naresh acl 1 proj

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1.1 PETROLEUM INDUSTRY IN INDIA

The petroleum industry in India stands out as an example of the strides made by

the country in its march towards economic self-reliance. The India Petroleum

Industry is a case in point for exhibiting the giant leaps India has taken after its

independence towards its march to attain self-reliant economy. The testimony of

its vigour and success during the past five decades is the significant increase in

crude oil production from 0.25 to 33 million tonnes per annum and refining

capacity from 0.3 to 103 million metric tonnes per annum (MMTpa).

The world at present is experiencing a lot of changes of mammoth proportions.

The Petroleum Industry in India is one of the harbingers of huge economic

growth. The arena for business has now gone global since trade boundaries are

fast dissolving. These developments present India with tremendous opportunities

in the future to be one of the major players in the export of petrochemical

intermediaries.

The main problems with the Petroleum Industry in India are related to

infrastructural developments. The lack of proper storage facilities, enhancements

in refining capacities, and fluctuating import prices plays important role in the

development of the sector. The target of improvement for the growth of the

economy for India should be in the area of the petrochemical sector. The need for

intermediary products for the manufacturing of the end use products is an

important sector to tap in. With the per capita consumption for the petrochemical

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products in India being low and the production of these products being high, India

may become one of the leading exporters of such intermediary products.

The long-term energy strategies of India have to emphasize on the methods of

using energy effectively and efficiently, and to enhance energy self-sufficiency.

To lift the Indian economy to enhanced economic standards innovation,

diplomacy, creativity and vision are the need of the hour

1.2 NEED FOR THE STUDY

Petroleum Industry in India has come a long way and is a vital sector for the

energy security and economy of the country because the investments made are

large and the returns are fair.The petroleum industry in India has good potential

for growth and hence investment in the stocks of petroleum firms is a good option

to gain good return . At present there are many petroleum firms operating in India

and choosing the stocks of the firms which can benefit the investor is essential.

Hence the significance of the study is, from the particular stocks, to identify the

stocks with high risk and low risk and the stocks yielding high returns and low

returns and make suggestions accordingly.

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1.3 OBJECTIVES

1. The purpose of doing study is to understand the security pricing theories

2. viz, CAPM and SML by practical application

3. To find the pricing status of securities of petroleum firms.

4. Test of asset pricing theories such as CAPM.

5. The study deals with the return and risk of the stocks.

1.4 SCOPE

1. The study is based on the securities listed on the national stock exchange

of India Ltd.

2. The studys scope is confined to securities of petroleum and natural gasFirms like:

Oil and Natural Gas Corporation. (ONGC)Bharat Petroleum Corporation Ltd. (BPCL)Hindustan Petroleum Ltd (HPL)Reliance Petroleum Ltd.(Rel.Petro.)

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1.5 METHODOLOGY

Research design:

Research is conducted on the equity shares listed in the National Stock Exchange.

Research consists of analyzing the equity shares and calculation of return and

betas of the stocks.

Data collection methods and techniques:

The collection of data is through secondary research.

Secondary research:

1. Internal secondary data: The data generated within the organization such as

financial reports, share prices at different time periods.

2. External secondary data: The data generated by sources outside the

organization such as government reports, data collected by syndicate.

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2.1 Oil and gas - India is hungry for investments

By Dr. Uday Lal Pai

Exclusively for InvestorIdeas.com

posted October 23, 2006

Though the rising crude oil prices in recent times have been posing major

challenges for the Oil Refinery and Marketing Companies, the investment

potential that the country hold is simply tremendous.

India ranks sixth in the world in terms of petroleum demand and by 2010, India is

projected to replace South Korea and emerge as the fourth-largest consumer of

energy, after the United States, China and Japan.

The the current investment wave, it appears that day would not take long in

arriving. With clear policies in place, India is becoming an attractive destination

for global companies in the oil and gas government of India is working on

increasing the country's investment potential to US$ 250 billion. And with sector.

The government has also decided to rope in public sector oil companies to anchor

the proposed investments in the country.

Companies like Oil and Natural Gas Corporation (ONGC), Indian Oil (IOCL),

Hindustan Petroleum (HPCL), Bharat Petroleum (BPCL) and Gail could take a

lead in the seven zones identified by the government.

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2.2 Oil & gas: Nothing to cheer about5 Jan 2009, 1710 hrs IST, ET Bureau

The December '08 quarter is expected to be somber for India's oil and gas majors.

While companies like ONGC and Cairn India could be hit by over 55%

decline in the crude oil prices, refiners could be hit by inventory losses besides

low gross refining margins. There has also been a sharp fall in the prices of

downstream petrochemicals and polymers, which is likely to hit integrated players

such as Reliance Industries and Gail India.

ONGC's average gross realization is likely to crash to $61 per barrel, which is

nearly half of September '08 quarter. Considering the stagnation in ONGC's crude

oil production, it's expected to report a sharp 30% fall in net profit during the

quarter. Reliance Industries is expected to post double-digit gross refining

margins (GRMs) despite the fall in crude oil prices in the December '08 quarter.

Profitability of public sector oil marketing companies could be under pressure

from inventory and low GRMs. We expect BPCL to post losses for thirdconsecutive quarter. Gail could take a hit on its petrochemicals and liquid

hydrocarbons business, while transmission business is likely to post healthy

growth in the December '08 quarter.

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http://economictimes.indiatimes.com/Features/Investors_Guide/Oil__gas_Nothing_to_cheer_about_/articleshow/3938326.cmshttp://economictimes.indiatimes.com/Features/Investors_Guide/Oil__gas_Nothing_to_cheer_about_/articleshow/3938326.cmshttp://economictimes.indiatimes.com/Features/Investors_Guide/Oil__gas_Nothing_to_cheer_about_/articleshow/3938326.cmshttp://economictimes.indiatimes.com/Features/Investors_Guide/Oil__gas_Nothing_to_cheer_about_/articleshow/3938326.cmshttp://economictimes.indiatimes.com/Features/Investors_Guide/Oil__gas_Nothing_to_cheer_about_/articleshow/3938326.cms


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2.3 Investopedia explainsSecurity Market Line SML

The SML essentially graphs the results from the capital asset pricing model

(CAPM) formula. The x-axis represents the risk (beta), and the y-axis represents

the expected return. The market risk premium is determined from the slope of the

SML.

The security market line is a useful tool in determining whether an asset being

considered for a portfolio offers a reasonable expected return for risk. Individual

securities are plotted on the SML graph. If the security's risk versus expected

return is plotted above the SML, it is undervalued because the investor can expect

a greater return for the inherent risk. A security plotted below the SML is

overvalued because the investor would be accepting less return for the amount of

risk assumed

2.4 Beta

What DoesBeta Mean?

A measure of the volatility, or systematic risk, of a security or a portfolio in

comparison to the market as a whole. Beta is used in the capital asset pricing

model (CAPM), a model that calculates the expected return of an asset based on

its beta and expected market returns..

Also known as "beta coefficient".

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2.5 EXPECTED RETURNS

Historical or ex-post returns: the proper measurement of return generated by an

investment must account for both the price change and the cash flow derived

during the period the asset was held i.e. the return from the investment includes

both current income and capital gain or losses due to appreciation or depreciation

in the prices of the security. Then the income is expressed as a percentage of the

total annual income and capital gain as percentage of investment.

