ma831 ezekiel peeta-imoudu disso

Ezekiel Peeta-Imoudu 1201252

MA831 FINAL YEAR PROJECT

A Review of the Capital Asset Pricing Model (CAPM):Testing the validity of the CAPM on the Volatility.

Ezekiel Peeta-Imoudu

1201252

BSc Economics and Mathematics

May 2015

Supervisor: Dr Haslifah Hasim

2

Department of Mathematical Sciences


Abstract

Ever since the derivation of The Capital Asset Pricing Model (CAPM), a

large number of studies have been dedicated to investigating and

assessing its validity and performance. These studies have significantly

impacted the field of financial economics, with some empirical studies

supporting the model, while others disputing and opposing the model. This

paper provides a comprehensive review of the CAPM, with the first part discussing the

theory, as well as the main literature on the continuing academic debate of its validity. The

second part is empirical, paying particular attention to testing validity by estimating Beta for

12 selected companies on the London Stock Exchange (LSE) over the period 2001-2010, and

comparing it to actual Beta results by a paired sample t-test, regression analysis, Pearson

correlation and a Kruskal-Wallis test.

Research results show that the CAPM is almost completely valid in the LSE, with 11 out of

12 of the companies showing no significant differences between the estimated Betas and the

actual beta, hence providing evidence in support of the model. The overall result demonstrates

the CAPM is valid in the LSE.

Keywords: Asset, Pricing Model, CAPM, Security, Beta, Risk, Expected return, and Market portfolio.

3


Acknowledgments

Completing this dissertation without support and encouragement from friends and family

would have been impossible. For that reason I would like to thank them. I also wish to thank

Dr. Aris Peperoglou, for always willing to help and give his best suggestions.

Massive thanks to Dr. Haslifah Hasim, my supervisor, for her excellent guidance, caring,

patience, and provision throughout the course of this project. My deepest gratitude goes

towards her. She encouraged and challenged my growth and development as a writer,

researcher, experimentalist, a problem solver and someone who thinks independently. Not a

lot of supervisors give their students the opportunity to develop and embrace a sense of self-

sufficiency and individuality, by letting them carry out independent work, whilst still being

constantly available in case of help or clarity; however, you have done for me this

remarkably. Therefore for this and everything you did for me, I appreciate you. Thank you

once again for agreeing to work with me on this project; it definitely would not have been

possible without your help.

Furthermore, I would like to thank the Department of Mathematical Sciences of Essex

University for this wonderful opportunity to enable students like me to contribute to the world

of research, both theoretically and empirically whilst developing and learning new skills in

the process. Thank you for this challenge.

Finally, I would like to thank the Almighty God for his grace and strength, which saw me

through this project from start to finish, despite the difficulties and problems encountered. For

this I say, Glory Be to God.

4


Table of Contents

1. Introduction..........................................................................................................................................................5

1.1 Overview of Asset Pricing Models......................................................................................................................7

1.2 CAPM Introduction...........................................................................................................................................11

1.3 Research Objectives...........................................................................................................................................13

2. Literature Review..............................................................................................................................................15

2.1 Introduction.......................................................................................................................................................15

2.2 CAPM Theory...................................................................................................................................................16

2.3 Evidence and Critique of the CAPM...............................................................................................................23

2.4 Advancements to the CAPM............................................................................................................................28

2.5 CAPM and Arbitrage Pricing Model (APT) Debate.....................................................................................31

2.6 Conclusion..........................................................................................................................................................35

3. Methodology and Data......................................................................................................................................37

3.1 Sample Selection................................................................................................................................................37

3.2 Data Selection....................................................................................................................................................38

3.3 Beta Estimating and Testing Method..............................................................................................................39

4. Empirical Results and Analysis.......................................................................................................................43

4.1 Empirical Results..............................................................................................................................................43

4.2 Descriptive Statistics.........................................................................................................................................45

4.3 Kruskal-Wallis Test..........................................................................................................................................46

4.4 Regression and Time-Series Analysis..............................................................................................................46

5. Conclusion..........................................................................................................................................................50

5.1 Future Research................................................................................................................................................51

6. Appendix............................................................................................................................................................53

7. Bibliography/References...................................................................................................................................54

5


1. Introduction

Asset Pricing Theory

Accurately measuring the trade-off that exists between the expected return and risk is one of

the main problems in a financial market, and the Theory of Asset Pricing helps to address this.

Professional investors and other people who in their daily life invest their money in one form

or the other will need to make key decisions from time to time; the behaviour of asset prices is

useful for this. To expand on this, an individual saving or investing in one financial form or

the other will make that choice depending on what they think of the risks and returns that are

related with the various forms of investment. Risk is an important factor for investors when it

comes to making investments as for example, the greater the risk of the investment, the less

likely it is for a person who is risk-averse to want to take the risk and make that investment,

unless the amount they get in return is large enough to compensate them for taking on board

the high risk investment. The Asset Pricing theory is aimed at recognising and measuring

these risks, and also assigning rewards for subsequently bearing these risks.

The theory explains and lets us understand important things for example, why expected

returns can change overtime, why two totally different stocks can have completely different

expected returns, and also why we can calculate for example, an expected return much higher

on like a stock than that of a short-term government bond. It also helps us to evaluate various

reasonable rates of return for various assets, as through financial awareness we are made to

recognize that investors like to hold well-diversified portfolios, and do not like lower

expected returns in comparison to higher expected returns. Well-diversified portfolios are

portfolios that contain a variation of securities with risks, which are closely approximated to

the market systematic risk, with the unsystematic ones diversified out.

6


The information on the rate of return for the particular asset is crucial, as investors need to

understand the risk they encounter with a particular portfolio. This will help in their critical

investment decisions, which could possibly range from evaluating projects to forming

investment portfolios. These investment portfolios can even be assessed and the overvalued

and undervalued assets can be identified. If we view it from a corporate scenery, we realise

that companies can also look at the characterised risks of their potential acquisitions and

projects, whilst allocating a discount rate to reflect the risk, and then choose the project that

has a higher promised rate of return than what would be presumed by the risk theory, to help

them create value.

Asset pricing as a finance theory, helps to answer the fundamental question of how an

investment’s expected return is affected by its risk. Contrasting macroeconomic events and

frictions in the financial market are also linked with the risk related with the returns of asset

price, as a lot of significant decisions in economics that have to do with consumption and

physical investments rely on this. The fundamental role asset pricing plays is high, as the

mispricing of assets could contribute to financial crises, which could cause damage to the

economy, for example the recent economic recession in the UK.

In order to provide some insights into this and aid in in the prevention of mispricing assets, a

variety of Asset Pricing models have been produced to achieve this, although not every model

can be said to be faultless or impractical. The most dominating and significant of the Asset

Pricing models is the Capital Asset Pricing Model (CAPM); I will be discussing the

framework of the model, both theoretically and empirically in a lot more detail later on in the

paper, especially with regards to its validity.

7


The remainder of this paper is organised as follows. The first part of the paper will give an

overview of Asset Pricing Models. Accordingly, the next part will introduce the CAPM

briefly and then research objectives will follow next, where I’ll briefly describe the main

purpose of the research. The Literature Review will then follow suit and comprise of further

expansion on CAPM by reviewing literature, discussing the background theory in a lot more

detail, and highlighting the various critiques of the model. I will correspondingly be outlining

observations made by previous researchers who came up with predictions of the Model after

theoretical and empirical evidence to support or contradict to the model.

The next section, Methodology, will address and discuss how and why we intend to achieve

the research objectives. Furthermore, we’ll move on to Analysis and Results, where we

examine the calculations and empirical analysis and explain the implications. Finally, the final

part of the paper will then be the conclusion section, which concludes the paper and gives an

answer to the relevant parts of the research objectives.

1.1 Overview of Asset Pricing Models

Asset Pricing Models formalize the accurate relationship between a financial asset’s expected

return and the way its risk is measured. They have majorly contributed to the world of finance

by their attempt to understand how these two variables are formalized, through calculating

and determining the appropriate return of a financial asset. The prices or the returns we expect

from financial assets in financial markets are described by the models, by using one or more

variables to determine an asset’s fundamental worth. By financial assets we mean assets such

as bonds, futures contracts, common stocks, etc.

8


Investors who invest in financial assets do so in the hope of attaining some return for their

investments or financial wealth without losing the worth of their investment. With this there

exists a risky asset, and a risk-free asset; the asset labelled as risk-free having a return which

is certain, and the risky asset the asset with variability in expected returns which brings about

uncertainty, and the asset pricing models help explain and measure these risks so the investors

can make their decisions based on that information.

Moreover, these models are quite distinctive, for example, their different assumptions, and

they fit at least one of the specific circumstances. However amongst this, they still possess

few similarities, which are established on one or more of the subsequent concepts; the law of

one price, no arbitrage principle and the financial market principle, which are 3 economic

concepts.

Asset Pricing Models can be single or multifactor, depending on how many factors the model

looks at, with single factor models like the Capital Asset Pricing Model (CAPM) that uses a

single factor Beta to compare a portfolio to that of the whole market. This was proposed by

William Sharpe, as he realised that the return we expect on an asset relies only on its Beta. He

figured this by deducing that we cannot diversify a systematic risk, and the unsystematic risk

is specific to the earnings of a company, which can be moved through appropriate

diversification.

This single factor in the model is used to determine the expected return of an investment by

calculating the amount of risk in the investment. Single factor models use systematic risk,

according to William Sharpe, which we define as the risk of being in the market.

9


Multi-factor models, on the other hand are quite different from Single factor models; they are

suggested to be an alternative to single factor ones, as they incorporate more than one risk, as

they allow the asset to have more than one measure of systematic risk, portfolios built could

contain either a risk factor itself or one that that contained a lot of stocks that had a relation

with a risk factor which was not observable. A model such as the CAPM with extra factors

added its formula can afterwards be considered as a multifactor model. An example of a

multi-factor model would be the Intertemporal CAPM (ICAPM) developed by Robert

Merton.

