naresh acl 1 proj
TRANSCRIPT
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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
Standard deviation (x) = 19.07876
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.
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Table 4.3: Calculation of returns and standard deviation of HPL
Mean return (Rx) =0.5991Variance (x) = 272.5359
Standard deviation (x) = 16.50866
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
Standard deviation (x) = 20.43002
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
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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)
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= 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.
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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
Calculation of covariance and correlation between stocks
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
----------------------------
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(13.20385)( 16.50866)
= 0.466
Cov (oh)=covariance between ONGC and HPL
o = Standard deviation of ONGC
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
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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
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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
Calculation of covariance and correlation between stocks
ONGC and Rel petroleum:
Cov (or) = 1 (Ro-Ro) (Rr-Rr)
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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
o = Standard deviation of ONGC
r= Standard deviation of Rel Petroleum
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-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
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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
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Table 4.8: Covariance between BPCL and HPL
Calculation of covariance and correlation between stocks
BPCL and HPL:
Cov(bh) = 1 (Rb-Rb)( Rh-Rh)
N-1
= 1 (6935.962)
23
=301.5636
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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
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-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
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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
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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
Calculation of covariance and correlation between stocks
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
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= 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
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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
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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
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Calculation of covariance and correlation between stocks
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.
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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.
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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 -
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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.
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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
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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/