Comparison of CAPM & APT

A Comparison of CAPM & Arbitrage Pricing Theory

M.P.BIRLA INSTITUTE OF MANAGEMENT 1


Submitted in partial fulfillment of the requirements of The M.B.A Degree Course of Bangalore University

By

RAKESH KUMAR (REGD.NO: 05XQCM6071)

Under the Guidance Of

Dr. T. V. Narasimha Rao

M.P.BIRLA INSTITUTE OF MANAGEMENT Associate Bharatiya Vidya Bhavan

43, Race Course Road, Bangalore-560001

2005-2007



DECLARATION

I hereby declare that this dissertation work entitled “A Comparison

of CAPM & Arbitrage Pricing Theory” is a bonafide study,

completed under the guidance and supervision of Dr. T.V.N.Rao

and submitted in partial fulfillment for the award of MASTERS

OF BUSINESS ADMINISTRATION degree at Bangalore

University.

I further declare that this project is the result of my own effort and

that it has not been submitted to any other university/institution for

the award of any degree or diploma or any other similar title of

recognition.

BANGALORE RAKESH KUMAR DATE: Reg No: 05XQCM6071



PRINCIPAL’S CERTIFICATE

I here by certify that this project dissertation report is undertaken

and completed by Mr. Rakesh Kumar bearing Reg. No.

05XQCM6071 on “Comparison of CAPM & Arbitrage Pricing

Theory” under the guidance of Dr: T. V. N RAO Adjunct

Professor, M P Birla Institute of Management, Bangalore.

Place: Bangalore Dr Nagesh S Malavalli

Date: (Principal, MPBIM)



GUIDE CERTIFICATE

I here by certify that project work embodied in the dissertation

entitled is the result of an study undertaken and completed by

Mr. Rakesh Kumar bearing Reg No: 05XQCM6071 on “A

Comparison of CAPM & Arbitrage Pricing Theory” under my

guidance and supervision.

Place: Bangalore

DATE: Dr: T. V. N RAO



ACKNOWLEDGEMENT

As students collect accolades in the form of grades for the success

in his endeavors and his success depends on adequate preparation

and in domination and most important of all the support received

from his guide. So the accolades I earn of this project, I would like

to share with all those who have played a notable part in its making

In these two months I have worked on it, I feel indebted to many

and extend my heart full gratitude and profusely thank those

people who not only gave assistance to me but also participated in

the making of this project.

I sincerely thank to Dr .T.V.N Rao my esteemed project guide for

his valuable advice, assistance and guidance provided. I also

remain grateful to all my friends for their assistance to prepare this

project successfully.

My gratitude will not be complete without thanking the almighty

god and my loving parents who have been supportive through out

the project.

Rakesh Kumar



TABLE OF CONTENTS

CHAPTERS PARTICULARS

PAGE NO.

ABSTRACT 01 1 INTRODUCTION AND THEORETICAL

BACKGROUND 02

2 REVIEW OF LITERATURE 10 3 RESEARCH METHODOLOGY 14

3.1 PROBLEM STATEMENT 15 3.2 OBJECTIVE OF THE STUDY 15 3.3 SAMPLE SIZE AND DATA SOURCES 16 4 CONCLUSION 17 5 BIBLIOGRAPHY 19 6 ANNEXURE 24

7 REFERENCES 26



ABSTRACT

This research presents some new evidence that Arbitrage Pricing Theory may lead to

different and better estimates of expected return than the Capital Asset Pricing Model,

particularly in the case of cost of capital. Results for monthly portfolio returns for 2001-

2006 lead to the conclusion that regulators should not adopt the single-factor risk

approach of the CAPM as the principal measure of risk, but give greater weight to APT,

whose multiple factors provide a better indication of asset risk and a better estimate of

expected return.

