A study on construction of optimal portfolio using sharpe’s single index model

CONSTRUCTION OF OPTIMAL PORTFOLIO USING SHARPE’S SINGLE INDEX MODEL

INTRODUCTION

EXECUTIVE SUMMARY

Capital market comprising the new issues market and secondary markets or stock
exchanges, is one of the most sensitive markets in the whole economy. The secondary
market enables investors to continuously rearrange their assets if they so desire by
divesting themselves of such assets while others can use their surplus funds to acquire
them. This rearrangement is not a product of instant decisions but a thorough research.
The major tools used for this are Fundamental analysis and technical analysis. Of which
fundamental analysis requires a large amount of inside data regarding the companies
concerned and also requires lot of calculations and deep knowledge. Where as technical
analysis is comparatively a simpler tool for an investor to decide his short/medium term
investment decisions. By closely watching the price changes, its trend can be analyzed
and the timings of entry and exit can be decided. In short his decisions such as when to
buy or when to sell particular scrip or when to reorganize his portfolio can be influenced
by the technical analysis, moving averages method where in the daily prices are
compared with average of certain number of days.

1.Objective of the study:

“Construction of optimal portfolio using Sharpe’s single index model”

2.Methodology and research design

1. In this study Secondary Data source is used
2. We also consider the movement of share prices, expected returns, standard
deviation and beta values.
3. A brief profile of the company is created for the application of Sharpe’s model
4. The stock price movements, closing index points of the companies and beta
values for the past 5 years are collected for analysis
5. The risk free rate of return is known

H.R.I.H.E, Hassan. Page1


6. All the values obtained above are interpreted and analyzed using Sharpe’s single
index model

3.Scope of the study:

1. Selections of companies are restricted to Sensex index only
2. Of the 30 companies of the index, the companies are chosen and analyzed based
on their performance in the past five years
3. No other factors other than the share price movements, index movements, rate of
return on government securities and beta values for the securities for the past 5
years are taken for analysis

4.Limitations:

1. Only 5 years data has been considered for the construction of optimal Portfolio
2. The portfolio is constructed purely on the basis of Sharpe’s model which
basically considers the stock price movements and does not take into
consideration company specific factors, industry specific factors and economic
specific factors.

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2.LITERATURE REVIEW

2.1 Evolution of Indian Stock Market

Indian Stock Markets are one of the oldest in Asia. Its history dates back to nearly 200
years ago. The earliest records of security dealings in India are meager and obscure. The
East India Company was the dominant institution in those days and business in its loan
securities used to be transacted towards the close of the eighteenth century.

By 1830's business on corporate stocks and shares in Bank and Cotton presses took
place in Bombay. Though the trading list was broader in 1839, there were only half a
dozen brokers recognized by banks and merchants during 1840 and 1850.

The 1850's witnessed a rapid development of commercial enterprise and brokerage
business attracted many men into the field and by 1860 the number of brokers increased
into 60. In 1860-61 the American Civil War broke out and cotton supply from United
States of Europe was stopped; thus, the 'Share Mania' in India begun. The number of
brokers increased to about 200 to 250. However, at the end of the American Civil War, in
1865, a disastrous slump began (for example, Bank of Bombay Share which had touched
Rs 2850 could only be sold at Rs. 87).

At the end of the American Civil War, the brokers who thrived out of Civil War in
1874, found a place in a street (now appropriately called as Dallal Street) where they
would conveniently assemble and transact business. In 1887, they formally established in
Bombay, the "Native Share and Stock Brokers' Association" (which is alternatively
known as “The Stock Exchange "). In 1895, the Stock Exchange acquired a premise in the
same street and it was inaugurated in 1899. Thus, the Stock Exchange at Bombay was
consolidated.

Trading Pattern of the Indian Stock Market

Trading in Indian stock exchanges is limited to listed securities of public limited
companies. They are broadly divided into two categories, namely, specified securities
(forward list) and non-specified securities (cash list). Equity shares of dividend paying,
growth-oriented companies with a paid-up capital of at least Rs.50 million and a market



capitalization of at least Rs.100 million and having more than 20,000 shareholders are,
normally, put in the specified group and the balance in non-specified group.

Two types of transactions can be carried out on the Indian stock exchanges: (a) spot
delivery transactions "for delivery and payment within the time or on the date stipulated
when entering into the contract which shall not be more than 14 days following the date
of the contract”: and (b) forward transactions "delivery and payment can be extended by
further period of 14 days each so that the overall period does not exceed 90 days from the
date of the contract". The latter is permitted only in the case of specified shares. The
brokers who carry over the outstanding pay carry over charges (can tango or
backwardation) which are usually determined by the rates of interest prevailing.

A member broker in an Indian stock exchange can act as an agent, buy and sell
securities for his clients on a commission basis and also can act as a trader or dealer as a
principal, buy and sell securities on his own account and risk, in contrast with the practice
prevailing on New York and London Stock Exchanges, where a member can act as a
jobber or a broker only.

The nature of trading on Indian Stock Exchanges are that of age old conventional
style of face-to-face trading with bids and offers being made by open outcry. However,
there is a great amount of effort to modernize the Indian stock exchanges in the very
recent times.

2.1.a. National Stock Exchange (NSE)

With the liberalization of the Indian economy, it was found inevitable to lift the
Indian stock market trading system on par with the international standards. On the basis
of the recommendations of high powered Pherwani Committee, the National Stock
Exchange was incorporated in 1992 by Industrial Development Bank of India, Industrial
Credit and Investment Corporation of India, Industrial Finance Corporation of India, all
Insurance Corporations, selected commercial banks and others.

Trading at NSE can be classified under two broad categories:



(a) Wholesale debt market and

(b) Capital market.

Wholesale debt market operations are similar to money market operations -
institutions and corporate bodies enter into high value transactions in financial
instruments such as government securities, treasury bills, public sector unit bonds,
commercial paper, certificate of deposit, etc.

There are two kinds of players in NSE:

(a) Trading members and

(b) Participants.

Recognized members of NSE are called trading members who trade on behalf of
themselves and their clients. Participants include trading members and large players like
banks who take direct settlement responsibility.

Trading at NSE takes place through a fully automated screen-based trading
mechanism which adopts the principle of an order-driven market. Trading members can
stay at their offices and execute the trading, since they are linked through a
communication network. The prices at which the buyer and seller are willing to transact
will appear on the screen. When the prices match the transaction will be completed and a
confirmation slip will be printed at the office of the trading member.

NSE has several advantages over the traditional trading exchanges. They are as
follows:

NSE brings an integrated stock market trading network across the nation.

Investors can trade at the same price from anywhere in the country since inter-market
operations are streamlined coupled with the countrywide access to the securities.

Delays in communication, late payments and the malpractice’s prevailing in the
traditional trading mechanism can be done away with greater operational efficiency and
informational transparency in the stock market operations, with the support of total
computerized network.



Unless stock markets provide professionalized service, small investors and foreign
investors will not be interested in capital market operations. And capital market being one
of the major sources of long-term finance for industrial projects, India cannot afford to
damage the capital market path. In this regard NSE gains vital importance in the Indian
capital market system.

2.1.b. Bombay Stock Exchange (BSE):

The Stock Exchange, Mumbai, popularly known as "BSE" was established in 1875 as
"The Native Share and Stock Brokers Association". It is the oldest one in Asia, even older
than the Tokyo Stock Exchange, which was established in 1878. It is a voluntary non-
profit making Association of Persons (AOP) and is currently engaged in the process of
converting itself into demutualised and corporate entity. It has evolved over the years into
its present status as the premier Stock Exchange in the country. It is the first Stock
Exchange in the Country to have obtained permanent recognition in 1956 from the Govt.
of India under the Securities Contracts (Regulation) Act, 1956.

The Exchange, while providing an efficient and transparent market for trading in
securities, debt and derivatives upholds the interests of the investors and ensures
reprisal of their grievances whether against the companies or its own member-brokers.
It also strives to educate and enlighten the investors by conducting investor education
programmers and making available to them necessary informative inputs. A Governing
Board having 20 directors is the apex body, which decides the policies and regulates the
affairs of the Exchange. The Governing Board consists of 9 elected directors, who
are from the broking community (one third of them retire ever year by rotation),
three SEBI nominees, six public representatives and an Executive Director & Chief
Executive Officer and a Chief Operating Officer.

