial asset will have a certain level of each of these characteristics.
Investment avenues
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There are a large number of investment avenues for savers in India. Some of them are marketable and liquid, while others are non-marketable. Some of them are highly risky while some others are almost risk less. Investment avenues can be broadly categorized under the following head. 1. Corporate securities 2. Equity shares. 3. Preference shares. 4. Debentures/Bonds. 5. Derivatives. 6. Others.
Corporate Securities
Joint stock companies in the private sector issue corporate securities. These include equity shares, preference shares, and debentures. Equity shares have variable dividend and hence belong to the high risk-high return category; preference shares and debentures have fixed returns with lower risk.The classification of corporate securities that can be chosen as investment avenues can be depicted as shown below:
Equity Shares
Preference shares
Bonds
Warrants
Derivatives
METHODOLOGY OF THE STUDY
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OBJECTIVES OF THE STUDY: The objectives of the study are as follows: To study the investment pattern and its related risks & returns. To find out optimal portfolio, which gave optimal return at a minimize risk To see whether the portfolio risk is less than individual risk on whose basis To see whether the selected portfolios is yielding a satisfactory and constant To understand, analyze and select the best portfolio.
? ?
to the investor. ? the portfolios are constituted. ? return to the investor. ?
SCOPE OF STUDY:
This study covers the Markowitz model. The study covers the calculation of correlations between the different securities in order to find out at what percentage funds should be invested among the companies in the portfolio. Also the study includes the calculation of individual Standard Deviation of securities and ends at the calculation of weights of individual securities involved in the portfolio. These percentages help in allocating the funds available for investment based on risky portfolios.
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DATA COLLECTION METHODS The data collection methods include both the primary and secondary collection methods. ? Primary collection methods: This method includes the data collection from the personal discussion with the authorized clerks and members of the exchange. ? Secondary collection methods: The secondary collection methods includes the lectures of the superintend of the department of market operations and so on, also the data collected from the news, magazines of the ISE and different books issues of this study
LIMITATIONS OF THE STUDY
The study confines to the past 2-3 years and present system of the trading procedure in the ISE and the study is confined to the coverage of all the related issues in brief. The data is collected from the primary and secondary sources and thus is subject to slight variation than what the study includes in reality. Hence accuracy and correctness can be measured only to the extend of what the sample group has furnished. This study has been conducted purely to understand Portfolio Management for investors. Construction of Portfolio is restricted to two companies based on Markowitz Very few and randomly selected scripts / companies are analyzed from BSE
?
model. ? listings.
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?
Data collection was strictly confined to secondary source. No primary data is Detailed study of the topic was not possible due to limited size of the
associated with the project. ? project. There was a constraint with regard to time allocation for the research study i.e. for a period of two months.
PORT FOLIO MANAGEMENT MEANING:
A portfolio is a collection of assets. The assets may be physical or financial like Shares, Bonds, Debentures, Preference Shares, etc. The individual investor or a fund manager would not like to put all his money in the sares of one company, that would amount to great risk. He would therefore, follow the age old maxim that one should not put all the egges into one basket. By doing so, he can achieve objective to maximize portfolio return and at the same time minimizing the portfolio risk by diversification. Portfolio management is the management of various financial assets which Portfolio management is a decision – support system that is designed with a According to Securities and Exchange Board of India Portfolio Manager is
?
comprise the portfolio. ? view to meet the multi-faced needs of investors. ? defined as: “portfolio means the total holdings of securities belonging to any person”.
?
PORTFOLIO MANAGER means any person who pursuant to a contract
or arrangement with a client, advises or directs or undertakes on behalf of the client
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(whether as a discretionary portfolio manager or otherwise) the management or administration of a portfolio of securities or the funds of the client.
?
DISCRETIONARY PORTFOLIO MANAGER means a portfolio
manager who exercises or may, under a contract relating to portfolio management exercises any degree of discretion as to the investments or management of the portfolio of securities or the funds of the client.
FUNCTIONS OF PORTFOLIO MANAGEMENT:
? To frame the investment strategy and select an investment mix to achieve
the desired investment objectives To provide a balanced portfolio which not only can hedge against the
?
inflation but can also optimize returns with the associated degree of risk To make timely buying and selling of securities To maximize the after-tax return by investing in various tax saving
?
?
investment instruments. STRUCTURE / PROCESS OF TYPICAL PORTFOLIO MANAGEMENT
In the small firm, the portfolio manager performs the job of security analyst. In the case of medium and large sized organizations, job function of portfolio manager and security analyst are separate.
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RESEARCH (e.g. Security Analysis)
PORTFOLIO MANAGERS
OPERATIONS (e.g. buying and selling of Securities)
CLIENTS
CHARACTERISTICS OF PORTFOLIO MANAGEMENT: Individuals will benefit immensely by taking portfolio management services for the following reasons: Whatever may be the status of the capital market, over the long period
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capital markets have given an excellent return when compared to other forms of investment. The return from bank deposits, units, etc., is much less than from the stock market. The Indian Stock Markets are very complicated. Though there are thousands
?
of companies that are listed only a few hundred which have the necessary liquidity. Even among these, only some have the growth prospects which are conducive for investment. It is impossible for any individual wishing to invest and sit down and analyze all these intricacies of the market unless he does nothing else. Even if an investor is able to understand the intricacies of the market and
?
separate chaff from the grain the trading practices in India are so complicated that it is really a difficult task for an investor to trade in all the major exchanges of
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India, look after his deliveries and payments. This is further complicated by the volatile nature of our markets which demands constant reshuffing of portfolios.
TYPES OF PORTFOLIO MANAGEMENT:
1. DISCRETIONARY (DPMS): In this type of service, the client parts with his money in favour of the manager, who in return, handles all the paper work, makes all the decisions and gives a good return on the investment and charges fees. In the Discretionary Portfolio Management Service, to maximise the yield, almost all portfolio managers park the funds in the money market securities such as overnight market, 18 days treasury bills and 90 days commercial bills. Normally, the return of such investment varies from 14 to 18 percent, depending on the call money rates prevailing at the time of investment. 2. NON-DISCRETIONARY PORTFOLIO MANAGEMENT SERVICE (NDPMS): The manager functions as a counsellor, but the investor is free to accept or reject the manager‘s advice; the paper work is also undertaken by manager for a service charge. The manager concentrates on stock market instruments with a portfolio tailor-made to the risk taking ability of the investor. PORTFOLIO MANAGEMENT SERVICE
IMPORTANCE OF PORTFOLIO MANAGEMENT:
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Emergence of institutional investing on behalf of individuals. A number of
financial institutions, mutual funds and other agencies are undertaking the task of investing money of small investors, on their behalf. Growth in the number and size of investigable funds – a large part of
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household savings is being directed towards financial assets. Increased market volatility – risk and return parameters of financial assets
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are continuously changing because of frequent changes in government‘s industrial and fiscal policies, economic uncertainty and instability. Greater use of computers for processing mass of data. Professionalization of the field and increasing use of analytical methods (e.g.
?
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quantitative techniques) in the investment decision – making Larger direct and indirect costs of errors or shortfalls in meeting portfolio
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objectives – increased competition and greater scrutiny by investors.
STEPS IN PORTFOLIO MANAGEMENT:
? Specification and qualification of investor objectives, constraints, and
preferences in the form of an investment policy statement. Determination and qualification of capital market expectations for the
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economy, market sectors, industries and individual securities.
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?
Allocation of assets and determination of appropriate portfolio strategies for
each asset class and selection of individual securities. Performance measurement and evaluation to ensure attainment of investor
?
objectives. Monitoring portfolio factors and responding to changes in investor
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objectives, constrains and / or capital market expectations. Rebalancing the portfolio when necessary by repeating the asset allocation, portfolio strategy and security selection.
CRITERIA FOR PORTFOLIO DECISIONS:
? In portfolio management emphasis is put on identifying the collective
importance of all investors holdings. The emphasis shifts from individual assets selection to a more balanced emphasis on diversification and risk-return interrelationships of individual assets within the portfolio. Individual securities are important only to the extent they affect the aggregate portfolio. In short, all decisions should focus on the impact which the decision will have on the aggregate portfolio of all the assets held. Portfolio strategy should be moulded to the unique needs and characteristics
?
of the portfolio‘s owner.
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?
Diversification across securities will reduce a portfolio‘s risk. If the risk and
return are lower than the desired level, leverages (borrowing) can be used to achieve the desired level. Larger portfolio returns come only with larger portfolio risk. The most
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important decision to make is the amount of risk which is acceptable. The risk associated with a security type depends on when the investment
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will be liquidated. Risk is reduced by selecting securities with a payoff close to when the portfolio is to be liquidated. Competition for abnormal returns is extensive, so one has to be careful in evaluating the risk and return from securities. Imbalances do not last long and one has to act fast to profit from exceptional opportunities.
QUALITIES OF PORTFOLIO MANAGER:
1.
SOUND GENERAL KNOWLEDGE: Portfolio management is an
exciting and challenging job. He has to work in an extremely uncertain and confliction environment. In the stock market every new piece of information affects the value of the securities of different industries in a different way. He must be able to judge and predict the effects of the information he gets. He must have sharp memory, alertness, fast intuition and self-confidence to arrive at quick decisions.
2.
ANALYTICAL ABILITY: He must have his own theory to arrive at
the instrinsic value of the security. An analysis of the security‘s values, company,
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etc. is s continuous job of the portfolio manager. A good analyst makes a good financial consultant. The analyst can know the strengths, weaknesses, opportunities of the economy, industry and the company.
3.
MARKETING SKILLS: He must be good salesman. He has to
convince the clients about the particular security. He has to compete with the stock brokers in the stock market. In this context, the marketing skills help him a lot.
4.
EXPERIENCE: In the cyclical behaviour of the stock market history
is often repeated, therefore the experience of the different phases helps to make rational decisions. The experience of the different types of securities, clients, market trends, etc., makes a perfect professional manager.
PORTFOLIO BUILDING:
Portfolio decisions for an individual investor are influenced by a wide variety of factors. Individuals differ greatly in their circumstances and therefore, a financial programme well suited to one individual may be inappropriate for another. Ideally, an individual‘s portfolio should be tailor-made to fit one‘s individual needs.
Investor‘s Characteristics: An analysis of an individual‘s investment situation requires a study of personal characteristics such as age, health conditions, personal habits, family
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responsibilities, business or professional situation, and tax status, all of which affect the investor‘s willingness to assume risk.
Stage in the Life Cycle:
One of the most important factors affecting the individual‘s investment objective is his stage in the life cycle. A young person may put greater emphasis on growth and lesser emphasis on liquidity. He can afford to wait for realization of capital gains as his time horizon is large.
Family responsibilities:
The investor‘s marital status and his responsibilities towards other members of the family can have a large impact on his investment needs and goals. Investor‘s experience: The success of portfolio depends upon the investor‘s knowledge and experience in financial matters. If an investor has an aptitude for financial affairs, he may wish to be more aggressive in his investments. Attitude towards Risk: A person‘s psychological make-up and financial position dictate his ability to assume the risk. Different kinds of securities have diffferent kinds of risks. The higher the risk, the greater the opportunity for higher gain or loss. Liquidity Needs: Liquidity needs vary considerably among individual investors. Investors with regular income from other sources may not worry much about instantaneous liquidity, but individuals who depend heavily upon investment for meeting their
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general or specific needs, must plan portfolio to match their liquidity needs. Liquidity can be obtained in two ways: 1. by allocating an appropriate percentage of the portfolio to bank deposits, and 2. by requiring that bonds and equities purchased be highly marketable. Tax considerations: Since different individuals, depending upon their incomes, are subjected to different marginal rates of taxes, tax considerations become most important factor in individual‘s portfolio strategy. There are differing tax treatments for investment in various kinds of assets.
Time Horizon: In investment planning, time horizon become an important consideration. It is highly variable from individual to individual. Individuals in their young age have long time horizon for planning, they can smooth out and absorb the ups and downs of risky combination. Individuals who are old have smaller time horizon, they generally tend to avoid volatile portfolios. Individual‘s Financial Objectives: In the initial stages, the primary objective of an individual could be to accumulate wealth via regular monthly savings and have an investment programme to achieve long term capital gains. Safety of Principal:
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The protection of the rupee value of the investment is of prime importance to most investors. The original investment can be recovered only if the security can be readily sold in the market without much loss of value.
Assurance of Income: `Different investors have different current income needs. If an individual is dependent of its investment income for current consumption then income received now in the form of dividend and interest payments become primary objective. Investment Risk: All investment decisions revolve around the trade-off between risk and return. All rational investors want a substantial return from their investment. An ability to understand, measure and properly manage investment risk is fundamental to any intelligent investor or a speculator. Frequently, the risk associated with security investment is ignored and only the rewards are emphasized. An investor who does not fully appreciate the risks in security investments will find it difficult to obtain continuing positive results.
RISK AND EXPECTED RETURN:
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There is a positive relationship between the amount of risk and the amount of expected return i.e., the greater the risk, the larger the expected return and larger the chances of substantial loss. One of the most difficult problems for an investor is to estimate the highest level of risk he is able to assume. Risk is measured along the horizontal axis and increases from the left to
? right.
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Expected rate of return is measured on the vertical axis and rises from
bottom to top. The line from 0 to R (f) is called the rate of return or risk less investments
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commonly associated with the yield on government securities. The diagonal line form R (f) to E(r) illustrates the concept of expected rate
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of return increasing as level of risk increases.
TYPES OF RISKS: Risk consists of two components. They are
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1. Systematic Risk 2. Un-systematic Risk
1. Systematic Risk:
Systematic risk is caused by factors external to the particular company and uncontrollable by the company. The systematic risk affects the market as a whole. Factors affect the systematic risk are ? ? ? economic conditions political conditions sociological changes
The systematic risk is unavoidable. Systematic risk is further sub-divided into three types. They are a) b) c) Market Risk Interest Rate Risk Purchasing Power Risk
a). Market Risk: One would notice that when the stock market surges up, most stocks post higher price. On the other hand, when the market falls sharply, most common stocks will drop. It is not uncommon to find stock prices falling from time to time while a company‘s earnings are rising and vice-versa. The price of stock may fluctuate widely within a short time even though earnings remain unchanged or relatively stable.