Not withstanding initial skepticism and recent challenges, the Capital Asset Pricing

Model (CAPM) has been used to develop project screening rates, value companies,

measure the impact of policy change on risk, and construct portfolios. Recently, the

Federal Energy Regulatory Commission (FERC) proposed it as the principal measure of

risk for the electric utilities it regulates. It would be ironic for acceptance of CAPM by

policymakers to occur just as Arbitrage Pricing Theory (APT) threatens to replace it as an

explanation of the relationship between return and risk. And it would be a pity if FERC

were to adopt the single risk factor approach of CAPM when it could be demonstrated

that the multiple factors of APT provide a better indication of asset risk and a better

estimate of expected return. This paper presents some new evidence that APT may lead

to different and better estimates of expected return than CAPM and that it may be more

helpful to policymakers as a result. We describe CAPM and APT, note work done by

others, show how estimates of required returns for utilities developed by applying each

model may differ, and finally report the evidence that convinces us that if one model is to

be relied upon for policy purposes, APT would be the better choice.



CHAPTER 1

INTRODUCTION AND

THEORETICAL BACKGROUND



INTRODUCTION AND THEORETICAL BACKGROUND

The estimation of firm’s cost of capital remains one of the most critical and challenging

issues faced by financial managers, analysts, and academicians. Although theory provides

several broad approaches, recent survey evidence reports that among large firms and

investors, the Capital asset pricing model (CAPM) is by far the most widely used model.

The Arbitrage Pricing Theory (APT),originally formulated by Ross, and extended by

Huberman and Connor, is an asset pricing model that explains the cross-sectional

variation in asset returns. Like the Capital Asset Pricing Model (CAPM) of Sharpe,

Lintner, and Black, the APT begins with an assumption on the return generating process:

each asset return is linearly related to several, say k, common "global" factors plus its

own idiosyncratic disturbance.

Capital Asset Pricing Model (CAPM): It is used in finance to determine a theoretically

appropriate required rate of return (and thus the price if expected cash flows can be

estimated) of an asset, if that asset is to be added to an already well-diversified portfolio,

given that asset's non-diversifiable risk. The CAPM formula takes into account the asset's

sensitivity to non-diversifiable risk (also known as systematic risk or market risk), in a

number often referred to as beta (β) in the financial industry, as well as the expected

return of the market and the expected return of a theoretical risk-free asset.

The model was introduced by Jack Treynor, William Sharpe, John Lintner and Jan

Mossin independently, building on the earlier work of Harry Markowitz on



diversification and modern portfolio theory. Sharpe received the Nobel Memorial Prize in

Economics (jointly with Harry Markowitz and Merton Miller) for this contribution to the

field of financial economics.

The formula

The CAPM is a model for pricing an individual security (asset) or a portfolio. For

individual security perspective, we made use of the security market line (SML) and its

relation to expected return and systematic risk (beta) to show how the market must price

individual securities in relation to their security risk class. The SML enables us to

calculate the reward-to-risk ratio for any security in relation to that of the overall market.

Therefore, when the expected rate of return for any security is deflated by its beta

coefficient, the reward-to-risk ratio for any individual security in the market is equal to

the market reward-to-risk ratio, thus:

Individual security’s = Market’s securities (portfolio)

Reward-to-risk ratio Reward-to-risk ratio

The market reward-to-risk ratio is effectively the market risk premium and by rearranging

the above equation and solving for E (Ri), we obtain the Capital Asset Pricing Model

The APT model



Arbitrage pricing theory (APT), in Finance, is a general theory of asset pricing, that has

become influential in the pricing of shares. The theory was initiated by the economist

Stephen Ross in 1976.

APT holds that the expected return of a financial asset can be modeled as a linear

function of various macro-economic factors or theoretical market indices, where

sensitivity to changes in each factor is represented by a factor specific beta coefficient.

The model derived rate of return will then be used to price the asset correctly - the asset

price should equal the expected end of period price discounted at the rate implied by

model. If the price diverges, arbitrage should bring it back into line.

If APT holds, then a risky asset can be described as satisfying the following relation:

where

• E(rj) is the risky asset's expected return,

• RPk is the risk premium of the factor,

• rf is the risk-free rate,

• Fk is the macroeconomic factor,

• bjk is the sensitivity of the asset to factor k, also called factor loading,

• and εj is the risky asset's idiosyncratic random shock with mean zero.

That is, the uncertain return of an asset j is a linear relationship among n factors.

Additionally, every factor is also considered to be a random variable with mean zero.