These Asset-Pricing Models have been an important contribution to the financial world; proof

of this is in its wide usage and its continuous research by academics and constant effortless

domination in financial textbooks, but due to the simplicity, rational presumptions and

imaginative observations, the CAPM has still been the main utilised model and has not really

still found much competition, although it has come under rigorous testing on its validity and

validity of its assumptions. This has generally resulted in some people favouring it, and others

not.

Consequently through this, new inventive models have also emerged, which try to side-step

the problems of CAPM through contrasting approaches in how they compute their

calculations of asset prices alongside their presumptions, which challenges prevalent models.

To give a well-rounded overview of some of the major Asset Pricing Models, especially the

mainly few recent asset pricing models which are innovatively developed from the basis of

CAPM, I was able to construct the following table;

10


Model Developed By

Year Single or Multifactor

Model

Brief Outline

Capital Asset Pricing Model

(CAPM)

Sharpe and Litner

1964 and 1965

respectivelySingle

Explores risk and return relationship by expected return

using the Beta (, and measures risks with the return of the stock market covariance to that of the

securitiesConsumption based CAPM

(CCAPM)

Rubinstein, Lucas and Breeden

1976, 1978 and 1979

respectively

Single Similar to CAPM but here Beta sensitivity is measured in relation

to the changes in aggregate consumption.

Intertemporal CAPM

Merton 1973 Multifactor The model assumes that there is a continuous flow of time.

Arbitrage Pricing Theory (APT)

Stephen Ross

1976 Multifactor Has the assumption that the return of each asset back to the investor has several factors that control it, but these factors are independent.

International CAPM

Stulz 1981, 1995 Single Here the expected return is calculated by measuring the

sensitivity is measure to the world market index.

Conditional CAPM (Cond-CAPM)

Jaggannathan and Wang

1996 MultifactorIn this model the return we expect on an asset is related to the degree of responsiveness of changes in the economic state.

Fama and French 3

Factor Model

Fama and French

1992, 1993 Multifactor For this model, Fama and French figured out that beta did not explain the cross section of the returns on stocks. They did this by outspreading the traditional CAPM to include explanatory variables such as size and book-to-market in explaining this stock returns cross-section.

Carhart 4CH Model

Carhart 1997 Multifactor The only difference between this model and the Fama and French three-factor model is the addition of a price momentum factor.

Liquidity- Adjusted

Asset Pricing Model

Archaya and

Pederson

2005 Multifactor They both discovered through studies that liquidity also affects the portfolio investment performance, so to incorporate this, they devised this model to help explain the effect of liquidity

11


risk on asset prices.

Fig 1. Table of some Asset Pricing Models including brief general background information.

From Fig 1 we can really see how Asset-Pricing Models as a whole, have acquired a long

history of theoretical and empirical investigation, which indicates how much authors have

attempted and successfully contributed to the development of the models, in order to progress

Asset Pricing in the world of finance and financial markets. It also shows the contribution

overtime of Researchers to Asset pricing in general through their studies and development of

models, through mostly the CAPM.

1.2 CAPM Introduction

Brief History

The Capital Asset Pricing Model (CAPM) was one of the major contributions to the financial

economics that transpired in the 1960s. The CAPM, as the first asset-pricing model, is

deemed as the most conspicuous model in the history of asset pricing. During this period

(1960s), a couple of researchers studied and used the Markowitz’s portfolio theory, to

formulate for financial assets, a theory of price information, which subsequently derived the

Asset Pricing Model famously known as CAPM. For this contribution to economic sciences,

in 1990, the researchers involved in this-Harry Markowitz were awarded the Alfred Nobel

Memorial prize.

Markowitz portfolio selection theory (1952), forms and originates the basis of the CAPM.

Briefly, it is a theory that examined the ways in which risks could be reduced, and even

though assets might differ in terms of their risks returns that we expect, we can still optimally

invest our wealth in them.

12


Before Sharpe, the theory was developed by Tobin (1958), who presented the Separation

theorem and the efficient linear set theorem. Years later after this, Sharpe and Litner finally

developed the relationship between determining an asset’s return whilst taking into account its

risk, hereby introducing the CAPM. Merton Miller (who introduced the Intertemporal CAPM

later on in 1973) and William Sharpe were also presented the famous Nobel Prize in 1990

alongside Markowitz.

Furthermore, the introduction of CAPM has overtime brought about a wave of empirical

studies done by scholars and people in the field of research. The studies have all included

heavy debates concerning the results, which brings about disputes on the model, which I will

consequently highlight later on in the detailed literature review besides the paper’s own

approach to checking its validity.

Brief Overview

The CAPM is an equilibrium theory on expected return and risk measurement. It integrates a

Beta () factor or beta value of a share, which is very significant to the CAPM, particularly in

the formula. This Beta value contributes to the volatility and risk of the whole portfolio of the

market, which contains risky securities. Therefore any share which has an assigned beta co-

efficient value of below 1, will not have as much impact on the total portfolio of the market,

whereas we would expect shares that have an assigned beta coefficient above 1 to have an

higher than average effect on the total market portfolio.

Through the manner in which the equilibrium price is formed on the capital market that is

efficient, we can generate the relations between an asset’s Beta value, its expected return and

its risk premium, and state that the latter two will change in direct proportion to the former

one. An accurate composed portfolio, which contains risky securities, can allow an investor to

13


choose to bare himself to a sizeable amount of risk. For the attitudes of the investors towards

risk, this can be seen in their selection of a risky portfolio combination and an investment

which is risk-free, but in CAPM in regards to the model stressing on what the optimal risky

portfolio should be composed of, it should depend on the investors’ future predicted

calculations of various securities. If the investors do not have as much information as their

counterparts with regards to investing, they are better off holding the same portfolio of shares

as the other investors. We choose to call this the market portfolio of shares.

One of the main significant contributions of CAPM is the measure of risk, which it provides

for an individual security, which is said to be very constant with the portfolio theory. (Weston

and Copeland, 1986). This can also then allow us to evaluate in a well-diversified portfolio,

the risks which are not diversifiable, known as un-diversifiable risk. (Weston and Copeland,

1986).

1.3 Research Objectives

The main purpose of this project is to fully review the CAPM model by providing a detailed

well rounded research on the CAPM, and also test the accuracy, by checking its validity to see

if it holds. For this research/project, the main objectives are to:

1. Provide a full comprehensive and detailed understanding of the Capital Asset Pricing

Model (CAPM) – Overall revision of its theoretical and empirical framework through

existing literature (Theory and Evidence, including disputations and advancements) in the

Literature Review.

14


2. Estimate and Analyse Beta, where Beta is a way of measuring risk based on Volatility of

the stocks. So here we will be predicting estimates of Beta of these 12 companies listed on

the London Stock Exchange for a 10 year period and compare it to actual results. Also, we

will be able to analyse the Beta values, observing its various levels of volatility, in order

to explain and interpret the relative risk and return level of the stocks in question in

comparison to the market (FTSE100) and the actual Beta values for the time period

selected.

3. Further analyse the relationship between the estimated Betas and actual Betas graphically

and statistically by performing tests, to further explain the results/findings observed, and

further test the accuracy of the CAPM.

15


2. Literature Review

2.1 Introduction

Asset pricing models produced from Finance theory all have quite a long history of theoretical

and empirical investigation, and the existing literature for these models is vastly increasing, as

studies are continuously carried out on them. If we consider the Capital Asset Pricing Model

(CAPM) in particular, which was the first ever known asset-pricing model and an uncommon

revolution and valuable addition to economics, we notice that ever since its conception,

enormous efforts have been devoted to evaluating its validity. This research on the CAPM

also led to a lot academic researchers in the field of economics developing and advancing it,

hence emanating the innovation of other asset-pricing models, with CAPM as the basis from

which they were developed. Extraordinarily, studies conducted on CAPM over time have

also appeared to have given rise to numerous debates which has led to some people becoming

advocates to CAPM principles, with others not in full support of the model.

These distinctions in the already led studies have right now served as a real fortifying element

to this paper’s interest in the CAPM, but in order to undertake a test of its validity, we would

need to revise the underlying economic theory and existing literature for the CAPM- ranging

from the main literature of its derivation all the way to innovative advancements to the model.

Literature also containing evidence and critiques of the model by some academic researchers

who carried out theoretical and empirical studies to contribute to the evaluation of the validity

of the model, albeit in support or in opposition of it, will all be explored within the review.

The review will consequently address 4 main themes (which are adequately interlinked),

which we think have proved to be the most prevalent aspects within the scope of CAPM’s

literature. Ultimately, we will discuss how this research can contribute to the topic.

These themes are as follows:

16


CAPM Theory - Theory, Economic Intuition and Assumptions, Graph and Formulae

Critique of the CAPM - Predictions, Evidence, Theory and Empirical tests

Advancements to the CAPM

CAPM and The Arbitrage Pricing Model (APT) Debate

2.2 CAPM Theory

The relationship between the risk and the return on an asset was advanced by Sharpe and

Litner in 1965 through the Capital Asset Pricing Model (CAPM). Originally, the model was

derived from the Markowitz theory of portfolio selection (1952), and although the Mean

Variance Analysis was developed by Tobin (1958) when he presented the concepts of the

Linear Efficient set and Separation theorem, the theory which involves mean variance

analysis, is an essential basis of the CAPM.

The MVA follows the assumption that during asset/portfolio selection by investors, the ones

which delivers the least possible variance for an expected return that is given or offers the

biggest expected return for a level of variance that is given are chosen. We call any selection

of this sort Mean variance efficient, else not efficient. Showing all the available combinations

of assets that either provide minimum amount of variance for given expected return, or

provide maximum amount of return for a given variance level, we get what we call the

Efficient Frontier (EF) which allows for all asset combinations in portfolio;

Figure 2.1- Diagram of The Efficient Frontier - Source: R. E. Bailey (2005)

17


The point MR, the minimum risk portfolio, signifies for all potential expected return values

the minimum variance, and the FF curve on the upper part of the MRP represents the actual

efficient frontier portfolios there are considered to be efficient, and those on the inside

inefficient. The portfolios outside the FF curve are not considered to be feasible. This moves

us forward to the diagram of the mean variance with a slope called Sharpe ratio, which

measures the amount one-unit risk that can be compensated by excess return. So with this risk

level we are given we can see that, the lower the ratio, the lower a portfolios’ excess return,

and vice versa. (Bailey R, 2005)

Therefore if we were to consider which portfolio was efficient, we would look at the one that

has the highest slope. Here the efficient frontier is illustrated by the Capital Market Line

(CML), which can be described as the steepest tangent line to the FF frontier for risky assets,

as seen below.