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b). Interest Rate Risk: Interest rate risk is the risk of loss of principal brought about the changes in the interest rate paid on new securities currently being issued. c). Purchasing Power Risk: The typical investor seeks an investment, which will give him current income and / or capital appreciation in addition to his original investment. 2. Un-systematic Risk: Un-systematic risk is unique and peculiar to a firm or an industry. The nature and mode of raising finance and paying back the loans, involve the risk element. Financial leverage of the companies that is debt-equity portion of the companies differs from each other. All these factors Factors affect the un-systematic risk and contribute a portion in the total variability of the return. ? Managerial inefficiently ? Technological change in the production process ? Availability of raw materials ? Changes in the consumer preference ? Labour problems The nature and magnitude of the above mentioned factors differ from industry to industry and company to company. They have to be analyzed separately for each industry and firm. Un-systematic risk can be broadly classified into: a) Business Risk b) Financial Risk
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a.
Business Risk:
Business risk is that portion of the unsystematic risk caused by the operating environment of the business. Business risk arises from the inability of a firm to maintain its competitive edge and growth or stability of the earnings. The volatibility in stock prices due to factors intrinsic to the company itself is known as Business risk. Business risk is concerned with the difference between revenue and earnings before interest and tax. Business risk can be divided into.
i). Internal Business Risk
Internal business risk is associated with the operational efficiency of the firm. The operational efficiency differs from company to company. The efficiency of operation is reflected on the company‘s achievement of its pre-set goals and the fulfillment of the promises to its investors.
ii). External Business Risk
External business risk is the result of operating conditions imposed on the firm by circumstances beyond its control. The external environments in which it operates exert some pressure on the firm. The external factors are social and regulatory factors, monetary and fiscal policies of the government, business cycle and the general economic environment within which a firm or an industry operates. b. Financial Risk:
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It refers to the variability of the income to the equity capital due to the debt capital. Financial risk in a company is associated with the capital structure of the company. Capital structure of the company consists of equity funds and borrowed funds.
PORTFOLIO ANALYSIS:
Various groups of securities when held together behave in a different manner and give interest payments and dividends also, which are different to the analysis of individual securities. A combination of securities held together will give a beneficial result if they are grouped in a manner to secure higher return after taking into consideration the risk element. There are two approaches in construction of the portfolio of securities. They are ? Traditional approach ? Modern approach TRADITIONAL APPROACH: Traditional approach was based on the fact that risk could be measured on each individual security through the process of finding out the standard deviation and that security should be chosen where the deviation was the lowest. Traditional
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approach believes that the market is inefficient and the fundamental analyst can take advantage fo the situation. Traditional approach is a comprehensive financial plan for the individual. It takes into account the individual needs such as housing, life insurance and pension plans. Traditional approach basically deals with two major decisions. They are a) Determining the objectives of the portfolio
Selection of securities to be included in the portfolio
MODERN APPROACH:
Modern approach theory was brought out by Markowitz and Sharpe. It is the combination of securities to get the most efficient portfolio. Combination of securities can be made in many ways. Markowitz developed the theory of diversification through scientific reasoning and method. Modern portfolio theory believes in the maximization of return through a combination of securities. The modern approach discusses the relationship between different securities and then draws inter-relationships of risks between them. Markowitz gives more attention to the process of selecting the portfolio. It does not deal with the individual needs.
MARKOWITZ MODEL:
Markowitz model is a theoretical framework for analysis of risk and return and their relationships. He used statistical analysis for the measurement of risk and mathematical programming for selection of assets in a portfolio in an efficient manner. Markowitz apporach determines for the investor the efficient set of portfolio through three important variables i.e. ? Return
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? Standard deviation ? Co-efficient of correlation Markowitz model is also called as an “Full Covariance Model“. Through this model the investor can find out the efficient set of portfolio by finding out the trade off between risk and return, between the limits of zero and infinity. According to this theory, the effects of one security purchase over the effects of the other security purchase are taken into consideration and then the results are evaluated. Most people agree that holding two stocks is less risky than holding one stock. For example, holding stocks from textile, banking and electronic companies is better than investing all the money on the textile company‘s stock. Markowitz had given up the single stock portfolio and introduced diversification. The single stock portfolio would be preferable if the investor is perfectly certain that his expectation of highest return would turn out to be real. In the world of uncertainity, most of the risk adverse investors would like to join Markowitz rather than keeping a single stock, because diversification reduces the risk.
ASSUMPTIONS:
? All investors would like to earn the maximum rate of return that they can All investors have the same expected single period investment horizon. All investors before making any investments have a common goal. This is Investors base their investment decisions on the expected return and Perfect markets are assumed (e.g. no taxes and no transation costs) achieve from their investments. ? ?
the avoidance of risk because Investors are risk-averse. ? standard deviation of returns from a possible investment. ?
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?
The investor assumes that greater or larger the return that he achieves on his
investments, the higher the risk factor surrounds him. On the contrary when risks are low the rerturn can also be expected to be low. ? ? The investor can reduce his risk if he adds investments to his portfolio. An investor should be able to get higher return for each level of risk “by
determining the efficient set of securities“. An individual seller or buyer cannot affect the price of a stock. This Investors make their decisions only on the basis of the expected returns, Investors are assumed to have homogenous expectations during the The investor can lend or borrow any amount of funds at the riskless rate of
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assumption is the basic assumption of the perfectly competitive market. ? standard deviation and covariances of all pairs of securities. ? decision-making period ? interest. The riskless rate of interest is the rate of interest offered for the treasury bills or Government securities. ? Investors are risk-averse, so when given a choice between two otherwise Individual assets are infinitely divisible, meaning that an investor can buy a There is a risk free rate at which an investor may either lend (i.e. invest) There is no transaction cost i.e. no cost involved in buying and selling of identical portfolios, they will choose the one with the lower standard deviation. ? fraction of a share if he or she so desires. ? money or borrow money. ? stocks. There is no personal income tax. Hence, the investor is indifferent to the form of return either capital gain or dividend.
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THE EFFECT OF COMBINING TWO SECURITIES:
It is believed that holding two securities is less risky than by having only one investment in a person‘s portfolio. When two stocks are taken on a portfolio and if they have negative correlation then risk can be completely reduced because the gain on one can offset the loss on the other. This can be shown with the help of following example:
INTER- ACTIVE RISK THROUGH COVARIANCE:
Covariance of the securities will help in finding out the inter-active risk. When the covariance will be positive then the rates of return of securities move together either upwards or downwards. Alternatively it can also be said that the inter-active risk is positive. Secondly, covariance will be zero on two investments if the rates of return are independent. Holding two securities may reduce the portfolio risk too. The portfolio risk can be calculated with the help of the following formula:
CAPITAL ASSET PRICING MODEL (CAPM):
Markowitz, William Sharpe, John Lintner and Jan Mossin provided the basic structure of Capital Asset Pricing Model. It is a model of linear general equilibrium return. In the CAPM theory, the required rate return of an asset is having a linear relationship with asset‘s beta value i.e. undiversifiable or systematic risk (i.e. market related risk) because non market risk can be eliminated by diversification and systematci risk measured by beta. Therefore, the relationship between an assets
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return and its systematic risk can be expressd by the CAPM, which is also called the Security Market Line. Rp= Rf Xf+ Rm(1- Xf) Rp = Portfolio return Xf = The proportion of funds invested in risk free assets 1- Xf = The proportion of funds invested in risky assets Rf = Risk free rate of return Rm = Return on risky assets Formula can be used to calculate the expected returns for different situtions, like mixing riskless assets with risky assets, investing only in the risky asset and mixing the borrowing with risky 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 total value of all risky assets. For example, if Satyam Industry share represents 15% of all risky assets, then the market portfolio of the individual investor contains 15% of Satyam 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. Eg.: assume that borrowing and lending rate to be 12.5% and the return from the risky assets to be 20%. There is a trade off between the expected return and risk. If an investor invests in risk free assets and risky assets, his risk may be less
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than what he invests in the risky asset alone. But if he borrows to invest in risky assets, his risk would increase more than he invests his own money in the risky assets. When he borrows to invest, we call it financial leverage. If he invests 50% in risk free assets and 50% in risky assets, his expected return of the portfolio would be Rp= Rf Xf+ Rm(1- Xf) = (12.5 x 0.5) + 20 (1-0.5) = 6.25 + 10 = 16.25%
if there is a zero investment in risk free asset and 100% in risky asset, the return is Rp= Rf Xf+ Rm(1- Xf) = 0 + 20% = 20% if -0.5 in risk free asset and 1.5 in risky asset, the return is Rp= Rf Xf+ Rm(1- Xf) = (12.5 x -0.5) + 20 (1.5) = -6.25+ 30 = 23.75%
EVALUATION OF PORTFOLIO:
Portfolio manager evaluates his portfolio performance and identifies the sources of strengths and weakness. The evaluation of the portfolio provides a feed back about the performance to evolve better management strategy. Even though
36
evaluation of portfolio performance is considered to be the last stage of investment process, it is a continuous process. There are number of situations in which an evaluation becomes necessary and important.
i.
Self Valuation: An individual may want to evaluate how well he has
done. This is a part of the process of refining his skills and improving his performance over a period of time.
ii.
Evaluation of Managers: A mutual fund or similar organization
might want to evaluate its managers. A mutual fund may have several managers each running a separate fund or sub-fund. It is often necessary to compare the performance of these managers.
iii.
Evaluation of Mutual Funds: An investor may want to evaluate
the various mutual funds operating in the country to decide which, if any, of these should be chosen for investment. A similar need arises in the case of individuals or organisations who engage external agencies for portfolio advisory services. Evaluation of Groups: Academics or researchers may want to evaluate the performance of a whole group of investors and compare it with another group of investors who use different techniques or who have different skills or access to different information. NEED FOR EVALUATION OF PORTFOLIO: We can try to evaluate every transaction. Whenever a security is brought or
?
sold, we can attempt to assess whether the decision was correct and profitable.
37
?
We can try to evaluate the performance of a specific security in the portfolio We can try to evaluate the performance of portfolio as a whole during the
to determine whether it has been worthwhile to include it in our portfolio. ? period without examining the performance of individual securities within the portfolio. NEED & IMPORTANCE: Portfolio management has emerged as a separate academic discipline in India. Portfolio theory that deals with the rational investment decision-making process has now become an integral part of financial literature. Investing in securities such as shares, debentures & bonds is profitable well as exciting. It is indeed rewarding but involves a great deal of risk & need artistic skill. Investing in financial securities is now considered to be one of the most risky avenues of investment. It is rare to find investors investing their entire savings in a single security. Instead, they tend to invest in a group of securities. Such group of securities is called as PORTFOLIO. Creation of portfolio helps to reduce risk without sacrificing returns. securities into portfolios. Portfolio management deals with the analysis of individual securities as well as with the theory & practice of optimally combining
38
The modern theory is of the view that by diversification, risk can be reduced. The investor can make diversification either by having a large number of shares of companies in different regions, in different industries or those producing different types of product lines. Modern theory believes in the perspective of combinations of securities under constraints of risk and return.
PORTFOLIO REVISION:
The portfolio which is once selected has to be continuously reviewed over a period of time and then revised depending on the objectives of the investor. The care taken in construction of portfolio should be extended to the review and revision of the portfolio. Fluctuations that occur in the equity prices cause substantial gain or loss to the investors. The investor should have competence and skill in the revision of the portfolio. The portfolio management process needs frequent changes in the composition of stocks and bonds. In securities, the type of securities to be held should be revised according to the portfolio policy. An investor purchases stock according to his objectives and return risk framework. The prices of stock that he purchases fluctuate, each stock having its own cycle of fluctuations. These price fluctuations may be related to economic activity in a country or due to other changed circumstances in the market.
39
If an investor is able to forecast these changes by developing a framework for the future through careful analysis of the behavior and movement of stock prices is in a position to make higher profit than if he was to simply buy securities and hold them through the process of diversification. Mechanical methods are adopted to earn better profit through proper timing. The investor uses formula plans to help him in making decisions for the future by exploiting the fluctuations in prices.
FORMULA PLANS:
The formula plans provide the basic rules and regulations for the purchase and sale of securities. The amount to be spent on the different types of securities is fixed. The amount may be fixed either in constant or variable ratio. This depends on the investor‘s attitude towards risk and return. The commonly used formula plans are i. ii. iii. iv. Average Rupee Plan Constant Rupee Plan Constant Ratio Plan Variable Ratio Plan
ADVANTAGES:
? Basic rules and regulations for the purchase and sale of securities are
provided. ? ? The rules and regulations are rigid and help to overcome human emotion. The investor can earn higher profits by adopting the plans.
40
? ? ?
A course of action is formulated according to the investor‘s objectives. It controls the buying and selling of securities by the investor. It is useful for taking decisions on the timing of investments.
DISADVANTAGES: The formula plan does not help the selection of the security. The selection of
?
the security has to be done either on the basis of the fundamental or technical analysis. ? ? It is strict and not flexible with the inherent problem of adjustment. The formula plans should be applied for long periods, otherwise the
transaction cost may be high. Even if the investor adopts the formula plan, he needs forecasting. Market forecasting helps him to identify the best stocks.