Note that there are some assumptions and requirements that have to be fulfilled for the

latter to be correct: There must be perfect competition in the market, and the total number

of factors may never surpass the total number of assets (in order to avoid the problem of

matrix singularity),



Arbitrage mechanics

In the APT context, arbitrage consists of trading in two assets – with at least one being

mispriced. The arbitrageur sells the asset which is relatively too expensive and uses the

proceeds to buy one which is relatively too cheap.

Under the APT, an asset is mispriced if its current price diverges from the price predicted

by the model. The asset price today should equal the sum of all future cash flows

discounted at the APT rate, where the expected return of the asset is a linear function of

various factors, and sensitivity to changes in each factor is represented by a factor-

specific beta coefficient.

A correctly priced asset here may be in fact a synthetic asset - a portfolio consisting of

other correctly priced assets. This portfolio has the same exposure to each of the

macroeconomic factors as the mispriced asset. The arbitrageur creates the portfolio by

identifying x correctly priced assets (one per factor plus one) and then weighting the

assets such that portfolio beta per factor is the same as for the mispriced asset.

When the investor is long the asset and short the portfolio (or vice versa) he has created a

position which has a positive expected return (the difference between asset return and

portfolio return) and which has a net-zero exposure to any macroeconomic factor and is

therefore risk free (other than for firm specific risk). The arbitrageur is thus in a position

to make a risk free profit:

Where today's price is too low:

The implication is that at the end of the period the portfolio would have appreciated at the

rate implied by the APT, whereas the mispriced asset would have appreciated at more

than this rate. The arbitrageur could therefore:

Today:

1 short sells the portfolio

2 buy the mispriced-asset with the proceeds.

At the end of the period:

1 sells the mispriced asset

2 use the proceeds to buy back the portfolio

3 pocket the difference.



Where today's price is too high:

The implication is that at the end of the period the portfolio would have appreciated at the

rate implied by the APT, whereas the mispriced asset would have appreciated at less than

this rate. The arbitrageur could therefore:

Today:

1 short sells the mispriced-asset

2 buy the portfolio with the proceeds.

At the end of the period:

1 sells the portfolio

2 use the proceeds to buy back the mispriced-asset

3 pocket the difference.

Relationship with the capital asset pricing model

The APT along with the capital asset pricing model (CAPM) is one of two influential

theories on asset pricing. The APT differs from the CAPM in that it is less restrictive in

its assumptions. It allows for an explanatory (as opposed to statistical) model of asset

returns. It assumes that each investor will hold a unique portfolio with its own particular

array of betas, as opposed to the identical "market portfolio". In some ways, the CAPM

can be considered a "special case" of the APT in that the securities market line represents

a single-factor model of the asset price, where Beta is exposure to changes in value of the

Market.

Additionally, the APT can be seen as a "supply side" model, since its beta coefficients

reflect the sensitivity of the underlying asset to economic factors. Thus, factor shocks

would cause structural changes in the asset's expected return, or in the case of stocks, in

the firm's profitability.



On the other side, the capital asset pricing model is considered a "demand side" model.

Its results, although similar to those in the APT, arise from a maximization problem of

each investor's utility function, and from the resulting market equilibrium (investors are

considered to be the "consumers" of the assets).

Identifying the factors

As with the CAPM, the factor-specific Betas are found via a linear regression of

historical security returns on the factor in question. Unlike the CAPM, the APT, however,

does not itself reveal the identity of its priced factors - the number and nature of these

factors is likely to change over time and between economies. As a result, this issue is

essentially empirical in nature. Several a priori guidelines as to the characteristics

required of potential factors are, however, suggested:

1. Their impact on asset prices manifests in their unexpected movements

2. They should represent undiversifiable influences (these are, clearly, more likely to

be macroeconomic rather than firm-specific in nature)

3. Timely and accurate information on these variables is required

4. The relationship should be theoretically justifiable on economic grounds

Chen, Roll and Ross identified the following macro-economic factors as

significant in explaining security returns:

• Surprises in inflation;

• Surprises in GNP as indicted by an industrial production index;

• Surprises in investor confidence due to changes in default premium in

corporate bonds;

• Surprise shifts in the yield curve.