Figure 2.2- Diagram of the Capital Market Line (CML) - Source: R. E. Bailey (2005)

From Figure 2.2, we see that the

optimal portfolios of different investors, are located along the CML, with the investors

holding distinct amounts of the risk-free asset depending on their behaviour towards risk, and

this is what the CAPM envisages. The point M represents the expected rate and standard

deviation of return, depicted by MM respectively. This is also the point that identifies 18


the market portfolio where the share of each asset that is risky equates its share in the whole

market. The CML goes through the r0 point on the vertical axis and lies in tangent at the

point M to FF, which is the portfolio frontier for risky assets only. The MV Efficient

portfolios are those laying along the CML, the only difference between them is their

proportion out of the total portfolio which got invested in the risk free asset. The tangent point

is the portfolio that only has the risky asset, with the portfolio consisting of just the asset that

is risk-free asset being the point on it. From the diagram we see how efficient portfolios are in

market equilibrium if every investor had the same conviction on means and variances. (Bailey

R, 2005)

This derivation of the Efficient Frontier clues in the Separation Theorem, a proposition

according to Sharpe (1964, pp.426). This states that by merging any other two portfolios in

the frontier, we can acquire every portfolios expected return and variance. So we can hence

breakdown the process of selecting portfolios by firstly selecting a combination of unique and

optimum risky assets, and secondly making a choice which is separate concerning how the

funds are allocated in the combination as well as the riskless single asset. Hence, the portfolio

which is the most preferred is distinct from the individuals risk attitude. Investors ready to

combine the market portfolio with the risk-free asset will find the relationship tracing out the

efficient combinations and risk (CML), available. So through the CML, these investors are

wise enough to identify the advantages of building a well-diversified portfolio which will

trace out all their optimal risk-return combinations (Richard Pike and Bill Neale, 2009).

Richard Pike and Bill Neale (2009) speaks about how in order for a theory to simplify an

analysis and expose the vital relationships between key variables, it relies on assumptions.

Generally, validating a theory will not depend on the practicality of its assumptions, but on

the empirical correctness of its predictions, which if they do not match with reality due to no

empirical errors or random influences, then we can re-assess the assumptions.

19


Hence why the assumptions of a theory are important. Therefore, outlining the most important

assumptions of the CAPM for all investors according to Richard Pike and Bill Neale (2009),

they are;

Maximizing expected utility enjoyed from wealth-holding is an aim for all investors.

Common single-period planning horizon is what all investors operate on.

All investors choose from alternative investment opportunities by considering the risks

and expected return.

All investors are rational and are risk-averse.

All investors arrive at comparable assessments of the probability distributions of

expected returns from securities, which are traded.

Expected returns are normal for all such distributions.

Unlimited amounts can be borrowed or lent by all investors at a similar common

interest rate.

In trading securities, there are no transaction costs involved.

Both dividends and capital gains are taxed at the same rates.

All investors are price takers which means that not one investor can influence the

market price through the scale of their own transactions.

All securities are highly divisible meaning they can be traded in small portions.

The CAPM calculates the Expected return of a security/asset with the emphasis of investors

needing to know the Risk Premium for the total portfolio, which is the extra amount that is

needed to compensate an investor for taking a risky investment, and Beta of the security

against the market, which is the degree that the security is an alternative for market investing.

The premium of this security is calculated by the part of its return that perfectly correlates

with the market, with the parts that do not perfectly correlate diversified away without

demanding a risk premium. According to the CAPM model, the expected return of an

investment to an investor will equal to the Risk-free rate, which is just the rate of return on an

investment with no risk (return of that investment acknowledged with certainty); for example

Government treasury bills, plus a whole security premium which is greater than that of the

risk-free rate, times the risk factor for bearing the investment.

20


Mathematically, this can be expressed as;

j = Ro + βj (m – Ro)………………………… Equation (2.1)

Where

1. j is the Expected Return on the asset j,2. Ro represents the Risk-Free rate,3. βj as the value of the Beta of asset j which signifies its risk,4. m signifying the market’s expected return, and5. m – Ro) representing the market Premium.

This relationship is what the CAPM predicts, revealing a function of the expected return of an

asset j and the market expected return with a slope of j, and this can be further illustrated as

the Characteristic line, as shown next;

Figure 2.3- Diagram of the Characteristic line - Source: R. E. Bailey (2005)

This characteristic line shown above uses the prediction of the CAPM we know to be j – r0 =

(M – r0) j, as a linear association amongst (j- r0) and (M – r0) with slope of j, and with

every of the assets having its own characteristic line, but distinct, depending to the value of j.

(Bailey. R, 2005)

Equation (2.1) above makes us understand that a linear combination of portfolio M return and

the return that is risk-free, will give us the expected return on a security (j), with the co-

21


efficient Beta (measuring the security’s risk and relating it to the security’s covariance

with the portfolio M tangency. So therefore, this expected return on the security will be equal

to the addition of the risk premium and the risk-free asset which would depend on how risky

the security is. This equation of the CAPM, depicted by Equation (2.1), is commonly denoted

as the Security Market line (SML).

Here (SML), we consider the returns we expect to be linear, and we can mathematically

express the co-efficient Beta value for an asset j as:

j = jm / 2m……………………………………Equation (2.2)

This SML line shows the associations which must be fulfilled amidst the beta and return of

the security, and also the return from the M portfolio. It is illustrated in 2 diagrams below;

Figure 2.4 and 2.5- Diagrams depicting the Security Market Line - Source: R. E. Bailey

(2005)

In Figure 2.4, the SML predicts that the all the beta-coefficients for all assets, its portfolios

and the average rates of return will be located along the SML, and it interprets as a linear

association between the Beta (j) and the expected return (j) of an asset (j), the CAPM

prediction, which is j = r0 + (M – r0)j. Figure 2.5 on the other hand, highlights the

disequilibrium in the CAPM, as from the diagram we can see 2 points A and B. The point A

lies above the SML, meaning the return rate on the asset A is higher than what the CAPM

22


predicted given the co-efficient of the Beta, whilst for asset B, it is lower than the prediction

of the CAPM. Hence, from this we say asset A and asset B are under-priced and overpriced

respectively, both of them conditional on the CAPM’s validity. (Bailey. R, 2005). When that

happens the CAPM is said to be in disequilibrium, as the points are not on the line.

All three main diagrams I have highlighted; The Capital Market Line (CML), Characteristic

line (CL) and the Security market Line (SML), all depict 3 key relationships for the CAPM.

The CML indicates the risk premium that is required for any portfolio that comprises of the

the market portfolio of risky assets and the risk-free asset, while the CL helps to express the

relationships between the expected return on a particular security for expected return values

on a portfolio that are given, and lastly the SML denotes the suitable appropriate return on

separate assets (and portfolios which are inefficient) (Richard Pike and Bill Neale, 2009).

Since the CAPM assumes for investors that when they calculate their rate of return, only risks

that are systematic will be considered, which just means any risk which affects a great amount

of assets either each one a greater or lesser degree (non-systematic only affects a single one

without effect on all the assets), the CAPM gives the ensuing 3 implications stated by Fama

and Macbeth (1974), some of which are considered to be testable and are as follows;

On a security, there exists a linear relationship between the risk (Beta) of a return and

its expected return.

Beta is seen as the total measure of risk of a security, so other variables would not be

explanatory so the intercept of the equation should be the risk-free return.

There is an association of Higher risk (high values of Beta) with Higher expected

return i.e. Rm) – Rg > 0.

Shortly after the birth of the CAPM, Black derived a modified version. Black (1972)

narrowed down the assumptions into three sets of conditions, which are:

Assets markets are in equilibrium.23


The behaviour of investors are in line with the principle of mean-variance

All investors possess homogenous beliefs about their decisions on the values of mean

variances and covariance means.

Black’s CAPM brought out the assumption of investors being able to lend or borrow any sum

with the notion that the risk-free asset does not exists. Black derived this same prediction by

mathematically expressing any asset j’s equilibrium expected return in equilibrium as;

j = R0 + j (m – R0) ………………………………...Equation 2.3

From Equation 2.3, R0 represents the return on assets with Zero value of Beta. The 0 beta

value imply that the there is no correlation with the market portfolio and the asset return.

Therefore the insinuations of Black CAPM, which are testable, are alike to the previous one

apart from the point that the intercept does not have to be the risk-free rate.

Overall, the CAPM proposes a way for investors and others to evaluate their investments, by

just assessing and comparing expected return and required return. If they find out that the

former is not favourable, then they would not embark on potential investment in that actual

security.

2.3 Evidence and Critique of the CAPM

As some considerable research has been conducted over the years in order to test validity of

the CAPM, some of the results have provided evidence backing the Capital Asset Pricing

Model (CAPM), while other findings have conferred substantial evidence, which has led to

questions on the validity of the model. The studies which provide support of the model are the

two classic studies; Black, Jensen and Scholes (1972) and Fama and Macbeth (1973), whilst 2

of the main prominent studies providing evidence not in favour of the CAPM are the Fama

and French study (1992) and the Powerful critique of all CAPM empirical tests made by

Richard Roll (1977). 24


Majority of these studies focused on the how effective Beta is in explaining the historical

returns of the portfolio, and tested on the New York Stock Exchange (NYSE), and there will

be a brief discussion and summary of these studies, alongside a few others that gave responses

on these studies, as these were the most prominent as discovered.

Black, Jensen and Scholes (1972) utilised the portfolio of the entirety of stocks which were

traded on the stock exchange as their market portfolio proxy, which was equally weighted.

They tested both the CAPM and the Black version (zero Beta) using time-series and cross

section methods, with the cross section methods carried out for the sub and whole period due

to how big the data was. They were able to compute the relationship between the portfolios

betas and the monthly average return between the years of 1926 to 1966 (40 years). Using this

massive amount of data, they came up with findings from this study, which showed an

astonishing close-fitting relationship between both variables.