ANALYSIS & INTERPRETION
CALCULATION OF AVERAGE RETURN OF COMPANIES: Average Return = (R)/N
41
ITC LTD: Opening Closing share price share price (P0) (P1) 696.70 628.25 628.25 1043.10 1043.10 1342.05 1342.05 2932 195.15 151.15 TOTAL RETURN Average Return = 180.79/5 = 36.16 (P1-P0)/ P0*100 -9.82 66.03 28.66 118.47 -22.55 180.79
ear 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(P1-P0) -68.45 414.85 298.95 1589.95 -44
DR REDDY LABORATORIES LTD:
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
Opening Closing share price share price (P0) (P1) 1090.95 916.30 916.30 974.35 974.35 739.15 739.15 1,421.40 1,421.40 1456.55 TOTAL RETURN
(P1-P0) -174.65 58.2 23.52 682.25 35.15
(P1-P0)/ P0*100 -16.00 6.33 -24.14 92.30 2.47 60.96
Average Return = 60.96/5 = 12.19
42
ACC: Opening Closing share price share price (P0) (P1) 153.40 138.50 138.50 254.65 254.65 360.55 360.55 782.20 782.20 735.25 TOTAL RETURN Average Return = 226.8/5 = 45.36 (P1-P0)/ P0*100 -9.7 83.86 41.58 116.95 -6.00 226.8
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(P1-P0) -14.19 116.15 105.9 421.61 -46.95
BHARAT HEAVY ELECTRICALS LTD: Opening Closing share price share price (P0) (P1) 169.00 223.15 223.15 604.35 604.35 766.40 766.40 2241.95 2241.95 2261.35 TOTAL RETURN Average Return = 423.08/5 = 84.62 (P1-P0)/ P0*100 32.04 170.83 26.81 192.53 0.87 423.08
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(P1-P0) 54.15 38.12 162.05 1475.55 19.4
HEROHONDA AUTOMOBILES LIMITED:
43
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
Opening Closing share price share price (P0) (P1) 338.55 188.20 188.20 490.60 490.60 548.00 548.00 890.45 890.45 688.75 TOTAL RETURN
(P1-P0) -150.35 302.40 57.40 342.45 -20.17
(P1-P0)/ P0*100 -44.40 160.68 11.70 62.50 -22.65 167.82
Average Return = 167.82/5 = 33.56
WIPRO: Opening Closing share price share price (P0) (P1) 1,700.60 1233.45 1,233.45 1361.20 1,361.20 2,012 670.95 559.7 559.70 559.40 TOTAL RETURN Average Return = 14.13/5 = 2.83 (P1-P0)/ P0*100 -27.47 10.36 47.87 -16.58 -0.05 14.13
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(P1-P0) -467.15 127.75 650.8 -111.25 -0.3
CALCULATION OF STANDARD DEVIATION:
Standard Deviation = Variance
44
Variance ITC LTD:
=
1/n (R-R)2
Year 2002-2003 2003-2004 2003-2004 2004-2005 2005-2006
Return Avg. (R) Return (R) -9.82 36.16 66.03 36.16 28.66 36.16 118.47 36.16 -22.55 36.16 TOTAL
(R-R) -45.98 29.87 -7.5 82.31 -58.71
(R-R)2 2114.16 892.22 56.25 6775 3447 13284
Variance = 1/n (R-R)2 = 1/5 (13284) = 2656.8 Standard Deviation = Variance = 2656.8 = 51.54
DR. REDDY: Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 Return Avg. (R) Return (R) -16.00 12.19 6.33 12.19 -24.14 12.19 92.30 12.19 2,47 12.19 TOTAL Variance = 1/n-1 (R-R)2 = 1/5 (8,661) = 1732.2 Standard Deviation = Variance = 1732.2= 41.62 (R-R) -28.19 -5.86 -36.33 80.11 -9.72 (R-R)2 795 34 1320 6418 94 8,661
ACC:
45
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
Return Avg. (R) Return (R) -9.7 45.36 83.86 45.36 41.58 45.36 116.95 45.36 -6.00 45.36 TOTAL
(R-R) -55.06 38.5 -3.78 71.59 -51.36
(R-R)2 3032 1482 13.69 5125 2638 12,291
Variance = 1/n-1 (R-R)2 = 1/5 (12,291) = 2458 Standard Deviation = Variance = 2458 = 49.58
WIPRO: Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 Return Avg. (R) Return (R) -27.47 2.83 10.36 2.83 47.87 2.83 -16.58 2.83 -0.05 2.83 TOTAL Variance = 1/n-1 (R-R)2 = 1/5 (3388) = 847 Standard Deviation = Variance = 847 =33.09 BHEL:
46
(R-R) -30.29 7.53 45.04 -19.41 -2.88
(R-R)2 917 57 2029 377 8 3388
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
Return Avg. (R) Return (R) 32.04 84.62 170.83 84.62 26.81 84.62 192.53 84.62 0.87 84.62 TOTAL
(R-R) -52.58 86.21 -57.81 107.91 -83.75
(R-R)2 2765 7432 3342 11645 7014 32,198
Variance = 1/n-1 (R-R)2 = 1/5 (32198) = 6440 Standard Deviation = Variance = 6440 = 80.25
HERO HONDA: Year 2002-2003 2002-2003 2004-2005 2005-2006 2006-2007 Return Avg. (R) Return (R) -44.40 33.56 160.68 33.56 11.70 33.56 62.50 33.56 -22.65 33.65 TOTAL Variance = 1/n-1 (R-R)2 = 1/5 (26,715) = 5343 Standard Deviation = Variance = 5343 = 73.09 (R-R) -77.97 127.12 -21.86 28.94 -56.21 (R-R)2 6079 16160 478 838 3160 26,715
CALCULATION OF CORRELATION:
Covariance (COV ab) = 1/n (RA-RA)(RB-RB) Correlation Coefficient = COV ab/?a*? b
47
i. ACC (RA) & ITC (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -55.06 38.5 -3.78 71.59 -51.36 (RB-RB) (RA-RA) (RB-RB) -45.98 2532 29.87 1149.99 -7.5 28.35 82.31 5892.57 -58.71 3015 TOTAL 12617.9
Covariance (COV ab) = 1/5 (12617.9) = 2523.58 Correlation Coefficient = COV ab/?a*? b ?a = 49.57 ; ?b = 51.54 = 2523.58/(49.57)(51.54) = 0.98 ii) ACC (RA) & WIPRO (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -52.58 86.21 -57.81 107.91 -83.75 TOTAL (RB-RB) (RA-RA) (RB-RB) -77.97 4099.66 127.12 10959.01 -21.86 1263.72 28.94 3122.91 -56.21 4707.58 24152.88
Covariance (COV ab) = 1/5 (24152.88) = 4830.57 Correlation Coefficient = COV ab/?a*? b ?a = 26 ; ?b = 41.62 = 4830.57/(80.25)(73.09) = 0.82 iii. WIPRO (RA) & DR REDDY (RB) YEAR (RA-RA) (RB-RB) (RA-RA) (RB-RB)
48
2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
-30.29 7.53 44.98 -19.41 -2.88 TOTAL
-28.19 -5.86 -36.33 80.11 -9.72
853.87 -44.12 -1634.12 -1554.93 27.99 -2351.31
Covariance (COV ab) = 1/5 (-2351.31) = 470.26 Correlation Coefficient = COV ab/?a*? b ?a = 26.00 ; ?b = 41.62 = -470.26/(26.00)(41.62) = -0.43
v.
ITC (RA) & BHEL (RB)
YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(RA-RA) -45.98 -29.87 -7,5 82.31 -58.71 TOTAL
(RB-RB) (RA-RA) (RB-RB) -52.58 2417.63 86.21 -2575.09 -57.81 -433.58 107.91 8882.07 -83.75 4916.96 14075.15
Covariance (COV ab) = 1/5 (14075.15) = 2815.03 Correlation Coefficient = COV ab/?a*? b ?a = 51.54 ; ?b = 80.25 = 2815.03/(51.54)(80.25) = 0.68
49
v. ACC (RA) & BHEL (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -55.06 38.5 -3.7 71.59 -51.3 TOTAL (RB-RB) (RA-RA) (RB-RB) -52.58 2895.05 86.21 3319.08 -57.81 213.89 107.91 7725.27 -83.75 4296.37 18449.66
Covariance (COV ab) = 1/5 (18449.66) = 3689.93 Correlation Coefficient = COV ab/?a*? b ?a = 49.57 ; ?b = 80.25 = 18449.66/(49.57)(80.25) = 0.92
2. Correlation between ACC & other Companies: i. ACC (RA) & HEROHONDA (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -55.06 38.5 -3.78 71.59 -51.36 TOTAL (RB-RB) (RA-RA) (RB-RB) -77.97 4293.02 127.12 4894.12 -21.86 82.63 28.94 2071.81 -56.21 2886.95 14228.53
Covariance (COV ab) = 1/5 (14228.53) = 2845.70 Correlation Coefficient = COV ab/?a*? b ?a = 49.58 ; ?b = 73.04 = 2845.70/(49.57)(26.00) = 0.78
50
ii. ACC (RA) & WIPRO (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -55.06 38.5 -3.78 71.59 -51.36 TOTAL Covariance (COV ab) = 1/5 (546) = 109.2 Correlation Coefficient = COV ab/?a*? b ?a = 49.57; ?b = 26.00
= 109.2/(49.57)(26.00) = 0.08
(RB-RB) (RA-RA) (RB-RB) -30.29 1667.77 7.53 289.90 44.98 -170.02 -19.41 -1389.56 -2.88 147.91 546
iii. ACC (RA) & DR REDDY (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -55.06 38.5 -3.78 71.59 -51.36 TOTAL (RB-RB) (RA-RA) (RB-RB) -28.19 552.14 -5.86 -225.61 -36.33 137.33 80.11 5735.07 -9.72 499.21 7698.14
Covariance (COV ab) = 1/5 (7698.14) = 1539.63 Correlation Coefficient = COV ab/?a*? b ?a = 49.57 ; ?b = 41.62 = 1539.63/(49.57)(41.62) = 0.74 iv. ITC (RA) & HERO HONDA (RB)
51
YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(RA-RA) -45.98 29.87 -7.5 82.31 -58.71 TOTAL
(RB-RB) (RA-RA) (RB-RB) -77.97 3585.06 127.12 3797.07 -21.86 163.95 28.94 2382.05 -56.21 3300.08 13228.21
Covariance (COV ab) = 1/5 (13228.21) = 2645.64 Correlation Coefficient = COV ab/?a*? b ?a = 51.54 ; ?b = 73.09 = 2645.64/(51.54)(73.09) = 0.70 3. Correlation Between DR REDDY & Other Companies i. ITC(RA) & WIPRO: YEAR 2002-2003 2002-2003 2003-2004 2004-2005 2005-2006 (RA-RA) -16.024 -26.574 -3.684 -34.724 81.006 TOTAL (RB-RB) (RA-RA) (RB-RB) -10.89 174.50 -46.94 1,247.38 -8.7 32.05 -26.98 936.85 93.53 7,576.49 9,967.28
Covariance (COV ab) = 1/5-1 (9967.28) = 2491.82 Correlation Coefficient = COV ab/?a*? b ?a = 46.75 ; ?b = 54.48 = 2491.82/(46.75)(54.48) = 0.978
52
ii. DR. REDDY (RA) & &ITC (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -28.19 -5.86 -36.33 80.11 -9.72 TOTAL YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -28.19 -5.86 -36.33 80.11 -9.72 TOTAL (RB-RB) (RA-RA) (RB-RB) -45.98 1296.17 29.87 -175.03 -7.5 272.47 82.31 6593.85 -58.71 570.66 8558.12 (RB-RB) -77.97 127.12 -21.86 28.94 -56.21 (RA-RA) (RB-RB) 2197.97 744.92 794.17 2318.38 546.36 6601.8
Covariance (COV ab) = 1/5 (8558.12) = 1711.62 Correlation Coefficient = COV ab/?a*? b ?a = 41.62 ; ?b = 51.54 = 1711.62/(41.62)(51.54) = 0.79
iv.
DR REDDY (RA) &HEROHONDA(RB)
Covariance (COV ab) = 1/5 (6601.8) = 1320.36 Correlation Coefficient = COV ab/?a*? b ?a = 41.62 ; ?b = 73.09
53
= 1320.36/(41.62)(73.09) = 0.43 4. Correlation Between HLL & Other Companies i. HEROHONDA (RA) & WIPRO(RB)
Covariance (COV ab) = 1/5 (1934.51) = 386.90 Correlation Coefficient = COV ab/?a*? b ?a = 73.09; ?b = 26.00 = 386.90/(73.09)(26.00) = 0.20 ii. DR REDDY (RA) & BHEL(RB)
YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(RA-RA) -77.97 127.12 -21.86 28.94 -56.21 TOTAL
(RB-RB) (RA-RA) (RB-RB) -30.29 2361.71 7.53 957.21 45.04 -984.57 -19.41 -561.72 -2.88 161.88 1934.51
54
YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(RA-RA) -28.19 -5.86 -36.33 80.11 -9.72 TOTAL
(RB-RB) (RA-RA) (RB-RB) -52.58 1482.23 86.21 -505.19 -57.81 2100.24 107.91 8644.67 -83.75 814.05 12536
Covariance (COV ab) = 1/5 (12536) =
386.90 Correlation Coefficient = COV ab/?a*? b ?a = 41.62; ?b = 80.25 = 2507.2/(41.62)(80.25) = 0.93
5. CORRELATION BETWEEN BHEL(RA) & WIPRO(RB)
YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(RA-RA) -52.58 86.21 -57.81 107.91 -83.75 TOTAL
(RB-RB) (RA-RA) (RB-RB) -30.29 1592.65 7.53 649.16 45.04 -2603.76 -19.41 -2094.53 -2.88 241.2 -2215.28
Covariance (COV ab) = 1/5 (-2215.28) = -443.05 Correlation Coefficient = COV ab/?a*? b ?a = 80.25; ?b = 26.00 = -443.05/(80.25)(26.00) = -0.21
55
CALCULATION OF PORTFOLIO WEIGHTS: FORMULA : Wa =
?b [?b-(nab*?a)] ?a2 + ?b2 - 2nab*?a*?b
Wb = 1 – Wa CALCULATION OF WEIGHTS OF ITC & OTHER COMPANIES: i. ITC(a) & WIPRO (b)
?a = 51.54 ?b = 26.00 nab = -0.02
Wa =
26.00 [26.00-(-0.02*51.54)] (51.54) + (26.00) 2 – 2(-0.02)*(51.54) *(26.00)
2
Wa =
690 3386
Wa =0.20 Wb = 1 – Wa Wb = 1-0.20 = 0.8
ii. HEROHONDA(a) & WIPRO(b)
?a = 73.09 ?b = 26.00 nab = 0.20
56
Wa =
26.00 [26.00-(0.20*73.09)] (73.09) + (26.00) 2 – 2(0.20)*(73.09) *(26.00)
2
Wa =
296 5258
Wa =0.05 Wb = 1 – Wa Wb = 1-0.05 = 0.95
CALCULATION OF WEIGHTS OF BHEL & WIPRO:
?a = 80.25 ?b = 26.00 nab = -0.21
Wa =
26.00 [26.00-(-0.21*80.25)] (80.25) 2 + (26.00) 2 – 2(-0.21)*(80.25) *(26.00) 1114 7992
Wa =
Wa =0.14 Wb = 1 – Wa Wb = 1-0.14 = 0.86
CALCULATION OF WEIGHTS OF WIPRO & OTHE COMPANIES:
i.