Any investment always expects a good rate of return from his investment. Rate

of return is defined as the total income the investor receives during the holding

period of the assets. The return is calculated by using the formula:

Ending period value- beginning period value dividendRETURNS= beginning period value

The best proxy for return is the future expected return. Therefore the basic

equation for measuring return for annual period is given as:

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Ri= (Pi-Po) +DiPo

Where:

Po is the beginning price of the security.Pi is the ending price of the security.

Di is the amount of dividend.

Rate of return can be stated semi annually or annually or to compare different

investment alternatives available. If the investment alternative is a stock the investor

gets a dividend and the capital appreciation. If it is a debt instrument, the investor

gets the interest and capital appreciation and the debt instrument is redeemed above

the face value.

2.6 EXPECTED RISK

In the context of security analysis risk is interpreted essentially in terms of

variability of security returns and the most common measures of a security are the

standard deviation and variance of returns.

Standard deviation commonly denoted as of return. It measures the extent of

deviation of return from the average value of return. In other words standard

deviation of return is the square root of the average of square of deviation of the

observed return from their expected value of return.

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The square of standard deviation is called variance; hence variance of security

returns is the average value of the square of deviations of the observed returns

from the expected value of returns.

Ex:-A step increase in the crude oil prices is almost certain to affect the entire

market adversely hence no amount of diversification can make a portfolio totally

free from such risk even though diversification may reduce this risk up to a point.

Therefore this level of systematic risk below which the riskness of a portfolio

cannot be reduced is called unavoidable risk.

The Non-Diversifiable Risk of a Portfolio: - To understand why a certainamount of risk is always present in a portfolio or the nature of the risk that cannot

be diversified away, consider the case of n securities, the proportion of

investments in each security being 1/n-1. The variance of the portfolio return will

be given by

1Variance (X) = ------------ { (Rx Rx )}

N 1

The residual risk in a well diversified portfolio equals the average covariance of

the securities in the portfolio representing the market risk. This is the amount of

risk that cannot be diversified always no matter how much the reducing risk by

diversification.

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Risk Decomposition: - The total risk of a security is measured in terms of

variance or standard deviation of its returns. Apart from this we know that the risk

comprises of both systematic and unsystematic components. The way or method

to split the total risk into the systematic or unsystematic risk components is

known as risk decomposition. And this is relatively simple.

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2.7 CAPITAL MARKET THEORY

Capital market theory (CMT) is an economic theory about asset valuation

that is similar in many respects to the arbitrage pricing theory (APT) of both

theory consider all investments thet is thousands of stocks, bonds, options,

commodities, diamonds golds, art objects and other things all at same time . Both

APT and CMT explain how the market price of all assets is determined. Some

important parts of both APT and CMT is pricing of financial assets. Total risk,systematic or undiversifiable risk unsystematic or diversifiable risk, and the

efficient frontier were introduced in this theory it pulls these and some other new

ideas as well together and shows how they interact. The main conclusion that both

APT and the CMT have in common is that it is the undiversifiable (or systematic)

portion of an assets total risk that causes risk averse inverse investors to demand

higher rates of returns.

The risk averse and rational investor would like to maximize expected return

for a given risk or would like to minimize risk for a given expected return.

Portfolio theory provides a normative approach for the analysis and identification

of such minimizing portfolios.

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One important implication of the normative approach provided by portfolio

theory is pricing of financial assets. If all investors act in a manner that

maximized expected returns for a given level of risk. Capital market theory relates

to the pricing of financial assets and equilibrium relation between risk and

expected return.

Capital market theory is an extension of the portfolio theory of markovitz.

The portfolio theory explains how rational investors should build efficientportfolio based on their risk return preference. Capital market assets pricing

model (capm) incorporates a relationship explaining how assets should be priced

in the capital market.

The capital market theory provides the following two models to maximize

expected return they

1) MARKOWITZ PORTFOLIO THEORY

2) CAPITAL ASSET PRICING MODEL (CAPM)

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2.7.1 MARKOWITZ PORTFOLIO THEORY

As with any model building exercise Markowitz portfolio is also based on few

assumptions. They are

1) Investor is risk averse and thus has preference for expected return and

dislike for risk this is general behaviors of rational investor, an investor would

like to get highest return possible for given risk or would like to minimize the risk

for a given expected rate of return

2) Investor act as if they make investment decision on the basis of the expected

return and variance standard deviation about security returns distribution i.e.

investors measures their preference and dislike investment through expected

return and or standard deviation of security return

Markowitz model of portfolio analysis generates an efficient frontier which is a

set of efficient portfolios. A portfolio is said to efficient if it offers maximum

expected return for a given level of risk or offers minimum risk for a given level

of expected returns.

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2.7.2 CAPITAL ASSET PRICING MODEL (CAPM)

Capital asset pricing model (CAPM): The CAPM was developed in mid 1960s.

The model has been attributed to William Sharpe but John linter and Yam Mossin

made similar independent derivation consequently. The model is often referred to

as Sharpe Linter-Mossin (SLM) CAPM. The CAPM explains the relationship that

should exist between securitys expected returns and their risk in terms of the

mean and standard deviation about security returns.

Definition:

The Capital asset pricing model is a linear relationship in which the expected rate

of return from an asset is determined by that assets undiversfiable (systematic)

risk. The CAPM is represented mathematically by the formula below:

E (ri) =R+ [E (rm) R] bi

Where

(bi)= independent variable representing the systematic risk of the ith asset that

determines the dependent variable.

E (ri) = is the expected rate of return for the ith asset,

The CAPM intersects the vertical axis at the risk less rate, R; and the quantity

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[E (rm) R] is the slope of the CAPM. The risk less interest rate, R is the

appropriate rate of return for an asset with zero risk in the CAPM.

Diversifiable risk can easily eliminated by simple diversification. Therefore

investors will tend to focus only on assets undiversifiable risk when they search

for asset that will minimize their risk exposure at whatever level of expected

return they seek. In seeking the most desirable assets investors will bid up the

prices of assets with low systematic risk (that is, low beta coefficients). In

contrast, assets with high beta coefficients will experience low demand andmarket prices that are low relative to assets expected income. Stated differently,

assets with high levels of systematic risk must also yield high expected returns to

induce investors to buy assets with large amount of risk that cannot be eliminated

by diversification.

ESTIMATING BETA

The systematic risk cannot be diversified away, unsystematic risk can be. Hence

the relevant risk is systematic risk also referred to as non-diversifiable risk. To

calculate this systematic risk beta, of a stock we have to calculate the slope of the

regression as follows

Ri= + Rm + e

Where

Ri is dependant variable and represents the return on security.

Rm is independent variable representing the return on the market portfolio, and

e is the error term.

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To calculate beta the following model is used

i = im

m

Where i = estimate of the beta of stock i

im = variance between the stock i and the return on the market portfolio.

m = variance of the return on market portfolio.

The CAPM or the SML as it is also called. This graphically depicts the result ofprice adjustments from the risk averse trading described above. In passing, it is

interesting to know that the CAPM in the figure is identical to the single factor

arbitrage pricing line shown in figure when the only risk factor used to develop

arbitrage pricing model as the market portfolio.

The CAPM is an extension of Markovitz portfolio theory. The assumptions on

which Markovitz is based are also applicable to CAPM also. The assumptions of

CAPM are:

1. Investors make their investment decisions on the basis of risk return

assessments measured in terms of expected returns and standard deviation of

returns.

2. The purchase or sale of a security can be undertaken in infinitely divisible

units.

