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“COMPARISON BETWEEN EXPECTED RETURN AS CALCULATED BY CAPM MODELAND ACTUAL RETURNS”
A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF
THE CURRICULUM REQUIREMENTS FORTHE AWARD OF THE DEGREE OF
MASTER OF BUSINESS ADMINISTRATIONOF BANGALORE UNIVERSITY
Submitted by:
GAURAV GUPTA
Register Number05XQCM6023
Under the guidanceof
Dr. Nagesh MalavalliPrincipal
M.P.Birla Institute of Management,Associate Bharatiya Vidya Bhavan,
Bangalore 5600012005-07
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DECLARATION
I hereby declare that the research work embodied in the dissertation entitled
“COMPARISON BETWEEN EXPECTED RETURN AS CALCULATED BY CAPM MODELAND ACTUAL RETURNS” is the result of research work carried out by me, under the
guidance and supervision of Dr. Nagesh Malavalli, M.P.Birla Institute of Management,
Bangalore.
I also declare that this report has not been submitted to any other University or Institute for
award of any Degree or Diploma.
Place: Bangalore (GAURAV GUPTA)
Date: Reg. no. 05XQCM6023
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PRINCIPAL’S CERTIFICATE
This is to certify that the Project titled “COMPARISON BETWEEN EXPECTED RETURN
AS CALCULATED BY CAPM MODEL AND ACTUAL RETURNS” has been prepared by
Mr. GauravGupta bearing registration number 05XQCM6023, under the guidance
of Dr. Nagesh Malavalli , M.P.Birla Institute of Management, Associate Bharatiya
Vidya Bhavan, Bangalore.
Place: Bangalore Dr. NAGESH MALAVALLI
Date: (Principal)
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GUIDE CERTIFICATE
This is to certify that the Project titled “COMPARISON BETWEEN EXPECTED RETURNAS CALCULATED BY CAPM MODEL AND ACTUAL RETURNS” has been prepared by
Mr. Gaurav Gupta bearing registration number 05XQCM6023, under the
guidance of Dr. Nagesh Malavalli, M.P.Birla Institute of Management, Associate
Bharatiya Vidya Bhavan, Bangalore.
Place: Bangalore
Date: (Dr. NAGESH MALAVALLI)
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ACKNOWLEDGEMENT
The completion of the research would have been impossible without the valuable
contributions of people from the academics, family and friends.
I hereby wish to express my sincere gratitude to all those who supported me throughout the
study.
I am thankful to Dr. Nagesh Malavalli (Finance), for his valuable guidance, academic and
moral support which made this report a reality.
I am greatly thankful to Prof. T.V. Narasimha Rao (Senior Faculty), M.P.Birla Institute of
Management, Bangalore, Prof. Santhanam (Statistics) and Prof. Rudramurthy (Finance)
for their support in completion of this report.
I also thank my family members and friends whose support and encourage has meant a lot to
me personally and also for the completion of the report.
(Gaurav Gupta)
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CONTENTS
Phase’s PARTICULARS
1.
Introduction
o Background
o
Purpose of the studyo Problem statement
o Objectives of the study
o Limitations of the study
2. Theoritical Framework
3.
Review of Literature
4. Methodology
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5. Data analysis and Interpretation
6. Bibliography
7.Annexure
o Sample data
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Phase: 1
Introduction
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The CAPM as a model is used for calculating the expected returns by 3 out of 4
financial managers. In case where a firm’s capital structure involves equity
capital, expected returns have a bearing on the cost of capital.
Recent research indicates that actual return may differ greatly from the returns
predicted by CAPM model. CAPM uses market risk premium for estimating the
expected returns. Recent research indicates that the true market risk premium
may differ greatly from market risk premium used in CAPM model. As a result of
result of which wrong cost of capital may be estimated.
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Purpose of the Study:
CAPM i.e Capital Asset Pricing Model is widely used tool for estimating the
expected returns. This research aims to check that up to what extent returns
predicted through CAPM matches the actual returns.
Statement of the problem:
Does the CAPM holds true in calculating expected returns?
Objectives of the study:
To see whether the expected returns as calculated by CAPM model matches
with ‘actual return’.