The Executive Director as the Chief Executive Officer is responsible for the day-
to-day administration of the Exchange and he is assisted by the Chief Operating Officer
and other Heads of Departments. The Exchange has inserted new Rule No.126 A in its
Rules, Bye-laws & Regulations pertaining to constitution of the Executive Committee of
the Exchange. Accordingly, an Executive Committee, consisting of three elected
directors, three SEBI nominees or public representatives, Executive Director & CEO and



Chief Operating Officer has been constituted. The Committee considers judicial & quasi
matters in which the Governing Board has powers as an Appellate Authority, matters
regarding annulment of transactions, admission, continuance and suspension of member-
brokers, declaration of a member-broker as defaulter, norms, procedures and other
matters relating to arbitration, fees, deposits, margins and other monies payable by the
member-brokers to the Exchange, etc.………………………………………………….

2.1.c.Optimal portfolio construction
Portfolio is a combination of securities such as stocks, bonds and money market
instruments. The process of blending together the broad asset classes so as to obtain
optimum return with minimum risk is called portfolio construction. Diversification of
investments helps to spread risk over many assets. A diversification of securities gives the
assurance of obtaining the anticipated return on portfolio. In a diversified portfolio, some
securities may not perform as expected, but others may exceed the expectation and
making the actual return of the reasonably close to the anticipated one.

Keeping a portfolio of single security may lead to a greater likelihood of the
actual return some what different from that of the expected return. Hence it is a common
practice to diversify securities in the portfolio. Keeping this fact in mind I have tried to
construct portfolio with diversification of investments in all sectors.

The steps followed in constructing optimal portfolio is as follows:

 Determination of objectives
 Selection of securities based on the objectives
 Choose a suitable approach for construction portfolio
 Apply the approach and construct the portfolio
 Assessment of risk and return.

2.1.d. Value of a stock
There are various factors that determine the value of a stock. understanding
these will help you to pay a price that reflects the true value of a stock.



 Demand and supply:
In the short term, the basic economic theory of demand and supply determines a
stock’s worth. so. when the demand for a stock exceeds its supply (that is, there
are more buyers than sellers), its price tends to rise and when supply overtakes
demand (that is, sellers exceed buyers),the stock loses value. However these are
short term market trend to get evened out over a period of time. In the medium to
long term, a stock is driven by the companies fundamental strength i.e. business
potential, past performance, competence and credibility of its promoters and
management, etc.

 Growth potential:
Investors are willing to pay a premium for stocks of companies that have the
potential to increase their revenues and net profit. the greater this growth
potential, the higher the premium given to the stock. if a company proves that it
is capable of sustaining growth, the market will continue to give it high
valuations.and,that’s likely to be the major driver for stock valuations.

 Fundamentals:
A companies growth outlook is linked to its business prospects and how well its
management is capitalizing on the existing opportunities. the quality of a
companies management is crucial.so,pay attention to the management practices
of a company and its level of corporate governance.

2.1.e.Various method of constructing optimal portfolio:

Some of the famous methods for constructing optimal portfolio are’

 Markowitz model
 Sharpe’s single index model

Single index model:
Casual observations of the stock prices over a period of time reveals that most of
the stock prices move with the market index. when the sensex increases, stock prices also



tend to increase and vice-versa. This indicates that some underlying factors affect the
market index and this relationship could be used to estimate the return on stock. towards
this purpose, the following equation can be used:

Ri = αi+βiRm+ei
Where,Ri-expected return on security i
αi-intercept of the straight line or alpha co-efficient i.e., the amount by
which a fund has out performed its bench mark taking into account its exposure to market
risk.
βi-slope of straight line or beta co-efficient i.e., a measure of a fund’s
sensitivity to market movements.

Rm-the rate of return on market index.
ei - error term
According to the equation the return of the stock can be divided into 2
components, the return due to the market and the return independent of the market.βi
indicates the sensitiveness of the stock return to the changes in the market return. the
single index model is based on the assumption that stocks vary together because of the
common movement in the stock market and there are no effects beyond the market that
accounts the stock co-movement. the expected return, standard deviation and co-variance
of the single index model represents the joint movement of securities.

The co variance of returns between securities i and j = βi βj
The variance of security’s return,σ 2= βi σ m2 + σ ei 2

The variance of the security has two components namely, systematic risk or
market risk and unsystematic risk or unique risk. the variance explained by the index is
referred to systematic risk. the unexplained variance is called residual variance or
unsystematic risk.
systematic risk = βi 2 * variance of market index.
= βi 2 σ m2

unsystematic risk=total variance - systematic risk



ei 2 = σ ei 2 - systematic risk
ei 2 = σ ei 2 - βi 2 σ m2

Thus total risk = systematic risk + unsystematic risk
= βi 2 σ m2 + ei 2

From this point ,the portfolio variance can be derived

σp2=[ (Xi βi)2 σ m2 + [ Xi 2 ei 2]

were i vary from 1 to N
σp2 = variance of portfolio

σ m2 =expected variance of index

ei 2 = variation in security ‘s return not related to the market index

Xi =the portion of stock I in the portfolio.

2.1.f. Sharpe’s optimal portfolio:

Sharpe had provided a model for the selection of appropriate securities in a
portfolio. the selection of any stock is directly related to its excess return beta ratio.Ri-Rf.



βi
The excess return is the difference between the expected return on the stock and the
risk less rate of interest such as offered on government securities or treasury bill. the
excess return to beta ratio measures the additional return on a security(excess of the risk
less asset return) per unit of systematic risk or non-diversifiable risk. this ratio provides a
relationship between potential risk and return. Ranking of the stocks are done on the basis
of their excess return to beta.portfoilo managers would like to include stocks with higher
ratios. the selection of stocks depend on unique cut-off rate such as all stocks with higher
ratios of (Ri-Rf)/ βi are included and the stocks with lower rank are let off. the cut-off
point is denoted by C *. The stocks ranked above C* have high excess returns to beta than
the cut-off point Ci and are included in the optimal portfolio.

Methodology:

Step 1: A brief profile of each of the 30 companies of sensex index is chosen.

Step 2: for a period of 5 years data of the each companies have been recorded.

Step 3: for applying Sharpe’s index model Ri,Rm, σ ei 2, βi, σ m2,Rf values are
required. so all these data are collected and calculated for proceeding further.

Step 4: the cut-off point C* is calculated using the formula:
σm2∑(Ri-Rf)βi
Ci= . σei2 .
1+σm2∑βi2
σei2
Step 5:after Ci for the companies are calculated the value got were put in a table and then
the interpretations were made.

Step 6:the Ci values go on increasing up to a certain point and then start decreasing. the
highest point is called cut-off point(C*).the securities which are above C* point are
chosen to the portfolio.



Step 7:Once the securities for portfolio are chosen, the proportion in which they should
be invested is to be determined. this can be done using a formula where Xi denotes the
proportion,

Xi=Zi
∑Zi
Where Zi= βi[Ri-Rf ] -C*
σei2 βi

Step 8:Return on portfolio can be made known with the formula
Rp=∑XiRi

Step 9: σp2 gives the risk associated with portfolio.

3.DATA COLLECTION

3.1 Selection of companies:

The companies constituting the sensex index have chosen for applying Sharpe’s
single index model and hence construct optimal portfolio. Bombay stock exchange


limited is the oldest stock exchange in Asia with a rich heritage popularly known as
“BSE”,it was established as “THE NATIVE SHARE & STOCK BROKERS
ASSOCIATION” in 1875.it is the first stock exchange in the country to obtain permanent
recognition in 1956 from the government of India under the securities
contracts(regulation) act,1956.the exchange’s pre-eminent role in the development of the
Indian capital market is widely recognized and its index, SENSEX,is tracked worldwide.
SENSEX ,first compiled in 1986, was calculated on a “market capitalization
weighed”methology of 30 component stocks representing a sample of large, well-
established and financially sound companies. the base year of SENSEX is 1978-1979.the
index is widely reported both in domestic and international markets through print as well
as electronic media.