As a practical matter, indices or spot or futures market prices may be used in place of

macro-economic factors, which are reported at low frequency (e.g. monthly) and often

with significant estimation errors. Market indices are sometimes derived by means of

factor analysis. More direct "indices" that might be used are:

• short term interest rates;



• The difference in long-term and short term interest rates;

• A diversified stock index such as the S&P 500 or NYSE Composite Index;

• oil prices

• gold or other precious metal prices

Currency exchange rates

Factor Analysis and the Estimation of the Factor Loadings:

The procedure to estimate factor loadings (i.e., the b,,'s) for all assets corresponding to

the same set of common factors is quite involved and expensive. We first do a factor

analysis on an initial subset of assets, and then we extend the factor structure of the

subset to the entire sample. This is accomplished via a large scale mathematical

programming exercise. Section I1 contains a brief outline.

It is clear that the development of the theory of arbitrage pricing is quite separate from

the factor analysis. We use factor analysis here only as statistical tools to uncover the

pervasive forces (factors) in the economy by examining how asset returns covary

together. As with any statistical method, its result is meaningful only when the method is

applied to a representative sample. In the present context, the initial subset to which the

factor analysis is applied should consist of a large random sample of securities of net

positive supply in the economy; thus the sample would be closely representative of the

risks borne by investors. In a recent article, Shanken [37] points out some of the potential

pitfalls of testing the APT, when the factored covariance matrix is unrepresentative of the

co variation of assets in the economy.



CHAPTER 2

REVIEW OF LITERATURE



REVIEW OF LITERATURE

Review of literature .means examining and analyzing the various literatures available in

any field either for references purposes or for further research.

Further research can be done by identifying the areas which have not been studied and in

turn undertaking research to add value to the existing literature.

For the purpose of literature review various sources of information have been used.

Sources include books, journals as well as some literature papers.

Nai fu chen :– Some Empirical Tests of the Theory of Arbitrage Pricing

In his project Nai fu Chen, had done some empirical tests of the theory of arbitrage, it

estimate the parameters of APT. Using daily return data during the 1963-78 period, this

project compare the evidence on the APT and the Capital Asset Pricing Model (CAPM)

as implemented by market indices and find that the APT performs well. The theory is

further supported in that estimated expected returns depend on estimated factor loadings,

and variables such as own variance and firm size do not contribute additional explanatory

power to that of the factor loadings.



Empirical Result:

Based on the empirical evidence gathered so far, the APT cannot be rejected in favor of

any alternative hypothesis, and the APT performs very well against the CAPM as

implemented by the S&P 500, value weighted, and equally weighted indices. Therefore,

the APT is a reasonable model for explaining cross-sectional variation in asset returns.

K C John Wei: - An Asset Pricing Theory Unifying the CAPM and APT

This study shows that the competitive-equilibrium version of the APT may be extended

to develop an exact model if idiosyncratic risks obey the Ross separating distribution.

The results indicate that one only need add the market portfolio as an extra factor to the

factor model in order to obtain an exact asset-pricing relation. Thus, this study presents

an extension and integration of the CAPM and APT. The "empirical" APT is also

generalized to allow for some factors to be omitted from the econometric model

employed to test the theory. The developed model is extremely robust and may be

reduced to the CAPM or expanded to approximate Ross's APT depending upon the

number of omitted factors. Further, the importance of the market portfolio is shown to be

a monotonic increasing function of the number of omitted factors. Finally, the study

demonstrates that, in a finite economy, the pricing-error bound of the Ross APT in a

correlated-residuals factor structure is an increasing function of the absolute value of

market-residual beta, rather than the weight of the asset in the market portfolio as is the

case of uncorrelated factor residuals. However, under the normality assumption, the

pricing error becomes an extra component related to the market-portfolio factor, and the

exact asset-pricing relation is once again obtained.

Conclusion: The APT emphasizes the role of the covariance between asset returns and exogenous

factors, while the CAPM stresses the covariance between asset returns and the



endogenous market portfolio. In this study, the positive aspects of each model are

combined to derive a theory unifying both models. The approach is based upon Connor's

competitive-equilibrium version of the APT and Ross's separating distribution. The

derived results demonstrate that one need only add the market portfolio as an extra factor

to the factor model in order to obtain an exact asset-pricing relation.