Although the slope and intercept from their study appeared to be significantly distinct and

larger than the mean risk-free rate of return across the period studied, they observed and

deduced a positive linear relationship between the beta and average return, which is why they

chose not to reject this prediction of linearity by the CAPM. Also, the beta value explained

most of the variations in the returns as the R-square value of 0.98. Even in the time-series test

where there was a regression of every portfolio excess return versus that of the market, results

consistent with the CAPM prediction were found, as the results of 10 regressions done has

intercepts done for every portfolio which were mostly insignificantly distinct from zero.

There was however the intercept change which was not random; high risk portfolios were

negative whilst other portfolios were positive which led to strict CAPM rejection, but Black,

Jensen and Scholes demonstrated the model with zero-beta having a positive relation, which

holds therefore the empirical results suit the Black Model better, as with the intercept of the

Black CAPM, there is no worry.

25


The Fama and MacBeth study (1973, 1974) also provided evidence similar which favours the

CAPM. Fama and Macbeth (1973, 1974), carried out the test using about 20 portfolios from

NYSE securities (similar time period as Black, Jensen and Scholes) to address the problem of

measurement error on beta. The tests concentrated on two of CAPM implications, which were

i) how linear was the expected return of portfolio beta, and ii) whether the expected return

was determined only by the portfolio beta and not the portfolio residual variance.

The portfolios are built such that the portfolio beta has a minimised measurement error. In

summary, the study divided the period of 15 years of the stocks into three 5-year periods and

grouped the stocks according to Beta ranks, then ensured unbiased beta estimation in every

portfolio after which regressions were done portfolios betas in the third sub-period

The regression, which was cross-sectional was carried out separately each month to obtain co-

efficients each month, with the all monthly average values calculated for each co-efficient and

then a t-test to was further carried out for testing significance. The main logic of the test that

one of the values would be equal to the average risk-free rate, the second equal to excess

return on market and the last two from the equation developed equal to 0. However the first

value did not equal the risk-free rate, which is a fail but did not contradict the Black CAPM,

while the second and last 2 values where greater than 0 (positive) and not considerably

distinct from 0 respectively. Therefore the overall study favoured the CAPM theory, as it

revealed the positive relationship between the betas and returns whilst even variables like the

residual variance did not explain the variation in the return.

Despite these evidences to support the model, the CAPM was still subject to critique, which

arose as a result of the conducted empirical studies. One of the most prominent contradictions

to the CAPM was done by Fama and French (1992, 2004). This study was also done with

traded stocks on the NYSE and other stock markets, but between 1963 and 1990.

26


Here the same method as the Fama and Macbeth (1973) was used by regressing the returns on

the various combinations of the explanatory variables which range from beta, Earnings to

price ratio (E/P), debt to equity ratio, the Book-market ratio (B/M), etc. which resulted in

different results to the Fama and Macbeth study.

By analysing the beta size and market size, they get an insignificant and negative co-efficient

value of beta, with the market size co-efficient also negative but significant. The other study

found the same consistent result. However, leaving the Beta alone as the sole variable brings

about worse results as it leads to a t-statistic, which is smaller, implying that in explaining

returns, Beta does not play a significant role, and this challenges the early study of CAPM.

Fama and French insinuated an explanation for this, saying that in representing the population

one of the sample periods may not be appropriate so; the difference in results is brought about

by the difference in time period. Also, regressing the (B/M) and the (E/P) alone show that in

explaining returns, they all play an important role, which is in dissimilarity to when the Beta

was left alone. To conclude, Fama and French deduced that size of market and (B/M) are

decisive variables in explaining returns, with Beta not as significant in explaining returns.

Therefore size of the firm and variables other than beta predict returns observed better, which

is why they oppose the CAPM, as it lays emphasis on Beta as the main explanatory variable

for returns.

One famous critique, presented by Richard Roll, famously called Roll’s Critique provided

additional dispute to all attempts to test the CAPM, and gave a conclusion that the CAPM

cannot be tested. He uses the basis for this critique as the efficient of the market portfolio

insinuation in CAPM, since market portfolios include all type of assets held as an investment

by anyone, ranging from bonds to stocks etc.

27


When applying, it means that the market portfolio is considered to be one that is not

observable, and individuals regularly use a stock index as a proxy replacement for the market

portfolio that is true. This substitution was debated by Roll as not safe and could result to

false interpretations of CAPM’s validity. Due to this inability, he believes that the CAPM

might not be testable empirically, and empirical tests done for the CAPM must comprise of all

assets available to investors.

Further evidence of Rolls worry of the CAPM not only being an empirical problem is

presented by Campbell et al. (1997). Here some of the studies indicated rejecting the CAPM

with a proxy would also imply the rejecting the market portfolio CAPM that is true, provided

correlation between true market and proxy market return surpasses around 0.70.

This shows that Rolls worry of the CAPM is not an empirical problem as even Stambaugh

(1982) conclusions, which were similar even when a proxy containing just stocks or also

stocks, bonds, etc. were used. This implied that a proxy that is good does not essentially have

to comprise of a wide range of assets.

Closer to that same year of Stambaugh, Banz (1981) and Reinganum (1981) both published

studies which provides evidence against the CAPM, with Reinganum’s study analysing

various anomalies that challenge CAPM such as the grouping of the portfolios by the market

value or the price earnings ratio (P/E) and the Banz (1981) study regressing returns on 25

portfolios on their Betas from a period of 1926- 1975.

By usually splitting his data into 6 sub-periods he realised a negative and significant market

size coefficient from 4 of 6 of the sub and the whole periods. His studies was one of the first

studies to find the “small-firm” effect, which was that of the CAPM predicting lower returns

than the returns on firm stocks that possessed market value that was relatively small.

Therefore the value of the Beta as a whole does not apprehend the whole risk.

28


Reinganum also came up with a conclusion which was consistent with Banz, which was that

the firms size which related the price earning ratio and market value is a likely missing factor,

as he found out in his portfolio groupings that the portfolios with a either a low P/E or a low

market value inclines to higher returns than prediction. He also found out that the effect of the

P/E is negligible we run together with Beta, market value and P/E. This is also consistent with

Banz.

2.4 Advancements to the CAPM

To further highlight the significance of the CAPM, numerous different expansions of this

model were presented after it. I will now provide a synopsis on some of the various literatures

I have researched on a few of the innovative asset pricing models derived from the basis of

the CAPM. The first two expansions of the CAPM we observed from the research on CAPM

literature are the Intertemporal CAPM (ICAPM) and the Arbitrage Pricing Theory (APT).

They are multifactor models introduced through Merton (1973) and Ross (1976) respectively.

The Intertemporal CAPM was Introduced by Merton as the CAPM was viewed as a static

model, as in CAPM the amount put into assets was set for a given time period, and this was

deemed to be improbable for the reason that the portfolio of investors can be rebalanced at

any time. Therefore according to Merton, he developed an equilibrium asset pricing model

(ICAPM) which had the same straightforwardness and empirical accordance of the CAPM,

consistent with the limited liability of assets and expansion of expected utility, and also makes

sure there is a consistency between the empirical evidence and the specification of

relationship among yields. The APT of Ross (1976) approached the idea that the long average

return is only affected by a minimal amount of systematic influences. The APT has been

presumed as a better alternative to CAPM by some, which will be discussed in the next

section.

29


The Consumption Capital Asset Pricing Model (CCAPM) of Rubinstein (1976), Lucas (1978)

and Breeden (1979) is another advancement of the CAPM, but based on the consumption in

the economy. Breeden (1979), did not base this model on financial wealth, as in comparison

to consumption, consumption was an adequate statistic for a dollar’s marginal utility.

Meaning that when we are not comfortable financially, we would more than welcome a few

more dollars to spend on consumption, than if we were comfortable. The model is similar to

the conventional CAPM as it allows assets to be priced with a single beta, but it measures this

beta by using the covariance of the assets return with aggregate future consumption, rather

than wealth.

Also, Fama and French in 1996 disputed that the CAPM Beta cannot explain the expected

return of Stocks, alone. Hence to address this, Fama and French (1993, 1996 and 1998)

derived a multifactor model commonly known as the 3-Factor model to help use numerous

factors like book to market and market capitalisation to explain the average return on an asset.

In 1996, another version of the CAPM was derived by Jagannathan and Wang. They derived

this by considering a dynamic economic and an unobservable return on portfolio of total

wealth, which according to them they subsequently denoted that the assumption of the CAPM

as being dynamic allows its betas and expected return to differ over time, then the statistical

rejections and effect of model requirements become weaker. They justified this by taking the

assumption of Beta (change with the business cycle. This version is called the Conditional

CAPM (CCAPM).

Literature on stock market efficiency by Jegadeesh and Titman (1993) posited the one year

momentum and also stated how stocks which normally perform best (worst) over a three- to

12-month period will usually continue to perform well (poorly) over the subsequent three to

30


12 months, as they possess the tendency to produce positive abnormal returns of about

1percent in the following year, per month. This one year momentum ideology was captured

by Carhart (1997), and he added a fourth factor (price momentum factor) to the Fama and

French 3 factor model, extending it. He extended this model by adding a price momentum

factor, which would explain the abnormal returns in momentum-sorted portfolios, wherein

which the price momentum represents the tendency of firms with positive past returns to earn

positive future returns, and vice versa. We know this model as the 4-factor model.

Since investors not only invest domestically but abroad, some researchers tried to address

this, as they felt that existing asset pricing models all considered domestic assets with the

assumption of investors all based in the same country. One researcher called Stulz (1981),

mentioned his ideology of the proportionality of the real expected return of an risky asset with

the covariance of the assets’ home country with changes in the rate of consumption in the

world. His argument also highlighted the Traditional CAPM, as being only appropriate for an

asset in traded in a closed financial market. This subsequently brought about an extension of

the CAPM known as The International Capital Asset Pricing Model (Int-CAPM), which has

given a theoretical structure for incorporating investments made abroad in asset pricing.