List of companies constituting SENSEX index:
Table :3.1



Si No Company Industry
1 ACC Cement & cement products
2 Bajaj automobiles Automobiles 2-3 wheelers
3 BHEL Electrical equipment
4 Bharathi airtel Communication
5 Cipla pharmaceutical
6 Dr.reddy’s laboratories pharmaceutical
7 Grasim industries Cement & cement products
8 Gujarat ambuja cements Cement & cement products
9 HDFC Finance housing
10 HDFC bank bank
11 Hero Honda motors Automobile 2-3 wheelers
12 HLL diversified
13 Hindalco India aluminum
14 ICICI bank bank
15 Infosys technology Computer software
16 ITC cigarettes
17 L&T engineering
18 Maruthi udyog Automobile 4 wheelers
19 Birla cement Cement
20 ONGC Oil exploration
21 Ranbaxy laboratories Pharmaceutical
22 Reliance communication Communication
23 PCS Software
24 Reliance industries Manufacturing
25 JP associates Computer software
26 SBI Bank
27 Tata motors Automobiles 4 wheelers
28 Tata steel Steel & steel products
29 TCS Computer software
30 Wipro Computer software



3.2 Risk-free rate of return: -
Risk free security has zero variance or standard deviation. The risk free securities
have no risk of default. The government T-bills or bonds are approximate example of risk
free securities as they have no risk of default. The 364 days Treasury bill rate return is
considered as the risk free rate of return for our calculation purpose. The 364 days T-Bills
rate for five years from 31st Dec 2004 to Dec 31st 2008 is as shown in the following table.

Year Weighted Avg Return
2005 4.67
2006 5.15
2007 5.87
2008 6.99
2009 7.33

Therefore the risk free rate of return for the whole five years is the average of all the values
in the table mentioned above.

Rf = 4.67+5.15+5.87+6.99+7.33
5
Rf = 6.002.



3.3 Return on Market: -
The return on the market is the return obtained by the companies constituting the
sensex index. The returns of all the 30 companies purpose are considered and only the
yearly values are shown in the table below for calculating purpose. The detailed
fluctuation of sensex index points during five years period can be seen clearly in the
following table.
Period (Rm - Rm') (Rm - Rm')2
2005 28.45841034 809.8811193
2006 -31.3579682 983.3221704
2007 -2.08752556 4.35776295
2008 2.902918708 8.426937024
2009 2.084164718 4.343742571

The volatility in the stock returns of index companies is given by
:- σ m2 = ∑(Rp- RP')2
N-1
=1810.331732

4.ANALYSIS



ACC: - {Associated Cement Companies Limited to ACC Limited}

ACC Limited was incorporated in the year 1936. ACC is India's foremost
manufacturer of cement and concrete. The company has been a trendsetter and important
benchmark for the cement industry in respect of its production, marketing and personal
management process. The company has 14 cement plants all over India, three refractory
plants and 6 Ready Mix Concrete plants near to four metro cities of India. It has also
extended its services overseas to the Middle East, Africa and South America, where it has
provided technical and managerial consultancy to a variety of consumers, and also helps
in the operation and maintenance of cement plants abroad. The company has received
Good Corporate Citizen Award for the year 2005-06. ACC received this award in
recognition of its corporate achievements and its ongoing endeavors in improving the
quality of life of the community
Table :4.1.

Date Cls – Return (RP - (Rm - (RP - RP') (RP - RP')2 (Rm - Rm')2
price RP RP') Rm') *(Rm -
Rm')
2005 534.2 57.7206 11.5336 28.4584 328.2278 133.0239 809.8811193
2006 1085.55 103.2104 57.0234 -31.3579 -1788.134 3251.6681 983.3221704
0
2007 1024.8 -5.5962 -51.783 -2.0875 108.0974 2681.4998 4.35776295
2
2008 477.90 43.12 -3.067 2.9029 -8.90319 9.4064 8.426937024
2009 948 32.48 -13.707 2.0841 -28.5667 187.8818 4.343742571
TOTAL 230.9348 -0.0002 -1389.278 6263.48 1810.331732
6
RP'= ∑Ri
N
230.9348÷5
RP' = 46.187
σRp2= ∑(Rp- RP')2
N-1
σRp2 = 15.65

βp = ∑( RP - RP')*(Rm - Rm')


∑(Rm - Rm')2

Βp = -0.767,
σei 2=σi2 -ßi2 σm2 =16.417

Bajaj Auto Limited:-
Manufactures and markets Bajaj scooters, motorcycles, three-wheelers and spare
parts. Incorporated in 1945 as a private limited company, it went public in 1960.
Currently the company has four plants at Akurdi, Waluj, Chakan and
Pantnagar(Uttarakhand) with an combined installed capacity to produce 4,050,000 nos. of
two wheelers and three wheelers. Further the company has an installed capacity to
produce 65.20 MW of Wind power.
In 1974-75, Bajaj Auto co-promoted a joint-sector company, Maharashtra Scooters. A
plant was set up at Satara and production of Priya scooters commenced in 1976. The
company introduced a new ungeared scooter called Wave for which the engine is
powered by DTSi.In 2006-07, Bajaj Auto entered into a Joint Venture in Indonesia with a
local financial consultancy group Boentaro and formed PT. Bajaj Auto Indonesia, where
the company has 95 per cent equity ownership. This joint venture company will be used
for assemble and sell three-wheelers and high-end motorcycles

Table: 4.2
Date Cls – Return (RP - (Rm - (RP - RP')* (RP - RP')2 (Rm -
price RP RP') Rm') (Rm - Rm') Rm')2
2005 2000.8 76.8350 50.158 28.4584 1427.4164 2515.8249 809.8811
2006 2618.85 30.8901 4.2131 -31.3579 -132.1139 17.7502 983.3221
2007 2795 6.7262 -19.958 -2.08752 41.6644 398.3536 4.357
8



2008 2795 4.654 -22.023 2.9029 -63.9305 485.0125 8.4269
2009 2900 14.28 -12.397 2.08416 -25.8373 153.6856 4.34374
Total 133.385 -0.0077 1247.1991 3570.6268 1810.3317
3
RP'= ∑Ri
N

133.3853÷5

RP' = 26.6770

N-1

σRp2 =8.926

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2

Βp = 0.6889 ,

σei 2=σi2 -ßi2 σm2 =8.2371

BHEL: {Bharat Heavy Electricals Ltd}
Incorporated as a government owned organization in 1950. After liberalization of
Indian economy, the government decided to divest a portion of its holding. In 1991-92, it
has divested a part of its equity shares to public and financial institutions. At present the
government of India holds 67.72% in the total equity capital of the company.
BHEL is the largest engineering and manufacturing enterprise in India in the energy-
related/infrastructure sector, today. The company's operations are organized around three



business sectors, namely Power, Industry (includes Transmission, Transportation,
Telecommunication and Renewable Energy) and Overseas Business. This enables the
organization to have a strong customer orientation, to be sensitive to his needs and
respond quickly to the changes in the market
BHEL has won International Asia Pacific Quality Award (IAPQA 2005) from the
International Asia Pacific Quality Organization (APQO) through its Ranipet Unit. It is the
first engineering & Manufacturing organization and the first PSU in the country to
receive this award.

Table:4.3



Date cls Return (RP - RP') (Rm - (RP - RP')* (RP - RP')2 (Rm -
price RP Rm') (Rm - Rm')2
Rm')
2005 693.13 80.0571 17.8862 28.4584 509.0126 319.916 809.8811
2006 1149.0 65.7813 3.6104 -31.3579 -113.2145 13.0349 983.3221
8
2007 2589.7 125.375 63.2050 -2.0875 -131.9404 3994.8720 4.3577
5 9
2008 1696.5 25.32 -36.8508 2.9029 -106.9742 1357.9814 8.4269
0
2009 2201 14.32 -47.8508 2.0841 -99.7258 2289.6991 4.3437
Total 310.854 0 57.1577 7975.5034 1810.3317
3
RP'= ∑Ri
N