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3. Purchases and sales by a single investor cannot affect prices. This means

that there is perfect competition where investors in total determine prices by their

actions.

4. There are no transaction costs. Given the fact that transaction costs are

small. They are probably of minor importance in investment decision making, and

hence they are ignored.

5. There are no personal income taxes. Alternatively, that tax rates on dividend

income and capital gains are the same, thereby making the investors indifferent to

the form in which the returns on the investment is received.6. The investors can lend or borrow any amount of funds desired at a rate of

interest equal to the rate for risk less securities.

7. The investors can sell short any amount of any share.

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Figure 2.1: GRAPHICAL REPRESENTATION OF CAPM

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2.8 SECURITY MARKET LINE (SML)

SECURITY MARKET LINES: - one of the contributions of modern portfolio

theory to the field of investment is the concept of security market line (SML).

The SML simply represent the average or normal trade off between risk and

return for a group of security.

Risk is measured typically in terms of security betas.

Ex-post SML: - In the Ex-post (SML) average historical rates of return for

security are plotted against their betas for a particular time period. Then a straight

line is fitted to the plots by regression and this is called the SML.

Hence the SML represents the normal or average trade off between return and

risk.

The securities which plot above the ex-post SML generate above the normal

returns and the securities which plot below this SML generate below average

returns.

The amount by which a security return differs from the normal returns for its level

of risk is simply the vertical distance of SML. The vertical distance is called the

securities abnormal return or its alpha .

The securities which plot above the ex-post SML generate normal returns for their

risk which are measured by their beta for the particular time period used in

constructing the SML.

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In case of portfolio involving complete diversification where the unsystematic

risk tends to be zero, there is only systematic risk measured by (). The only

dimension of a security which concerns us is expected return and betas.

The equation of security market line (SML) is

Ri= + i (Rm-Rf)

Or

Ri=Rf + i (Rm-Rf)

Where = Rf = risk free return

Rm= market return

i= beta

Covariance is to be as much as possible negative interactive effect among the

securities within the portfolio and co-efficient of correlation to be 1 (negative).

So that the overall risk of the portfolio as a whole is nil or neglible. Then the

securities have to be combined in a manner that standard deviation is zero.

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For building up an efficient set of portfolio, we need to look into these important

parameters:

1. Expected return.

2. Variability of return as measured by standard deviation from the mean.

3. Covariance or variance of one asset return to other asset return.

In general the higher the expected return the lower is the standard deviation or

variance and lower is the correlation the better will be the security for the investor

choice.

Whatever is the risk of the individual securities in isolation, the total risk of allsecurities may be lower, if the covariance of their returns is negative or neglible.

Application:

1. Evaluating the performance of portfolio manager.

2. Test of asset pricing theories such as CAPM.

3. Test of Market efficiency.

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Figure 2.2: GRAPHICAL REPRESENTATION OF SML.

Normal return N (ri) = ro + ri imro=intercept of Ex-post SML.ri= slope of ex-post SML. = ri- N (ri) + > ri- (ro+ riim)

If > 0 then security has above normal returns.< 0 then security has below normal returns.

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3.1 Introduction of the company

Stock Trading Centre (STCprofit) is a franchise of India Infoline. STC was

established in the year 2006 by expert professionals keeping in view the

challenging needs arising out of stock market broking business in India with a

Capital of Rs.200000.

STC services

1. Providing investment information and knowledge.

2. Online/ offline trading. (NSE, BSE, NCDEX & MCX).

3. Money making ideas and advice

4. Monitory plan for clients growth.

5. Individual portfolio management.

6. Personal attention and service.

7. Financial planning.

8. Assistance for income tax returns filing and processing PAN- card etc.

Total number of customers served at present is 320-350.

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Indian Infoline was founded by Mr. Nirmal Jain in the year 1995 as a company

offering various kinds of financial services like equity research, equity and

derivatives trading, commodity trading, portfolio management, mutual funds, life

insurance, etc.

Currently India Infoline operates from over 785 locations across 360 cities

through its own offices and various franchises and channel partners across the

country.

The aim of the company is to bring its financial services to every household in the

country, for this 5paise trading softwarehas been developed using which retailinvestors can trade directly with the stock exchanges (BSE & NSE) at their

convenience from their home itself.

India Infoline provides its customers a wide range of technical analysis, live

quotes from NSE & BSE, intraday charts and various tips and suggestions which

would help the retail investors in making investment decisions on their own.

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4.1 CALCULATION OF RETURNS, VARIANCE AND

STANDARD DEVIATION

Calculation of monthly return:

Return (Rx)= Closing- opening* 100Opening

Calculation of average return:

Rx

Mean return (Rx) = -------------

N

Calculation of variance:1

Variance (x) = ------------- { (Rx - Rx) }N-1

Calculation of standard deviation:

S.D (x) = variance

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Calculation of Returns and Standard deviation ofOil and Natural Gas Corporation

Month Opening Closing Returns (Rx-Rx) (Rx-Rx)Jan-08 880 911.4 3.568182 26.7842 717.3934

Feb-08 912 788.05 -13.591 -13.591 184.7155

Mar-08 788.05 880.8 11.76956 11.76956 138.5225

Apr-08 875 913.85 4.44 4.44 19.7136

May-08 923.85 922.3 -0.16778 -0.16778 0.028149

Jun-08 944.45 905.55 -4.1188 -4.1188 16.96451

Jul-08 906 914.55 0.943709 0.943709 0.890586

Aug-08 914 860 -5.9081 -5.9081 34.9056

Sep-08 860 971 12.90698 12.90698 166.59

Oct-08 962 1250 29.93763 29.93763 896.2617Nov-08 1268.9 1168.25 -7.93207 -7.93207 62.91769

Dec-08 1160 1238 6.724138 6.724138 45.21403

Jan-09 1240 1018 -17.9032 -17.9032 320.5255

Feb-09 995.05 1012 1.703432 1.703432 2.901681

Mar-09 1024.4 986 -3.74854 -3.74854 14.05152

Apr-09 1000 1031.3 3.13 3.13 9.7969

May-09 1044 861.6 -17.4713 -17.4713 305.2451

Jun-09 870 804 -7.58621 -7.58621 57.55054

Jul-09 829.95 992 19.52527 19.52527 381.2363

Aug-09 980.2 1023.75 4.442971 4.442971 19.73999

Sep-09 1019 1034.8 1.55054 1.55054 2.404174

Oct-09 1064.4 684 -35.7384 -35.7384 1277.236

Nov-09 700 687.05 -1.85 -1.85 3.4225

Dec-09 724.85 668 -7.843 -7.843 61.51268

= -23.216 = 4739.741

Table 4.1: Calculation of returns and standard deviation of ONGC

Mean return (Rx) = -0.96733

Variance (x) = 174.3417

Standard deviation (x) = 13.203

Calculation of mean returns and standard deviation of

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Bharat Petroleum Corporation limited.9

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Month

Opening

Closing

Return (RxRx)

(Rx-Rx)