In addition to this derivation, they have also proved that the new approach may be

applied to generalize the "empirical" APT with some factors omitted from the

econometric model. This generalized theory is shown to be an integrated model of the

CAPM and APT. If all factors are omitted, the new model reduces to the CAPM. When

none of the factors is omitted, the new model becomes either the Ross APT in an infinite

economy or the unified asset-pricing theory in a finite economy.

Philip H Dybvig; Stephen A Ross : - Yes, The APT is Testable

The Arbitrage Pricing Theory (APT) has been proposed as an alternative to the

meanvariance Capital Asset Pricing Model (CAPM). This paper considers the testability

of the APT and points out the irrelevance for testing of the approximation error. We

refute Shanken's objections, including his assertion that Roll's critique of the CAPM is

applicable to the APT. We also explain the testability of the APT on subsets, and we

explore the relationship between the APT and the CAPM.

The Arbitrage Pricing Theory uses a factor model for asset returns to capture the intuition

that there are many close substitutes in asset markets. The word "arbitrage" in the name

comes from the limiting case in which there is no idiosyncratic noise. In this case, the

linearity of expected returns in factor loadings is a direct consequence of the absence of

arbitrage, since in this case portfolios with identical factor loadings are perfect

substitutes. More generally, the APT follows in theoretical models with assumptions

ensuring that portfolios with identical factor loadings are close substitutes. Empirically,



the APT should be tested as an equality. Understanding these definitions lies at the heart

of the relationship between the theory and empirics of the APT.

CHAPTER 3

RESEARCH METHODOLOGY



3.1 Statement of Problem

CAPM and APT have many uses in real life. They can be used for testing the efficiency

of the market, to describe the return generating process and so on. Among the various

uses, they are prominently employed for calculating the cost of capital. Hence, a study of

their applicability will be usefull to the practitioners of Corporate Finance.

3.2 Objectives

To compare the applicability of Equilibrium Asset Pricing Models such as CAPM and

APT.



SAMPLE SIZE AND DATA SOURCES

In this study S&P CNX Nifty index has been considered as a proxy for the stock market

and accordingly the closing index values were collected from Jan 1,2001 till December

31, 2006.

Out of the total observations the data pertaining to Jan 1, 2001 till December 2005

totaling 60 months observations of NIFTY were used for estimation of the model

parameters and the remaining observations will be used for out of sample forecasting also

known as hold out sample. Therefore the first month for which out of sample forecasts

are obtained is January, 2006 and the out of sample forecasts were constructed for 12

months till December 2006. The monthly average prices were converted into continuous

compounded returns in the standard method as the log differences:

Rt = ln (It / It-1)

Where, It stands for the closing index value on day‘t’;



CHAPTER

CONCLUSION



Conclusion

The APT emphasizes the role of the covariance between asset returns and exogenous

factors, while the CAPM stresses the covariance between asset returns and the

endogenous market portfolio. The approach is based upon Connor's competitive-

equilibrium version of the APT and Ross's separating distribution. The derived results

demonstrate that one need only add the market portfolio as an extra factor to the factor

model in order to obtain an exact asset-pricing relation. If all factors are omitted, the new

model reduces to the CAPM. When none of the factors is omitted, the new model

becomes either the Ross APT in an infinite economy or the unified asset-pricing theory in

a finite economy.

While calculating CAPM in this study,

• Value of R square is very low, so it does not have explanatory power • Value of F test is less than its 5% significant level, so it is not significant • Value of T test is less than 2 so it is not significant • Calculated expected return is undervalued

CAPM is not valid.

In factor analysis we have taken 9 factors out of which only 2 factors are priced , but it is

not possible to recognize the factor. Factor 3 is showing negative t value and factor 7 is

showing positive t value.