To see what could be the probable reasons if the above two vary.
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Limitations of the study:
The study is limited to Indian 70 only
The study is limited to a period of six years.
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Phase: 2
Theoretical
Framework
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Capital Asset Pricing Model (CAPM)
The CAPM establishes a linear relationship between the required rate of return on a
security and its systematic or non-diversifiable risk as measured by Beta.
Mathematically, it is represented as
k j= Rf + (km- Rf)
where k j is the required rate of return on the security, km is the return on market portfolio,
and Rf is the risk free rate of return.
The term (km- Rf) indicates the risk premium on the security and the term (km- Rf)
indicates the market risk premium
Assumptions under the CAPM model:
1. Investors are risk-averse.
2. Investors make their decisions based on a single- period horizon.
3. There are no transactions costs in the financial markets.
4. Taxes do not affect the choice of buying an asset.
5. All individuals assume that they can buy assets at the going market price and
they all agree on the nature of risk and returns associated with each investment.
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The CAPM model can be graphically represented by the security market line.
• Any individual’s expected return and beta should lie on the SML.
• Rf is the intercept of the SML.
• km-Rf is the slope of the SML.
Using SML to evaluate securities
If the expected rate of return on a security is greater than the required rate of return, it
indicates that the security is undervalued because its average return is high for the level of
risk it bears. Such a stock lies above the SML.
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-If the expected rate of return is less than the required rate of return then the security is
over-valued. Such a stock is unattractive as it is expected to produce a rate of return lower
than the stocks with similar betas and it lies below the SML.
-The above two categories of stocks should move towards equilibrium by going through a
temporary price adjustment. The expected return on the security is computed as:
.
Assuming that Betas remain the same, the expected return of the undervalued stock has
to be brought down to be equal to the required rate of return by increasing the purchase
price of the security.
Similarly for the overpriced security, the purchase price of the security has to be broughtdown so that its expected rate of return rises and becomes equal to its required rate of
return.
Concept of return
When an asset is bought, the gain (or loss) from that investment is called the return on
investment.
It is the major factor that motivates an investor to invest in an asset. Assessing the return
of an asset is important because of the following reasons:
a. It facilitates comparison between various alternatives.
b. It helps in analyzing the past performance.
c. It helps in forecasting the future returns.
Returns can be classified as:
1. Realized return; 2. Expected return
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Realized return (or ex-post) is the return that was realized or could have been realized
from an asset whereas expected return is the return that an investor expects to earn over
some time in future. Expected return is affected by uncertainty
Components of return
Return usually has two components
1. The income component or yield : The cash that the investor receives whilehe owns an investment is called the income component. For e.g. the dividend that
the equity-holders get when they own a company’s shares constitutes the income
component.
The component of dividend yield is measured as , where Dt is the dividend paid on
the stock during the year and Pt-1 is the price of the stock at the beginning of the year.
(Note: In case of bonds or debenture, Dt will represent coupon payments).
2. The capital gain (or loss): The value of the asset that an investor has will
often change; and depending upon the increase (or decrease) in the value of an
asset there will be a capital gain (or loss).
• The Capital gain yield is measured as
(pt-pt-1)/pt-1
, where Pt is the price of the
stock at the end of the year
Concept of Return Concept of Return
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•
Measurement of returns
• The component of dividend yield is measured as ,
• The Capital gain yield is measured as
(pt-pt-1)/pt-1
,
• The total percentage return is measured as the sum of the dividend yield and
the capital gain yield
Hence the total (percentage) return on an investment is given by
Dt + (pt-pt-1)/pt-1
Probability and rate of return
The future returns are characterized by uncertainty. Whenever the probabilities associated
with various possible returns are known, then the expected return can be computed as the
weighted average of the various returns, the weights being the probabilities associated
with the returns.
Expected rate of return
where Pi is the probability associated with the ith outcome and ki is the rate of return from
the ith possible outcome.
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Concept of risk
• Risk can be defined as the variability in the actual return emanating from a project in
future over its working life, in relation to the estimated return that was forecasted at
the time of selecting the project. The greater the variability between the actual and
estimated return, the more risky is the project.