ACC (a) & ITC (b):
?a = 49.57 ?b = 51.54 nab = 0.98
57
Wa =
51.54 [51.54-(0.98*49.57)]
(49.57) 2 + (51.54) 2 – 2(0.98)*(49.57) *(51.54) Wa = 152 106 Wa =1.43 Wb = 1 – Wa Wb = 1-1.43 = - 0.43
ii. BHEL (a) & HEROHONDA (b)
?a = 80.25 ?b = 73.09 nab = 0.82
Wa =
73.09 [73.09-(0.82*80.25)] (80.25) 2 + (73.09) 2 – 2(0.82)*(80.25) *(73.09)
2163
Wa =
533 Wa =0.24 Wb = 1 – Wa Wb = 1-0.24 = 0.76
iii.
WIPRO (a) & DR REDYY (b)
?a = 26.00 ?b = 41.62 nab = -0.43
Wa =
41.62 [41.62-(-0.43*26.00)] (26.00) 2 + (41.62) 2 – 2(-0.43)*(41.62) *(26.00)
58
Wa = 2198 1477 Wa =1.49 Wb = 1 – Wa Wb = 1-1.49 = -0.49
iv.
ITC (a) & BHEL (b)
?a = 51.54 ?b = 80.25 nab = 0.68
Wa =
80.25 [80.25-(0.68*51.54)] (51.54) 2 + (80.25) 2 – 2(0.68)*(51.54) *(80.25)
Wa = 3628 3471 Wa =1.04 Wb = 1 – Wa Wb = 1-1.04 =0.04
v. ACC (a) & BHEL (b)
?a = 49.57 ?b = 80.25 nab = 0.92
Wa =
80.25 [80.25-(0.92*49.57)] (49.57) 2 + (80.25) 2 – 2(0.92)*(49.57) *(80.25)
Wa = 2781
59
1577 Wa =1.76 Wb = 1 – Wa Wb = 1-1.76 = -0.76
CALCULATION OF WEIGHTS OF ACC & OTHER COMPANIES: iii. ACC (a) & HEROHONDA (b)
?a = 49.57 ?b = 73.09 nab = 0.78
Wa =
73.09 [73.09-(0.78*49.57)] (49.57) 2 + (73.09) 2 – 2(0.78)*(49.57) *(73.09)
Wa = 2516 2148 Wa =1.17 Wb = 1 – Wa Wb = 1-1.17 = -0.17
iv. ACC(a) & WIPRO (b)
?a = 49.57 ?b = 26.00 nab = 0.08
Wa =
26.00 [26.00-(0.08*49.57)] (49.57) 2 + (26.00) 2 – 2(0.08)*(49.57) *(26.00) 573 2927
60
Wa =
Wa =0.19 Wb = 1 – Wa Wb = 1-0.19 = 0.81
v. ACC (a) & DR REDDY (b)
?a = 49.57 ?b = 41.62 nab = 0.74
Wa =
41.62 [41.62-(0.74*49.57)] (49.57) 2 + (41.62) 2 – 2(0.74)*(49.57) *(41.62) 206 1136
Wa =
Wa =0.18 Wb = 1 – Wa Wb = 1-0.18 = 0.82
vi. ITC(a) & HERO HONDA (b)
?a = 51.54 ?b = 73.09 nab = 0.70
Wa =
73.09 [73.09-(0.70*51.54)] (51.54) + (73.09) 2 – 2(0.70)*(51.54) *(73.09)
2
Wa =
2706 2724
Wa =0.99 Wb = 1 – Wa
61
Wb = 1-0.99 = 0.01
CALCULATION OF WEIGHTS OF DRREDDY & OTHER COMPANIES: vii. DRREDDY (a) & ITC (b)
?a = 41.62 ?b = 51.54 nab = 0.79
Wa =
51.54 [51.54-(0.79*41.62)] (41.62) 2 + (51.54) 2 – 2(0.79)*(41.62) *(51.54)
Wa =
962 999 Wa =0.96 Wb = 1 – Wa Wb = 1-0.96 = 0.04
viii. DRREDDY (a) & HEROHONDA (b)
?a = 41.62 ?b = 73.09 nab = 0.43
Wa =
73.09 [73.09-(0.43*41.62)] (41.62) + (73.09) 2 – 2(0.43)*(41.62) *(73.09)
2
Wa =
4034 4458
Wa =0.90 Wb = 1 – Wa Wb = 1-0.90 = 0.10
ix. DRREDDY (a) & BHEL (b)
62
?a = 41.62 ?b = 80.25 nab = 0.75
Wa =
80.25 [80.25-(0.75*41.62)] (41.62) 2 + (80.25) 2 – 2(0.75)*(41.62) *(80.25) 3935 3162
Wa =
Wa =1.24 Wb = 1 – Wa Wb = 1-1.24 = -0.24
CALCULATION OF PORTFOLIO RISK:
RP =
?a2*Wa2 + ?b2*Wb2 + 2nab*?a*?b*Wa*Wb
CALCULATION OF PORTFOLIO RISK OF WIPRO & OTHER COMPANIES: i. Wipro (a) & ITC (b):
?a = 33.09 ?b = 56.09 = 2/3 = 1/3 Nab = 0.98
RP = (2/3)2(49.57)2+(1/3) 2(0.51.54)2+2(49.57)(51.54) *(0.98) *(2/3)*(1/3)
= ? 2505
= 50.04
63
ii.
BHEL (a) & HEROHONDA (b):
?a = 80.25 ?b = 73.09 = 2/3 = 1/3 nab = 0.82
RP = (2/3)2(80.25)2+(1/3) 2(73.09)2+2(80.25)(73.09) *(0.82) *(2/3)*(1/3)
= ? 5613
iii.
= 74.91
WIPRO (a) & DR REDDY (b):
?a = 41.62 ?b = 26.00 = 2/3 = 1/3 nab = 0.43
RP = (2/3)2(41.62)2+(1/3) 2(26.00)2+2(41.62)(26.00) *(0.43) *(2/3)*(1/3)
= ? 647
iv.
= 25.43
ITC (a) & BHEL (b):
?a = 51.54 ?b = 80.25 = 1/3 = 2/3 nab = 0.68
64
RP =
(1/3)2(51.54)2+(2/3) 2(80.25)2+2(51.54)(80.25) *(0.68) *(2/3)*(1/3)
= ? 4434
v.
=
66.58
ACC (a) & BHEL (b):
?a = 49.57 ?b = 80.25 = 2/3 =1/3 nab = 0.92
RP = (2/3)2(49.57)2+(1/3) 2(80.25)2+2(49.57)(80.25) *(0.92) *(2/3)*(1/3)
= ? 4786
= 69.18
I.
CALCULATION OF PORTFOLIO RISK OF ACC & OTHER COMPANIES
vi.
ACC(a) & HEROHONDA(b):
?a = 49.57 ?b = 73.09 = 2/3 = 1/3 nab = 0.78
RP = (2/3)2(49.57)2+(1/3) 2(73.09)2+2(49.57)(73.09) *(0.78) *(2/3)*(1/3)
= ? 2944 = 54.25
vii.
ACC (a) & WIPRO (b):
65
?a = 49.57 ?b = 26.00 = 2/3 = 1/3 nab = 0.08
RP = (2/3)2(49.57)2+(1/3) 2(26.00)2+2(49.57)(26.00) *(0.08) *(2/3)*(1/3)
= ? 1226 = 35.01
viii.
ACC (a) & DR REDDY (b):
?a = 49.57 ?b = 41.62 = 2/3 = 1/3 nab = 0.74
RP = (2/3)2(49.57)2+(1/3) 2(41.62)2+2(49.57)(41.62) *(0.74) *(2/3)*(1/3)
= ? 1972 = 44.40
ix.
ITC (a) & HEROHONDA (b):
?a = 51.54 ?b = 73.09 = 2/3 = 1/3 nab = 0.70
RP = (2/3)2(51.54)2+(1/3) 2(73.09)2+2(51.54)(73.09) *(0.70) *(2/3)*(1/3)
= ? 2949
= 54.30
66
II.
x.
CALCULATION OF PORTFOLIO RISK OF DR REDDY & OTHER COMPANIES DRREDDY (a) & ITC (b):
?a = 41.62 ?b = 51.54 = 1/3 = 2/3 nab = 0.79
RP = (1/3)2(41.62)2+(2/3) 2(51.54)2+2(41.62)(51.54) *(0.79) *(2/3)*(1/3)
= ? 2135
xi.
= 46.2
DRREDDY (a) & HEROHONDA (b):
?a = 41.62 ?b = 73.09 = 1/3 = 2/3 nab = 0.43
RP =
(1/3)2(41.62)2+(2/3) 2(73.09)2+2(41.62)(73.09) *(0.43) *(2/3)*(1/3)
= ? 3172
xii.
= 56.32
DRREDDY (a) & BHEL (b):
?a = 41.62 ?b = 80.25 = 1/3 = 2/3
67
nab = 0.878
RP = (1/3)2(41.62)2+(2/3) 2(80.25)2+2(41.62)(80.25) *(0.75) *(2/3)*(1/3)
= ? 4197
III.
= 64.78
CALCULATION OF PORTFOLIO RISK OF ITC & OTHER COMPANIES
xiii.
ITC (a) & WIPRO (b):
?a = 51.54 ?b = 26.00 = 2/3 = 1/3 nab = -0.02
RP =
(2/3)2(51.54)2+(1/3) 2(26.00)2+2(51.54)(26.00) *(26.00) *(2/3)*(1/3)
= ? 1281
xiv.
= 35.79
HEROHONDA (a) & WIPRO (b):
?a = 73.09 ?b = 26.00 = 2/3 = 1/3 nab = 0.20
RP =
(2/3)2(73.09)2+(1/3) 2(26.00)2+2(73.09)(26.00) *(0.20) *(0.67)*(0.33)
68
= ? 2646 = 51.44
IV.
CALCULATION OF PORTFOLIO RISK OF BHEL (a) &WIPRO (b)
?a = 80.25 ?b = 26.00 =2/3 =1/3 nab = -0.21
RP (2/3)2(80.25)2+(1/3) 2(26.00)2+2(80.25)(26.00) *(?0.21)*(2/3)*(1/3)
=
= ? 2778
= 52
69
CONCLUSION
For any investment the factors to be considered are the return on the investment and the risk associated with that investment. Diversification in the investment into different assets can reduce the risk. There fore by following modern portfolio theorem, risk can be reduced for a required return
.
70
BIBILOGRAPHY
1.SECURITY ANALYSIS AND PORTFOLIO MANAGEMENT -Donald.E.Fisher, Ronald.J.Jordan 2.INVESTMENTS -William .F.Sharpe,gordon,J Alexander and Jeffery.V.Baily 3.PORTFOLIOMANAGEMENT -Strong R.A
WEB REFERENCES
http;//www.nseindia.com http;//www.bseindia.com http;//www.economictimes.com http;//www.answers.com
71
doc_362707189.doc
This is to certify that the project work entitled “A Case Study on Portfolio Management” with reference to Inter-Connected Stock Exchange of India Limited [ISE]; Hyderabad has been carried out by Krishna under my guidance in partial fulfillment of the Requirements for the award of Master of Business Administration.
PROJECT REPORT ON “A CASE STUDY ON PORT FOLIO MANAGEMENT ”
CERTIFICATE
This is to certify that the project work entitled “A Case Study on Portfolio Management” with reference to Inter-Connected Stock Exchange of India Limited [ISE]; Hyderabad has been carried out by XXXXX under my guidance in partial fulfillment of the Requirements for the award of –
MASTER OF BUSINESS ADMINISTRATION
(Faculty – Finance) (Director)
(Course Co-ordinator)
CONTENTS
1. 2. 3.
4.
COMPANY PROFILE INTRODUCTION PORTFOLIO ANALYSIS ANALYSIS & INTERPRETION CALCULATION OF AVERAGE RETURN OF COMPANIES CALCULATION OF PORTFOLIO RISK CALCULATION OF PORTFOLIO WEIGHTS CONCLUSION BIBILOGRAPHY
5. 6. 7. 8. 9.
5
COMPANY PROFILE
Inter-connected stock exchange of India limited [ISE] has been promoted by 14 Regional stock exchanges to provide cost-effective trading linkage/connectivity to all the members of the participating Exchanges, with the objective of widening the market for the securities listed on these Exchanges. ISE aims to address the needs of small companies and retail investors with the guiding principle of optimizing the existing infrastructure and harnessing the potential of regional markets, so as to transform these into a liquid and vibrant market through the use of state-of-the-art technology and networking. The participating Exchanges of ISE in all about 4500 stock brokers, out of which more than 200 have been currently registered as traders on ISE. In order to leverage its infrastructure and to expand its nationwide reach, ISE has also appointed around 450 Dealers across 70 cities other than the participating Exchange centers. These dealers are administratively supported through the regional offices of ISE at Delhi [north], kolkata [east], Coimbatore, Hyderabad [south] and Nagpur [central], besides Mumbai.
6
ISE has also floated a wholly-owned subsidiary, ISE securities and services limited [ISS], which has taken up corporate membership of the National Stock Exchange of India Ltd. [NSE] in both the Capital Market and Futures and Options segments and The Stock Exchange, Mumbai In the Equities segment, so that the traders and dealers of ISE can access other markets in addition to the ISE markets and their local market. ISE thus provides the investors in smaller cities a one-stop solution for cost-effective and efficient trading and settlement in securities. With the objective of broad basing the range of its services, ISE has started offering the full suite of DP facilities to its Traders, Dealers and their clients.
OBJECTIVES OF THE COMPANY:
1. Create a single integrated national level solution with access to multiple markets for providing high cost-effective service to millions of investors across the country. 2. Create a liquid and vibrant national level market for all listed companies in general and small capital companies in particular. 3. Optimally utilize the existing infrastructure and other resources of participating Stock Exchanges, which are under-utilized now. 4. Provide a level playing field to small Traders and Dealers by offering an opportunity to participate in a national markets having investment-oriented business. 5. Reduce transaction cost. 6. Provide clearing and settlement facilities to the Traders and Dealers across the Country at their doorstep in a decentralized mode. 7. Spread demat trading across the country
7
SAILENT FEATURES Network of intermediaries:
As at the beginning of the financial year 2003-04, 548 intermediaries (207 Traders and 341 Dealers) are registered on ISE. A broad of members forms the bedrock for any Exchange, and in this respect, ISE has a large pool of registered intermediaries who can be tapped for any new line of business.