Annexure

Table 1

SUMMARY OUTPUT

Regression Statistics Multiple R 0.093422 R Square 0.008728 Adjusted R Square -0.00449 Standard Error 0.024928 Observations 77 ANOVA

df SS MS F Significance

F Regression 1 0.00041 0.00041 0.660342 0.419011285 Residual 75 0.046606 0.000621 Total 76 0.047016

Coefficients Standard

Error t Stat P-value Lower 95% Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.004153 0.007683 0.540484 0.590465-

0.011153056 0.019458 -0.01115 0.01945834

X Variable 1 0.006266 0.007711 0.812614 0.419011-

0.009095149 0.021627 -0.0091 0.02162745



Table 2

Rotated Component Matrix(a) 1 2 3 4 5 6 7 8 9aurophar 0.5109 0.1203 0.046 0.3762 0.0364 0.1894 0.204 0.1807 0.3552gail 0.222 0.3164 0.5245 0.1958 0.2908 0.3106 0.1908 0.1546 -0.126kotakmahin 0.4871 0.3458 0.392 0.0857 0.0096 -0.044 0.2063 0.1703 0.2545ttml 0.1923 0.2672 -0.021 0.1126 0.6198 0.3564 -0.078 0.1553 0.0969cpcl 0.1081 0.3751 0.4158 0.4081 0.1977 0.2204 -0.019 -0.31 0.1709ing 0.1445 0.6375 0.2661 0.0452 0.3027 0.0774 0.0598 0.2434 0.118ingersol 0.293 0.4629 0.2759 0.3818 0.0431 0.0025 -0.146 0.226 0.191punjabtrac 0.193 0.1752 0.1873 0.3222 0.0383 0.4243 0.3657 0.3479 0.0679hcl 0.803 0.0312 0.0614 0.2216 0.2046 0.0797 0.1902 0.0398 -0.007moserbaer 0.0535 0.3116 0.1843 0.0671 -0.005 0.0681 0.6254 0.233 -0.027hdfcl 0.2078 0.335 0.2124 0.2603 0.5473 0.0085 0.1673 0.3601 0.0189nicholus 0.3475 0.3343 0.2169 0.4588 0.2781 0.0699 0.0919 0.0338 0.1895polaris 0.6999 0.2201 0.1924 0.1679 0.0746 0.1797 0.1944 -0.129 -0.112siemens 0.2733 0.2714 0.3148 0.5175 0.0643 0.1048 0.2713 0.0964 0.2355sydicatebnk 0.0984 0.7893 0.1345 0.1801 0.0659 0.219 0.2091 0.0528 0.1168lic 0.1345 0.5169 0.4018 0.1423 0.1234 0.2211 0.1395 0.3078 -0.014ipcl 0.2461 0.0646 0.5565 0.0783 -0.096 0.6097 0.0537 -0.066 0.1204iob 0.0222 0.7881 0.185 0.1728 0.032 0.1692 0.195 -0.155 0.0542lupin -0.074 0.0209 -0.087 0.1185 -0.029 0.0663 -0.133 0.2146 0.7627mphasis 0.7727 0.1418 0.2284 0.1077 -0.189 0.0668 0.0975 0.1934 0.1142mtnl 0.2197 0.24 0.3661 0.2266 0.2796 0.2879 0.2038 0.0884 0.1525tvs 0.333 0.1517 0.4456 0.2657 -0.142 0.3417 0.0869 0.4027 0.3129raymond 0.3814 0.2223 0.1643 0.6521 0.1174 0.284 0.1333 0.1873 0.097sterlite 0.0394 0.0348 -0.015 0.0103 0.1481 -0.078 0.6185 0.1373 0.2609indhotel 0.4449 0.1327 0.2314 0.4201 0.2344 0.159 0.3674 0.1766 -0.079andhrabnk -0.029 0.8309 0.0185 0.1514 -0.055 0.2172 0.0677 0.0336 0.1212wokhardt 0.3205 0.1208 0.1646 0.2001 0.4477 -0.036 0.0634 -0.071 0.5227containercorp 0.3052 0.351 0.5912 0.0912 0.105 0.2235 0.0364 0.1333 0.1531