• The financial decisions of the firm are inter-related and jointly affect the market value
of its shares by influencing the return and risk of the firm. The relationship between
return and risk can be simply expressed as:Return = Risk-free rate + Risk premium
• A proper balance between return and risk should be maintained to maximize the
market value of a firm’s shares. Such a balance is called risk-return trade off. The
finance manager, in a bid to maximize the shareholder’s wealth should strive to
maximize returns in relation to the given risk and should seek courses of actions that
avoid unnecessary risks.
Sources of risk
The various sources from which a risk can arise are:
1. Interest rate risk: Variability in security’s return due to changes in the level of
interest rates. The price of a security moves inversely to the changes in interest
rates. Hence if there is a rise in the interest rate, the price of the security will fall.
2. Market rate risk: Variability in the security’s return due to fluctuations in the
securities market. This risk arises as a result of factors that affect the entire
economy, e.g recession, war etc.
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3. Inflation risk: The reduction in the purchasing power of money due to rise in
inflation is referred to as inflation risk. Inflation risk directly affects the interest rate
risk as the interest rates increase with rise in inflation.
4. Business risk: It is the risk of doing business in a particular industry or
environment. This risk is unique in nature and arises as a result of uncertainties
associated with a company or an industry.
5. Financial risk: It is the risk arising due to the use of debt financing (i.e.
financial leverage). It can also be defined as the variability in the return on equity
and earnings per share of the firm due to increase in financial leverage.
6. Liquidity risk: It is the risk associated with the secondary market in which the
security is traded. Securities like treasury bills which can be sold without asignificant price concession are considered to be more liquid.
Measurement of risk
The degree of uncertainty involved can be analyzed using the measures of dispersion.
The various measures of dispersion are:
1. Range: It can be computed as the difference between the highest possible
return and the lowest possible return. It is not a popular measure of risk as it is
based on two extreme values which can (may) misrepresent the actual risk
involved.
2. Standard deviation: Standard deviation is an absolute measure of deviation.
It’s very useful in comparing the risks involved in different projects that have similaroutlays. It is defined as the square root of the mean deviations where the deviation
is the difference between an outcome and the expected mean value of all
outcomes. Further, each deviation is assigned a weight equal to its probability of
occurrence.
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Let ki be the rate of return associated with the ith possible outcome and Pi be the
corresponding probability and be the mean return, then the standard deviation for the
security can be computed as:
.
The greater the standard deviation of a probability distribution, the greater is the
dispersion or the variability of the outcomes around the expected (mean) value.
Graphically, a distribution having a wider normal distribution indicates greater risk.
Portfolio risk:
The risk (as measured by standard deviation) of the portfolio is not a simple weighted
average of the risk of the individual securities in it; the portfolio’s risk will be smaller than
the weighted average of the standard deviations of the assets.
The basic formula for computing the standard deviation of an n-security portfolio is:
=
where, is the standard deviation of the portfolio,
wi is the weight of the ith security
w j is the weight of the jth security
is the standard deviation of the ith security
is the standard deviation of the jth security.
is the correlation coefficient between the ith and the jth security.
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Risks Affecting a Portfolio:
The total risk in the case of an individual security can be divided into two parts:
1. Diversifiable risk or unsystematic risk: It affects a single asset or only a
small group of assets. Since these risks are specific to individual companies or
assets, they are sometimes referred to as unique or asset-specific risks. This risk
arises from the uncertainties which are unique to individual securities and which are
diversifiable if a large number of securities are combined to form well-diversified
portfolios.
Examples of unsystematic risks :
• Workers declare strike in a company.
• The R&D expert of a company leaves.
• The company is not able to obtain adequate quantity of raw material from the
supplier.
2. Non-Diversifiable or systematic risk: It influences a large number of assets,
each to a greater or lesser extent. This risk arises on account of economy-wide
uncertainties and the tendency of the securities to move together with changes in
the market. It is also referred to as market risk. This part of the risk cannot be
reduced through diversification. Thus investors are exposed to market risk even
when they hold well-diversified portfolios of securities.