Robust Operational Systems:
The trading, settlement and funds transfer operations of ISE and ISS are completely automated and state-of-the-art systems have been deployed. The communication network of ISE, which has connectivity with over 400 trading members and is spread across46 cities, is also used for supporting the operations of ISS. The trading software and settlement software, as well as the electronic funds transfer arrangement established with HDFC Bank and ICICI Bank, gives ISE and ISS the required operational efficiency and flexibility to not only handle the secondary market functions effectively, but also by leveraging them for new ventures.
Skilled and experienced manpower:
ISE and ISS have experienced and professional staff, who have wide experience in Stock Exchanges/ capital market institutions, with in some cases, the experience going up to nearly twenty years in this industry. The staff has the skillset required to perform a wide range of functions, depending upon the requirements from time to time.
8
Aggressive pricing policy:
The philosophy of ISE is to have an aggressive pricing policy for the various products and services offered by it. The aim is to penetrate the retail market and strengthen the position, so that a wide variety of products and services having appeal for the retail market can be offered using a common distribution channel. The aggressive pricing policy also ensures that the intermediaries have sufficient financial incentives for offering these products and services to the endclients.
Trading, Risk Management and Settlement Software Systems:
The ORBIT (Online Regional Bourses Inter-connected Trading) and AXIS (Automated Exchange Integrated Settlement) software developed on the Microsoft NT platform, with consultancy assistance from Microsoft, are the most contemporary of the trading and settlement software introduced in the country. The applications have been built on a technology platform, which offers low cost of ownership, facilitates simple maintenance and supports easy up gradation and enhancement. The soft wares are so designed that the transaction processing capacity depends on the hardware used; capacity can be added by just adding inexpensive hardware, without any additional software work. Vibrant Subsidiary Operations: ISS, the wholly owned subsidiary of ISE, is one of the biggest Exchange subsidiaries in the country. On any given day, more than 250 registered intermediaries of ISS traded from 46 cities across the length and breadth of the country.
9
Name of the Board of directors
1. Prof. P. V. Narasimham 2. Shri V. Shankar 3. Dr. S. D. Israni 4. Dr. M. Y. Khan 5. Mr. P. J. Mathew 6. M. C. Rodrigues 7. Mr. M. K. Ananda Kumar 8. Mr. T.N.T Nayar 9. Mr. K. D. Gupta 10. Mr. V. R. Bhaskar Reddy 11. Mr. Jambu Kumar Jain Public Interest Director Managing Director Public Interest Director Public Interest Director Shareholder Director Shareholder Director Shareholder Director Shareholder Director Shareholder Director Shareholder Director Trading Member Director
INTRODUCTION
10
Investment may be defined as an activity that commits funds in any financial form in the present with an expectation of receiving additional return in the future. The expectations bring with it a probability that the quantum of return may vary from a minimum to a maximum. This possibility of variation in the actual return is known as investment risk. Thus every investment involves a return and risk. Investment is an activity that is undertaken by those who have savings. Savings can be defined as the excess of income over expenditure. An investor earns/expects to earn additional monetary value from the mode of investment that could be in the form of financial assets. • The three important characteristics of any financial asset are:
Return-the potential return possible from an asset. • Risk-the variability in returns of the asset form the chances of its value
going down/up. • Liquidity-the ease with which an asset can be converted into cash. Investors tend to look at these three characteristics while deciding on their individual preference pattern of investments. Each financial asset will have a certain level of each of these characteristics.
Investment avenues
11
There are a large number of investment avenues for savers in India. Some of them are marketable and liquid, while others are non-marketable. Some of them are highly risky while some others are almost risk less. Investment avenues can be broadly categorized under the following head. 1. Corporate securities 2. Equity shares. 3. Preference shares. 4. Debentures/Bonds. 5. Derivatives. 6. Others.
Corporate Securities
Joint stock companies in the private sector issue corporate securities. These include equity shares, preference shares, and debentures. Equity shares have variable dividend and hence belong to the high risk-high return category; preference shares and debentures have fixed returns with lower risk.The classification of corporate securities that can be chosen as investment avenues can be depicted as shown below:
Equity Shares
Preference shares
Bonds
Warrants
Derivatives
METHODOLOGY OF THE STUDY
12
OBJECTIVES OF THE STUDY: The objectives of the study are as follows: To study the investment pattern and its related risks & returns. To find out optimal portfolio, which gave optimal return at a minimize risk To see whether the portfolio risk is less than individual risk on whose basis To see whether the selected portfolios is yielding a satisfactory and constant To understand, analyze and select the best portfolio.
? ?
to the investor. ? the portfolios are constituted. ? return to the investor. ?
SCOPE OF STUDY:
This study covers the Markowitz model. The study covers the calculation of correlations between the different securities in order to find out at what percentage funds should be invested among the companies in the portfolio. Also the study includes the calculation of individual Standard Deviation of securities and ends at the calculation of weights of individual securities involved in the portfolio. These percentages help in allocating the funds available for investment based on risky portfolios.
13
DATA COLLECTION METHODS The data collection methods include both the primary and secondary collection methods. ? Primary collection methods: This method includes the data collection from the personal discussion with the authorized clerks and members of the exchange. ? Secondary collection methods: The secondary collection methods includes the lectures of the superintend of the department of market operations and so on, also the data collected from the news, magazines of the ISE and different books issues of this study
LIMITATIONS OF THE STUDY
The study confines to the past 2-3 years and present system of the trading procedure in the ISE and the study is confined to the coverage of all the related issues in brief. The data is collected from the primary and secondary sources and thus is subject to slight variation than what the study includes in reality. Hence accuracy and correctness can be measured only to the extend of what the sample group has furnished. This study has been conducted purely to understand Portfolio Management for investors. Construction of Portfolio is restricted to two companies based on Markowitz Very few and randomly selected scripts / companies are analyzed from BSE
?
model. ? listings.
14
?
Data collection was strictly confined to secondary source. No primary data is Detailed study of the topic was not possible due to limited size of the
associated with the project. ? project. There was a constraint with regard to time allocation for the research study i.e. for a period of two months.
PORT FOLIO MANAGEMENT MEANING:
A portfolio is a collection of assets. The assets may be physical or financial like Shares, Bonds, Debentures, Preference Shares, etc. The individual investor or a fund manager would not like to put all his money in the sares of one company, that would amount to great risk. He would therefore, follow the age old maxim that one should not put all the egges into one basket. By doing so, he can achieve objective to maximize portfolio return and at the same time minimizing the portfolio risk by diversification. Portfolio management is the management of various financial assets which Portfolio management is a decision – support system that is designed with a According to Securities and Exchange Board of India Portfolio Manager is
?
comprise the portfolio. ? view to meet the multi-faced needs of investors. ? defined as: “portfolio means the total holdings of securities belonging to any person”.
?
PORTFOLIO MANAGER means any person who pursuant to a contract
or arrangement with a client, advises or directs or undertakes on behalf of the client
15
(whether as a discretionary portfolio manager or otherwise) the management or administration of a portfolio of securities or the funds of the client.
?
DISCRETIONARY PORTFOLIO MANAGER means a portfolio
manager who exercises or may, under a contract relating to portfolio management exercises any degree of discretion as to the investments or management of the portfolio of securities or the funds of the client.
FUNCTIONS OF PORTFOLIO MANAGEMENT:
? To frame the investment strategy and select an investment mix to achieve
the desired investment objectives To provide a balanced portfolio which not only can hedge against the
?
inflation but can also optimize returns with the associated degree of risk To make timely buying and selling of securities To maximize the after-tax return by investing in various tax saving
?
?
investment instruments. STRUCTURE / PROCESS OF TYPICAL PORTFOLIO MANAGEMENT
In the small firm, the portfolio manager performs the job of security analyst. In the case of medium and large sized organizations, job function of portfolio manager and security analyst are separate.
16
RESEARCH (e.g. Security Analysis)
PORTFOLIO MANAGERS
OPERATIONS (e.g. buying and selling of Securities)
CLIENTS
CHARACTERISTICS OF PORTFOLIO MANAGEMENT: Individuals will benefit immensely by taking portfolio management services for the following reasons: Whatever may be the status of the capital market, over the long period
?
capital markets have given an excellent return when compared to other forms of investment. The return from bank deposits, units, etc., is much less than from the stock market. The Indian Stock Markets are very complicated. Though there are thousands
?
of companies that are listed only a few hundred which have the necessary liquidity. Even among these, only some have the growth prospects which are conducive for investment. It is impossible for any individual wishing to invest and sit down and analyze all these intricacies of the market unless he does nothing else. Even if an investor is able to understand the intricacies of the market and
?
separate chaff from the grain the trading practices in India are so complicated that it is really a difficult task for an investor to trade in all the major exchanges of
17
India, look after his deliveries and payments. This is further complicated by the volatile nature of our markets which demands constant reshuffing of portfolios.
TYPES OF PORTFOLIO MANAGEMENT:
1. DISCRETIONARY (DPMS): In this type of service, the client parts with his money in favour of the manager, who in return, handles all the paper work, makes all the decisions and gives a good return on the investment and charges fees. In the Discretionary Portfolio Management Service, to maximise the yield, almost all portfolio managers park the funds in the money market securities such as overnight market, 18 days treasury bills and 90 days commercial bills. Normally, the return of such investment varies from 14 to 18 percent, depending on the call money rates prevailing at the time of investment. 2. NON-DISCRETIONARY PORTFOLIO MANAGEMENT SERVICE (NDPMS): The manager functions as a counsellor, but the investor is free to accept or reject the manager‘s advice; the paper work is also undertaken by manager for a service charge. The manager concentrates on stock market instruments with a portfolio tailor-made to the risk taking ability of the investor. PORTFOLIO MANAGEMENT SERVICE
IMPORTANCE OF PORTFOLIO MANAGEMENT:
18
?
Emergence of institutional investing on behalf of individuals. A number of
financial institutions, mutual funds and other agencies are undertaking the task of investing money of small investors, on their behalf. Growth in the number and size of investigable funds – a large part of
?
household savings is being directed towards financial assets. Increased market volatility – risk and return parameters of financial assets
?
are continuously changing because of frequent changes in government‘s industrial and fiscal policies, economic uncertainty and instability. Greater use of computers for processing mass of data. Professionalization of the field and increasing use of analytical methods (e.g.
?
?
quantitative techniques) in the investment decision – making Larger direct and indirect costs of errors or shortfalls in meeting portfolio
?
objectives – increased competition and greater scrutiny by investors.
STEPS IN PORTFOLIO MANAGEMENT:
? Specification and qualification of investor objectives, constraints, and
preferences in the form of an investment policy statement. Determination and qualification of capital market expectations for the
?
economy, market sectors, industries and individual securities.
19
?
Allocation of assets and determination of appropriate portfolio strategies for
each asset class and selection of individual securities. Performance measurement and evaluation to ensure attainment of investor
?
objectives. Monitoring portfolio factors and responding to changes in investor
?
objectives, constrains and / or capital market expectations. Rebalancing the portfolio when necessary by repeating the asset allocation, portfolio strategy and security selection.
CRITERIA FOR PORTFOLIO DECISIONS:
? In portfolio management emphasis is put on identifying the collective
importance of all investors holdings. The emphasis shifts from individual assets selection to a more balanced emphasis on diversification and risk-return interrelationships of individual assets within the portfolio. Individual securities are important only to the extent they affect the aggregate portfolio. In short, all decisions should focus on the impact which the decision will have on the aggregate portfolio of all the assets held. Portfolio strategy should be moulded to the unique needs and characteristics
?
of the portfolio‘s owner.
20
?
Diversification across securities will reduce a portfolio‘s risk. If the risk and
return are lower than the desired level, leverages (borrowing) can be used to achieve the desired level. Larger portfolio returns come only with larger portfolio risk. The most
?
important decision to make is the amount of risk which is acceptable. The risk associated with a security type depends on when the investment
?
will be liquidated. Risk is reduced by selecting securities with a payoff close to when the portfolio is to be liquidated. Competition for abnormal returns is extensive, so one has to be careful in evaluating the risk and return from securities. Imbalances do not last long and one has to act fast to profit from exceptional opportunities.
QUALITIES OF PORTFOLIO MANAGER:
1.
SOUND GENERAL KNOWLEDGE: Portfolio management is an
exciting and challenging job. He has to work in an extremely uncertain and confliction environment. In the stock market every new piece of information affects the value of the securities of different industries in a different way. He must be able to judge and predict the effects of the information he gets. He must have sharp memory, alertness, fast intuition and self-confidence to arrive at quick decisions.
2.
ANALYTICAL ABILITY: He must have his own theory to arrive at
the instrinsic value of the security. An analysis of the security‘s values, company,
21
etc. is s continuous job of the portfolio manager. A good analyst makes a good financial consultant. The analyst can know the strengths, weaknesses, opportunities of the economy, industry and the company.
3.
MARKETING SKILLS: He must be good salesman. He has to
convince the clients about the particular security. He has to compete with the stock brokers in the stock market. In this context, the marketing skills help him a lot.
4.
EXPERIENCE: In the cyclical behaviour of the stock market history
is often repeated, therefore the experience of the different phases helps to make rational decisions. The experience of the different types of securities, clients, market trends, etc., makes a perfect professional manager.
PORTFOLIO BUILDING:
Portfolio decisions for an individual investor are influenced by a wide variety of factors. Individuals differ greatly in their circumstances and therefore, a financial programme well suited to one individual may be inappropriate for another. Ideally, an individual‘s portfolio should be tailor-made to fit one‘s individual needs.
Investor‘s Characteristics: An analysis of an individual‘s investment situation requires a study of personal characteristics such as age, health conditions, personal habits, family
22
responsibilities, business or professional situation, and tax status, all of which affect the investor‘s willingness to assume risk.
Stage in the Life Cycle:
One of the most important factors affecting the individual‘s investment objective is his stage in the life cycle. A young person may put greater emphasis on growth and lesser emphasis on liquidity. He can afford to wait for realization of capital gains as his time horizon is large.