Jan-08

338 360.4 6.627219

4.573581

20.91764

Feb08

355 311.25

-12.3239 -14.3776

206.7149

Mar08

314.8 302.75

-3.82783 -5.88147

34.59163

Apr0

8

302.5 333.2

5

10.1652

9

8.111

651

65.7988

9May08

335 361.2 7.820896

5.767258

33.26126

Jun-08

355 340.45

-4.09859 -6.15223

37.84993

Jul-08

341 321.3 -5.77713 -7.83076

61.32086

Aug08

320 311 -2.8125 -4.86614

23.6793

Sep-08

310.05

362 16.75536

14.70172

216.1407

Oct-08

361 345.9 -4.18283 -6.23646

38.89348

Nov08

347.6 389 11.91024

9.856604

97.15264

Dec-08

393.9 518 31.50546

29.45182

867.4097

Jan-09

529.7 357 -32.6034 -34.657

1201.108

Feb-09

369.9 466.85

26.20979

24.15615

583.5195

Mar09

451.3 404 -10.4808 -12.5345

157.113

Apr09

408.4 409 0.146915

-1.90672

3.635593

May09

400.55

362 -9.62427 -11.6779

136.3735

Jun09

362.4 221.2 -38.9625 -41.0161

1682.321

Jul09 232 326 40.51724

38.4636

1479.449

Aug09

325 302 -7.07692 -9.13056

83.36714

sep-09

300 358.85

19.61667

17.56303

308.46

Oct-09

358 286 -20.1117 -22.16

54

491.3036

Nov09

290 363 25.17241

23.11878

534.4778

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Table 4.2: Calculation of returns and standard deviation of BPCL

Mean return (Rx) = 2.0536

Variance (x) = 363.9991


Calculation of Returns and Standard deviation ofHindustan petroleum ltd

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Month

Opening

Closing

Returns

(Rx-Rx)((Rx-Rx)

Jan-08

280.00

312.100

11.46429

10.86512118.0508

Feb08

311.00

271.600

-12.6688 -13.268176.0393

Mar08

273.00

247.800

-9.23077 -9.8299496.62767

Apr08

250.00

270.100

8.04 7.44083255.36598

May08

273.95

294.700

7.574375

6.97520748.65351

Jun-08

294.00

270.650

-7.94218 -8.5413472.95457

Jul-08

265.50

257.650

-2.95669 -3.5558512.64409

Aug0

8

254.9

5

235.0

00

-7.82506 -8.4242370.9676

8Sep-08

237.60

266.000

11.95286

11.35369128.9064

Oct-08

255.00

239.400

-6.11765 -6.7168245.11561

Nov08

241.10

272.650

13.08586

12.48669155.9174

Dec-08

277.00

364.100

31.44404

30.84488951.4063

Jan-09

356.25

252.000

-29.2632 -29.8623891.7585

Feb-

09

255.0

0

301.2

00

18.1176

517.51848

306.897

1Mar09

300.00

256.000

-14.6667 -15.2658233.0457

Apr09

252.00

256.700

1.865079

1.2659111.602531

May09

260.00

247.900

-4.65385 -5.2530127.59416

Jun-09

247.50

172.050

-30.4848 -31.084966.2161

Jul-09

184.80

220.300

19.20996

18.61079346.3615

Aug0

9

218.0

0

202.0

00 -7.33945 -7.93862

63.0216

5Sep-09

197.50

242.400

22.73418

22.13501489.9586

Oct-09

241.50

190.000

-21.3251 -21.9242480.6714

Nov09

193.00

238.500

23.57513

22.97596527.8948

Dec-09

239.00

238.500

-0.20921 -0.808370.653467

=14.38

003

=6268.

325

31


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Table 4.3: Calculation of returns and standard deviation of HPL

Mean return (Rx) =0.5991Variance (x) = 272.5359


Calculation of Returns and Standard deviation ofReliance petroleum

Month

Opening

Closing returns Rx-Rx` (Rx-Rx`)2

Jan-08

62.85 65.3 3.89817 1.484852

2.204785

Feb08

65.3 66.85 2.37366 -0.03966

0.001573

Mar08

66.8 71.55 7.110778

4.69746 22.06613

Apr08

71.4 80.95 13.37535

10.96203

120.1661

May08 81.3 100.25 23.30873 20.89541 436.6184Jun-08

99.9 111.1 11.21121

8.797893

77.40292

Jul-08

112 111.65 -0.3125 -2.72582

7.430085

Aug08

110.9 115.9 4.508566

2.095248

4.390064

Sep-08

118.75

153.35 29.13684

26.72352

714.1467

Oct-08

154 247.25 60.55195

58.13863

3380.1

Nov08

250 217.4 -13.04 -15.4533

238.805

Dec-08

215 223.15 3.790698

1.377379

1.897174

Jan-09

223.8 161 -28.0608 -30.4741

928.67

Feb-09

162.9 174.25 6.967465

4.554146

20.74025

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Mar09

169 156.1 -7.63314 -10.0465

100.9312

Apr09

157.25

201.2 27.94913

25.53581

652.0775

May09

203.6 175.05 -14.0226 -16.4359

270.1392

Jun-09

203.6 170.5 -16.2574 -18.6707

348.5945

Jul-09

171 164.75 -3.65497 -6.06829

36.82413

Aug09

165 157 -4.84848 -7.2618 52.73378

Sep-09

156.6 143.2 -8.55683 -10.9702

120.3442

Oct-09

144.1 87.3 -39.4171 -41.8304

1749.782

Nov0

9

90 72.75 -19.1667 -21.58 465.695

8Dec-09

73.5 87.25 18.70748

16.29416

265.4998

=57.91964

=10017.26

Table 4.4: Calculation of returns and standard deviation of Reliance Petroleum Ltd.

Mean return (Rx) = 2.4133

Variance (x) = 417.3859


4.2. CALCUALTION OF COVARIANCES AND

CORRELATION OF COVARIANCE.

Muitiply the monthly returns of one stock with that of other companies stock.

Covariance has to be calculated for all stocks with that of other stocks.

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Formula for covariance:

Cov (ob) = 1 (Ro-Ro) ( Rb-Rb)

N-1

Correlation of coefficient:

= cov (ob) o b

Let:Ro= returns of ONGC

Rb= returns of BPCL

Rh=returns of HPL

Rr=returns of REL PETRO.

Covariance between the stocks of ONGC and BPCL

Month Ro-Ro

Rb-Rb

(Ro-Ro) (Rb-Rb)

Jan-08

4.53552

4.57358 20.7435

Feb08 -12.624

-14.37

8 181.498

Mar08

12.7369

-5.881

5 -74.912

Apr08

5.40733

8.11165 43.8624

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May08

0.79956

5.76726 4.61126

Jun-08 -3.1515

-6.152

2 19.3885

Jul-08

0.94371

-7.830

8 -7.39

Aug08 -4.9408

-4.866

1 24.0424

Sep-08

13.8743

14.7017 203.976

Oct-08 30.905

-6.236

5 -192.74

Nov08 -6.9647

9.8566 -68.649

Dec-08

7.69147

29.4518 226.528

Jan-09 -16.936

-34.65

7 586.947

Feb-09

2.67077

24.1561 64.5154

Mar09 -2.7812

-12.53

4 34.8609

Apr09

4.09733

-1.906

7 -7.8125

May09 -16.504

-11.67

8 192.731

Jun-09 -6.6189

-41.01

6 271.48

Jul-09

20.4926

38.4636 788.219

Aug09 5.4103

-9.130

6 -49.399

Sep-09

2.51787

17.563 44.2215

Oct- -34.771 - 770.715

35


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09

22.165

Nov09 -0.8827

23.1188 -20.406

Dec-

09 -6.8757

2.668

58 -18.348

=3038.69Table 4.5: Covariance between ONGC and BPCL

Calculation of covariance and correlation between stocks

ONGC and BPCL:Cov (ob) = 1 (Ro-Ro)( Rb-Rb)

N-1

= 1 (3038.69)

23

= 132.1168

Correlation of coefficient = cov (ob)

o b

= 132.1168

----------------------------

(13.20385)(19.07876)

36


37/76

= 0.524

Cov (ob) =covariance between ONGC and BPCL

o = Standard deviation of ONGC

b = Standard deviation of BPCL.