Examples of Systematic risk:
• The Reserve Bank of India introduces a restrictive credit policy.
• The corporate tax is increased.
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• The inflation rate increases.
Note: Since the systematic risk present in an asset cannot be eliminated by diversification,
the expected return on a risky asset depends only on that asset’s systematic risk. As
unsystematic risk can be eliminated by diversification, there is no reward for bearing it
From the above graph we observe that,
i. Diversification reduces only the unsystematic risk whereas the systematic risk remains
constant.
ii. Beyond a certain point, the diversifying effect of each additional stock diminishes due to
increase in the positive correlation between the assets.
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Beta: A measure of systematic risk
Beta measures the relative risk associated with an individual portfolio as measured in
relation to the risk of the market portfolio.
The Market Portfolio represents the most diversified portfolio of risky assets an investor
could buy since it includes all risky assets.
The expected return and the risk premium on an asset depend only on its systematic risk.
Since assets with larger betas have greater systematic risks, they will have greater
expected returns. Mathematically beta can be expressed as:
If Beta is greater than 1, it indicates that the stock is more risky when compared to the
market portfolio.
If Beta=1 then it indicates average risk.
If beta is less than 1, then it indicates that the security is less risky than the market
portfolio.
Beta of a Portfolio: The beta of a portfolio is a weighted average of the beta of the
individual securities, where the weights represent the proportion of the individual securities
in the portfolio.
, where
is the beta of the portfolio,
wi is the weight associated with the ith security, and
is the beta associated with the ith security
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Phase: 3
Literature Review
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It was tried to investigate the appropriateness of CAPM model for calculating
expected returns and the cost of equity capital. The results indicated that the
expected returns predicted by CAPM model may vary greatly from actual
returns due to market risk premium.
This research paper explains why the cost of capital may not be a critical input
based on the theory of real options. Further it extends the analysis to
continuous time and demonstrates that, when the firm has substantial real
options, the project selection decision will be near optimal even when the wrong
cost of capital is used.
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Phase: 4
Methodology
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Methodology
Study Design
a) Study Type: The study type is analytical, quantitative and historical.
Analytical because facts and existing information is used for the analysis,
Quantitative as relationship is examined by expressing variables in measurable terms and
also Historical as the historical information is used for analysis and interpretation.
b) Study population: population is the entire stocks and all indices of all the countries.
c) Sampling frame: Sampling Frame would be 70 stocks of Indian companies choosen from
CNX Nifty for individual stock returns and Sensex for market return.
d) Sample: Sample chosen is monthly average values of 70 stocks and monthly average
values of Sensex.
e) Sampling technique: Deliberate sampling is used because only particular units are
selected from the sampling frame. Such a selection is undertaken as these unitsrepresent the population in a better way and reflect better relationship with the other
variable.
Data gathering procedures and instruments:
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Data: Historical monthly average share prices and Historical monthly average values of
Sensex.
Data Source: Historical share prices of the sample companies and the index points for the
period has been taken from the database of Capital Market Publishers (India) Ltd.,
Sensex has been taken because CNX Nifty and BSE Sensex are considered as trust
worthy indices of India, to see whether both the indices move in the same direction or not.