Family responsibilities:
The investor‘s marital status and his responsibilities towards other members of the family can have a large impact on his investment needs and goals. Investor‘s experience: The success of portfolio depends upon the investor‘s knowledge and experience in financial matters. If an investor has an aptitude for financial affairs, he may wish to be more aggressive in his investments. Attitude towards Risk: A person‘s psychological make-up and financial position dictate his ability to assume the risk. Different kinds of securities have diffferent kinds of risks. The higher the risk, the greater the opportunity for higher gain or loss. Liquidity Needs: Liquidity needs vary considerably among individual investors. Investors with regular income from other sources may not worry much about instantaneous liquidity, but individuals who depend heavily upon investment for meeting their
23
general or specific needs, must plan portfolio to match their liquidity needs. Liquidity can be obtained in two ways: 1. by allocating an appropriate percentage of the portfolio to bank deposits, and 2. by requiring that bonds and equities purchased be highly marketable. Tax considerations: Since different individuals, depending upon their incomes, are subjected to different marginal rates of taxes, tax considerations become most important factor in individual‘s portfolio strategy. There are differing tax treatments for investment in various kinds of assets.
Time Horizon: In investment planning, time horizon become an important consideration. It is highly variable from individual to individual. Individuals in their young age have long time horizon for planning, they can smooth out and absorb the ups and downs of risky combination. Individuals who are old have smaller time horizon, they generally tend to avoid volatile portfolios. Individual‘s Financial Objectives: In the initial stages, the primary objective of an individual could be to accumulate wealth via regular monthly savings and have an investment programme to achieve long term capital gains. Safety of Principal:
24
The protection of the rupee value of the investment is of prime importance to most investors. The original investment can be recovered only if the security can be readily sold in the market without much loss of value.
Assurance of Income: `Different investors have different current income needs. If an individual is dependent of its investment income for current consumption then income received now in the form of dividend and interest payments become primary objective. Investment Risk: All investment decisions revolve around the trade-off between risk and return. All rational investors want a substantial return from their investment. An ability to understand, measure and properly manage investment risk is fundamental to any intelligent investor or a speculator. Frequently, the risk associated with security investment is ignored and only the rewards are emphasized. An investor who does not fully appreciate the risks in security investments will find it difficult to obtain continuing positive results.
RISK AND EXPECTED RETURN:
25
There is a positive relationship between the amount of risk and the amount of expected return i.e., the greater the risk, the larger the expected return and larger the chances of substantial loss. One of the most difficult problems for an investor is to estimate the highest level of risk he is able to assume. Risk is measured along the horizontal axis and increases from the left to
? right.
?
Expected rate of return is measured on the vertical axis and rises from
bottom to top. The line from 0 to R (f) is called the rate of return or risk less investments
?
commonly associated with the yield on government securities. The diagonal line form R (f) to E(r) illustrates the concept of expected rate
?
of return increasing as level of risk increases.
TYPES OF RISKS: Risk consists of two components. They are
26
1. Systematic Risk 2. Un-systematic Risk
1. Systematic Risk:
Systematic risk is caused by factors external to the particular company and uncontrollable by the company. The systematic risk affects the market as a whole. Factors affect the systematic risk are ? ? ? economic conditions political conditions sociological changes
The systematic risk is unavoidable. Systematic risk is further sub-divided into three types. They are a) b) c) Market Risk Interest Rate Risk Purchasing Power Risk
a). Market Risk: One would notice that when the stock market surges up, most stocks post higher price. On the other hand, when the market falls sharply, most common stocks will drop. It is not uncommon to find stock prices falling from time to time while a company‘s earnings are rising and vice-versa. The price of stock may fluctuate widely within a short time even though earnings remain unchanged or relatively stable.
27
b). Interest Rate Risk: Interest rate risk is the risk of loss of principal brought about the changes in the interest rate paid on new securities currently being issued. c). Purchasing Power Risk: The typical investor seeks an investment, which will give him current income and / or capital appreciation in addition to his original investment. 2. Un-systematic Risk: Un-systematic risk is unique and peculiar to a firm or an industry. The nature and mode of raising finance and paying back the loans, involve the risk element. Financial leverage of the companies that is debt-equity portion of the companies differs from each other. All these factors Factors affect the un-systematic risk and contribute a portion in the total variability of the return. ? Managerial inefficiently ? Technological change in the production process ? Availability of raw materials ? Changes in the consumer preference ? Labour problems The nature and magnitude of the above mentioned factors differ from industry to industry and company to company. They have to be analyzed separately for each industry and firm. Un-systematic risk can be broadly classified into: a) Business Risk b) Financial Risk
28
a.
Business Risk:
Business risk is that portion of the unsystematic risk caused by the operating environment of the business. Business risk arises from the inability of a firm to maintain its competitive edge and growth or stability of the earnings. The volatibility in stock prices due to factors intrinsic to the company itself is known as Business risk. Business risk is concerned with the difference between revenue and earnings before interest and tax. Business risk can be divided into.
i). Internal Business Risk
Internal business risk is associated with the operational efficiency of the firm. The operational efficiency differs from company to company. The efficiency of operation is reflected on the company‘s achievement of its pre-set goals and the fulfillment of the promises to its investors.
ii). External Business Risk
External business risk is the result of operating conditions imposed on the firm by circumstances beyond its control. The external environments in which it operates exert some pressure on the firm. The external factors are social and regulatory factors, monetary and fiscal policies of the government, business cycle and the general economic environment within which a firm or an industry operates. b. Financial Risk:
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It refers to the variability of the income to the equity capital due to the debt capital. Financial risk in a company is associated with the capital structure of the company. Capital structure of the company consists of equity funds and borrowed funds.
PORTFOLIO ANALYSIS:
Various groups of securities when held together behave in a different manner and give interest payments and dividends also, which are different to the analysis of individual securities. A combination of securities held together will give a beneficial result if they are grouped in a manner to secure higher return after taking into consideration the risk element. There are two approaches in construction of the portfolio of securities. They are ? Traditional approach ? Modern approach TRADITIONAL APPROACH: Traditional approach was based on the fact that risk could be measured on each individual security through the process of finding out the standard deviation and that security should be chosen where the deviation was the lowest. Traditional
30
approach believes that the market is inefficient and the fundamental analyst can take advantage fo the situation. Traditional approach is a comprehensive financial plan for the individual. It takes into account the individual needs such as housing, life insurance and pension plans. Traditional approach basically deals with two major decisions. They are a) Determining the objectives of the portfolio
Selection of securities to be included in the portfolio
MODERN APPROACH:
Modern approach theory was brought out by Markowitz and Sharpe. It is the combination of securities to get the most efficient portfolio. Combination of securities can be made in many ways. Markowitz developed the theory of diversification through scientific reasoning and method. Modern portfolio theory believes in the maximization of return through a combination of securities. The modern approach discusses the relationship between different securities and then draws inter-relationships of risks between them. Markowitz gives more attention to the process of selecting the portfolio. It does not deal with the individual needs.
MARKOWITZ MODEL:
Markowitz model is a theoretical framework for analysis of risk and return and their relationships. He used statistical analysis for the measurement of risk and mathematical programming for selection of assets in a portfolio in an efficient manner. Markowitz apporach determines for the investor the efficient set of portfolio through three important variables i.e. ? Return
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? Standard deviation ? Co-efficient of correlation Markowitz model is also called as an “Full Covariance Model“. Through this model the investor can find out the efficient set of portfolio by finding out the trade off between risk and return, between the limits of zero and infinity. According to this theory, the effects of one security purchase over the effects of the other security purchase are taken into consideration and then the results are evaluated. Most people agree that holding two stocks is less risky than holding one stock. For example, holding stocks from textile, banking and electronic companies is better than investing all the money on the textile company‘s stock. Markowitz had given up the single stock portfolio and introduced diversification. The single stock portfolio would be preferable if the investor is perfectly certain that his expectation of highest return would turn out to be real. In the world of uncertainity, most of the risk adverse investors would like to join Markowitz rather than keeping a single stock, because diversification reduces the risk.
ASSUMPTIONS:
? All investors would like to earn the maximum rate of return that they can All investors have the same expected single period investment horizon. All investors before making any investments have a common goal. This is Investors base their investment decisions on the expected return and Perfect markets are assumed (e.g. no taxes and no transation costs) achieve from their investments. ? ?
the avoidance of risk because Investors are risk-averse. ? standard deviation of returns from a possible investment. ?
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?
The investor assumes that greater or larger the return that he achieves on his
investments, the higher the risk factor surrounds him. On the contrary when risks are low the rerturn can also be expected to be low. ? ? The investor can reduce his risk if he adds investments to his portfolio. An investor should be able to get higher return for each level of risk “by
determining the efficient set of securities“. An individual seller or buyer cannot affect the price of a stock. This Investors make their decisions only on the basis of the expected returns, Investors are assumed to have homogenous expectations during the The investor can lend or borrow any amount of funds at the riskless rate of
?
assumption is the basic assumption of the perfectly competitive market. ? standard deviation and covariances of all pairs of securities. ? decision-making period ? interest. The riskless rate of interest is the rate of interest offered for the treasury bills or Government securities. ? Investors are risk-averse, so when given a choice between two otherwise Individual assets are infinitely divisible, meaning that an investor can buy a There is a risk free rate at which an investor may either lend (i.e. invest) There is no transaction cost i.e. no cost involved in buying and selling of identical portfolios, they will choose the one with the lower standard deviation. ? fraction of a share if he or she so desires. ? money or borrow money. ? stocks. There is no personal income tax. Hence, the investor is indifferent to the form of return either capital gain or dividend.
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THE EFFECT OF COMBINING TWO SECURITIES:
It is believed that holding two securities is less risky than by having only one investment in a person‘s portfolio. When two stocks are taken on a portfolio and if they have negative correlation then risk can be completely reduced because the gain on one can offset the loss on the other. This can be shown with the help of following example:
INTER- ACTIVE RISK THROUGH COVARIANCE:
Covariance of the securities will help in finding out the inter-active risk. When the covariance will be positive then the rates of return of securities move together either upwards or downwards. Alternatively it can also be said that the inter-active risk is positive. Secondly, covariance will be zero on two investments if the rates of return are independent. Holding two securities may reduce the portfolio risk too. The portfolio risk can be calculated with the help of the following formula:
CAPITAL ASSET PRICING MODEL (CAPM):
Markowitz, William Sharpe, John Lintner and Jan Mossin provided the basic structure of Capital Asset Pricing Model. It is a model of linear general equilibrium return. In the CAPM theory, the required rate return of an asset is having a linear relationship with asset‘s beta value i.e. undiversifiable or systematic risk (i.e. market related risk) because non market risk can be eliminated by diversification and systematci risk measured by beta. Therefore, the relationship between an assets
34
return and its systematic risk can be expressd by the CAPM, which is also called the Security Market Line. Rp= Rf Xf+ Rm(1- Xf) Rp = Portfolio return Xf = The proportion of funds invested in risk free assets 1- Xf = The proportion of funds invested in risky assets Rf = Risk free rate of return Rm = Return on risky assets Formula can be used to calculate the expected returns for different situtions, like mixing riskless assets with risky assets, investing only in the risky asset and mixing the borrowing with risky 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 total value of all risky assets. For example, if Satyam Industry share represents 15% of all risky assets, then the market portfolio of the individual investor contains 15% of Satyam 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. Eg.: assume that borrowing and lending rate to be 12.5% and the return from the risky assets to be 20%. There is a trade off between the expected return and risk. If an investor invests in risk free assets and risky assets, his risk may be less
35
than what he invests in the risky asset alone. But if he borrows to invest in risky assets, his risk would increase more than he invests his own money in the risky assets. When he borrows to invest, we call it financial leverage. If he invests 50% in risk free assets and 50% in risky assets, his expected return of the portfolio would be Rp= Rf Xf+ Rm(1- Xf) = (12.5 x 0.5) + 20 (1-0.5) = 6.25 + 10 = 16.25%
if there is a zero investment in risk free asset and 100% in risky asset, the return is Rp= Rf Xf+ Rm(1- Xf) = 0 + 20% = 20% if -0.5 in risk free asset and 1.5 in risky asset, the return is Rp= Rf Xf+ Rm(1- Xf) = (12.5 x -0.5) + 20 (1.5) = -6.25+ 30 = 23.75%
EVALUATION OF PORTFOLIO:
Portfolio manager evaluates his portfolio performance and identifies the sources of strengths and weakness. The evaluation of the portfolio provides a feed back about the performance to evolve better management strategy. Even though
36
evaluation of portfolio performance is considered to be the last stage of investment process, it is a continuous process. There are number of situations in which an evaluation becomes necessary and important.
i.
Self Valuation: An individual may want to evaluate how well he has
done. This is a part of the process of refining his skills and improving his performance over a period of time.
ii.
Evaluation of Managers: A mutual fund or similar organization
might want to evaluate its managers. A mutual fund may have several managers each running a separate fund or sub-fund. It is often necessary to compare the performance of these managers.
iii.
Evaluation of Mutual Funds: An investor may want to evaluate
the various mutual funds operating in the country to decide which, if any, of these should be chosen for investment. A similar need arises in the case of individuals or organisations who engage external agencies for portfolio advisory services. Evaluation of Groups: Academics or researchers may want to evaluate the performance of a whole group of investors and compare it with another group of investors who use different techniques or who have different skills or access to different information. NEED FOR EVALUATION OF PORTFOLIO: We can try to evaluate every transaction. Whenever a security is brought or
?
sold, we can attempt to assess whether the decision was correct and profitable.
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?
We can try to evaluate the performance of a specific security in the portfolio We can try to evaluate the performance of portfolio as a whole during the
to determine whether it has been worthwhile to include it in our portfolio. ? period without examining the performance of individual securities within the portfolio. NEED & IMPORTANCE: Portfolio management has emerged as a separate academic discipline in India. Portfolio theory that deals with the rational investment decision-making process has now become an integral part of financial literature. Investing in securities such as shares, debentures & bonds is profitable well as exciting. It is indeed rewarding but involves a great deal of risk & need artistic skill. Investing in financial securities is now considered to be one of the most risky avenues of investment. It is rare to find investors investing their entire savings in a single security. Instead, they tend to invest in a group of securities. Such group of securities is called as PORTFOLIO. Creation of portfolio helps to reduce risk without sacrificing returns. securities into portfolios. Portfolio management deals with the analysis of individual securities as well as with the theory & practice of optimally combining
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The modern theory is of the view that by diversification, risk can be reduced. The investor can make diversification either by having a large number of shares of companies in different regions, in different industries or those producing different types of product lines. Modern theory believes in the perspective of combinations of securities under constraints of risk and return.
