Gaurav Gupta-Return as Calculated by CAPM Model & Actual Returns

8/3/2019 Gaurav Gupta-Return as Calculated by CAPM Model & Actual Returns

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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



2

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



3

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)



4

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)



5

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)



6

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



7

5. Data analysis and Interpretation

6. Bibliography

7.Annexure

o Sample data



8

Phase: 1

Introduction



9

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.



10

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.



11

Limitations of the study:

The study is limited to Indian 70 only

The study is limited to a period of six years.



12

Phase: 2

Theoretical

Framework



13

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.



14

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.



15

-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



17

•

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.



20

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.



21

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.



23

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



24

Phase: 3

Literature Review



25

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.



26

Phase: 4

Methodology



27

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:



28

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



30

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



32

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.



34

Phase 8

BIBLIOGRAPHY



35

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



36

• 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



37

Phase 9

ANNEXURES



38

Calculation of betas for different companies

HDFC

SUMMARY OUTPUT


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


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



39

Dabur India Ltd

SUMMARY

OUTPUT


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


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



40

Housing Development Finance Corporation Ltd

SUMMARY OUTPUT


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


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



41

Indian Hotels Co Ltd

SUMMARY OUTPUT


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


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



42

Bank of Baroda

SUMMARY OUTPUT


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


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



43

Syndicate Bank

SUMMARY OUTPUT


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


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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Tata Steel Ltd

SUMMARY OUTPUT


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


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


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


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


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


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



47

Sun Pharmaceuticals Industries Ltd

SUMMARY OUTPUT


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


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



48

National Aluminium Company Ltd

SUMMARY OUTPUT


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


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



49

Satyam Computer Services Ltd

SUMMARY OUTPUT


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


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



50

Cummins India Ltd

SUMMARY OUTPUT


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


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



51

Punjab Tractors Ltd

SUMMARY OUTPUT


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


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



52

Kotak Mahindra Bank Ltd

SUMMARY OUTPUT


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


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



53

Aurobindo Pharma Ltd

SUMMARY OUTPUT


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


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



54

LIC Housing Finance Ltd

SUMMARY OUTPUT


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


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



55

Oil & Natural Gas Corpn Ltd

SUMMARY OUTPUT


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


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



56

Industry :Banks - Private Sector

SUMMARY OUTPUT


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


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



57

Indian Overseas Bank

SUMMARY OUTPUT


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


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



58

Bharat Electronics Ltd

SUMMARY OUTPUT


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


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



59

MphasiS Ltd

SUMMARY OUTPUT


Multiple R 0.469773

R Square 0.220686Adjusted RSquare 0.203745StandardError 0.167761

Observations 48

ANOVA


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



60

Industrial Development Bank of India Ltd

SUMMARY OUTPUT


Multiple R 0.557742

R Square 0.311076Adjusted RSquare 0.296099

StandardError 0.135531

Observations 48

ANOVA


F

Regression 1 0.381528 0.381528 20.77075 3.82E-05

Residual 46 0.844952 0.018369

Total 47 1.22648

Coefficients

Standard


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



Cadila Healthcare Ltd

SUMMARY OUTPUT


Multiple R 0.323429

R Square 0.104606Adjusted RSquare 0.085141StandardError 0.095489

Observations 48

ANOVA


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

Gaurav Gupta-Return as Calculated by CAPM Model & Actual Returns

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Transcript of Gaurav Gupta-Return as Calculated by CAPM Model & Actual Returns