List of companies taken for study:
Raymond Nirma Ltd
Hindalco State Bank of India
Ibp Polaris Software Lab Ltd
Ingersoll ABB Ltd
M & M Indian Petrochemicals Corporation Ltd
Tata Motors Siemens Ltd
Rel Cap Container Corporation Of India Ltd
IFCI Infosys Technologies Ltd
Chennai Petro Larsen & Toubro Ltd
Glaxo Smithline Hindustan Lever Ltd
Bharat Heavy Electricals Ltd Corporation Bank
Bajaj Auto Ltd Cadila Healthcare Ltd
Tata Power Company Ltd
Industrial Development Bank of India
Ltd
ITC Ltd MphasiS Ltd
Cipla Ltd Bharat Electronics Ltd
Ashok Leyland Ltd Indian Overseas Bank
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Bank of India ICICI Bank - Private Sector
Apollo Tyres Ltd Oil & Natural Gas Corpn Ltd
ING Vysya Bank Ltd LIC Housing Finance Ltd
GAIL (India) Ltd Aurobindo Pharma Ltd
Dr Reddys Laboratories Ltd Kotak Mahindra Bank Ltd
Asian Paints Ltd Punjab Tractors Ltd
Ranbaxy Laboratories Ltd Cummins India Ltd
Bharat Forge Ltd Satyam Computer Services Ltd
Aventis Pharma Ltd National Aluminium Company Ltd
Moser Baer (India) Ltd Sun Pharmaceuticals Industries Ltd
HCL Technologies Ltd Bharat Petroleum Corporation Ltd
Lupin Ltd Mahanagar Telephone Nigam Ltd
ACC Ltd Tata Steel Ltd
Hindustan Petroleum CorporationLtd Syndicate Bank
Steel Authority of India Ltd Bank of Baroda
Nicholas Piramal India Ltd Indian Hotels Co Ltd
Grasim Industries Ltd Housing Development Finance Corporation Ltd
Hero Honda Motors Ltd Dabur India Ltd
TVS Motor Company Ltd HDFC Bank Ltd
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A BRIEF PROCESS SUMMARY:
First of all the monthly average prices data for 70 stocks were taken from capitaline for the
period of 6 years starting from 2001 to 2006. Same was done for Sensex also. Now total
period was divided into two parts as follows:
Estimation period- 01-012001 to 31-12-2004
Testing period- 01-01-2005 to 31-12-2006
Estimation period: In this period the log natural of all stocks and Sensex was taken for
the purpose of calculating beta also the return of the market.
Beta for each stock was calculated by regressing the stock returns on market returns.
Testing period: in this period the average return for each stock was caculated through
log naturals and these average returns were regressed on betas calculated under
estimating period.
How to check whether CAPM holds true or not- The final regression results (in testing
period) provides with 3 important values. Which are intercept, x variable and t statistic.
Here intercept should be equal to risk free rate of return (Rf during estimation period).
Which has been around 6-6.5%. The x variable should be equal to Rm-Rf during
estimation period.
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Phase 5
Tests and Results
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Tests and Results
The primary test was regression analysis for this study
Regression; The results were as follows-
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.1026737
R Square 0.0105419
Adjusted R
Square -0.004009
Standard Error 0.0200304
Observations 70
ANOVA
df SS MS F
Significance
F
Regression 1 0.000291 0.000291 0.724486 0.397664
Residual 68 0.027283 0.000401
Total 69 0.027573
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.026512 0.005951 -4.4551 3.21E-05 -0.03839 -0.01464 -0.03839 -0.014
X Variable 1 0.0065529 0.007699 0.851168 0.397664 -0.00881 0.021915 -0.00881 0.0219
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DATA ANALYSIS AND INTERPRETATION:
Now it is clear from the above summary output that intercept does not match to risk free
rate of return as well as x variable also does not match to Rm-Rf. Hence it can be said as
per this study that CAPM does not hold true. In other words expected returns as
calculated by CAPM model does not match to actual returns.
If we see the test statistic in the above summary output, then also we can say that it is not
significant at 5% level of significance.