RP' = 62.17086

N-1

σRp2 =19.9387

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2

βp = 0.03157

σei 2=σi2 -ßi2 σm2 = 19.90713



BHARTI AIRTEL LTD :
Was incorporated on 7th July, 1995, for promoting investments in diversified
telecom service projects. The company was formed as a 80:20 joint venture between the
Bharti Group through its subsidiary Bharti Telecom and STET International Netherlands
NV, a company promoted by Telecom Italia, Italy.Bharti is one of India's leading private
sector provider of telecom services with more than 39.01 million customers in India
comprising of 37 million mobile and approximately 1.9 million broadband & telephone
customers and is the first to have an all India presence. The company is structured into
three main units, Mobile Services which offers GSM Mobiles Servies and Infotel
Services which provides broadband & Telephone,long distance and enterprise services
which offers carriers and corporates. The company was first GSM Operator to have more
than ten million customers and also the first telecom company to cover all the 23 telecom
circles of India, which this coverage facility the company became the first operator to
have an All-India footprint. All the services of company is been provided under brand
name AIRTEL
Table:4.4

Date Cls- Return (RP - RP') (Rm - (RP - RP') (RP - RP')2 (Rm -
price RP Rm') *(Rm - Rm') Rm')2
2005 345.7 60.3432 -82.7043 28.4584 -2353.6321 6840 809.8811
2006 628.85 81.9062 -61.1413 -31.3579 1917.2628 3738.258 983.3221
5
2007 996.4 58.4479 -84.5996 -2.0875 176.6017 7157.092 4.3577
2008 358.50 253.54 110.4925 2.9029 320.7487 12208.59 8.4269
2009 315 261 117.9525 2.0841 245.8248 13912.79 4.3437
2
Total 715.237 -0.0002 306.8059 43856.74 1810.3317
3
RP'= ∑Ri

715.2373÷5

143.0475




N-1

σRp2=109.64

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2

βp = 0.1695 ,

σei 2=σi2 -ßi2 σm2

= 109.4705

Cipla Ltd:-
Incorporated in the year 1935. Today Cipla is one of the largest manufacturer and
marketer in bulk drugs and formulations. It has been ranked as first in India by
ORG IMS ratings 2005 in terms of retail pharmaceutical sales. All the bulk drug facilities
have been approved by the US FDA and the formulation facilities have been approved by
the Medicine Control Agency, UK; the Medicine Control Council, South Africa; the
Therapeutic Goods Administration, Australia and other international agencies. It has
manufacturing facilities at Kurkumbh, Bangalore, Patalganda and Vikroli in Mumbai.
The company's products are currently registered in over 150 countries.
Cipla has a very wide product range which includes antibiotics, anti-bacterial, anti-
asthmatics, anti-inflammatory anthelminites, anti-cancer and cardiovasculars. In domestic
formulation market, antibiotics are the mainstay, which contributes around 50% of the
company's revenue. The company expanded its facilities at Baddi in Himachal Pradesh.
The company is planning to set up a large drug formulation manufacturing facility for
various dosage forms as a Special Economic Zone (SEZ) in Goa and also planned major
additions to its manufacturing facilities at Kurkumbh and Bangalore.

Table :4.5



Date Cls – Return (RP - (Rm - Rm') (RP - (RP - RP')2 (Rm -
price RP RP') RP')*(Rm - Rm')2
Rm')
2005 177.3 39.763 20.7401 28.4584 590.2300 430.1517 809.8811
6 5
2006 250.7 41.350 22.3275 -31.3579 -700.1435 498.1572 983.3221
9
2007 212.6 -15.197 -34.220 -2.0875 71.4359 1171.0631 4.3577
4 8
2008 218.0 14.20 -4.8234 2.9029 -14.0018 23.2652 8.4269
5
2009 263 15 -4.0234 2.0841 -8.3852 16.1877 4.3437
Total 95.117 0 -60.8646 2139.1849 1810.3317

RP'= ∑Ri
N

95.117÷5

RP' = 19.0234

N-1

σRp2=5.3479

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2

βp = -0.03362
σei 2=σi2 -ßi2 σm2
= 5.3815



Dr. Reddy's Laboratories:-
Established in 1984, is a leading Indian pharmaceutical company with vertically
integrated operations. The company develops, manufactures and markets a wide range of
pharmaceutical products in India and overseas. Dr. Reddy's produces finished dosage
forms, active pharmaceutical ingredients, diagnostic kits, critical care and biotechnology
products. The company has over 190 finished dosage brands and 60 active
pharmaceutical ingredients currently in production. In 2006, The company involved de-
bottlenecking of existing capacities and adding new lines, especially to meet growing
international demand for generics and customs pharmaceuticals services. During the year
company has made two major acquisitions. The first was the purchase of Roche's API
Business, its order-book and its manufacturing plant at Cuernavaca in Mexico. The
another acquisition was that a betapharm, Germany

Table :4.6

Date Cls- Return (RP - (Rm - (RP - RP')* (RP - RP')2 (Rm -
price RP RP') Rm') (Rm - Rm') Rm')2
2005 489.2 13.0821 -10.6492 28.4584 -303.0591 113.4055 809.8811
5
2006 811.2 65.8048 42.0735 -31.3579 -1319.3366 1170.1794 983.3221
2007 735.3 -9.3503 -33.0816 -2.0875 69.0578 1094.3923 4.3577
5
2008 403.1 12.23 -11.5013 2.9029 -33.3871 132.2799 8.4269
0
2009 1098 36.89 13.1587 2.08416 27.4240 173.1514 4.3437
Total 118.656 -1559.301 2683.4085 1810.3317
6

RP'= ∑Ri
N

118.6566÷5

RP' = 23.7313



Rp2= ∑(Rp- RP')2
N-1

σRp2= 6.7085

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2

βp = - 0.86133 ,

σei 2=σi2 -ßi2 σm2 = 7.56983

Grasim Industries:-
Aditya Birla Group was originally incorporated as Gwalior Rayon Silk
Manufacturing (Weaving) Company in 1947. The company's key business are Viscose
Stable Fiber and Cement. It also produces sponge Iron, Chemicals and textiles.
Grasim which commenced operation in 1950 by manufacturing fabrics using imported
rayon ( a manmade cellulosic fibre) at Gwalior has now grown to become one of India's
top ten largest private sector companies in terms of assets and sales. The company's foray
into cement has became a successful diversification and the company has became the
third largest producer of cement in India.
Grasim's subsidiaries are Dakshin Cements Ltd, Narmada Cement Company Ltd, Sun
God Trading & Investments Ltd, Samruddhi Swastik Trading & Investments ltd, Shree
Digvijay Cement Company Ltd, UltraTech Cement Ltd and UltraTech Ceylinco Pvt Ltd.
The company which has hived off its software business to Birla Technologies Ltd(BTL),
a subsidiary of the company in 2000-01 has divested its entire holding in BTL to PSI
Data Systems, a group company for an consideration of Rs.11.3 Crores during the year
2006-07

.



Table:4.7

Date Cls- Return (RP – (Rm – (RP – RP’)* (RP – RP’)2 (Rm -
price RP RP’) Rm’) (Rm – Rm')2
Rm’)
2005 1391.2 5.2104 -28.2196 28.4584 -803.08466 796.3458 809.8811
5
2006 2789.1 100.474 67.044 -31.357 -2102.3590 4494.8979 983.3221
3 9
2007 3651.6 30.9239 -2.5061 -2.0875 5.23148 6.2805 4.3577
2008 1774.7 10.652 -22.778 2.9029 -66.1222 518.8373 8.4269
0
2009 2480 19.89 -13.54 2.0841 -28.2187 183.3316 4.3437
Total 167.150 0 -2994.553 5999.69 1810.3317
6
RP'= ∑Ri
N
167.1506÷5
RP' = 33.43

Rp2= ∑(Rp- RP')2
N-1
σRp2= 14.999

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2

βp =-1.654

σei 2=σi2 -ßi2 σm2 = 16.653



Gujarat Ambuja Cements Ltd:-
Started out as a joint sector co. with public sector Gujarat Industrial Investment
Corporation (GIIC) and Narottam Sekhsaria & Associates in 1981. Later with private
partners buying out GIIC's stake , the company became a private sector venture. It is
having six cement plants at Ambujanagar (Gujarat), Darlaghat (Himachal Pradesh),
Upperwahi (Maharashtra), Rabriyawas (Rajasthan), Daburji (Punjab) and in Bhatinda
district(Punjab). It is also having three Bulk Cement Terminals at Muldwarka (Gujarat),
Gavier (Gujarat) and in Ulwa (Maharashtra).During June 2005 the company has sub-
divided its face value of equity share from Rs.10/- per share to Rs.2/- per share. Further
the company has issued bonus equity share to its shareholders in the ratio of 1:2.The
company has increased its installed capacity of Cement by 440000 MT and with this
expansion the total installed capacity of Cement has been increased to 13300000 MT.