Finally, liquidity risk has an effect on stock pricing, and there is pretty much strong evidence

for this (Amihud and Mendelson (1986) and Archarya and Pedersen (2005)). Acharya and

Pederson (2005), derived one of the most recent asset pricing models,which gives an intuition

of the effect of liquidity risk on asset prices. Archarya and Pederson (2005) made a reference

in their paper to Chordia et al., (2000); Hasbrouck and Seppi, (2001); Huberman and Halka,

(1999), which are previous studies that comment that the performance of an investment

portfolio, which is important in calculating expected returns, are affected by liquidity. The

finance term “liquidity” in this case, said to be generally denoted as the ability to exchange

vast amounts rapidly, and effortlessly without moving the price (Pastor and Stambaugh,

31


2003). The study suggested that if this liquidity is important for an investor, since it affects

the portfolio investment performance, it should be priced, which is why it got developed from

the traditional CAPM to become the Liquidity Adjusted Pricing Model (LAPM).

2.5 CAPM and Arbitrage Pricing Model (APT) Debate

There have been various remarks towards both the CAPM and the APT; a few studies

comparing and contrasting both asset pricing models, and other studies proposing the APT as

a better or demonstrable alternative to the traditional Sharpe-Litner CAPM, as they see the

APT as new and different approach to asset pricing determination, due to the differences in

certain parts of its assumptions, insinuation and method. Both models show are in the market

equilibrium, risky assets are priced and also provide investors with estimates on required rate

of return on their respective investments, or securities. Both models are built on the standard

of Capital Market Efficiency. However, the main difference between both however, would be

one of CAPM being a single factor model with systematic risk (Beta) being the sole

determinant of expected return, whilst the expected return of the APT on the other hand has

more than one single factor as its determinant, so the APT is considered to be a multi-factor

model. The APT does not try to explicate the causes of the returns of securities, while the

CAPM does, which is another difference.

The theory was developed by Stephen Ross (1976), the economist, and is represented by the

equation;

rj = ojC FC jD FDjK FK j……….. Equation (2.4)

Identifying the variables in the equation, we have rj as the rate of return expected on random

security variable j, FC and FD representing non-diversifiable factors C and D respectively

which could continuously go on, hence the “…”, osignifies the estimated return levels for j,

32


with all indices possessing a zero value, jK indicates the sensitivity to factor k of the j

security return; and finally j is the residual term or characteristic risk, independent across

securities.

In John Wei (1988), the assumptions that are for the most part utilized in the derivation of the

APT are i) All Investors display homogenous beliefs that the stochastic properties of the

capital assets return are consistent with a K factors structure which is linear, ii) Its either a

competitive equilibrium is what the capital markets are in, or no arbitrage opportunities, iii)

The large numbers theory are applied to the amount of securities in that economy, as they are

either so huge or infinite, and iv) the amount of factors, k, can either be already known (in

advance) or the investigator estimates it accurately.

This APT model and the CAPM model both differ on what they both emphasize in regards to

returns on asset and the role of the covariance in this; the former stresses the role between

asset returns and exogenous, whilst the other accentuates the co-variance between asset

returns and the endogenous market portfolio instead (John Wei, 1988).

Creating a well-diversified portfolio with no senilities to each factor is possible with adequate

securities, hence enabling the portfolio to offer a zero risk premium as it is effectively risk

free. This is what the APT illustrates, and literature from Brealy and Myers (1981) also

deduced a difference between the CAPM and the APT in what the risk premium depends on.

With the APT, the risk premium of securities bank on the sensitivity of these securities to

each of the factors and how related the risk premiums are with one another.

This is different from the instance of the CAPM, where the risk premium in this model is

decided by the securities risk level which we know to be systematic, times the risks’ market

price. The systematic risk specified is total risk times the extent of the correlation of its

returns to that of the market portfolio. 33


Brealy and Myers (1981) further made an interesting statement, by stating that the CAPM and

the APT can be equal if there is proportionality between the risk premium expected from each

portfolios and the market risk of the portfolio. In regards to similarity, Weston and Copeland

(1986) highlighted that the CAPM and the APT are very similar in the aspect of its

application; in the sense of using the models to determine how much capital cost for

estimation and its budgeting, both of them can be utilised as part of literally the same way.

When testing the APT empirically, we get a process called factor analysis which has been

used to identify applicable factors, and a range of these factors have risen to be likely

determinants of the actual value of common security returns (Emmery and Finnerty, 1991).

The factors could not be identified easily, and the APT does not really say which of the

factors have relevance in regards to the economy and their behaviour, but it suggests the

relationship between a limited amount of factors and returns on securities (Van Horne, 1989).

Moreover, the APT has lot of Beta factors and is derived in a totally different way than the

CAPM, and according to Weston and Copeland 1986), the return of an asset cannot be easily

analysed against randomly factors found, but in order to extract the factors underlying all

security returns, the same factor analysis mentioned earlier must be employed. This I believe

is quite different from the CAPM as with CAPM we regress the return of an asset that of the

market portfolio when estimating it.

34


Literature studies on both the CAPM and the APT have debated which model is preferred to

the other. Although some have viewed the CAPM to have simplicity as its plus side, on

testing it, they come across 2 problems, one being the CAPM only focusing on expected

returns as its concern and also the issue that all risky investment should be involved in the

market portfolio, whereas majority of the market indexes only hold a sample of common

stocks (Brealy and Myers, 1981).

With respect to the debate of how much advancement can be achieved when utilising the APT

instead of using the CAPM, the study of Roll and Ross (1980) claimed that APT is more

susceptible to testing than CAPM. The study claimed this because all assets returns it’s not

essential to test them, and also, there is no distinct role for the market portfolio.

Weston and Copeland (1986) deemed the CAPM as not a good tool for making decisions and

with the CAPM; accurate beta estimation is tough since the Betas tend to change overtime.

Moreover, despite these comments on CAPM, Cooley and Roden (1986) still believe that in

any occasion the CAPM offers us a comprehension of how investors act, and their market

dynamics. The model might not be considered as perfect, however it is useful as it provides a

few noteworthy perspectives in to the main considerations of security price determination.

This has also aided in predictive ability for companies for instance, the idea that low beta

securities are less volatile and produce a much lower return than high beta securities.

However, studies of Chen (1983) and Roll and Ross (1983) looked to suggest that the APT is

an upgrade of the CAPM, notably when some CAPM anomaly has been found in the security

returns.

35


Regardless of this conjectural dispute, and the struggle of finding correct Betas, the CAPM is

still used by investors as they like how it shows the interaction of key variables, and how it

relates risk and returns systematically (Cooley and Roden, 1986). Even additional studies

such as the Brown and Weinstein (1983) study did not really find any noteworthy differences

between both the CAPM and APT.

The question of replacing CAPM with APT has been subject to much debate by many, and I

believe that to determine this, sufficient research is compulsory. Both models are two hugely

important asset pricing theories; nevertheless, according to Van Horne (1989), the APT could

well become the main asset pricing theory, with the CAPM as a theme of it, according to Van

Horne (1989).

2.6 Conclusion

In a lot of empirical studies on the CAPM, the CAPM was advised as invalid and not able to

explain expected return by its market Beta alone. However, Beta as a measure of risk is still

useful and despite all the empirical evidence against using the CAPM, it still remains a

valuable tool for approximating cost of capital as well as studying market efficient events, and

evaluation of performance (Laubscher, 2002). In relation to this, another extensively held

argument was the market proxies utilised adequately representing the efficient market

required by CAPM, and this further gave rise to the argument of the unachievable CAPM

equilibrium.

Furthermore, the ATP now outdoes the CAPM as it has been proven to succeed empirically,

and the mere fact that it incorporates multiple factors affecting asset returns rather than just

one like the CAPM, makes it more realistic in financial markets.

36


Also, the ATP enables investors to select variables, making it more aligned to the

requirements of a pricing model which can be considered as universal. However in cases

where appropriate the same factor could result to misuse of the APT.

A thorough review of the existing literature for CAPM has revealed that there is still a

considerable amount of research that could still be done. Some of the literature chosen and

discussed casted light on both theoretical and empirical studies on CAPM, addressing and its

validity. This is one of the major reasons which encouraged and inspired me

to carry out research/study in an area (London Stock exchange) where I

can also contribute to this testing, empirically. Therefore, the contribution of this

study will be to examine CAPM, by empirically estimating the Beta of 12 company Stocks

listed on the London Stock Exchange (LSE) over a 10 year period, and analysing it to see if

the CAPM holds in its ability to accurately predict Beta, in that industry by comparing it with

the actual Beta for the same time period.

37


3. Methodology and Data

This section introduces the methods of testing the validity of the CAPM. It

presents the data outsourced and describes the method applied to

conduct studies. The methodology is used to obtain outcomes for further

analysis.

3.1 Sample Selection

A period of ten (10) years is covered by the data utilised in this study, from 2001-01-01 to

2010-12-01. This period was selected as a result of historical Beta which was not available for

a few Bank Stocks required from the financial databases. Initially the focus of the study was

up to 10 UK banks with duration of 5 years, but it was realised that having a longer

duration/span of years rather than number of companies will make the result more accurate

and efficient. Therefore in order to provide an extended time frame and adequate number of

observations, 12 firms and 10 years was chosen. It was also soon realised that there were no

12 UK banks with each of them having at least 10 years’ worth of historical prices/Beta on

the London Stock Exchange (LSE). Therefore it was decided to instead have a combination of

the few banks which had the data required, alongside other companies from other working

sectors. The companies selected include some of the most prestigious and internationally

renowned companies in the UK. The list of companies comprise of 4 Banks, 2 oil companies,

2 pharmaceutical companies, 2 supermarkets, one tobacco firm and one huge retailer, all

listed on the LSE. They are; Barclays Bank, RBS, Standard Chartered, HSBC, Tesco,

Sainsbury, Glaxo-Smith Kline, AstraZeneca, BP, Premier Oil, Imperial Tobacco and Marks

and Spencer Group.

38


3.2 Data Selection

In the course of this study, data for the selected range of companies listed on the LSE for a

period of ten (10) years is required, and Yahoo Finance was able to provide this. One of the

key data required for the stocks from Yahoo Finance was the “Adjusted Close” in particular,

as it is an essential part in the calculation for the Beta estimates because it helps calculate the

return on the stocks.