PORTFOLIO REVISION:
The portfolio which is once selected has to be continuously reviewed over a period of time and then revised depending on the objectives of the investor. The care taken in construction of portfolio should be extended to the review and revision of the portfolio. Fluctuations that occur in the equity prices cause substantial gain or loss to the investors. The investor should have competence and skill in the revision of the portfolio. The portfolio management process needs frequent changes in the composition of stocks and bonds. In securities, the type of securities to be held should be revised according to the portfolio policy. An investor purchases stock according to his objectives and return risk framework. The prices of stock that he purchases fluctuate, each stock having its own cycle of fluctuations. These price fluctuations may be related to economic activity in a country or due to other changed circumstances in the market.
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If an investor is able to forecast these changes by developing a framework for the future through careful analysis of the behavior and movement of stock prices is in a position to make higher profit than if he was to simply buy securities and hold them through the process of diversification. Mechanical methods are adopted to earn better profit through proper timing. The investor uses formula plans to help him in making decisions for the future by exploiting the fluctuations in prices.
FORMULA PLANS:
The formula plans provide the basic rules and regulations for the purchase and sale of securities. The amount to be spent on the different types of securities is fixed. The amount may be fixed either in constant or variable ratio. This depends on the investor‘s attitude towards risk and return. The commonly used formula plans are i. ii. iii. iv. Average Rupee Plan Constant Rupee Plan Constant Ratio Plan Variable Ratio Plan
ADVANTAGES:
? Basic rules and regulations for the purchase and sale of securities are
provided. ? ? The rules and regulations are rigid and help to overcome human emotion. The investor can earn higher profits by adopting the plans.
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? ? ?
A course of action is formulated according to the investor‘s objectives. It controls the buying and selling of securities by the investor. It is useful for taking decisions on the timing of investments.
DISADVANTAGES: The formula plan does not help the selection of the security. The selection of
?
the security has to be done either on the basis of the fundamental or technical analysis. ? ? It is strict and not flexible with the inherent problem of adjustment. The formula plans should be applied for long periods, otherwise the
transaction cost may be high. Even if the investor adopts the formula plan, he needs forecasting. Market forecasting helps him to identify the best stocks.
ANALYSIS & INTERPRETION
CALCULATION OF AVERAGE RETURN OF COMPANIES: Average Return = (R)/N
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ITC LTD: Opening Closing share price share price (P0) (P1) 696.70 628.25 628.25 1043.10 1043.10 1342.05 1342.05 2932 195.15 151.15 TOTAL RETURN Average Return = 180.79/5 = 36.16 (P1-P0)/ P0*100 -9.82 66.03 28.66 118.47 -22.55 180.79
ear 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(P1-P0) -68.45 414.85 298.95 1589.95 -44
DR REDDY LABORATORIES LTD:
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
Opening Closing share price share price (P0) (P1) 1090.95 916.30 916.30 974.35 974.35 739.15 739.15 1,421.40 1,421.40 1456.55 TOTAL RETURN
(P1-P0) -174.65 58.2 23.52 682.25 35.15
(P1-P0)/ P0*100 -16.00 6.33 -24.14 92.30 2.47 60.96
Average Return = 60.96/5 = 12.19
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ACC: Opening Closing share price share price (P0) (P1) 153.40 138.50 138.50 254.65 254.65 360.55 360.55 782.20 782.20 735.25 TOTAL RETURN Average Return = 226.8/5 = 45.36 (P1-P0)/ P0*100 -9.7 83.86 41.58 116.95 -6.00 226.8
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(P1-P0) -14.19 116.15 105.9 421.61 -46.95
BHARAT HEAVY ELECTRICALS LTD: Opening Closing share price share price (P0) (P1) 169.00 223.15 223.15 604.35 604.35 766.40 766.40 2241.95 2241.95 2261.35 TOTAL RETURN Average Return = 423.08/5 = 84.62 (P1-P0)/ P0*100 32.04 170.83 26.81 192.53 0.87 423.08
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(P1-P0) 54.15 38.12 162.05 1475.55 19.4
HEROHONDA AUTOMOBILES LIMITED:
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Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
Opening Closing share price share price (P0) (P1) 338.55 188.20 188.20 490.60 490.60 548.00 548.00 890.45 890.45 688.75 TOTAL RETURN
(P1-P0) -150.35 302.40 57.40 342.45 -20.17
(P1-P0)/ P0*100 -44.40 160.68 11.70 62.50 -22.65 167.82
Average Return = 167.82/5 = 33.56
WIPRO: Opening Closing share price share price (P0) (P1) 1,700.60 1233.45 1,233.45 1361.20 1,361.20 2,012 670.95 559.7 559.70 559.40 TOTAL RETURN Average Return = 14.13/5 = 2.83 (P1-P0)/ P0*100 -27.47 10.36 47.87 -16.58 -0.05 14.13
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(P1-P0) -467.15 127.75 650.8 -111.25 -0.3
CALCULATION OF STANDARD DEVIATION:
Standard Deviation = Variance
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Variance ITC LTD:
=
1/n (R-R)2
Year 2002-2003 2003-2004 2003-2004 2004-2005 2005-2006
Return Avg. (R) Return (R) -9.82 36.16 66.03 36.16 28.66 36.16 118.47 36.16 -22.55 36.16 TOTAL
(R-R) -45.98 29.87 -7.5 82.31 -58.71
(R-R)2 2114.16 892.22 56.25 6775 3447 13284
Variance = 1/n (R-R)2 = 1/5 (13284) = 2656.8 Standard Deviation = Variance = 2656.8 = 51.54
DR. REDDY: Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 Return Avg. (R) Return (R) -16.00 12.19 6.33 12.19 -24.14 12.19 92.30 12.19 2,47 12.19 TOTAL Variance = 1/n-1 (R-R)2 = 1/5 (8,661) = 1732.2 Standard Deviation = Variance = 1732.2= 41.62 (R-R) -28.19 -5.86 -36.33 80.11 -9.72 (R-R)2 795 34 1320 6418 94 8,661
ACC:
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Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
Return Avg. (R) Return (R) -9.7 45.36 83.86 45.36 41.58 45.36 116.95 45.36 -6.00 45.36 TOTAL
(R-R) -55.06 38.5 -3.78 71.59 -51.36
(R-R)2 3032 1482 13.69 5125 2638 12,291
Variance = 1/n-1 (R-R)2 = 1/5 (12,291) = 2458 Standard Deviation = Variance = 2458 = 49.58
WIPRO: Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 Return Avg. (R) Return (R) -27.47 2.83 10.36 2.83 47.87 2.83 -16.58 2.83 -0.05 2.83 TOTAL Variance = 1/n-1 (R-R)2 = 1/5 (3388) = 847 Standard Deviation = Variance = 847 =33.09 BHEL:
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(R-R) -30.29 7.53 45.04 -19.41 -2.88
(R-R)2 917 57 2029 377 8 3388
Year 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
Return Avg. (R) Return (R) 32.04 84.62 170.83 84.62 26.81 84.62 192.53 84.62 0.87 84.62 TOTAL
(R-R) -52.58 86.21 -57.81 107.91 -83.75
(R-R)2 2765 7432 3342 11645 7014 32,198
Variance = 1/n-1 (R-R)2 = 1/5 (32198) = 6440 Standard Deviation = Variance = 6440 = 80.25
HERO HONDA: Year 2002-2003 2002-2003 2004-2005 2005-2006 2006-2007 Return Avg. (R) Return (R) -44.40 33.56 160.68 33.56 11.70 33.56 62.50 33.56 -22.65 33.65 TOTAL Variance = 1/n-1 (R-R)2 = 1/5 (26,715) = 5343 Standard Deviation = Variance = 5343 = 73.09 (R-R) -77.97 127.12 -21.86 28.94 -56.21 (R-R)2 6079 16160 478 838 3160 26,715
CALCULATION OF CORRELATION:
Covariance (COV ab) = 1/n (RA-RA)(RB-RB) Correlation Coefficient = COV ab/?a*? b
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i. ACC (RA) & ITC (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -55.06 38.5 -3.78 71.59 -51.36 (RB-RB) (RA-RA) (RB-RB) -45.98 2532 29.87 1149.99 -7.5 28.35 82.31 5892.57 -58.71 3015 TOTAL 12617.9
Covariance (COV ab) = 1/5 (12617.9) = 2523.58 Correlation Coefficient = COV ab/?a*? b ?a = 49.57 ; ?b = 51.54 = 2523.58/(49.57)(51.54) = 0.98 ii) ACC (RA) & WIPRO (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -52.58 86.21 -57.81 107.91 -83.75 TOTAL (RB-RB) (RA-RA) (RB-RB) -77.97 4099.66 127.12 10959.01 -21.86 1263.72 28.94 3122.91 -56.21 4707.58 24152.88
Covariance (COV ab) = 1/5 (24152.88) = 4830.57 Correlation Coefficient = COV ab/?a*? b ?a = 26 ; ?b = 41.62 = 4830.57/(80.25)(73.09) = 0.82 iii. WIPRO (RA) & DR REDDY (RB) YEAR (RA-RA) (RB-RB) (RA-RA) (RB-RB)
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2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
-30.29 7.53 44.98 -19.41 -2.88 TOTAL
-28.19 -5.86 -36.33 80.11 -9.72
853.87 -44.12 -1634.12 -1554.93 27.99 -2351.31
Covariance (COV ab) = 1/5 (-2351.31) = 470.26 Correlation Coefficient = COV ab/?a*? b ?a = 26.00 ; ?b = 41.62 = -470.26/(26.00)(41.62) = -0.43
v.
ITC (RA) & BHEL (RB)
YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(RA-RA) -45.98 -29.87 -7,5 82.31 -58.71 TOTAL
(RB-RB) (RA-RA) (RB-RB) -52.58 2417.63 86.21 -2575.09 -57.81 -433.58 107.91 8882.07 -83.75 4916.96 14075.15
Covariance (COV ab) = 1/5 (14075.15) = 2815.03 Correlation Coefficient = COV ab/?a*? b ?a = 51.54 ; ?b = 80.25 = 2815.03/(51.54)(80.25) = 0.68
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v. ACC (RA) & BHEL (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -55.06 38.5 -3.7 71.59 -51.3 TOTAL (RB-RB) (RA-RA) (RB-RB) -52.58 2895.05 86.21 3319.08 -57.81 213.89 107.91 7725.27 -83.75 4296.37 18449.66
Covariance (COV ab) = 1/5 (18449.66) = 3689.93 Correlation Coefficient = COV ab/?a*? b ?a = 49.57 ; ?b = 80.25 = 18449.66/(49.57)(80.25) = 0.92
2. Correlation between ACC & other Companies: i. ACC (RA) & HEROHONDA (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -55.06 38.5 -3.78 71.59 -51.36 TOTAL (RB-RB) (RA-RA) (RB-RB) -77.97 4293.02 127.12 4894.12 -21.86 82.63 28.94 2071.81 -56.21 2886.95 14228.53
Covariance (COV ab) = 1/5 (14228.53) = 2845.70 Correlation Coefficient = COV ab/?a*? b ?a = 49.58 ; ?b = 73.04 = 2845.70/(49.57)(26.00) = 0.78
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ii. ACC (RA) & WIPRO (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -55.06 38.5 -3.78 71.59 -51.36 TOTAL Covariance (COV ab) = 1/5 (546) = 109.2 Correlation Coefficient = COV ab/?a*? b ?a = 49.57; ?b = 26.00
= 109.2/(49.57)(26.00) = 0.08
(RB-RB) (RA-RA) (RB-RB) -30.29 1667.77 7.53 289.90 44.98 -170.02 -19.41 -1389.56 -2.88 147.91 546
iii. ACC (RA) & DR REDDY (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -55.06 38.5 -3.78 71.59 -51.36 TOTAL (RB-RB) (RA-RA) (RB-RB) -28.19 552.14 -5.86 -225.61 -36.33 137.33 80.11 5735.07 -9.72 499.21 7698.14
Covariance (COV ab) = 1/5 (7698.14) = 1539.63 Correlation Coefficient = COV ab/?a*? b ?a = 49.57 ; ?b = 41.62 = 1539.63/(49.57)(41.62) = 0.74 iv. ITC (RA) & HERO HONDA (RB)
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YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(RA-RA) -45.98 29.87 -7.5 82.31 -58.71 TOTAL
(RB-RB) (RA-RA) (RB-RB) -77.97 3585.06 127.12 3797.07 -21.86 163.95 28.94 2382.05 -56.21 3300.08 13228.21
Covariance (COV ab) = 1/5 (13228.21) = 2645.64 Correlation Coefficient = COV ab/?a*? b ?a = 51.54 ; ?b = 73.09 = 2645.64/(51.54)(73.09) = 0.70 3. Correlation Between DR REDDY & Other Companies i. ITC(RA) & WIPRO: YEAR 2002-2003 2002-2003 2003-2004 2004-2005 2005-2006 (RA-RA) -16.024 -26.574 -3.684 -34.724 81.006 TOTAL (RB-RB) (RA-RA) (RB-RB) -10.89 174.50 -46.94 1,247.38 -8.7 32.05 -26.98 936.85 93.53 7,576.49 9,967.28
Covariance (COV ab) = 1/5-1 (9967.28) = 2491.82 Correlation Coefficient = COV ab/?a*? b ?a = 46.75 ; ?b = 54.48 = 2491.82/(46.75)(54.48) = 0.978
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ii. DR. REDDY (RA) & &ITC (RB) YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -28.19 -5.86 -36.33 80.11 -9.72 TOTAL YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 (RA-RA) -28.19 -5.86 -36.33 80.11 -9.72 TOTAL (RB-RB) (RA-RA) (RB-RB) -45.98 1296.17 29.87 -175.03 -7.5 272.47 82.31 6593.85 -58.71 570.66 8558.12 (RB-RB) -77.97 127.12 -21.86 28.94 -56.21 (RA-RA) (RB-RB) 2197.97 744.92 794.17 2318.38 546.36 6601.8
Covariance (COV ab) = 1/5 (8558.12) = 1711.62 Correlation Coefficient = COV ab/?a*? b ?a = 41.62 ; ?b = 51.54 = 1711.62/(41.62)(51.54) = 0.79
iv.