Table :4.8

price RP Rm') *(Rm - Rm') Rm')2
2005 79.6 48.6738 25.26 28.4584 718.8591 638.0676 809.8811
2006 141.3 77.5125 54.10 -31.3579 -1696.46 2926.81 983.3221
2007 146.9 3.9631 -19.448 -2.0875 40.5977 378.2247 4.3577
2008 76.00 -15.43 -38.842 2.9029 -112.754 1508.700 8.4269
9
2009 98 2.34 -21.072 2.0841 -43.916 444.029 4.3437
Total 117.059 -1093.6732 5895.832 1810.3317
4 2

RP'= ∑Ri
N
117.0594÷5

RP' = 23.412

Rp2= ∑(Rp- RP')2
N-1



σRp2= 14.7395

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2

βp = -0.604

σei 2=σi2 -ßi2 σm2 =15.3436

HDFC :{Housing Development Finance Corporation}
HDFC was promoted by the Industrial Credit and Investment Corporation of India
with initial equity reservation for the International Finance Corporation (Washington) and
his Royal Highness, the Aga Khan. The corporation provides housing loans to
individuals, corporates and developers. Its Centre for Housing Finance (CHF) provides
technical assistance to national governments and housing finance institutions in
developing countries in South Asia and Africa. It is also a co-ordinator of the coalition of
housing finance institutions in Asia and the Pacific, a public and private sector
partnership project, funded by the United Nations Development Programme (UNDP). The
company, which has been working closely with National Housing Bank to frame,
appropriate foreclosure norms so that securitization of housing debt is possible
In the year 2007, The company has opened an office in London to cater to the needs of
non-resident Indians (NRIs). The company was selected as the best Indian company in the
'Financial Institutions/Non-Banking Financial Companies/Financial Services' category at
the Dun & Bradstreet - American Express Corporate Awards 2006.



Table :4.9

Date Cls- Return (RP - (Rm - (RP - RP')* (RP - (Rm -
price RP RP') Rm') (Rm - RP')2 Rm')2
Rm')
2005 1205.3 57.3358 1.706 28.4584 48.55 2.910436 809.8811
5
2006 1624.5 34.7782 -20.8516 -31.3579 653.86 434.789 983.3221
5
2007 2872.4 76.8151 21.1853 -2.0875 -44.2243 448.816 4.3577
5
2008 336.12 47.13 -8.4998 2.9029 -24.6741 72.246 8.4269
2009 1664 62.09 6.4602 2.0841 13.4637 41.734 4.3437
Total 278.141 646.9753 1000.49 1810.3317
9

RP'= ∑Ri
N
278.1491÷5

RP' = 55.6298

Rp2= ∑(Rp- RP')2
N-1

σRp2= 2.5

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2

=0.3573

σei 2=σi2 -ßi2 σm2 = 2.1427



HDFC Bank:-
HDFC was promoted by the Industrial Credit and Investment Corporation of India
with initial equity reservation for the International Finance Corporation (Washington) and
his Royal Highness, the Aga Khan. The corporation provides housing loans to
individuals, corporates and developers. Its Centre for Housing Finance (CHF) provides
technical assistance to national governments and housing finance institutions in
developing countries in South Asia and Africa. It is also a co-ordinator of the coalition of
housing finance institutions in Asia and the Pacific, a public and private sector
partnership project, funded by the United Nations Development Programme (UNDP). The
company, which has been working closely with National Housing Bank to frame,
appropriate foreclosure norms so that securitization of housing debt is possible. In the
year 2007, The company has opened an office in London to cater to the needs of non-
resident Indians (NRIs). The company was selected as the best Indian company in the
'Financial Institutions/Non-Banking Financial Companies/Financial Services' category at
the Dun & Bradstreet - American Express Corporate Awards 2006
Table:4.10

price RP Rm') *(Rm Rm')2
Rm')
2005 707.45 36.3496 0.8484 28.4584 24.144 0.7197 809.8811
2006 1069.7 51.2120 15.71 -31.3579 -492.633 246.8041 983.3221
5
2007 1727.8 61.5143 26.51 -2.0875 -55.3396 702.7801 4.3577
2008 1205.7 48.25 12.75 2.9029 37.0119 162.5625 8.4269
5
2009 1795 28.43 -7.07 2.0841 -14.7345 49.9849 4.3437
Total 177.505 -501.5512 1162.8513 1810.3317
9

RP'= ∑Ri
N
177.5059÷5



RP' = 35.50118

Rp2= ∑(Rp- RP')2
N-1
σRp2= 2.9071

βp = ∑(RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=-0.277
σei 2=σi2 -ßi2 σm2 = 3.1841

Hero Honda :-
Joint Venture company promoted by Hero Cycles of India and Honda Motor
Company of Japan, is the world's largest two wheeler manufacturing Company. Honda
Motors, Japan the Technical and Financial Collaborator holds 26% stake in the Company.
The market share of the company in the Indian motorcycle market is 39.4 per cent. The
company has launched 5 new models namely CD-Dawn, for entry segment, KARIZMA
for power+ sport segment, Passion Plus and Splendor Plus and AMBITION 135 for
premium segment. In line with its lineage of introducing the world's best technologies to
India, the company announced the launch of India's first motorcycles with Fuel Injection
(FI) technology in June 2006, with the launch of 125 cc Glamour FI. With this, Honda
Motor Co. will debuts this technology globally in 125 cc category, with Hero Honda The
company was the only two-wheeler company named amongst the top 10 companies in
India by the Asia 200 Leadership Report by the Wall Street Journal



Table :4.11
Date Cls- Return (RP - RP') (Rm - (RP - RP')* (RP - RP')2 (Rm -
price RP Rm') (Rm - Rm')2
Rm')
2005 859.7 50.5340 38.734 28.4584 1102.3077 1500.323 809.8811
2006 762.3 -11.323 -23.1237 -31.357 725.1106 534.705 983.3221
5 7 9
2007 697.6 -8.4869 -20.2869 -2.0875 42.3489 411.5583 4.3577
5
2008 804.1 9.364 -2.436 2.9029 -7.07146 5.9340 8.4269
2
2009 1187 18.93 7.13 2.0841 14.8596 50.8369 4.3437
Total 59.0174 1877.56 2503.359 1810.3317
3
RP'= ∑Ri
N
59.0174÷5

RP' = 11.80

Rp2= ∑(Rp- RP')2
N-1
σRp2= 6.2584

βp = ∑ RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=1.037

σei 2=σi2 -ßi2 σm2 =5.2214

HUL:-


The Company was Incorporated in the year 1933. In June 2007, The company has
changed its name from Hindustan Lever Ltd(HLL) to Hindustan Unilever Ltd (HUL).
With this, the company's new corporate identity represented by a new logo comes into
effect. During 2005, the companies subsidiaries Lever India Exports Ltd, Lipton India
Exports Ltd, Merry weather Food Products Ltd, Toc Disinfectants Ltd, International
Fisheries Ltd were merged with the company as of December 30, 2005 with effect from
the respective appointed dates stipulated in the Merger Scheme approved by the High
Court of Mumbai. Vasishti Detergents Ltd (VDL)also came in to the fold of the company
as a result of amalgamation of the Tata Oil Mills Company Ltd. VDL was merged with
the company on February 28, 2006 pursuant to a Scheme of Arrangement sanctioned by
the High Court of Mumbai with retrospective effect from July 1, 2005. The company
transferred the soap and soap intermediate manufacturing facilities at Sewari in Mumbai
to Bon Ltd on 17th July, 2005. In December 2004, the company obtained approval from
shareholders and transferred its Functionalized biopolymer business to Riddhi Siddhi
Gluco Biols Ltd

Table :4.12

price RP Rm') *(Rm - Rm')2
Rm')
2005 197.2 37.4564 24.3826 28.4584 693.4584 594.511 809.8811
5
2006 216.5 9.7845 -3.2893 -31.3579 103.1455 10.819 983.3221
5
2007 213.9 -1.2237 -14.2975 -2.0875 29.846 204.418 4.3577
2008 143.2 0.572 -12.5018 2.9029 -36.2915 156.295 8.4269
5
2009 223 18.78 5.7062 2.0841 11.8923 32.56 4.3437
Total 65.3692 802.482 998.603 1810.3317
RP'= ∑Ri
N
65.3692÷5

RP' = 13.0738



Rp2= ∑(Rp- RP')2
N-1

σRp2= 2.496

βp = ∑ RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=0.4433

σei 2=σi2 -ßi2 σm2 = 2.0527

HINDALCO INDIA:-
Hindalco Industries, a flagship company of the Aditya Birla Group, is India's
largest integrated aluminum producer. The company has also emerged as one of the
leading player in the Copper business in India with the acquisition of Copper business of
erstwhile Indo Gulf Corporation, a Aditya Birla Group company. The company is the
market leader with 41% marketshareIn 2006-07, the Installed capacity of Aluminum
Metal, Electricity, Electricity (Co-generation), Gold and Silver capacities was expanded
by enhancing to 6000 tonnes, 100 MW, 7.4 MW, 7.5 Tonnes and 75 tonnes respectively.
By enhancing, Installed capacity of Aluminum Metal, Electricity, Electricity (Co-
generation), Gold and Silver the total installed capacity stood as 461000 tonnes, 1009.2
MW, 212.8 MW, 15 Tonnes and 150 Tonnes respectively.