Subsequently, actual Beta values for the selected companies which aid in testing and

comparing the accuracy of the estimated Beta prediction needed to also be obtained but

Yahoo Finance did not have this unfortunately. This would have caused complications for the

research, however luckily they were able to be obtained from software called DataStream.

After learning to use DataStream, we were able to source out actual Beta values required for

the selected companies for the time period. During this process, the well-known UK Bank

“Santander” and oil company “Royal Dutch Shell” were even omitted, as they both did not

meet the periodic requirements; they possessed incomplete data which did not stretch back to

the time period needed, which is why they were never included as part of the 12 companies.

With regards to the Risk-Free rate needed to be selected for the research, the United Kingdom

Government Gilt 10 Year Bond Yield was decided as the proxy. It was a value of 1.65%

which was obtained from http://www.bloomberg.com/markets/rates-bonds/government-

bonds/uk/. This seemed the appropriate risk-free rate to use for the research as it will better

reflect long-term changes in the financial market, and also since the duration of the data is a

10 year period, it seemed fit to select a risk-free rate that matches it.

39

http://www.bloomberg.com/markets/rates-bonds/government-bonds/uk/

http://www.bloomberg.com/markets/rates-bonds/government-bonds/uk/


For the market portfolio proxy, the FTSE 100 index was used, from which the returns would

be utilised by carrying out the same calculations as similarly done with the Stocks to

collectively aid in the beta estimation. This is explained more in the next section.

3.3 Beta Estimating and Testing Method

The Sharpe-Litner CAPM formula for Expected Return is the main equation used to compute

the Beta estimates and return. It is also called the SML or CAPM Equation. To help compute

estimates for Beta, historical data from Yahoo Finance (https://uk.finance.yahoo.com/) had to

be extracted. After downloading the adjusted monthly stock prices for the selected companies,

the monthly index of the FTSE100 (market portfolio) for the same period was also

downloaded.

Since the adjusted prices table was sorted by date in descending order, to help conveniently

calculate the returns, it was better to have the table in increasing order by date. So the entire

table was selected and sorted in ascending order by date. Since for the data, we do not have

the price for the month preceding the first month in the table, we will not be able to calculate

the price for the first month, but for the subsequent months the formula for return of an asset

was used, which is mathematically depicted as:

Return = [ (Adjusted close t+1 / Adjusted close t) – 1 ] ………………….Equation 3.1

This equation (3.1) is well interpreted as the current month’s stock price divided by the last

month’s stock price.

40

https://uk.finance.yahoo.com/


The above equation was successful used to compute returns for each asset and the market to

provide the expected rate of return of each of the companies for that time period, as well as

the market portfolio (FTSE100) .After getting values from applying Equation 3.1 to the data

for each stock, excel syntax was used to compute an average for the values, which was

“=AVERAGE (value1: valuez)”, where z means the zth value of the data. The same average

was also computed for the monthly FTSE100 data as well as that helps generate the required

market portfolio for estimation of CAPM Beta.

Following this, we then use CAPM formula to calculate the Beta (i) for each of the 12

companies. Since from CAPM we know that the expected rate of return, denoted by i for

example, of one of the company assets will satisfy:

i – 0 = i (m – 0)…………………………………Equation 3.2

Equation 3.2 was re-arranged to make Beta the subject, that way we would be able to compute

our Beta values, using the risk-free rate, the market value and the expected return on the asset,

with the latter 2 needed to have previously been computed to aid in the new computation. Re-

arranging this, we have for the Beta of a Company asset i:

i= (m – 0)/i – 0 ……………………………………….Equation 3.3

Computing the above using excel syntax, we were able to get results for estimates for Beta for

each of the companies. For the actual Beta values obtained from Data Stream, they range from

the same monthly 10year period as well, so to be able to compare it to the estimates we have

to take averages for the Beta value, so we could get a general average for each of the

companies. That way we can compare the averaged actual Beta to the estimated Beta.

Looking at the estimated Beta and the actual Beta, we will then analyse both Beta values in

comparison to one another and in relation to the market as well.

41


When analysing Beta in general, we generally start by assuming that the Beta for the risk-free

rate is equal to 0, and the Beta of the market has a value of 1, therefore if the Beta of any of

the selected companies stock is greater (lesser) than this, we can say that overtime, it

fluctuates more (less) than the market. Moreover, that high (low) value of Beta will mean that

the stock is considered to be more (less) riskier, hence meaning that returns on that stock

would be potentially higher (lower).

Different values of Beta have different implications. For example, values of Beta that equal 0

do not necessarily mean that it’s the risk-free rate as it could also mean that the return on the

stock is not associated with the market’s movement. When the value is equal to 1, it means

that the stock for example the bank Barclays, moves similarly to the market (FTSE100). If

greater than 1, then we say the stock overtime is more volatile than the market’s, which means

that a rising of the market will mean that we anticipate the stock to also rise, but at a higher

level, and vice versa.

When the stock is between 0 and 1, it means that we presume the stock to also move with the

market, but at a slower rate. Therefore, a rise in the market will mean the stock rises too, but

not as significantly as the market. So here we have volatility which is less than that of the

market. Finally, when the value of the beta of the stock is less than 0, we can say that the

movement of the stock with the market has an inverse relationship.

42


This inverse relation depicts that when the market rises the stock would decrease instead of

increase. This does not really generally happen unless the stock is for example e.g. Gold. So

this is one major basic way in which we will be analysing the Beta values obtained from

DataStream and also the Beta values we have estimated using the method suggested earlier.

We will do this by utilising and observing the values of estimated Beta obtained to deduce

and explain how much they diverge from the market, since Beta is way to measure the

volatility of a stock in comparison to the market.

Furthermore, to gain more insight on the differences or similarities between the results of the

Beta estimates in comparison to the actual Beta values to aid in examining the accuracy of the

CAPM (final research objective), statistical analysis is required. Therefore we will be doing

the following.

1. Descriptive Statistics for both the estimated and actual betas of the 12 selected

companies is examined.

2. Pearson correlation co-efficient.

3. Kruskal-Wallis test, to help find out statistically if a significant difference between

the values of beta estimated by CAPM and actual beta values from DataStream exists.

43


4. Conduct a T-test, to check both actual and predicted beta estimates and see if there’s

a significant difference between them by using the t-statistic and the p-value. The hypothesis

for this is stated in chapter 4, and to undergo this t-test we would need to run a regression on

the data to also find the p-value and t value and comment on them afterwards. Using

Microsoft Excel Data Analysis tool, regressions to obtain t-statistic and p-values per company

will be run, by using the yearly expected return of the companies (average of the monthly

returns) in order to calculate yearly estimated betas for each stock using the CAPM formula.

So one company would have 10 estimated betas, one for each year and to match the actual

beta values to this, we’ll also average these values from Data stream. Therefore we will have

10 yearly predictions and actual values of Beta from CAPM and data stream respectively. We

had to do this as it will enable us to regress the data, as it needed more observations per

company in order to perform a regression. It was initially planned to average the whole 10

years “adjusted close” value, as well as the whole 10 year average of estimated Beta, but this

would not help us in running a t-test. From these we would be able to obtain the results of the

t-test, and subsequently analyse and comment on the results of rejecting or accepting the H0,

and its implications.

4. Empirical Results and Analysis

For this part, results attained from the using the empirical methods as basis for the test of the

CAPM conferred in the previous chapter are displayed. Correspondingly, obtained results

will be analysed within this section. Firstly initial results are presented alongside descriptive

44


statistics and Pearson Correlation. Subsequently we will present results from the Kruskal-

Wallis test, paired sample t-test and the results of regression analysis of Estimated and Actual

Beta results of 12 firms on the London Stock Exchange from 2001-2010.

4.1 Empirical Results

To help calculate estimates for Beta using CAPM, we had to use the risk-free rate and also the

computed expected market return of FTSE100 over the 10 year period using the methods

outlined in the methodology. Their values are seen in the table below;

Table 4.1 – Risk-free rate and Computed Expected Market Return (FTSE100) (Source: Authors

Calculation)

Computing the expected return on each stock for the 10 year time period as a whole, using the

methodology outlined in previous chapter gave me results of estimated beta in table 4.2,

which also includes the Actual beta taken from data stream that was averaged over the 10year

period as well to match the same approach of calculating estimated. The results are;

Table 4.2 – Table of Return, CAPM Estimated Beta and Actual Betas (Source: Authors

Calculation)

Analysis of these beta results from the table shows us that majority of the selected stocks have

the lowest values of beta co-efficient are the values calculated with CAPM. This is contrasting

45

10 year Risk-free rate 0.01680010 year Expected Mkt. return 4.3581E-04

Stock, iExpected return on

asset i10 year Beta (i) Estimate CAPM

Actual Beta (DataStream) 10 year Avg.

Barclays -0.003376 1.232906 1.442583333Royal Bank of Scotland (RBS) -0.012171 1.770420 1.32175Standard Chartered 0.012766 0.246534 1.686833333HSBC 0.004025 0.780669 1.29075Tesco 0.008576 0.502557 0.60525Sainsbury 0.005300 0.702784 0.73025Glaxo-Smith Kline (GSK) 0.001126 0.957816 0.48675AstraZeneca 0.004864 0.729390 0.616583333BP 0.003102 0.837050 0.878BG Group 0.015241 0.095289 0.655083333Imperial Tobacco 0.016571 0.014013 0.375166667Marks and Spencer Group (M and S) 0.011498 0.323975 0.514166667


to the Actual Beta values from DataStream, which has more of the majority of its stocks

having highest results of coefficients of beta. The lowest value of beta overall is the stock

Imperial Tobacco (0.014013) and this is from the CAPM estimate, and the CAPM estimate

also has the highest beta stock which is RBS (1.770420). None of the stocks in this sample

have negative Beta. Approximately ¾ of the stocks from the whole sample have values of

Beta between 0 and 1, which imply that these stocks move in the same direction like the

market does but not as volatile as the value is between 0 and 1. The remaining ¼ of beta

values in the table have Beta which is higher than 1 and this implies that their volatility in

comparison to the market is higher in general.