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Phase 8
BIBLIOGRAPHY
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Text Books
• Multinational Business Finance,
David K. Eieteman, Arthur I. Stonehill and Michel H. Moffett, (Tenth Edition)
• Research Methodology
Donald Cooper and Pamela Schindler , (Eighth Edition)
• Financial markets and services
Gordon and Natrajan, (Second Edition)
Websites
• www.investopedia.com
• www.nseindia.com
• www.bseindia.com
• www.exchangerate.com
• www.emeclai.com
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• www.icicidirect.com
• www.iciciresearch.com
• www.easy-forex.com
• www.indiainfoline.com
Database of Capital Market Publishers (India) Ltd., Capitaline 2000
Jstor Database
Reference:
Do we need capital budgeting? Ravi Jagannathan; Iwan Meier, Financial Management,
Vol-31,No.4(Winter,2002), pp. 55-77
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Phase 9
ANNEXURES
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Calculation of betas for different companies
HDFC
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.530112
R Square 0.281019
Adjusted R
Square 0.265389
Standard Error 0.041971
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.031672 0.031672 17.97945 0.000107
Residual 46 0.081031 0.001762
Total 47 0.112703
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.01249 0.006104 -2.04602 0.046496 -0.02478 -0.0002 -0.02478 -0.000
X Variable 1 0.368034 0.086796 4.240218 0.000107 0.193323 0.542746 0.193323 0.5427
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Dabur India Ltd
SUMMARY
OUTPUT
Regression Statistics
Multiple R 0.488125
R Square 0.238266
Adjusted R Square 0.221707Standard Error 0.067676
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.0659 0.0659 14.38855 0.000432
Residual 46 0.210683 0.00458
Total 47 0.276583
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Uppe
95.0%
Intercept -0.00188 0.009843 -0.19091 0.849433 -0.02169 0.017934 -0.02169 0.017
X Variable 1 0.530881 0.139955 3.793224 0.000432 0.249166 0.812597 0.249166 0.812
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40
Housing Development Finance Corporation Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.644206
R Square 0.415001
Adjusted R
Square 0.402284
Standard
Error 0.041872
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.057212 0.057212 32.6326 7.79E-07
Residual 46 0.080648 0.001753
Total 47 0.137861
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.01671 0.00609 -2.74367 0.008633 -0.02897 -0.00445 -0.02897 -0.00445
X Variable 1 0.49465 0.086591 5.712495 7.79E-07 0.320352 0.668949 0.320352 0.66894
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41
Indian Hotels Co Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.502037
R Square 0.252041
Adjusted R
Square 0.235782
Standard
Error 0.088131
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.120395 0.120395 15.50074 0.000277
Residual 46 0.357285 0.007767
Total 47 0.47768
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.00979 0.012818 -0.76357 0.449024 -0.03559 0.016014 -0.03559 0.01601
X Variable 1 0.71756 0.182256 3.937098 0.000277 0.350697 1.084422 0.350697 1.08442
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42
Bank of Baroda
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.35611
R Square 0.126814
Adjusted R
Square 0.107832
Standard
Error 0.119509
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.095416 0.095416 6.680666 0.012984
Residual 46 0.656989 0.014282
Total 47 0.752405
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.02445 0.017382 -1.40691 0.166176 -0.05944 0.010533 -0.05944 0.01053
X Variable 1 0.638798 0.247146 2.584698 0.012984 0.141319 1.136277 0.141319 1.13627
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43
Syndicate Bank
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.311814
R Square 0.097228
Adjusted R
Square 0.077603
Standard
Error 0.105668
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.055317 0.055317 4.954182 0.030969
Residual 46 0.513622 0.011166
Total 47 0.568939
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.03205 0.015369 -2.08528 0.042621 -0.06298 -0.00111 -0.06298 -0.0011
X Variable 1 0.486388 0.218523 2.225799 0.030969 0.046524 0.926251 0.046524 0.92625
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44
Tata Steel Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.623504
R Square 0.388758
Adjusted R
Square 0.37547
Standard
Error 0.084169
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.207265 0.207265 29.25656 2.2E-06
Residual 46 0.325882 0.007084
Total 47 0.533148
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.02149 0.012242 -1.75539 0.08585 -0.04613 0.003152 -0.04613 0.00315
X Variable 1 0.941492 0.174062 5.408933 2.2E-06 0.591122 1.291861 0.591122 1.29186