ifci 0.1546 0.5029 0.1895 0.1119 0.3214 0.5123 -0.088 0.2718 0.0446ibp 0.0626 -0.068 0.707 0.1216 0.2667 0.0311 0.0088 0.2917 0.075aventis 0.0667 0.1766 0.1107 0.7191 0.3854 0.0608 0.0214 0.0295 0.2683nirma 0.4718 0.3232 0.0778 0.4594 0.1629 0.1858 -0.037 0.1797 -0.04satyam 0.8525 -0.009 0.1192 0.1958 0.1302 0.1392 -0.005 0.1124 0.1026hpcl 0.1486 0.3387 0.7454 0.0759 0.0033 0.1508 0.1522 0.1575 0.0274brpl 0.0861 0.4353 0.278 0.278 0.0182 0.5112 -0.099 -0.043 0.1946ashokley 0.3035 0.292 0.335 0.1744 0.3311 0.3015 0.1714 0.3042 0.0701idbi 0.0838 0.4661 0.2167 0.2377 0.195 0.4995 0.167 0.0691 -0.004asianpaint 0.223 0.2975 0.1937 0.4103 0.2034 -0.093 -0.065 0.283 0.0471cummin 0.4206 0.2973 0.0968 0.3296 0.2734 0.18 0.1427 0.0721 0.2057wipro 0.8646 0.0412 0.0302 0.0677 0.2348 0.0302 -0.06 0.1207 0.0887m&m 0.5526 0.2199 0.2221 0.1548 0.1674 0.2403 0.32 0.1622 0.0643utibnk 0.4071 0.5818 0.1865 0.2695 0.2287 0.0656 0.1233 0.0926 0.0036corpbnk 0.0422 0.5564 0.3558 0.1119 0.3418 -0.08 0.2503 0.0858 0.1085tatamotor 0.5344 0.2415 0.2308 0.0888 0.2056 0.3443 0.2126 0.2956 0.1966hindalco 0.3064 0.1774 0.2773 0.2985 0.2144 0.3863 0.4541 0.126 -0.067apollo 0.5545 0.4244 0.0441 0.1335 0.0116 0.3856 0.1679 0.0134 -0.004cadila 0.2017 0.1191 0.1149 0.19 0.2478 0.2664 0.2509 -0.02 0.7005pfizer 0.1479 0.2139 0.1731 0.7506 0.1403 0.1471 0.0647 0.1349 0.1319abb 0.3019 0.3046 0.3838 0.3341 0.2684 0.047 0.4045 0.0748 -0.065acc 0.4594 0.085 0.1405 0.0942 0.451 0.3523 0.3126 0.1542 0.0548bajaj auto 0.3526 0.0287 0.2423 0.1249 0.1716 0.402 0.0705 0.497 0.2435bhel 0.3769 0.3261 0.3956 0.1779 0.2006 0.1921 0.4497 0.091 -0.085bpcl 0.0333 0.2269 0.7439 0.1873 0.1148 0.2018 0.2186 0.1767 -0.059cipla 0.3515 0.011 0.0296 0.2686 0.4987 0.1024 0.2227 0.1564 0.2972dr reddy 0.1357 0.1521 0.0598 0.069 0.1933 0.0361 0.2498 0.6365 0.2093glaxo 0.2918 0.1272 0.2509 0.7117 0.068 0.0227 0.2476 0.0793 0.2321grasim 0.3283 0.2614 0.1701 0.139 0.4572 0.3191 0.4918 0.0129 0.0935gujambuja 0.4697 0.1383 0.2286 0.089 0.4148 0.3157 0.3183 -0.031 -1E-04hdfc 0.2083 0.3353 0.2119 0.2615 0.5461 0.0074 0.1649 0.3592 0.0189herohonda 0.2679 0.0625 0.2227 0.1688 0.0766 0.0137 0.0776 0.5234 0.186hind lever 0.0886 0.0759 0.1763 0.2153 0.45 0.0341 0.2496 0.5897 0.044icici 0.2639 0.4054 0.3045 0.2682 0.0437 0.1316 0.3251 0.2129 -0.105infosys 0.8235 -0.064 0.0552 0.0885 0.2436 0.0492 0.0258 0.0633 -0.012itpl 0.2471 0.0641 0.5581 0.0784 -0.096 0.6089 0.0536 -0.063 0.1156itc 0.2273 0.1578 0.1429 0.426 0.1449 0.1315 0.4743 0.1018 -0.131L N T 0.4843 0.0696 0.1451 0.3766 0.2577 0.2138 0.3063 0.2117 -0.212Nationalalum 0.0669 0.2251 0.5613 0.3126 0.0873 0.2414 0.3692 0.1487 -0.041ongc 0.1522 0.3323 0.6777 0.2532 0.1248 0.0138 0.0132 -0.042 0.0355ranbaxy 0.1128 0.3212 0.1395 0.172 0.0901 0.0692 0.0999 0.3332 0.5853reliance 0.3283 0.1579 0.4372 0.0446 0.2515 0.1229 0.4358 -0.155 0.149