Table:4.13



(RP - RP')*
Cls- Return (RP - (Rm - (Rm - (Rm -
Date price RP RP') Rm') Rm') (RP - RP')2 Rm')2
2005 143.4 6.8474 -8.855 28.4584 -251.999 78.41 809.8811
2006 174.1 21.4086 5.7062 -31.3579 -178.934 32.56 983.3221
214.8
2007 5 23.4060 7.7036 -2.0875 -16.0812 59.345 4.35776
-10.292
2008 90.8 5.41 4 2.9029 -29.8778 105.933 8.4269
2009 129 21.44 5.7376 2.0841 11.9577 32.92 4.3437
Total 78.512 -464.9343 309.168 1810.3317

RP'= ∑Ri
N
78.512÷5

RP' = 15.7024

Rp2= ∑(Rp- RP')2
N-1
σRp2= 0.7729

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=-0.2568

σei 2=σi2 -ßi2 σm2 =1.0297

ICICI Bank:-
ICICI Bank (ICICIBK) is a commercial bank promoted by ICICI Ltd, an Indian
Financial Institution. It was incorporated in Jan.'94 and received its banking license from


Reserve Bank of India in May.'94. It is the 2nd largest bank in India. The bank has over
755 branches & extension counters across India and over 3271 ATMs across the country.
During 2006-07, Sangli Bank Ltd was merged with ICICI Bank Ltd and RBI approved
the scheme of amalgamation effective April 19, 2007.The Board of Directors of ICICI
Bank at its meeting held on March 1-3 2007 approved the incorporation of a new wholly
owned subsidiary. The Bank has proposed to transfer its holding in ICICI Prudential Life
Insurance Company, ICICI Lombard General Insurance Company Ltd, ICICI Prudential
Asset Management Company Ltd and ICICI Prudential Trust Ltd to its proposed new
wholly owned subsidiary.
Table:4.14

Date Cls- Return (RP - (Rm - (RP - RP')* (RP - (Rm -
price RP RP') Rm') (Rm - Rm') RP')2 Rm')2
2005 584.7 57.7073 25.7113 28.4584 731.7025 661.07 809.8811
2006 890.4 52.2832 202872 -31.3579 -636.1639 411.570 983.3221
2007 1232.4 38.4097 6.4137 -2.0875 -13.3885 41.135 4.3577
2008 728.1 10.40 -21.596 2.9029 -62.691 466.387 8.4269
2009 1109 1018 -30.816 2.0841 -64.2236 949.625 4.3437
Total 159..98 -44.7645 2529.787 1810.3317

RP'= ∑Ri
N
159.98÷5

RP' = 31.996

Rp2= ∑(Rp- RP')2
N-1

σRp2=6.32

βp = ∑ RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=-0.024
σei 2=σi2 -ßi2 σm2 = 6.3447



Infosys Technologies:-
Infosys Technologies Ltd (Infosys) was incorporated on July 2, 1981, as a private
ltd company. It became public limited company on June 1992 and subsequently the name
was also changed to Infosys Technologies Ltd. It was the first Indian company to be listed
on American Stock Exchange. The Company is one of India's leading information
technologies(IT) services companies. It is mainly engaged Out-Sourced application &
Infrastructure Services, Enterprise Services, Product R&D Services and Consulting
Services. The company also develops and markets certain company owned software
products.
The company has received award 'First Position in SAFA (South Asian Federation of
Accountants) Best presented Accounts Award 2004 in the Communication and
information Technology Sector based on the evaluation of the Annual report of the
company. Wired Magazine has ranked No.9 on Wired 40. The company was named
'India's Best Managed Company' based on a study Conducted by Business Today and A T
Kearney.

Table:4.15
Date Cls- Return RP (RP - (Rm - (RP - (RP - RP')2 (Rm - Rm')2
price RP') Rm') RP')*
(Rm -
Rm')
2005 1498.3 43.4542 18.4792 28.4584 525.888 341.48 809.8811
8
2006 2240.5 49.5281 24.5531 -31.357 -769.93 602.85 983.3221



9
2007 1768.4 -21.07711 -46.0520 -2.0875 96.134 2120.79 4.3577
2008 1394.9 27.6 2.625 2.9029 7.620 6.890 8.4269
0
2009 2643 25.37 0.395 2.0841 0.823 0.156 4.3437
Total 124.875 -139.465 3072.166 1810.331732

RP'= ∑Ri
N
124.975÷5

RP' = 24.975

Rp2= ∑(Rp- RP')2
N-1

σRp2= 7.68

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=-0.077
σei 2=σi2 -ßi2 σm2 = 7.757

ITC (Indian Tobacco Company):-
ITC Ltd. a leading FMCG Cigarette major is one of the most valuable companies
of India. Rated among the World's Best Big Companies by Forbes magazine. Even
though ITC is renowned for its Cigarette business it also has business interests in Hotels;
Paperboards, Paper & Packaging; agri exports and some other FMCG products like
branded packaged foods, safety matches, Incense Sticks and Greeting Cards etc. Being
the pioneer of manufacture of cigarettes in India, ITC maintains its leadership position



since 1910. ITC has diversified its brands across products categories. Its successful
brands include Gold Flake, Wills, Classic, Bristol and Scissors. It also sells two luxury
filter brands of its parent company Benson & Hedges and 555.
In 2005, the company was awarded the ISO 9001:2000 standard By M/s. Det Norske
Veritas as a recognition of its quality products and processes. The company's units at
Munger and Tiruvottiyur are certified to ISO 9000,14000 and 18000. The company has
also won three India stars, three Asia Stars and one World star Award for innovative
packaging

Table :4.16
Date Cls- Return (RP - RP') (Rm - (RP - RP')* (RP - RP')2 (Rm - Rm')2
price RP Rm') (Rm -
Rm')
2005 142 62.620 38.07 28.4584 1083.41 1449.324 809.8811
9
2006 175.9 23.90 -0.646 -31.3579 20.257 0.417 983.3221
5
2007 210.3 19.522 -5.0244 -2.0875 10.488 25.2445 4.3577
2008 192.3 9.38 -15.166 2.9029 -44.025 230 8.4269
0
2009 231 7.31 -17.2364 2.0841 -35.922 297.09 4.3437
Total 122.732 1034.208 2002.07 1810.331732

RP'= ∑Ri
N
122.732÷5

RP' =24.5464
Rp2= ∑(Rp- RP')2
N-1

σRp2= 5.055

βp = ∑ RP - RP')*(Rm - Rm')
∑(Rm - Rm')2



=0.571
σei 2=σi2 -ßi2 σm2 = 4.435

LARSEN & TOURBO:-

Founded in 1938 by two Danish engineers, Henning Holk Larsen and Soren Kristian
Toubro, as a partnership firm, Larsen & Toubro became a private limited company in
1946 and a public limited one in 1950.
Larsen & Toubro (L&T) is one of the largest engineering conglomerates in south east
Asia. It manufactures a wide range of engineering products like earthmoving, industrial
and chemical machinery, switchgears, valves and welding alloys. L&T diversified into
shipping, acquiring two bulk carriers from Japan in 1981-82. In 1983-84, it commenced
operations at its 1-mtpa cement plant at Awarpur, Maharashtra
The company enhanced its installed capacity of Steel structural fabrication and Ready
Mix Concrete by 2400 MTs & 942800 M3 respectively. With this expansion the total
installed capacity of Steel Structural Fabrication and Ready Mix Concrete increased to
18000 MTs & 3128000 M3 respectively.