-50

-40

-30

-20

-10

0

10

20

30

40

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

time in months

returns

monthlyReturns of ONGC Monthly Returns of BPCL

Fig 4.1:GRAPH SHOWING MONTHLY RETURNS OF ONGC SECURITIESAND BPCL SECURITIES FROM JAN 2008 TO DEC 2009.

37


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Covariance between the stocks of ONGC and HPL

Month (Ro-Ro) (Rh-Rh) (Ro-Ro)( Rh-Rh)

Jan-08 4.535516 10.86512 49.27891

Feb08 -12.6237 -13.268 167.4906

Mar08 12.73689 -9.82994 -125.203

Apr08 5.407334 7.440832 40.23506May0

8 0.799558 6.975207 5.577082

Jun-08 -3.15147 -8.54134 26.91775

Jul-08 0.943709 -3.55585 -3.35569

Aug08 -4.94076 -8.42423 41.62213Sep-

08 13.87431 11.35369 157.5247Oct-

08 30.90496 -6.71682 -207.583

Nov08 -6.96473 12.48669 -86.9665Dec-

08 7.691472 30.84488 237.2425

Jan-09 -16.9359 -29.8623 505.7451

Feb-09 2.670766 17.51848 46.78776

Mar09 -2.7812 -15.2658 42.45736

Apr09 4.097334 1.265911 5.186861May0

9 -16.5039 -5.25301 86.69538

Jun-09 -6.61887 -31.084 205.7412

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Jul-09 20.49261 18.61079 381.3836

Aug09 5.410305 -7.93862 -42.9503Sep-

09 2.517874 22.13501 55.73316Oct-

09 -34.7711 -21.9242 762.3295

Nov09 -0.88267 22.97596 -20.2801Dec-

09 -6.87567 -0.80837 5.558105

=2337.168

Table 4.6: Covariance between ONGC and HPL


ONGC and HPL:

Cov (ob) = 1 (Ro-Ro)( Rh-Rh)

N-1

= 1 (2337.168)

23

= 101.616

Correlation of coefficient = cov (oh)

o h

= 101.616

----------------------------

39


40/76

(13.20385)( 16.50866)

= 0.466

Cov (oh)=covariance between ONGC and HPL


h = Standard deviation of HPL.

-40

-30

-20

-10

0

10

20

30

40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

time in months

return

monthlyReturns of ONGC monthly Returns of HPL

Figure 4.2: GRAPH SHOWING MONTHLY RETURNS OF SECURITIES OFONGC AND HPL FROM JAN 2008 TO DEC 2009

40


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Covariance between the stocks of ONGC and Rel Petroleum

Month

Ro-Ro Rr-Rr

(Ro-Ro)(Rr-Rr)

Jan-08

4.535516

1.484852 6.73457

Feb08

-12.62

37

-0.039

66 0.500633Mar0

812.73

6894.697

46 59.83104Apr0

8

5.407

334

10.96

203 59.27537May

080.799

55820.89

541 16.7071

Jun-08

-3.151

478.797

893 -27.7263

Jul-08

0.943709

-2.725

82 -2.57238

Aug08

-4.940

762.095

248 -10.3521Sep-

0813.87

43126.72

352 370.7705Oct-

0830.90

49658.13

863 1796.772

Nov08

-6.964

73

-15.45

33 107.6282

41


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Dec-08

7.691472

1.377379 10.59408

Jan-09

-16.93

59

-30.47

41 516.1058Feb-

092.670

7664.554

146 12.16306

Mar09

-2.781

2

-10.04

65 27.94122Apr0

94.097

33425.53

581 104.6287

May09

-16.50

39

-16.43

59 271.2571

Jun-

09

-6.618

87

-18.67

07 123.5789

Jul-09

20.49261

-6.068

29 -124.355

Aug09

5.410305

-7.261

8 -39.2886

Sep-09

2.517874

-10.97

02 -27.6215

Oct-

09

-34.77

11

-41.83

04 1454.489

Nov09

-0.882

67 -21.58 19.04792

Dec-09

-6.875

6716.29

416 -112.033

=4614.077

Table 4.7: Covariance between ONGC and Reliance Petroleum Ltd


ONGC and Rel petroleum:

Cov (or) = 1 (Ro-Ro) (Rr-Rr)

42


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N-1

= 1 (4614.077)

23

= 200.612

Correlation of coefficient = cov (or)

o r

= 200.612

----------------------------

(13.20385)(20.43002)

= 0.742

Cov (or) =covariance between ONGC and Rel Petroleum


r= Standard deviation of Rel Petroleum

43


44/76

-60

-40

-20

0

20

40

60

80

1 3 5 7 9 11 13 15 17 19 21 23 25

time in months

return

monthlyReturns of ONGC monthly returns of Rel.Petro

Figure 4.3: GRAPHICAL REPRESENTATION OF MONTHLY RETURNS OFSECURITIES OF ONGC AND REL.PETROLEUM LTD FROM JAN 2008 TO

DEC 2009.

Covariance between the stocks of BPCL and HPL

44


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Month

Rb-Rb

Rh-Rh

(Rb-Rb)(Rh-Rh)

Jan-08

4.573581

10.86512 49.6925

Feb08

-14.37

76

-13.26

8 190.7614

Mar08

-5.881

47

-9.829

94 57.81443Apr0

8

8.111

651

7.440

832 60.35743May08

5.767258

6.975207 40.22781

Jun-08

-6.152

23

-8.541

34 52.54831

Jul-08

-7.830

76

-3.555

85 27.84505

Aug08

-4.866

14

-8.424

23 40.99347

Sep-08

14.70172

11.35369 166.9189

Oct-08

-6.236

46

-6.716

82 41.88917Nov0

89.856

60412.48

669 123.0763Dec-

0829.45

18230.84

488 908.4377

Jan-09

-34.65

7

-29.86

23 1034.939

Feb-09

24.15615

17.51848 423.179

Mar09

-12.53

45

-15.26

58 191.3492

Apr09

-1.906

721.265

911 -2.41374

May09

-11.67

79

-5.253

01 61.3442

Jun-09

-41.01

61

-31.08

4 1274.945Jul-

0938.46

3618.61

079 715.838

Aug09

-9.130

56

-7.938

62 72.48403Sep-

0917.56

30322.13

501 388.7578

Oct-

09

-22.16

54

-21.92

42 485.9584Nov09

23.11878

22.97596 531.1761

45


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Table 4.8: Covariance between BPCL and HPL


BPCL and HPL:

Cov(bh) = 1 (Rb-Rb)( Rh-Rh)

N-1

= 1 (6935.962)

23

=301.5636

46


47/76

Correlation of coefficient = cov (bh)

b h

= 301.5636

----------------------------

(19.07876)(16.50866)