Graphically showing the relationship between the estimated and actual values, we have;

Figure 4.1- Graph showing the relationship between Estimate Beta and Actual Beta

46

Barclay

s

Royal Ban

k of S

cotla

nd (RBS)

Standard

Chartere

dHSB

CTes

co

Sainsb

ury

Glaxo-Sm

ith Klin

e (GSK

)

Astraze

neca BP

BG Group

Imperi

al Tobacc

o

Marks &

Spen

cer Gro

up (M&S)

00.20.40.60.8

11.21.41.61.8

2

10 year CAPM Estimated BetaActual Beta (Datastream) 10 year Avg.


4.2 Descriptive Statistics

Table 4.3 shows us descriptive statistics of the CAPM estimated Beta and the DataStream

actual betas for the selected stocks. We can see from this table that the highest average of

beta is by the DataStream, whilst the lowest average of beta is from CAPM estimates, which

is similar to the earlier conclusions.

The estimated betas calculated by CAPM range from 0.014 (Imperial Tobacco) to 1.770

(RBS) for the selected stocks whilst Betas from DataStream for the same period range from

Imperial Tobacco company again (0.375) to 1.686 (Standard Chartered). Standard deviation is

higher in CAPM estimated Beta (0.499) than the Actual beta (0.436), but both values are

not too far off.

CAPM Estimated Beta Actual BetaMean 0.682784052 0.883597222Median 0.716087078 0.692666667Minimum 0.014013976 0.375166667Maximum 1.770420854 1.686833333Sample Variance 0.249193213 0.190219285Standard Deviation 0.499192561 0.436141359Skewness 0.73812501 0.71535939Kurtosis 0.712839148 -0.972448648Sum 8.193408625 10.60316667Sum Sq. Dev. 2.741126 2.092412729Observations 12 12

Table 4.3 – Descriptive Statistics of CAPM Estimated Beta and Actual Averaged Beta from

DataStream (Source: Authors Calculation)

Moreover, Results of Pearson Correlation between the CAPM Estimated beta and Actual

Beta have indicated a fairly positive correlation which exists between the variables, with a

value of 0.420 (rounded). Table 4.4 shows this.

47


CAPM Estimated Beta Actual BetaCapm Estimated Beta 1Actual Beta 0.419631957 1

Table 4.4- Pearson Correlation between Estimated Beta and Actual Beta. (Source: Authors Calculation)

4.3 Kruskal-Wallis Test

Results of this Test confirm that there is no statistically significant difference between the

estimated betas and the actual betas. Since KW= 0.853 and p= 0.3556 > 0.05, we do not reject

the H0 as there is not enough evidence to claim that some of the population medians are

unequal at the a = 0.05 significance level, which means that the samples come from

populations with equal medians. Also the X2= 0.853 which is less than or equal to X2u which

is 3.841 so we do not reject the null, as the rejection region for this Chi-Square test is R =

{X2: X2 > 3.841} at the degree of freedom which is one. This is summarised in Table 4.5.

Method degrees of freedom Value of H-statistic p-valueKruskal-Wallis 1 0.853 0.3556

Table 4.5- Kruskal-Wallis test (Source: Authors Calculation)

4.4 Regression and Time-Series Analysis

For this section, we had to estimate 10 Yearly Beta values per company (since the Data is 10

years monthly), by averaging the expected return values into yearly and plugging it into the

CAPM equation to find estimates for Beta. Actual Beta values from DataStream were also

averaged to match these estimates, by having 10 values (observations) for that. To statistically

analyse the CAPM model further to test the accuracy of the prediction of Beta, t-tests was

used for rejecting and accepting the hypothesis. The t-test applied by this study was a paired

sample t-test to find the p-value which would mainly indicate the significance of the

difference between the CAPM return and the actual return.

48


To analyse the results of the regression analysis, we choose a significance level of 95% as we

believe the statistics to be good enough to support the result with a confidence of 95%,

leaving the remaining 5% as the chance of being rejected. From the t-distribution, the critical

value for this 95% is 2.262. The table showing the results of the tests is shown below;

Stock, i

Expected return on

asset i

10 year CAPM

Beta (i) Estimate

10 year Actual Beta Avg. Difference

t-statistic from yearly averages regression

p-value from yearly averages regression

T-Stat for "9" degrees of freedom

Hypothesis Not rejected/Rejected

Barclays -0.003376 1.232906 1.4426 0.209676 -1.039833 0.328820 2.262Accepted Null Hypothesis

Royal Bank of Scotland (RBS) -0.012171 1.770420 1.3218 -0.448670 -0.802048 0.445693 2.262

Accepted Null Hypothesis

Standard Chartered 0.012766 0.246534 1.6868 1.440299 -0.221402 0.830325 2.262


HSBC 0.004025 0.780669 1.2908 0.510080 0.912665 0.388094 2.262Accepted Null Hypothesis

Tesco 0.008576 0.502557 0.6053 0.102692 0.106529 0.917785 2.262Accepted Null Hypothesis

Sainsbury 0.005300 0.702784 0.7303 0.027465 -0.563222 0.588716 2.262Accepted Null Hypothesis

Glaxo-Smith Kline 0.001126 0.957816 0.4868 -0.471066 1.701840 0.127198 2.262


AstraZeneca 0.004864 0.729390 0.6166 -0.112806 1.292644 0.232215 2.262Accepted Null Hypothesis

BP 0.003102 0.837050 0.8780 0.040949 0.251152 0.808026 2.262Accepted Null Hypothesis

BG Group 0.015241 0.095289 0.6551 0.559793 0.099317 0.923330 2.262Accepted Null Hypothesis

Imperial Tobacco 0.016571 0.014014 0.3752 0.361152 2.394902 0.043521 2.262

Rejected Null Hypothesis

Marks and Spencer Group 0.011498 0.323975 0.5142 0.190191 1.580541 0.152638 2.262


Table 4.6- Time-Series Regression Analysis computed on Microsoft Excel. (Source: Authors

Calculation)

For the time series analysis, the selected 12 individual stocks are given the appropriate

hypothesis. The Hypothesis Test for which would make us accept the null hypothesis is;

Null Hypothesis, depicted by Ho: , which implies that there’s not that much of a

significant difference between CAPM Beta and actual Beta, and we have the Alternative

hypothesis, depicted by H1: ≠, which means that there’s a significant difference.

Here the test statistic is given as: tstat = b0/Standard error (b0) ~ tn-g-1. We decide to reject the

null hypothesis if the tstat is > t n-g-1, α/2 or < - t n-g-1, α/2. We know t n-g-1, α/2 to be 2.262 from looking 49


at the t-table as t n-g-1, α/2 = t9, 0.025 = 2.3011 where α = 5%, therefore if we take for example the

tstat of Glaxo Smith-Kline which we found out to be 1.701840, evaluating this, we see if tstat

(1.701840) > tn-g-1, α/2 (2.262) or tstat (1.701840) < - tn-k-1, α/2 (-2.262). This is the decision rule

that helps us accept the null hypothesis against the alternative hypothesis which is 2-sided, at

a 5% level of significance, as the inequality does not satisfy. And from this we can say that

the CAPM does hold for the stock.

To further confirm this we can look at the P-value, where we know that if we have a

subsequent p-value which is <0.05 or <0.10, then we can conclude that there is a significant

difference between both Betas at 5% or 10% level of significance, which would lead us to

reject H0 in favour of H1, and vice-versa. However, the p-value for this stock is 0.127198;

therefore we do the opposite and accept the null-hypothesis instead as it implies that there is

no significant difference between both Betas. We can also say that 12.7198% is the lowest

significance level that the null hypothesis can be rejected by given the sample data we have.

Furthermore, The Hypothesis Test for which would make us reject the null hypothesis is

still; Null Hypothesis, depicted by Ho: , which implies like said earlier that there’s not

that much of a significant difference between CAPM Beta and actual Beta, and we have the

Alternative hypothesis, depicted by H1: ≠, which means that there’s a significant

difference.

The test-statistic decision rule is also the same. We decide to reject H0 if the tstat is > t n-g-1, α/2 or

< - t n-g-1, α/2. As we know t n-g-1, α/2 to be 2.262 from looking at the t-table since t n-g-1, α/2 = t9, 0.025 =

2.3011 where α = 5%, if we take as another example from Table 4.1, the tstat of Imperial

Tobacco which we found out to be 2.394902, evaluating this, we also check if tstat (2.394902)

> tn-g-1, α/2 (2.262) or tstat (2.394902) < - tn-k-1, α/2 (-2.262). Since the inequality is satisfied this

50


time around, we reject the null hypothesis in favour of the alternative hypothesis which is 2-

sided, at a 5% level of significance. And from this we can say that the CAPM does not hold

for that stock. To further confirm this result we also look at the P-value, which we find to be

0.043521; therefore we reject the null-hypothesis. The value 0.043521 is < 0.05, therefore

showing that there is some significance difference between both betas, hence why we reject

H0. We can also say that 4.3521% is the higher significance level that the null hypothesis can

be accepted by, given the sample data. Therefore, from table 4.6 which includes the

regression analysis, we figure out that that the CAPM Beta holds for about 91.6% of the data

and 8.3% does not hold in the CAPM. Therefore in this case, we can say that overall the

CAPM holds in regards to its ability to accurately predict beta.

Also from the report calculation, the values of the computed R2 of the individual stocks range

from 41.7570% (maximum) to a very low 0.60901% imply that for the stock with 41.7570%

R2 , 41.7570% of the total variation is explained by the regression line for that stock. The

closer the value of R2 for the stocks to be closer to 1, the better it is as it would mean that the

regression line would perfectly fit with the data. From Figure 4.1 we can see this, and this

means that the regression model is quite good at explaining the statistically significant beta,

so therefore from this we can deduce that the CAPM does hold despite the differences, as the

differences are not significant enough to disprove the model. The adjusted R2 does not really

matter as there’s only one variable being compared, if it was more than one then I would have

also given attention to the adjusted R squared coefficient of determination.