Table :4.17
Date Cls – Return (RP - (Rm - (RP - (RP - RP')2 (Rm -
price RP RP') Rm') RP')* Rm')2
(Rm -
Rm')
2005 922.1 87.800 10.977 28.4584 312.3879 120.4945 809.8811
1
2006 1442.9 56.485 -20.338 -31.357 637.7569 413.63 983.3221


5 9
2007 4171.8 189.11 112.28 -2.0875 -234.399 12608.37 4.3577
5 7
2008 1631.2 24.72 -52.103 2.9029 -151.2497 2714.72 8.4269
3
2009 1520 26 -50.823 2.0841 -105.92 2582.98 4.3437
Total 384.115 458.5761 18440.194 1810.33173
5 2

RP'= ∑Ri
N
384.115÷5

RP' = 76.823

Rp2= ∑(Rp- RP')2
N-1
σRp2= 46.10

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=0.253
σei 2=σi2 -ßi2 σm2 = 45.847

ONGC:-
Oil and Natural Gas Corporation (ONGC) was set up in 1956 with significant
contribution in industrial and economic growth of the country, is a leading National Oil
Company of India engaged mainly in exploration, development and production of crude
oil, natural gas and some value added products. It was subsequently converted into a
public limited company in Jun.'93 following new liberalized economic policy adopted by
the Government of India in July, 1991 sought to deregulate and delicense the core sector
(including petroleum sector) with partial disinvestment of Govt. equity in Public Sector
Undertakings and other measures. The company is developing a 740 MW Power Plant at
Palatana in Tripura Primarily to monetize idle gas. The project is scheduled to be


completed by 2008. The company is also taking initiatives to develop non-conventional
energy sources and has planned to set up two Wind Power Projects of 50 MW each at
Gujarat and Karnataka with approximate investment of Rs.5000 Million

Table:4.18
Date Cls- Return (RP - RP') (Rm - (RP - (RP - RP')2 (Rm - Rm')2
price RP Rm') RP')*
(Rm -
Rm')
2005 783.3 43.3643 21.4063 28.4584 609.189 458.2296 809.8811
0
2006 870.0 11.0749 -10.8831 -31.3579 341.271 118.4418 983.3221
5 2
2007 1236. 42.11 20.152 -2.0875 -42.0673 406.103 4.3577
5
2008 694.3 6.18 -15.778 2.9029 -45.8019 248.945 8.4269
5
2009 1096 7.07 -14.888 2.0841 -31.021 221.653 4.3437
Total 109.79 831.563 1453.372 1810.331732
4
RP'= ∑Ri
N
109.79÷5

RP' = 21.958
Rp2= ∑(Rp- RP')2
N-1

σRp2= 2.078

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=0.80
σei 2=σi2 -ßi2 σm2 = 1.278



RANBAXY LABORATORIES:-
Incorporated in Jun.'61 as a private limited company, Ranbaxy Laboratories
(RLL) manufactures and markets pharmaceutical dosage forms (for human health care),
animal health care products, bulk drugs and intermediates, diagnostics, laboratory
chemicals and reagents. It is the largest exporter of bulk drugs and pharmaceutical dosage
forms in India. The company has established a wholly owned subsidiary in Sweden
under the name of Ranbaxy Pharma AB. This Subsidiary would manage operations in the
territories of Sweden, Norway, Denmark & Finland.
During the year, the company has acquired Terapia SA (Romania), Ethimed (Belgium),
Allen(Italy), Mundogen (Spain) and Sentek PLC's Proprietary Technology. And also the
company has entered into an agreement for acquisition on 100% Equity stake in Bio-Tabs
Pharmaceuticals (Proprietary) Ltd (SA) and the transaction is expected to be complete
sometime in second quarter of 2007.
Table :4.19
Date Cls- Return RP (RP - (Rm - (RP - RP')* (RP - RP')2 (Rm - Rm')2
price RP') Rm') (Rm - Rm')
2005 391.8 -42.0888 -39.788 28.4584 -1132.3255 1583.148 809.8811
5
2006 425.9 8.1412 10.44 -31.357 -327.3765 108.99 983.3221
5 9
2007 613.7 8.7023 11.002 -2.0875 -22.967 121.04 4.3577
0
2008 180.9 6.130 8.43 2.9029 24.47 71.06 8.4269
0
2009 360 7.60 9.90 2.0841 20.633 98.01 4.3437
Total -11.515 1437.566 1982.248 1810.331732

RP'= ∑Ri
N
-11.515÷5

RP' = -2.30

Rp2= ∑(Rp- RP')2
N-1



σRp2= 4.956

βp = ∑( RP - RP')*(Rm - Rm')
∑(Rm - Rm')2 =0.79
σei 2=σi2 -ßi2 σm2 =4.166

RELIANCE INDUSTRIES:-
Reliance Industries Ltd (RIL) started its business operation in 1966 as a small
textile manufacturer. In May 8, 1973 RIL was incorporated and adopted its current name
in 1985. Initial business was the manufacturing of textiles products. Over the years, the
Company has transformed into a petrochemical major.
RIL is the largest private sector business enterprise in India. It's operations capture value
addition at every stage, from the production of crude oil and gas to polyester, polymer
and chemical products, and finally to the production of textiles. The company operates
mainly in India but has business activities and customers in more than 100 countries
around the world. It has production facilities at three major locations in India and a
further four locations in Europe. It also has exploration and production interests in India,
Yemen and Oman.
RIL is the world's largest producer of Polyester Fibre & Yarn. The Company is also the
world's - 4th largest producer of paraxylene (PX), 5th largest producer of mono ethylene
glycol (MEG), 7th largest producer of Purified terephthalic acid (PTA) & largest
producer of Polypropylene(PP). Within the country, the market share of the company is in
a leading position for all its major businesses in India

Table :4.20
Date Cls- Return RP (RP - RP') (Rm - (RP - RP')* (RP - RP')2 (Rm - Rm')2
Price Rm') (Rm –
R.m')
2005 604.5 15.27 -53.82 28.4584 -1531.63 2896.59 809.8811
2006 519.7 -14.01 -83.08 -31.357 2605.21 6902.28 983.3221
5 9
2007 2134. 310.69 241.62 -2.0875 -504.38 58380.22 4.3577
6



2008 1500 30.6 -38.47 2.9029 -111.67 1479.94 8.4269
2009 1087 2.82 -68.25 2.0841 -138.072 4389.06 4.3437
Total 345.35 0 319.458 74048.09 1810.331732

RP'= ∑Ri
N
345.35÷5

RP' = 69.07

Rp2= ∑(Rp- RP')2
N-1

σRp2= 185.12
βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=0.176
σei 2=σi2 -ßi2 σm2 =184.94

STATE BANK OF INDIA:-
State Bank of India's (SBI) origin goes back to in the first decade of the nineteenth
century with the establishment of the Bank of Calcutta in Calcutta on 2 June 1806. Three
years later the bank was re-designed as the Bank of Bengal on 2 January 1809. It was the
first joint-stock bank of British India sponsored by the Government of Bengal. Two other
banks the Bank of Bombay on 15 April 1840 and the Bank of Madras on 1 April 1843
started its operations. These three banks remained at the apex of modern banking in India
till their amalgamation as the Imperial Bank of India on 27 January 1921. This new bank
took on the triple role of a commercial bank, a banker's bank and a banker to the
government.



The Bank is actively involved in non-profit activity called community services banking
apart from its normal banking activity. All the branches and administrative offices
throughout the country sponsor and participate in large number of welfare activities and
social causes. It reflects that the bank touches the lives of people anywhere in many ways.