= 0.957

Cov (bh)=covariance between BPCL and HPL

b = Standard deviation of BPCL

h = Standard deviation of HPL

47


48/76

-50

-40

-30

-20

-10

0

10

20

30

40

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

TIME IN MONTHS

RETURN

Monthly Returns of BPCL monthly Returns of HPL

Figure 4.4: GRAPHICAL REPRESENTATION OF MONTHLY

RETURNS OF SECURITIES OF BPCL AND HPL FROM JAN

2008 AND DEC 2009

Covariance between the stocks of HPL and Rel Petroleum

Month

Rh-Rh Rr-Rr

(Rh-Rh)(Rr-Rr)

Jan-08

10.86512

1.484852 16.13309

48


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Feb08

-13.26

8

-0.039

66 0.526185

Mar08

-9.829

944.697

46 -46.1757

Apr08

7.440832

10.96203 81.56664

May08

6.975207

20.89541 145.7498

Jun-08

-8.541

348.797

893 -75.1458

Jul-08

-3.555

85

-2.725

82 9.692611

Aug08

-

8.42423 2.095248 -17.6509Sep-

0811.35

36926.72

352 303.4107

Oct-08

-6.716

8258.13

863 -390.506

Nov08

12.48669

-15.45

33 -192.961Dec-

0830.84

4881.377

379 42.4851

Jan-09

-29.8623

-30.4741 910.0271

Feb-09

17.51848

4.554146 79.78172

Mar09

-15.26

58

-10.04

65 153.3675Apr0

91.265

91125.53

581 32.32607

May

09

-5.253

01

-16.43

59 86.33808

Jun-09

-31.08

4

-18.67

07 580.3599

Jul-09

18.61079

-6.068

29 -112.936Aug0 - - 57.64868

49


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97.938

627.261

8

Sep-09

22.13501

-10.97

02 -242.824

Oct-09

-21.92

42

-41.83

04 917.0987Nov0

922.97

596 -21.58 -495.821

Dec-09

-0.808

3716.29

416 -13.1718

=1829.32Table 4.9: Covariance between HPL and Reliance Petroleum Ltd


HPL and Rel Petroleum:

Cov(hr) = 1 (Rh-Rh)( Rr-Rr)

N-1

= 1 (1829.32)

23

=79.53563

Correlation of coefficient = cov (hr)

h r

50


51/76

= 79.53563

----------------------------

(16.50866)(20.43002)

= 0.235

Cov (bh) =covariance between HPL and Rel.Petroleum ltd.

h = Standard deviation of HPL

r = Standard deviation of Rel. Petroleum ltd.

-60

-40

-20

0

20

40

60

80

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

time in months

return

monthly Returns of HPL monthly returns of Rel.Petro

51


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Figure 4.5: GRAPHICAL REPRESENTATION OF MONTHLY RETURNS OFSECURITIES OF HPL AND REL.PETROLEUM LTDFROM JAN 2008 TO DEC 2009.

Covariance between the stocks of BPCL and Rel Petroleum

Month

Rb-Rb Rr-Rr

(Rb-Rb)(Rr-Rr)

Jan-08

4.573581

1.484852 6.791091

Feb0

8

-14.37

76

-0.039

66 0.57019

Mar08

-5.881

474.697

46 -27.6279Apr0

88.111

65110.96

203 88.92018May

085.767

25820.89

541 120.5092

Jun-08

-6.152

238.797

893 -54.1267

Jul-08

-

7.83076

-

2.72582 21.34524

Aug08

-4.866

142.095

248 -10.1958Sep-

0814.70

17226.72

352 392.8819Oct- - 58.13 -362.579

52


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086.236

46 863

Nov08

9.856604

-15.45

33 -152.317Dec-

0829.45

1821.377

379 40.56633

Jan-09

-34.65

7

-30.47

41 1056.14Feb-

0924.15

6154.554

146 110.0106

Mar09

-12.53

45

-10.04

65 125.927

Apr0

9

-1.906

72

25.53

581 -48.6897

May09

-11.67

79

-16.43

59 191.937

Jun-09

-41.01

61

-18.67

07 765.7989

Jul-09

38.4636

-6.068

29 -233.408

Aug0

9

-9.130

56

-7.261

8 66.30434

Sep-09

17.56303

-10.97

02 -192.669

Oct-09

-22.16

54

-41.83

04 927.1861Nov0

923.11

878 -21.58 -498.903Dec-

092.668

58416.29

416 43.48235

=2377.854

Table 4.10: Covariance between BPCL and Reliance Petroleum Ltd

53


54/76


BPCL and Rel Petroleum:

Cov (br) = 1 (Rb-Rb) (Rr-Rr)

N-1

= 1 (2377.854)

23

=103.385

Correlation of coefficient = cov (br)

b r

= 103.385

----------------------------

(19.07876) (20.43002)

= 0.265

Cov (br) =covariance between BPCL and Rel Petroleum

b = Standard deviation of BPCL

r= Standard deviation of Rel Petroleum.

54


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-60

-40

-20

0

20

40

60

80

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

TIME IN MONTHS

RETURN

Monthly Returns of BPCL monthly returns of Rel.Petro

Figure 4.6: GRAPHICAL REPRESENTATION OF MONTHLY RETURNS OF

SECURITIES OF BPCL AND REL.PETROLEUM LTDFROM JAN 2008 TO DEC 2009.

55


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Table 4.11: Covariance between the stocks

1. Covariance shows the degree to which the returns of the two securities

Vary or change together

2. The stocks which are having high value of covariance are positively covariated

means that the returns of the two securities move in the same direction.

ONGC BPCL HPLRELPETROLUEM

ONGC -

132.116 101.616 200.612

BPCL 132.116 - 301.563 103.385

HPL 101.616 301.563 - 79.53

RELPETROLEUM 200.612 103.385 79.53 -

56


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3. The stocks which are having lesser value of covariance or negative covariance

imply that the returns of the two securities move in opposite direction.

4. Here the stocks of BPCL and HPL are highly covariated with a covariance of

301.56 between them indicating that the returns of these two stocks move in the

same direction.

5. The securities of HPL and Rel.Petroleum ltd are having least value of

covariance which implies that the returns of these two stocks do not move in the

same direction and hence may be preferred combination to inves

ONGC BPCL HPLRELPETROLEUM

ONGC - 0.524 0.466 0.742

BPCL 0.524 - 0.957 0.265

HPL 0.466 0.957 - 0.235

RELPETROLEUM 0.742 0.265 0.235 -

Table 4.12: Correlation of coefficient.

1. Coefficient of correlation reflects the degree of comovement between two

variables. Coefficient of correlation indicates the risk aspect of the two

stocks.

2. The correlation coefficient can vary between -1.0 and +1.0. A value of -1.0

means perfect negative correlation or comovement; a value of +1.0 means

perfect correlation or comovement in the same direction.

57


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3. The correlation coefficient between the securities of HPL and Rel

Petroleum ltd is the lowest and hence the risk will be least if investment is

made in the combination of these two.

4. The correlation coefficient between the securities of BPCL and HPL is the

highest indicating high comovement.

4.3. Calculation on market returns (Rm)

For the period 2008 and 2009

58


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Table 4.13: Calculation of market return.