sail 0.1957 0.3388 0.0642 0.0035 0.2955 0.7636 0.0292 0.0751 0.0891sbin 0.2277 0.5972 0.3049 0.0992 0.2383 0.1285 0.3136 0.2027 -0.043

sun pharma 0.3444 0.0208 0.2377 0.184 0.5911 -0.032 0.1694 0.1568 0.3497tata power 0.3582 0.3368 0.2897 0.0924 0.4172 0.3573 0.3759 0.0245 -0.079tata steel 0.3784 0.2259 0.1759 0.1791 0.2585 0.5837 0.3301 0.0376 0.057vsnl 0.2095 0.0964 0.3138 0.2919 0.4618 0.1323 0.2997 -0.02 -0.208zeel 0.6438 0.2004 0.1808 0.1289 0.2344 0.196 0.0272 0.1532 0.2042Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a Rotation converged in 14 iterations.

Table 3

Table 4

Unrotated

Coefficients(a)

Model Unstandardized Coefficients

Standardized Coefficients t Sig.

B Std. Error Beta 1 (Constant) 0.016539 0.01043 1.585734 0.117182

factors 1 -0.00054 0.01623 -0.00446 -0.0335 0.973369 2 -0.01549 0.020135 -0.08957 -0.76909 0.444354

Rotated Coefficients(a)

Model Unstandardized Coefficients

Standardized Coefficients t Sig.

B Std. Error Beta 1 (Constant) 0.01908 0.004277 4.461336 3.19E-05

factors 1 0.018485 0.012235 0.174944 1.51079 0.135544 2 -0.02006 0.013396 -0.17132 -1.49758 0.138939

3 -0.03 0.013907 -0.24794 -2.15685 0.034609 4 -0.02646 0.016681 -0.17829 -1.58636 0.117367 5 -0.01789 0.021533 -0.09272 -0.83099 0.40893 6 0.00366 0.016917 0.024004 0.21634 0.82938 7 0.059699 0.027403 0.239006 2.178585 0.032885 8 -0.00284 0.024151 -0.013 -0.11747 0.906843 9 -0.00917 0.019102 -0.05354 -0.48014 0.632691a Dependent Variable: VAR00001



3 0.027614 0.043689 0.07837 0.632049 0.529357 5 -0.07144 0.050484 -0.17545 -1.415 0.161378a Dependent Variable: VAR00001

BIBLIOGRAPHY

BOOKS

1. Basic Econometrics: By Damodar N. Gujrati

2. Introductory Econometrics: By Ramu Ramanathan

WEBSITES

1. www.nseindia.com

2. www.yahoofinance.com

3. www.capitaline.com

4. www.jstor.com

5. www.google.com

ECONOMETRICS SOFTWARE PACKAGES

1. SPSS



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G. Chamberlain. "Funds, Factors, and Diversification in Arbitrage Pricing Models."

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J. Jobson. "A Multivariate Linear Regression Test for the Arbitrage Pricing

Theory." Journal of Finance 37 (September 1982), 1037-42.

P. Pfleiderer. "A Short Note on the Similarities and the Differences between the

Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT)."

Graduate School of Business Working Paper, Stanford University, 1983.

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(December 1982), 1129-40.



M. Jensen, and M. Scholes. "The Capital Asset Pricing Model: Some Empirical

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Comparison of CAPM & APT

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