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Mahanagar Telephone Nigam Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.577036
R Square 0.332971
Adjusted R
Square 0.31847
Standard
Error 0.072414
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.120409 0.120409 22.96249 1.76E-05
Residual 46 0.241211 0.005244
Total 47 0.36162
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.011339 0.010532 1.076614 0.287267 -0.00986 0.032539 -0.00986 0.03253
X Variable 1 0.717601 0.149752 4.791919 1.76E-05 0.416165 1.019036 0.416165 1.01903
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Bharat Petroleum Corporation Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.478506
R Square 0.228968
Adjusted R
Square 0.212207
Standard
Error 0.099385
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.134927 0.134927 13.66031 0.000581
Residual 46 0.454357 0.009877
Total 47 0.589285
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.0166 0.014455 -1.14859 0.256664 -0.0457 0.012493 -0.0457 0.01249
X Variable 1 0.759632 0.205529 3.695985 0.000581 0.345924 1.173341 0.345924 1.17334
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Sun Pharmaceuticals Industries Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.492229
R Square 0.24229
Adjusted R
Square 0.225818
Standard
Error 0.058973
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.051157 0.051157 14.70923 0.00038
Residual 46 0.159981 0.003478
Total 47 0.211138
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.02178 0.008577 -2.53899 0.014564 -0.03904 -0.00451 -0.03904 -0.0045
X Variable 1 0.467739 0.121958 3.835261 0.00038 0.222251 0.713227 0.222251 0.71322
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48
National Aluminium Company Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.541229
R Square 0.292929
Adjusted R
Square 0.277558
Standard
Error 0.091515
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.159604 0.159604 19.0571 7.13E-05
Residual 46 0.385252 0.008375
Total 47 0.544856
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.02021 0.01331 -1.5181 0.135832 -0.047 0.006586 -0.047 0.00658
X Variable 1 0.826181 0.189255 4.365444 7.13E-05 0.445231 1.207131 0.445231 1.20713
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Satyam Computer Services Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.603246
R Square 0.363906
Adjusted R
Square 0.350078
Standard
Error 0.098423
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.254929 0.254929 26.31633 5.68E-06
Residual 46 0.445607 0.009687
Total 47 0.700536
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.009315 0.014315 0.650738 0.518453 -0.0195 0.03813 -0.0195 0.03813
X Variable 1 1.044151 0.20354 5.129944 5.68E-06 0.634445 1.453856 0.634445 1.45385
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Cummins India Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.532646
R Square 0.283712
Adjusted R
Square 0.26814
Standard
Error 0.074723
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.101732 0.101732 18.21996 9.73E-05
Residual 46 0.256843 0.005584
Total 47 0.358575
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.0024 0.010868 -0.22128 0.825857 -0.02428 0.019471 -0.02428 0.01947
X Variable 1 0.659603 0.154529 4.268484 9.73E-05 0.348553 0.970652 0.348553 0.97065
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51
Punjab Tractors Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.53206
R Square 0.283088
Adjusted R
Square 0.267503
Standard
Error 0.067873
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.083676 0.083676 18.16408 9.94E-05
Residual 46 0.211908 0.004607
Total 47 0.295585
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.003757 0.009872 0.380578 0.705268 -0.01611 0.023628 -0.01611 0.02362
X Variable 1 0.598212 0.140362 4.261934 9.94E-05 0.315679 0.880745 0.315679 0.88074
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52
Kotak Mahindra Bank Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.435344
R Square 0.189525
Adjusted R
Square 0.171906
Standard
Error 0.092116
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.091276 0.091276 10.75681 0.001985
Residual 46 0.39033 0.008485
Total 47 0.481606
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.02916 0.014214 -2.05116 0.045972 -0.05777 -0.00054 -0.05777 -0.00054X Variable 1 0.671103 0.20462 3.279757 0.001985 0.259225 1.082981 0.259225 1.08298
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53
Aurobindo Pharma Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.475613
R Square 0.226208
Adjusted R
Square 0.209387
Standard
Error 0.106415
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.152283 0.152283 13.44751 0.000634
Residual 46 0.520915 0.011324
Total 47 0.673198
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.001019 0.015477 0.065836 0.947794 -0.03014 0.032173 -0.03014 0.03217