To round up, in this case based on these results, we can say that the CAPM for an investor

would have been a useful investment procedure due to its fairly accurate prediction ability.

51


5. Conclusion

In this section of the paper, a summary of the obtained findings from the analysis is presented.

These findings form the basis of conclusion on the CAPM’s validity, from examined data in

the investigation. Comments will also be made on the reliability of the results. Finally, we will

present areas of interest for further future research purposes.

This study has been established to contribute to CAPM by providing a detailed

comprehensive review of the model, and also investigating its validity on London Stock

Exchange with regards to testing its accuracy of Beta estimations. For this study a sample of

12 firms listed on the London Stock Exchange, was selected with data dating from 2001-

2010. For each of the stocks monthly Beta are calculated and compared to the actual beta

values from DataStream to test the CAPM prediction. Research suggests through the Pearson

correlation that fairly positive correlation exists between both values. This suggests that there

is probably not much significant difference between estimated Betas and actual Betas.

These results are confirmed with the results from the Kruskal-Wallis test, which concludes

that there is not enough evidence of significant difference to conclude that the CAPM does

not hold.

Furthermore, the t-test aimed at sampling revealed results of analysis of significant difference

in only 1 out of the 12 companies; Imperial Tobacco. As results of 11 out of the 12 show that

there is no significant difference between actual return and CAPM return.

Therefore these findings confirm that the CAPM is valid on the London Stock Exchange for

11 of the 12 companies during the 10 year period selected. However it has to be pointed out

that this study is based on 12 companies, so more extensive study probably comprising of lot

more stocks and longer time period will need to be undertaken to draw final conclusions.

52


Moreover, even though the model from the results has predicted the Beta fairly accurately, it

means that the CAPM model holds, however that might not necessarily be the case, reason

being that external factors which actually happened could have contributed to the fluctuations

or differences in actual Beta from the estimates, which the model would not be aware about.

These are called market anomalies, so even though the CAPM estimate was not too far off, it

could have been worse, or not worse.

5.1 Future Research

Interest and inquisitiveness into CAPM stirred the selection of this research topic. At this

point, I am even more interested and would probably like to conduct further research on the

same topic (the validity of the CAPM), and as I mentioned earlier, if we used more stocks and

a longer time period, the estimates could have been much more accurate. In addition the t and

p values from statistical testing would have been more accurate as well if we computed more

than 10 estimates and actual values of Betas for each Bank, 10 each was only used, as a

monthly average was taken.

As an evaluation point, an aspect that could be considered for the selected data for the Beta

calculation must be the compromise between the accuracy and the significance. Explaining

this, the more years we use might increase the accuracy of Beta, so using a 15 year period

instead of 10 could have made the results more accurate, however, how relevant those data

points are, are in query. This is because the old trends from that period might not have much

bearing on new trends for the same stock. And although we could have been more accurate by

using either daily data or using weekly data to get more observations and more accuracy,

monthly was used instead as we thought that might provide some increased relevance because

of the nature of most investors needs. So that could have been one of the reasons.

53


Moreover, in Brown and Warner (1985) the daily prices are said to better in event

methodology for auto correlation, so data collected weekly and monthly might not provide a

very meaningful relationship between Beta and returns in general. So we could have probably

tested the CAPM model on daily data instead e.g. 90 days in a particular year, to see if we

would have gotten far better result.

For investment purposes to further expand the research, we could have created a portfolio

split into the 12 companies, and then calculate weighted average beta of the entire portfolio.

This would help any investor who has planning to invest, as it gives them a larger picture of

the volatility of Beta anticipated compared to the market, so they can make a wiser

investment, as according to Pellet, 47 (2004), on the individual stock level, Beta does not

work very well.

Finally for future research purposes, we could also try and focus on another industry other

than the Bank industry so for example, supermarkets or oil companies, and see how the

CAPM performs there. Or by testing another sample to go along with the sample of company

stocks that would have enhanced the research further. With regards to enhancing and

strengthening the research objective, we could have aimed to also try and predict expected

returns of assets using the Betas and empirically checking it with the actual to further test the

accuracy of the CAPM by testing this relationship between Beta and expected return. Also, it

will be of interest to consider the alternative models which have been previously mentioned in

this paper e.g. the APT and study the results in relation to CAPM.

54


6. Appendix

Table 6.1 List of 12 companies and their ticker/Abbreviation on the London Stock

Exchange

55

Company/Stock, i Ticker

Barclays BARC.L

Royal Bank of Scotland (RBS) RBS.L

Standard Chartered STAN.L

HSBC HSBA.L

Tesco TSCO.L

Sainsbury SBRY.L

Glaxo-Smith Kline (GSK) GSK.L

AstraZeneca AZN.L

BP BP.L

Royal Dutch Shell BG.L

Imperial Tobacco IMT.L

Marks and Spencer Group (M and S) MKS.L


7. Bibliography/References

-Acharya, V. and Pedersen, L. (2005): Asset pricing with liquidity risk. Journal of Financial

Economics 77, 375–410

-Bailey, R (2005): The Economics of Financial Markets. New York: Cambridge University

Press

- Banz, R. W. (1981): The Relationship Between Return and Market Value of Common

Stocks. Journal of Financial Economics, 9: 3-18

- Black, F. (1972): Capital Market Equilibrium with Restricted Borrowing. The Journal of

Business. 45 (3), p444-455.

- Black, F., Jensen, M.C. and Scholes, M. (1972): The Capital Asset Pricing Model: Some

empirical tests. Studies in the Theory of Capital Markets. New York: Praeger, 79-121

-Brealy, R and Myer, S (1981) Principles of Corporate Finance. Mc-Graw-Hill.

-Breeden, D.T. (1979): An intertemporal asset pricing model with stochastic consumption

and investment opportunities. Journal of Financial Economics 7, 265-296

- Brown, S., and Warner, J. (1985): Using daily stock returns: The case of event studies.

Journal of Financial Economics, 14, 3-31.

-Brown, Stephen J., and Mark I. Weinstein (1983): A New Approach to Testing Asset

Pricing Models: The Bilinear Paradigm. Journal of Finance 38 June): 711-43.

- Campbell, J.Y. Lo, A.W. and MacKinlay, A.C.(1997): The Econometrics of Financial

Markets. Princeton University Press, Princeton, NJ.

-Carhart, M. (1997): On Persistence in Mutual Fund Performance. The Journal of Finance,

Vol. 52, No. 1, 57-82.

-Chen N. F., Roll R W. and Ross S. A, (1983): Economic forces and the stock market:

testing the APT and alternative asset Pricing Theories, working paper No. 13-83.

-Cooly, P.L and Roden, P. F (1988): Business Financial Management, Holt, Rinehart and

56


Winston.

-Emery, R.D and Finnerty (1991): Principles of Finance with Corporate Applications. West

Publishing Co.

-Fama, E.F. and French, K. (1992): The cross-section of expected returns. Journal of

Finance 47, 427-465

-Fama, E.F. and French, K. (1993): Common Risk Factors in the Returns on Stocks and

Bonds. Journal of Financial Economics 33, 3–56

-Fama, E.F. and French, K. (2004): The Capital Asset Pricing Model: Theory and Evidence.

The Journal of Economic Perspectives, Vol. 18, No. 3. 25-46.

- Fama, E. F. and French, K. R. (1992): The Cross-Section of Expected Stock Returns.

Journal of Finance, 4 (2): 427-465,

-Fama, E. F. and French, K. R. (2004): The Capital Asset Pricing Model: Theory and

Evidence, Journal of Economic Perspectives, Vol.18, No. 3, pp. 25–46

- Fama, E.F. and MacBeth, J. (1973): Risk, return and equilibrium: Empirical tests. Journal

of Political Economy 81.

- Fama , E. F. and MacBeth (1974): Return, and Equilibrium: Empirical Tests, Journal of

Political Economy, 71

-Ferson, W.E. and Jagganathan, R. (1996): Econometric evaluation of asset pricing

models. Research department staff Report 206

-Jaggannathan, R. and Wang, Z. (1996): The conditional CAPM and the cross section of

expected returns. The Journal of Finance, Vol. 51, No. 1, 3-53.

-Jegadeesh, N. and S. Titman (1993): Returns to Buying Winners and Selling Losers:

Implications for Stock Market Efficiency. Journal of Finance, Vol. 48 Issue 1, 65-91

-Laubscher, R.E. (2002): A review of the theory of and evidence on the use of the capital

asset pricing model to estimate expected share returns. Meditari Accountancy Research Vol.

10.131–14657


-L. Pastor, R.F. Stambaugh (2003): Liquidity risk and expected stock returns. Journal of

Political Economy, 111, pp. 642–685

-Merton, R.C. (1973): An intertemporal capital asset pricing model. Econometrica 41, No.5.

867-887

- Pellet, J. (2004): Beta on it. Money. March 2004, 47.

- Pike Richard and Bill Neale (2009): Corporate Finance And Investment: Decisions And

Strategies. 6th ed. Pearson Education, Print, p227-250.

- Reinganum, M. R. (1981): A new empirical perspective on the CAPM. The journal of

financial and quantitative analysis vol. 16 no.14

-Roll, R and Ross, S.A (1980): An Empirical Investigation of the Arbitrage Pricing Theory,

The Journal of Finance, December, pp. 1073-1103.

-Ross, S.A. (1976): The arbitrage theory of capital asset pricing. Journal of Economic

Theory13, 341-360

- Sharpe, W. F. (1964): Capital Asset Prices: A Theory of Market Equilibrium Under

Conditions of Risk, Journal of Finance 19, no.3, September 1964, pp.425-442.

- Stambaugh, R. F. (1982): On the Exclusion of Assets from Tests of the Two-Parameter

Model: A Sensitivity Analysis, Journal of Financial Economics, 237-268

-Stulz, R.M. (1981): A model of international asset pricing. Journal of Financial Economics

9, 383–406.

-Van Horne, J. C (1989): Financial Management and Policy. Eight edition, Prentice-Hall

International Inc.London.

-Weston, J. F and Copeland, T. E (1986): Managerial Finance. Eighth edition, Holt

Rinehart and Winston Inc: London.

58

ma831 ezekiel peeta-imoudu disso

Documents