Month Opening ClosingReturn(Rm) (RmRm) (Rm-Rm)2

December'09 2755.15 2959.15 7.4 8.14 66.32832

November 2885.4 2755.1 -4.52 -3.78 14.25768

October 3921.85 2885.6 -26.42 -25.68 659.5946

September 4356.1 3921.2 -9.98 -9.24 85.44777August 4331.6 4360 0.66 1.4 1.947564

July 4039.75 4332.95 7.26 8 63.96448

June 4869.25 4040.55 -17.02 -16.28 265.0105

May 5265.3 4870.1 -7.51 -6.77 45.7766

April 4735.65 5165.9 9.09 9.83 96.53547

March 5222.8 4734.5 -9.35 -8.61 74.12326

February 5140.6 5223.5 1.61 2.35 5.534523

January '09 6136.75 5137.45 -16.28 -15.54 241.6147

December'08 5765.45 6138.6 6.47 7.21 52.01409

November 5903.8 5762.75 -2.39 -1.65 2.719975October 5021.5 5900.65 17.51 18.25 332.9757

September 4466.65 5021.35 12.42 13.16 173.149

August 4528.85 4464 -1.43 -0.69 0.4789

July 4318.3 4528.85 4.88 5.62 31.5357

June 4295.8 4318.3 0.52 1.26 1.596867

May 4087.9 4295.8 5.09 5.83 33.93814

April 3821.55 4087.9 6.97 7.71 59.43777

March 3745.3 3821.55 2.04 2.78 7.705007

February 4082.7 3745.3 -8.26 -7.52 56.6141

January'08 3944.55 4082.7 3.5 4.24 17.9963

=-17.76 =2390.29698

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Mean return of market index (Rx) = -0.74

Calculation of variance for market index:

m = (Rm-Rm)N-1

m = 2390.30 = 103.9223

Return(Rm)

-30

-25

-20

-15

-10

-5

0

5

10

15

20

1 3 5 7 9 11 13 15 17 19 21 23

time

returns

Return(Rm)

Figure 4.7: REPRESENTATION OF MARKET RETURNSDEC 2009-JAN 2008

4.4. CALCULATION OF BETA

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Calculation of beta for ONGC

month (Ro-Ro) (RmRm) (RoRo)(RmRm)

Jan08 4.535516 4.24 19.23059

Feb08 -12.6237 -7.52 94.93003

Mar08 12.73689 2.78 35.40856

Apr08 5.407334 7.71 41.69055

May08 0.799558 5.83 4.661423

Jun08 -3.15147 1.26 -3.97085

Jul-08 0.943709 5.62 5.303642

Aug08 -4.94076 -0.69 3.409126

Sep08 13.87431 13.16 182.5859

Oct08 30.90496 18.25 564.0156

Nov08 -6.96473 -1.65 11.49181

Dec08 7.691472 7.01 53.91722

Jan09 -16.9359 -15.54 263.1838

Feb09 2.670766 2.35 6.2763

Mar09 -2.7812 8.61 -23.9461

Apr09 4.097334 9.83 40.27679

May09 -16.5039 -6.77 111.7316

Jun09 -6.61887 -16.28 107.7552

Jul-09 20.49261 8 163.9409

Aug09 5.410305 1.4 7.574427

Sep09 2.517874 -9.24 -23.2652

Oct09 -34.7711 -25.68 892.9221

Nov09 -0.88267 -3.78 3.336477

Dec09 -6.87567 8.14 -55.9679

=2506.492

Table 4.14: Calculation of beta of ONGC

Calculation of covariance of ONGC & market index:

Cov(om) = (Ro-Ro)(Rm-Rm)N-1

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Cov(om)= 2506.492 = 108.98 24-1

Calculation of beta () for ONGC:

= Cov(om) m

= 108.98103.92

= 1.05

-40

-30

-20

-10

0

10

20

30

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Monthly Returns of ONGC Return(Rm)

Figure 4.8: CHART SHOWING THE MARKET RETURNS AND RETURNS

OF SECURITIES OF ONGC FROM JAN 2008 TO DEC 2009.

Calculation of beta for BPCL

Month (Rb-Rb) (RmRm) (RbRb)(RmRm)

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Jan08 4.573581 4.24 19.39198

Feb08 -14.3776 -7.52 108.1194

Mar08 -5.88147 2.78 -16.3505

Apr08 8.111651 7.71 62.54083

May08 5.767258 5.83 33.62311

Jun08 -6.15223 1.26 -7.75181

Jul-08 -7.83076 5.62 -44.0089

Aug08 -4.86614 -0.69 3.357635

Sep08 14.70172 13.16 193.4747

Oct08 -6.23646 18.25 -113.815

Nov08 9.856604 -1.65 -16.2634

Dec08 29.45182 7.01 206.4573

Jan09 -34.657 -15.54 538.5698

Feb09 24.15615 2.35 56.76695

Mar09 -12.5345 8.61 -107.922

Apr09 -1.90672 9.83 -18.7431

May09 -11.6779 -6.77 79.05941

Jun09 -41.0161 -16.28 667.7423

Jul-09 38.4636 8 307.7088

Aug09 -9.13056 1.4 -12.7828

Sep09 17.56303 -9.24 -162.282

Oct09 -22.1654 -25.68 569.2067

Nov09 23.11878 -3.78 -87.389

Dec09 2.668584 8.14 21.72228

=2280.432

Table 4.15: Calculation of beta of BPCL

Calculation of covariance of BPCL & market index:

Cov (bm) = (Rb-Rb)(Rm-Rm)N-1

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Cov (bm) = 2280.432 = 99.15 24-1

Calculation of beta () for BPCL:

= Cov(bm) m

= 99.15103.92

= 0.95

-40

-30

-20

-10

0

10

20

30

40

50

returns

1 2 3 4 5 6 7 8 9101112131415161718192021222324

time in months

Return

Return(Rm)

Figure 4.8: CHART SHOWING THE MARKET RETURNS AND THE RETURNSOF BPCL FROM JAN 2008 TO DEC 2009

Calculation of beta for HPL

month (Rh-Rh) (RmRm) (RhRh)(RmRm)

Jan08 10.86512 4.24 46.0681

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Feb08 -13.268 -7.52 99.7752

Mar08 -9.82994 2.78 -27.3272

Apr08 7.440832 7.71 57.36881

May08 6.975207 5.83 40.66546

Jun08 -8.54134 1.26 -10.7621

Jul-08 -3.55585 5.62 -19.9839

Aug08 -8.42423 -0.69 5.81272

Sep08 11.35369 13.16 149.4146

Oct08 -6.71682 18.25 -122.582

Nov08 12.48669 -1.65 -20.603

Dec08 30.84488 7.01 216.2226

Jan09 -29.8623 -15.54 464.0605

Feb09 17.51848 2.35 41.16843

Mar09 -15.2658 8.61 -131.439

Apr09 1.265911 9.83 12.44391

May09 -5.25301 -6.77 35.56291

Jun09 -31.084 -16.28 506.0478

Jul-09 18.61079 8 148.8863

Aug09 -7.93862 1.4 -11.1141

Sep09 22.13501 -9.24 -204.527

Oct09 -21.9242 -25.68 563.014

Nov09 22.97596 -3.78 -86.8491

Dec09 -0.80837 8.14 -6.58016

=1744.744 Table 4.16: Calculation of beta of HPL

Calculation of covariance of HPL & market index:

Cov (hm) = (Rh-Rh)(Rm-Rm)N-1

Cov (hm) =1744.744 = 75.86

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24-1

Calculation of beta () for HPL:

= Cov(hm) m

= 75.86103.92

= 0.73

-40

-30

-20

-10

0

10

20

30

40

returns

1 2 3 4 5 6 7 8 9 10 11 1213 1415 16 17 18 19 2021 22 23 24

time in months

monthlyReturns of HPL Return(Rm)