DR REDDY (RA) &HEROHONDA(RB)
Covariance (COV ab) = 1/5 (6601.8) = 1320.36 Correlation Coefficient = COV ab/?a*? b ?a = 41.62 ; ?b = 73.09
53
= 1320.36/(41.62)(73.09) = 0.43 4. Correlation Between HLL & Other Companies i. HEROHONDA (RA) & WIPRO(RB)
Covariance (COV ab) = 1/5 (1934.51) = 386.90 Correlation Coefficient = COV ab/?a*? b ?a = 73.09; ?b = 26.00 = 386.90/(73.09)(26.00) = 0.20 ii. DR REDDY (RA) & BHEL(RB)
YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(RA-RA) -77.97 127.12 -21.86 28.94 -56.21 TOTAL
(RB-RB) (RA-RA) (RB-RB) -30.29 2361.71 7.53 957.21 45.04 -984.57 -19.41 -561.72 -2.88 161.88 1934.51
54
YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(RA-RA) -28.19 -5.86 -36.33 80.11 -9.72 TOTAL
(RB-RB) (RA-RA) (RB-RB) -52.58 1482.23 86.21 -505.19 -57.81 2100.24 107.91 8644.67 -83.75 814.05 12536
Covariance (COV ab) = 1/5 (12536) =
386.90 Correlation Coefficient = COV ab/?a*? b ?a = 41.62; ?b = 80.25 = 2507.2/(41.62)(80.25) = 0.93
5. CORRELATION BETWEEN BHEL(RA) & WIPRO(RB)
YEAR 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
(RA-RA) -52.58 86.21 -57.81 107.91 -83.75 TOTAL
(RB-RB) (RA-RA) (RB-RB) -30.29 1592.65 7.53 649.16 45.04 -2603.76 -19.41 -2094.53 -2.88 241.2 -2215.28
Covariance (COV ab) = 1/5 (-2215.28) = -443.05 Correlation Coefficient = COV ab/?a*? b ?a = 80.25; ?b = 26.00 = -443.05/(80.25)(26.00) = -0.21
55
CALCULATION OF PORTFOLIO WEIGHTS: FORMULA : Wa =
?b [?b-(nab*?a)] ?a2 + ?b2 - 2nab*?a*?b
Wb = 1 – Wa CALCULATION OF WEIGHTS OF ITC & OTHER COMPANIES: i. ITC(a) & WIPRO (b)
?a = 51.54 ?b = 26.00 nab = -0.02
Wa =
26.00 [26.00-(-0.02*51.54)] (51.54) + (26.00) 2 – 2(-0.02)*(51.54) *(26.00)
2
Wa =
690 3386
Wa =0.20 Wb = 1 – Wa Wb = 1-0.20 = 0.8
ii. HEROHONDA(a) & WIPRO(b)
?a = 73.09 ?b = 26.00 nab = 0.20
56
Wa =
26.00 [26.00-(0.20*73.09)] (73.09) + (26.00) 2 – 2(0.20)*(73.09) *(26.00)
2
Wa =
296 5258
Wa =0.05 Wb = 1 – Wa Wb = 1-0.05 = 0.95
CALCULATION OF WEIGHTS OF BHEL & WIPRO:
?a = 80.25 ?b = 26.00 nab = -0.21
Wa =
26.00 [26.00-(-0.21*80.25)] (80.25) 2 + (26.00) 2 – 2(-0.21)*(80.25) *(26.00) 1114 7992
Wa =
Wa =0.14 Wb = 1 – Wa Wb = 1-0.14 = 0.86
CALCULATION OF WEIGHTS OF WIPRO & OTHE COMPANIES:
i.
ACC (a) & ITC (b):
?a = 49.57 ?b = 51.54 nab = 0.98
57
Wa =
51.54 [51.54-(0.98*49.57)]
(49.57) 2 + (51.54) 2 – 2(0.98)*(49.57) *(51.54) Wa = 152 106 Wa =1.43 Wb = 1 – Wa Wb = 1-1.43 = - 0.43
ii. BHEL (a) & HEROHONDA (b)
?a = 80.25 ?b = 73.09 nab = 0.82
Wa =
73.09 [73.09-(0.82*80.25)] (80.25) 2 + (73.09) 2 – 2(0.82)*(80.25) *(73.09)
2163
Wa =
533 Wa =0.24 Wb = 1 – Wa Wb = 1-0.24 = 0.76
iii.
WIPRO (a) & DR REDYY (b)
?a = 26.00 ?b = 41.62 nab = -0.43
Wa =
41.62 [41.62-(-0.43*26.00)] (26.00) 2 + (41.62) 2 – 2(-0.43)*(41.62) *(26.00)
58
Wa = 2198 1477 Wa =1.49 Wb = 1 – Wa Wb = 1-1.49 = -0.49
iv.
ITC (a) & BHEL (b)
?a = 51.54 ?b = 80.25 nab = 0.68
Wa =
80.25 [80.25-(0.68*51.54)] (51.54) 2 + (80.25) 2 – 2(0.68)*(51.54) *(80.25)
Wa = 3628 3471 Wa =1.04 Wb = 1 – Wa Wb = 1-1.04 =0.04
v. ACC (a) & BHEL (b)
?a = 49.57 ?b = 80.25 nab = 0.92
Wa =
80.25 [80.25-(0.92*49.57)] (49.57) 2 + (80.25) 2 – 2(0.92)*(49.57) *(80.25)
Wa = 2781
59
1577 Wa =1.76 Wb = 1 – Wa Wb = 1-1.76 = -0.76
CALCULATION OF WEIGHTS OF ACC & OTHER COMPANIES: iii. ACC (a) & HEROHONDA (b)
?a = 49.57 ?b = 73.09 nab = 0.78
Wa =
73.09 [73.09-(0.78*49.57)] (49.57) 2 + (73.09) 2 – 2(0.78)*(49.57) *(73.09)
Wa = 2516 2148 Wa =1.17 Wb = 1 – Wa Wb = 1-1.17 = -0.17
iv. ACC(a) & WIPRO (b)
?a = 49.57 ?b = 26.00 nab = 0.08
Wa =
26.00 [26.00-(0.08*49.57)] (49.57) 2 + (26.00) 2 – 2(0.08)*(49.57) *(26.00) 573 2927
60
Wa =
Wa =0.19 Wb = 1 – Wa Wb = 1-0.19 = 0.81
v. ACC (a) & DR REDDY (b)
?a = 49.57 ?b = 41.62 nab = 0.74
Wa =
41.62 [41.62-(0.74*49.57)] (49.57) 2 + (41.62) 2 – 2(0.74)*(49.57) *(41.62) 206 1136
Wa =
Wa =0.18 Wb = 1 – Wa Wb = 1-0.18 = 0.82
vi. ITC(a) & HERO HONDA (b)
?a = 51.54 ?b = 73.09 nab = 0.70
Wa =
73.09 [73.09-(0.70*51.54)] (51.54) + (73.09) 2 – 2(0.70)*(51.54) *(73.09)
2
Wa =
2706 2724
Wa =0.99 Wb = 1 – Wa
61
Wb = 1-0.99 = 0.01
CALCULATION OF WEIGHTS OF DRREDDY & OTHER COMPANIES: vii. DRREDDY (a) & ITC (b)
?a = 41.62 ?b = 51.54 nab = 0.79
Wa =
51.54 [51.54-(0.79*41.62)] (41.62) 2 + (51.54) 2 – 2(0.79)*(41.62) *(51.54)
Wa =
962 999 Wa =0.96 Wb = 1 – Wa Wb = 1-0.96 = 0.04
viii. DRREDDY (a) & HEROHONDA (b)
?a = 41.62 ?b = 73.09 nab = 0.43
Wa =
73.09 [73.09-(0.43*41.62)] (41.62) + (73.09) 2 – 2(0.43)*(41.62) *(73.09)
2
Wa =
4034 4458
Wa =0.90 Wb = 1 – Wa Wb = 1-0.90 = 0.10
ix. DRREDDY (a) & BHEL (b)
62
?a = 41.62 ?b = 80.25 nab = 0.75
Wa =
80.25 [80.25-(0.75*41.62)] (41.62) 2 + (80.25) 2 – 2(0.75)*(41.62) *(80.25) 3935 3162
Wa =
Wa =1.24 Wb = 1 – Wa Wb = 1-1.24 = -0.24
CALCULATION OF PORTFOLIO RISK:
RP =
?a2*Wa2 + ?b2*Wb2 + 2nab*?a*?b*Wa*Wb
CALCULATION OF PORTFOLIO RISK OF WIPRO & OTHER COMPANIES: i. Wipro (a) & ITC (b):
?a = 33.09 ?b = 56.09 = 2/3 = 1/3 Nab = 0.98
RP = (2/3)2(49.57)2+(1/3) 2(0.51.54)2+2(49.57)(51.54) *(0.98) *(2/3)*(1/3)
= ? 2505
= 50.04
63
ii.
BHEL (a) & HEROHONDA (b):
?a = 80.25 ?b = 73.09 = 2/3 = 1/3 nab = 0.82
RP = (2/3)2(80.25)2+(1/3) 2(73.09)2+2(80.25)(73.09) *(0.82) *(2/3)*(1/3)
= ? 5613
iii.
= 74.91
WIPRO (a) & DR REDDY (b):
?a = 41.62 ?b = 26.00 = 2/3 = 1/3 nab = 0.43
RP = (2/3)2(41.62)2+(1/3) 2(26.00)2+2(41.62)(26.00) *(0.43) *(2/3)*(1/3)
= ? 647
iv.
= 25.43
ITC (a) & BHEL (b):
?a = 51.54 ?b = 80.25 = 1/3 = 2/3 nab = 0.68
64
RP =
(1/3)2(51.54)2+(2/3) 2(80.25)2+2(51.54)(80.25) *(0.68) *(2/3)*(1/3)
= ? 4434
v.
=
66.58
ACC (a) & BHEL (b):
?a = 49.57 ?b = 80.25 = 2/3 =1/3 nab = 0.92
RP = (2/3)2(49.57)2+(1/3) 2(80.25)2+2(49.57)(80.25) *(0.92) *(2/3)*(1/3)
= ? 4786
= 69.18
I.
CALCULATION OF PORTFOLIO RISK OF ACC & OTHER COMPANIES
vi.
ACC(a) & HEROHONDA(b):
?a = 49.57 ?b = 73.09 = 2/3 = 1/3 nab = 0.78
RP = (2/3)2(49.57)2+(1/3) 2(73.09)2+2(49.57)(73.09) *(0.78) *(2/3)*(1/3)
= ? 2944 = 54.25
vii.
ACC (a) & WIPRO (b):
65
?a = 49.57 ?b = 26.00 = 2/3 = 1/3 nab = 0.08
RP = (2/3)2(49.57)2+(1/3) 2(26.00)2+2(49.57)(26.00) *(0.08) *(2/3)*(1/3)
= ? 1226 = 35.01
viii.
ACC (a) & DR REDDY (b):
?a = 49.57 ?b = 41.62 = 2/3 = 1/3 nab = 0.74
RP = (2/3)2(49.57)2+(1/3) 2(41.62)2+2(49.57)(41.62) *(0.74) *(2/3)*(1/3)
= ? 1972 = 44.40
ix.
ITC (a) & HEROHONDA (b):
?a = 51.54 ?b = 73.09 = 2/3 = 1/3 nab = 0.70
RP = (2/3)2(51.54)2+(1/3) 2(73.09)2+2(51.54)(73.09) *(0.70) *(2/3)*(1/3)
= ? 2949
= 54.30
66
II.
x.
CALCULATION OF PORTFOLIO RISK OF DR REDDY & OTHER COMPANIES DRREDDY (a) & ITC (b):
?a = 41.62 ?b = 51.54 = 1/3 = 2/3 nab = 0.79
RP = (1/3)2(41.62)2+(2/3) 2(51.54)2+2(41.62)(51.54) *(0.79) *(2/3)*(1/3)
= ? 2135
xi.
= 46.2
DRREDDY (a) & HEROHONDA (b):
?a = 41.62 ?b = 73.09 = 1/3 = 2/3 nab = 0.43
RP =
(1/3)2(41.62)2+(2/3) 2(73.09)2+2(41.62)(73.09) *(0.43) *(2/3)*(1/3)
= ? 3172
xii.
= 56.32
DRREDDY (a) & BHEL (b):
?a = 41.62 ?b = 80.25 = 1/3 = 2/3
67
nab = 0.878
RP = (1/3)2(41.62)2+(2/3) 2(80.25)2+2(41.62)(80.25) *(0.75) *(2/3)*(1/3)
= ? 4197
III.
= 64.78
CALCULATION OF PORTFOLIO RISK OF ITC & OTHER COMPANIES
xiii.
ITC (a) & WIPRO (b):
?a = 51.54 ?b = 26.00 = 2/3 = 1/3 nab = -0.02
RP =
(2/3)2(51.54)2+(1/3) 2(26.00)2+2(51.54)(26.00) *(26.00) *(2/3)*(1/3)
= ? 1281
xiv.
= 35.79
HEROHONDA (a) & WIPRO (b):
?a = 73.09 ?b = 26.00 = 2/3 = 1/3 nab = 0.20
RP =
(2/3)2(73.09)2+(1/3) 2(26.00)2+2(73.09)(26.00) *(0.20) *(0.67)*(0.33)
68
= ? 2646 = 51.44
IV.
CALCULATION OF PORTFOLIO RISK OF BHEL (a) &WIPRO (b)
?a = 80.25 ?b = 26.00 =2/3 =1/3 nab = -0.21
RP (2/3)2(80.25)2+(1/3) 2(26.00)2+2(80.25)(26.00) *(?0.21)*(2/3)*(1/3)
=
= ? 2778
= 52
69
CONCLUSION
For any investment the factors to be considered are the return on the investment and the risk associated with that investment. Diversification in the investment into different assets can reduce the risk. There fore by following modern portfolio theorem, risk can be reduced for a required return
.
70
BIBILOGRAPHY
1.SECURITY ANALYSIS AND PORTFOLIO MANAGEMENT -Donald.E.Fisher, Ronald.J.Jordan 2.INVESTMENTS -William .F.Sharpe,gordon,J Alexander and Jeffery.V.Baily 3.PORTFOLIOMANAGEMENT -Strong R.A
WEB REFERENCES
http;//www.nseindia.com http;//www.bseindia.com http;//www.economictimes.com http;//www.answers.com
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