X Variable 1 0.80701 0.220069 3.667084 0.000634 0.364035 1.249985 0.364035 1.24998
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54
LIC Housing Finance Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.543934
R Square 0.295864
Adjusted R
Square 0.280557
Standard
Error 0.09314
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.167674 0.167674 19.32833 6.45E-05
Residual 46 0.399052 0.008675
Total 47 0.566726
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.03053 0.013547 -2.25355 0.029034 -0.0578 -0.00326 -0.0578 -0.0032
X Variable 1 0.846811 0.192615 4.396399 6.45E-05 0.459098 1.234524 0.459098 1.23452
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Oil & Natural Gas Corpn Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.357595
R Square 0.127874
Adjusted R
Square 0.108915
Standard
Error 0.09783
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.064551 0.064551 6.744677 0.012585
Residual 46 0.440251 0.009571
Total 47 0.504802
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.03254 0.014229 -2.28682 0.026857 -0.06118 -0.0039 -0.06118 -0.0039
X Variable 1 0.525418 0.202313 2.597052 0.012585 0.118183 0.932654 0.118183 0.93265
8/3/2019 Gaurav Gupta-Return as Calculated by CAPM Model & Actual Returns
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56
Industry :Banks - Private Sector
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.46812
R Square 0.219136
Adjusted R
Square 0.202161
Standard
Error 0.084637
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.092473 0.092473 12.90912 0.000793
Residual 46 0.329517 0.007163
Total 47 0.421991
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.01161 0.01231 -0.94304 0.350586 -0.03639 0.01317 -0.03639 0.01317
X Variable 1 0.628871 0.17503 3.592926 0.000793 0.276553 0.981189 0.276553 0.98118
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57
Indian Overseas Bank
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.391424
R Square 0.153212
Adjusted R
Square 0.134804
Standard
Error 0.099978
Observations 48
ANOVA
df SS MS F
Significance
F
Regression 1 0.083192 0.083192 8.32295 0.00594
Residual 46 0.459795 0.009996
Total 47 0.542988
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept -0.0375 0.014541 -2.57879 0.013179 -0.06677 -0.00823 -0.06677 -0.00823
X Variable 1 0.596479 0.206755 2.884952 0.00594 0.180302 1.012656 0.180302 1.01265
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58
Bharat Electronics Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.570982
R Square 0.32602Adjusted RSquare 0.311368
StandardError 0.098577
Observations 48
ANOVA
df SS MS F Significance
F
Regression 1 0.216227 0.216227 22.25127 2.26E-05
Residual 46 0.447005 0.009718
Total 47 0.663232
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%Intercept -0.03688 0.014337 -2.57263 0.013385 -0.06574 -0.00803 -0.06574 -0.0080
X Variable 1 0.961631 0.203859 4.717125 2.26E-05 0.551283 1.371979 0.551283 1.37197
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59
MphasiS Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.469773
R Square 0.220686Adjusted RSquare 0.203745StandardError 0.167761
Observations 48
ANOVA
df SS MS F Significance
F
Regression 1 0.366609 0.366609 13.02629 0.000755
Residual 46 1.294613 0.028144
Total 47 1.661222
Coefficients Standard
Error t Stat P-value Lower 95% Upper 95%
Lower 95.0%
Upper95.0%
Intercept -0.00603 0.0244 -0.24726 0.80581 -0.05515 0.043081 -0.05515 0.04308
X Variable 1 1.252146 0.346932 3.609196 0.000755 0.553808 1.950484 0.553808 1.95048
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60
Industrial Development Bank of India Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.557742
R Square 0.311076Adjusted RSquare 0.296099
StandardError 0.135531
Observations 48
ANOVA
df SS MS F Significance
F
Regression 1 0.381528 0.381528 20.77075 3.82E-05
Residual 46 0.844952 0.018369
Total 47 1.22648
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%Intercept -0.01529 0.019712 -0.77584 0.441813 -0.05497 0.024385 -0.05497 0.02438
X Variable 1 1.27737 0.280279 4.557494 3.82E-05 0.713198 1.841542 0.713198 1.84154
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Cadila Healthcare Ltd
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.323429
R Square 0.104606Adjusted RSquare 0.085141StandardError 0.095489
Observations 48
ANOVA
df SS MS F Significance
F
Regression 1 0.049001 0.049001 5.374057 0.024938
Residual 46 0.419433 0.009118
Total 47 0.468434
Coefficients Standard
Error t Stat P-value Lower 95% Upper 95%
Lower 95.0%
Upper95.0%
Intercept -0.02118 0.013888 -1.52474 0.13417 -0.04913 0.00678 -0.04913 0.0067
X Variable 1 0.45778 0.197472 2.318201 0.024938 0.060289 0.855271 0.060289 0.85527
In the same way beta was calculated for other companies also