Figure 4.9: CHART SHOWING MARKET RETURNS AND RETURNS OF HPLFROM JAN 2008 TO DEC 2009

Calculation of beta for Rel Petroleum

month (Rr-Rr) (RmRm) (RrRr)(RmRm)

Jan08 1.484852 4.24 6.295772

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Feb08 -0.03966 -7.52 0.29823

Mar08 4.69746 2.78 13.05894

Apr08 10.96203 7.71 84.51727

May08 20.89541 5.83 121.8203

Jun08 8.797893 1.26 11.08535

Jul-08 -2.72582 5.62 -15.3191

Aug08 2.095248 -0.69 -1.44572

Sep08 26.72352 13.16 351.6816

Oct08 58.13863 18.25 1061.03

Nov08 -15.4533 -1.65 25.49798

Dec08 1.377379 7.01 9.65543

Jan09 -30.4741 -15.54 473.5673

Feb09 4.554146 2.35 10.70224

Mar09 -10.0465 8.61 -86.5

Apr09 25.53581 9.83 251.017

May09 -16.4359 -6.77 111.2711

Jun09 -18.6707 -16.28 303.9588

Jul-09 -6.06829 8 -48.5463

Aug09 -7.2618 1.4 -10.1665

Sep09 -10.9702 -9.24 101.3642

Oct09 -41.8304 -25.68 1074.204

Nov09 -21.58 -3.78 81.57234

Dec09 16.29416 8.14 132.6345

=4063.255 Table 4.17: Calculation of beta of Reliance Petroleum ltdCalculation of covariance of Rel Petro & market index:

Cov (rm) = (Rr-Rr)(Rm-Rm)N-1

Cov (rm)=4063.26 = 176.66 24-1

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Calculation of beta () for Rel Petroleum:

= Cov(rm) m

= 176.66103.92

= 1.7

-40

-30

-20

-10

0

10

20

30

40

50

60

70

returns

1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 1718 19 20 21 2223 24

time in months

Monthlyreturns of Rel Petro Return(Rm)

Figure 4.10:CHART SHOWING MARKET RETURNS AND RETURNS OFREL.PETROLEUM LTD. FROM JAN 2008 TO DEC 2009.

4.5. SECURITY MARKET LINE

Security market line (SML) equation:

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r= + (rm-rf)

rf = risk free rate, here assuming it to be 9% = beta of individual stock

rm = market return, here market return is -0.74.

Calculation of expected returns using SML

Security (1) ONGC with beta= 1.05r= rf + (rm-rf)= 0.09+ 1.05(-0.74-0.09)= - 0.7815 OR -78.15%

Security (2) BPCL with beta= 0.95

r= rf+ (rm-rf)= 0.09+ 0.95(-0.74-0.09)= - 0.6985 OR -68.86%

Security (3) HPL with beta= 0.73r= rf + (rm-rf)= 0.09+ 0.73(-0.74-0.09)= -0.5159 OR -51.59%

Security (4) Rel Petroleum ltd with beta=1.7

r= rf+ (rm-rf)= 0.09+ 1.7(-0.74-0.09)= -1.321 OR -132.1%

5.1.FINDINGS

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Table 6.2: valuation of shares

Actualreturn

(mean)

Expectedreturn

Beta value

ONGC -0.97 -0.781 1.05 Under priced

BPCL 2.05 -0.698 0.95 Under priced

HPL 0.59 -0.515 0.73 Under priced

RelPetrol

2.41 -1.321 1.70 Under priced

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-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0 0.5 1 1.5 2

beta

returns

expected returns market return Rf

Figure 6.1: Security market line of the Table 6.1

1. The actual returns of ONGC is -0.97 which is high compared to the

expected returns of -0.687, it is under priced, here beta is 1.05, which is

high.

2. The actual returns of BPCL is 2.05 when compared to expected returns

of-0.613 it is high, it is under priced, here beta is 0.95 which is average.

3. The actual returns of HPL are 0.59 is higher than the expected returns of

-0.45, it is also under valued, and here the beta is 0.73 which is low.

4. The actual returns of Relpetroleum is 2.45 which is quite higher than the

expected returns of -1.258, and here beta value is 1.70 which is the

highest when compared to that of other companys.

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5.2. CONCLUSION

1. The expected returns and the actual returns of the stocks are not equal and

there are wide disparities, the market is considered to be aggressive or

volatile.

2. The actual returns are better when compared to expected returns of the

stocks; hence it would be beneficial for an investor to make investments as

all the stocks are under priced.

3. The actual returns of the securities and the beta are directly proportional.

The stock with highest beta is also yielding the highest actual returns.

4. Those who want to take less risk must invest in securities which are having

less beta value.

5. The stocks of ONGC is having a high beta value and giving negative returns

indicating poor performance of the company

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5.3. SUGGESTIONS

1. As the markets are very volatile and the returns for the coming year or two

is not certain, an investor seeking to make investment for short period of

1-5 years is advised not to invest in equities.

2. It is a good opportunity for investors looking for a long term investments

in stocks as these would be available at low prices, but proper evaluation

has to be made.

3. Seeing the current trend the volatility of the market is expected to continue

for the next 12-18 months. So even if we buy stocks at lower prices there

would not be a notable increase in the values for these 12-18 months.

4. Investors are advised not to make investments in the stocks of ONGC as

its actual returns are negative and the beta is als high at 1.05

5. Investors who want to take low risk and are satisfied with low returns can

invest in the equities of Hindustan petroleum ltd.

6. Investors who want high returns and are ready to bear high risk can invest

in the shares of BPCL and Rel petroleum.

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5.4. LIMITATIONS

1. Future uncertainties: Future changes are largely unpredictable; more so when

the economic and business environment is buffeted by frequent winds of changes.

In an environment characterized by discontinuities, the past record is poor guide

to future performance.

2. Irrational market behavior: The market itself presents a major obstacle to the

analyst. On account of neglect of prejudice, undervaluation may persist fore

extended periods: likewise, overvaluation arising from unjustified optimism and

misplaced enthusiasm may endure for unreasonable lengths of time. The slow

correction of under or overvaluation poses a threat to the analyst. Before the

market eventually reflects the values established by the analyst, new forces may

emerge.

3. Inadequacies or incorrectness of data: An analyst has to often wrestle with

inadequacy or incorrect data. While deliberate falsification of data may be rare,

subtle misrepresentation and concealment are common. Often an experienced and

skilled analyst may be able to detect such ploys and cope with them. However, in

some instances, he too is likely to be misled by them into drawing wrong

conclusions.

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BIBLIOGRAPHY

1. Prasanna Chandra (2006),Investment Analysis and Portfolio Management

(2nd edition) Tata Mc.Graw-Hill Publishing Company limited, New Delhi.

2. Donald E.Fischer & Ronald J.Jordan(2006), Security Analysis and portfolio

Management(6th edition) Prentice-Hall of India Pvt limited, New Delhi.

3.ZVIBodie, Alex Kane, Alan J Marcus, Pitabas Mohanty (2006),Investments

(6th edition) Tata Mc.Graw-Hill Publishing Company limited, New Delhi.

Websites:

www.investopedia.com

www.economictimes.com

www.investorideas.com
http://www.investopedia.com/http://www.economictimes.com/http://www.investorideas.com/http://www.investopedia.com/http://www.economictimes.com/http://www.investorideas.com/

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