Table :4.21
price RP') Rm') (Rm -
Rm')
2005 907.4 39.08 -1.18 28.4584 -33.58 1.3924 809.8811
5
2006 1245. 37.29 -2.97 -31.3579 93.133 8.821 983.3221
9
2007 2371 90.30 50.04 -2.0875 -104.458 2504 4.3577
2008 1214 23.24 -17.02 2.9029 -49.407 289.68 8.4269
2009 1278 11.392 -28.868 2.0841 -60.164 833.36 4.3437
Total 201.30 -154.476 3637.25 1810.331732

RP'= ∑Ri
N
201.30÷5
RP' = 40.26

Rp2= ∑(Rp- RP')2
N-1

σRp2= 9.09

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=-0.085
σei 2=σi2 -ßi2 σm2 = 9.175



TATA MOTORS:-
Tata Motors Ltd (Formerly known as Tata Engineering and Locomotive Company
Ltd), Controlled by the House of Tatas, is the fifth-largest manufacturer of medium and
heavy commercial vehicle and the second largest medium and heavy bus manufacturer in
the world. The commercial diesel vehicles, which were called Tata Mercedes Benz, are
now sold under the name Tata after the expiry of the collaboration agreement with
Daimler-Benz, Germany. Apart from manufacturing light, medium and heavy commercial
vehicles, it also manufactures passenger cars, utility vehicles, excavators and machine
tools. The manufacturing units are located at Jamshedpur, Pune, Lucknow and Pant Nagar
in Uttarakhand.
In 2006-07, Tata Motors initiated steps for establishing a Small Car plant in Singur, West
Bengal with a capacity of 250,000 vehicles per annum. The company remains committed
to launching its new small car in the first half of 2008. The company also setting up a
green-field manufacturing facility in Uttarakhand. This plant will have manufacturing
capacity of 225,000 vehicles per annum.

Table :4.22
price RP') Rm') (Rm - Rm')
2005 653 29.26 16.71 28.4584 475.539 279.224 809.8811
2006 900.2 37.86 25.31 -31.3579 -793.668 640.59 983.3221
5
2007 742.1 -17.56 -30.11 -2.0875 62.855 906.61 4.3577
2008 356 12.9 0.35 2.9029 1.016 0.1225 8.4269
2009 812 0.28 -12.27 2.0841 -25.572 150.55 4.3437
Total 62.74 -279.83 1977.096 1810.331732

RP'= ∑Ri
N



62.74÷5

RP' = 12.55

Rp2= ∑(Rp- RP')2
N-1

σRp2= 4.94

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
= -0.154
σei 2=σi2 -ßi2 σm2 = 5.0945

TATA STEELS LTD:-
Tata Steel Ltd (formerly Tata Iron and Steel Company (TISCO)) was incorporated
in 1907. Over the Years, TISCO has diversified to manufacture, apart from saleable steel,
Welded-steel tubes, cold-rolled strips, seamless tubes, carbon and alloy Steel bearing
rings; alloy steel ball bearing rings, bearings, Ferro Manganese, Ferro chrome,
metallurgical machinery, etc.
The companies subsidiaries include Tata Refractories, Tata Pigments, Kalimati
Investment, Tata Korf, Tata Incorporated, Stewarts & Lloyds of India, Tata SSL, TM
International logistics Ltd, Lanka Special Tubes Ltd, Jamshedpur Utilities & Services Co
Ltd, The Indian Steel and wire products Ltd, NatSteel Asia Pte Ltd, Sila Eastern Ltd,
Hooghly Metcoke & Power company Ltd.



The company acquired Rawnet Ferrous Industries Pvt Ltd, in Orissa, a Ferro Alloys plant
with a capacity of 50,000 tpa of high carbon chrome
Table :4.23

Date Cls- Return (RP- (Rm- (RP - RP')* (RP - (Rm - Rm')2
price RP RP') Rm') (Rm - RP')2
Rm')
2005 336.1 -1.33 -44.868 28.4584 -1276.87 2013.137 809.8811
1
2006 426.2 29.82 -13.718 -31.3579 430.1676 188.18 983.3221
6
2007 934.8 119.30 75.762 -2.0875 -158.153 5739.88 4.3577
2008 698.9 29.9 -13.638 2.9029 -39.589 185.99 8.4269
5
2009 737 40 -3.538 2.0841 -7.3735 12.517 4.3437
Total 217.69 -1051.817 8139.704 1810.331732
9

RP'= ∑Ri
N
217.69÷5

RP' = 43.538

Rp2= ∑(Rp- RP')2
N-1

σRp2= 20.349

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
= -0.581
σei 2=σi2 -ßi2 σm2 = 20.93

MARUTI UDYOG:



• Maruti Udyog Limited (MUL), established in 1981, had a prime objective to meet
the growing demand of a personal mode of transport, which is caused due to lack
of efficient public transport system. The incorporation of the company was
through an Act of Parliament. Suzuki Motor Company of Japan was chosen from
seven other prospective partners worldwide. Suzuki was due not only to its
undisputed leadership in small cars but also to commitments to actively bring to
MUL contemporary technology and Japanese management practices (that had
catapulted Japan over USA to the status of the top auto manufacturing country in
the world). A licence and a Joint Venture agreement was signed between
Government of India and Suzuki Motor Company (now Suzuki Motor
Corporation of Japan) in Oct 1982.

In 2001, MUL became one of the first automobile companies, globally, to be
honoured with an ISO 9000:2000 certificate. The production/ R&D is spread across 297
acres with 3 fully-integrated production facilities. The MUL plant has already rolled out
4.3 million vehicles. The fact says that, on an average two vehicles roll out of the factory
in every single minute. The company takes approximately 14 hours to make a car. Not
only this, with range of 11 models in 50 variants, Maruti Suzuki fits every car-buyer's
budget and any dream

Table :4.24
RP'= ∑Ri
Date Cls- Return (RP - (Rm - (RP - (RP - (Rm - Rm')2
price RP RP') Rm') RP')* RP')2
(Rm -
Rm')
2005 578.35 97.2 60.68 28.4584 1726.86 3682.06 809.8811
2006 972 32.12 -4.40 -31.3579 137.974 19.36 983.3221
2007 741 31.4 -5.12 -2.0875 10.688 26.214 4.3577
2008 58.60 19.6 -16.92 2.9029 -49.117 286.26 8.4269
2009 1391 2.28 -34.24 2.0841 -71.359 1172.37 4.3437
7
Total 182.6 1755.046 5186.29 1810.331732
7


N
182.6÷5

RP' = 36.52

Rp2= ∑(Rp- RP')2
N-1

σRp2= 12.965

βp = ∑ (RP - RP')*(Rm - Rm')
∑(Rm - Rm')2
=0.969
σei 2=σi2 -ßi2 σm2 = 11.996

TCS (Tata Consultancy Service):

TCS is a leading provider of highly flexible financial management software that
powers mid-sized businesses.

Company mission is to maximise the business success of our customers through the
installation, maintenance, and support of superior financial management software
solutions.

We have set a number of strategic and tactical objectives that reflect our mission, aim and
collective goals:

• to establish the company as the best global organization for large-scale
deployment of financial management software solutions on the Caché platform.



• to establish a fully object-oriented component based application, which will
enable us to deliver robust software quicker and more efficiently than any
competitor.
• to ensure that customers can operate their business software solutions on
infrastructures that match their needs.

Expertise

• With a focus on the customer, we have the business and accounting skills
necessary to understand and implement the structure best suited to the customers
needs.
• With a focus on Inter Systems Caché, we have the technical expertise to
implement the latest innovations to ensure the maximum return on investment.
• Our people are our biggest asset, and at TCS we have individuals who combine
skills, backgrounds and cultures to provide a cohesive and outstanding team.

Table :4.25

Date Cls- Return (RP - (Rm - (RP - (RP - (Rm - Rm')2
price RP RP') Rm') RP')* RP')2
(Rm -
Rm')
2005 1569.21 43.4542 20.0712 28.4584 571.194 402.85 809.8811
2006 1650.75 49.5281 26.1415 -31.357 -819.855 683.57 983.3221
9
2007 1330 -21.07711 -44.46 -2.0875 92.81 1976.69 4.3577
2008 727.35 27.6 4.217 2.9029 12.24 17.78 8.4269
2009 778 17.14 -5.973 2.0841 -12.448 35.677 4.3437
Total 116.915 -156.059 3116.56 1810.331732
7


A study on construction of optimal portfolio using sharpe’s single index model

A study on construction of optimal portfolio using sharpe’s single index model

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