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Systematic risk in the capital asset pricing model for australia a clinical death

UNIVERSITY OF ECONOMICS
HO CHI MINH CITY
VIET NAM

ERASMUS UNVERSITY ROTTERDAM
INSTITUTE OF SOCIAL STUDIES
THE NETHERLANDS

VIETNAM – THE NETHERLANDS
PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS

SYSTEMATIC RISK IN THE CAPITAL ASSET PRICING
MODEL FOR AUSTRALIA: A CLINICAL DEATH?

BY

NGUYEN CONG THANG

MASTER OF ARTS IN DEVELOPMENT ECONOMICS

Ho Chi Minh City

December 2017


UNIVERSITY OF ECONOMICS
HO CHI MINH CITY
VIETNAM

INSTITUTE OF SOCIAL STUDIES
THE HAGUE
THE NETHERLANDS

VIETNAM - NETHERLANDS
PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS

SYSTEMATIC RISK IN THE CAPITAL ASSET PRICING
MODEL FOR AUSTRALIA: A CLINICAL DEATH?
A thesis submitted in partial fulfilment of the requirements for the degree of
MASTER OF ARTS IN DEVELOPMENT ECONOMICS

By

NGUYEN CONG THANG

Academic Supervisor:

Dr. VO HONG DUC

Ho Chi Minh City
December 2017


DECLARATION
I hereby declare, that the thesis entitled, “Systematic Risk in the Capital Asset Pricing Model
Australia: A Clinical Death?” written and submitted by me in fulfillment of the requirements
for the degree of Master of Art in Development Economics to the Vietnam – The Netherlands
program. This is my original work and conclusions drawn are bases on the material collected
by me.
I further declare that this work has not been submitted to this or any other university for the
award of any other degree, diploma or equivalent course.


Ho Chi Minh City, December 2017

Nguyen Cong Thang


ACKNOWLEDGEMENTS

I would like to express my special thanks of gratitude to my academic supervisor Dr. Duc Vo.
He gave me the golden opportunity to do this wonderful project on the topic of capital asset
pricing model. I know that, for the last 20 years, you has been spending your youth, your effort
to make your life and your future thrive in Australia. I appreciate this opportunity.
I did not realize that my high school knowledge, my skill I had developed as an Android
developer could help me jump over challenges during the process of thesis accomplishment.
On that way, I learnt Visual Basic and R and I expect that they are my friends when I struggle
with messy data. I want to say thanks for my supervisor and for those introducing Beta and R
to me.
I would also like to send my first few words to my friends at the Business and Economics
Research Group (BERG) at Ho Chi Minh City Open University MA. Thach Ngoc Pham and
MA. Anh The Vo. Your attitude at work makes me wisdom with a positive slogan “If my work
gets wrong, do it again”. Furthermore, drinking milk tea on every Thursday afternoon is a cute
moment to me at BERG.
After all, I leave my last few words to Mom and Dad. This thesis is for you. This work is my
gift to you. I have put all great effort to develop and complete this very first academic study.
From the bottom of my heart, I apologize for your tears. I should have focused on getting thing
done to have lived happily and planned carefully my future.
My dearest loved Mom and Dad! I am still a kid, are not I?


ABBREVIATIONS
C4F:

Cahart four-factor model.

CAL:

Capital allocation line.

CAPM:

Capital asset pricing model.

DDM:

Dividend-discount model.

FF3F:

Fama-French three-factor model.

GICS:

Global Industry Classification Standard.

HML:

High minus Low.

MPT:

Modern portfolio theory.

SMB:

Small minus Big.


ABSTRACT

On the ground of a well-known Markowitz (1952)’s Modern Portfolio Theory, Sharpe
(1964) and Lintner (1965) developed a specific relationship between risk and expected return,
which has been named as the Sharpe-Lintner Capital Asset Pricing Model (CAPM).
CAPM or the Sharpe-Lintner CAPM is a well-known and most widely used model for
estimating a rate of return/cost of capital. The CAPM confirms that only systematic risk –
denoted by ß (beta), does matter and investors are only compensated for taking systematic risk.
Since its introduction, many studies have been conducted in an effort to assess the validity of
the CAPM in practice. Practitioners and regulators around the world including Australia,
Germany, New Zealand and United Kingdom employed CAPM as a primary model to estimate
asset’s return.
However, various studies demonstrated that CAPM appears to underestimate returns for
low-beta assets and overestimate returns for high-beta assets. The criticism went further as
Fama and French (1992) introduced the three-factor model to estimate the asset’s return. The
Fama-French three-factor model has been proven to work well in the US market and that beta
is alive in the American context. However, in contrast to the US market, Vo (2015) argued
that the Fama-French three-factor model has been proven to not work well in the Australian
context. A work by Savor and Wilson (2014) concluded that beta, or systematic risk, is still
alive in the US market. A similar question is that whether or not beta is still alive in Australia
because Vo (2015) has never tested this hypothesis? We are not aware of any study on the issue
which has been conducted. This study is conducted to fill in the gap.
This study examines the validity of the Capital Asset Pricing Model (1965) in the context
of Australia on the ground of the pioneering work by Savor and Wilson (2014) for the US. The
choice of Australia is important because, among all nations in the Asia-Pacific region, Australia
is one of a few which has required data for the analysis to be conducted.
In the heart of the CAPM, beta is considered an important measure of systematic risk
which is generally defined as an uncertainty about general economic conditions, such as GNP,
interest rates, or inflation. From that perspective, a key purpose of this study is to examine and
quantify whether or not systematic risk is responsive on the days when macroeconomics
news/events are announced or scheduled for announcement.


On the ground of Savor and Wilson (2014), four different types of portfolios are
considered in this study including: (i) 10 beta-sorted portfolios; (ii) 10 idiosyncratic risk-sorted
portfolios (iii) 25 Fama-French size and book-to-market portfolios; and (iv) industry portfolios.
In addition, macroeconomic events include announcements in relation to growth, inflation,
employment, central bank announcements, bonds, housing, consumer surveys, business surveys
and speeches from the Prime Minister or the Governor of the Reserve Bank of Australia. Days
with these events are allocated into the group (the so-called a-day) which is separated from the
n-day (non-announcement days) group.
In addition, in this study, a sensitivity check, which is beyond Savor and Wilson (2014),
by adopting different definition1 of the a-day group including (i) macroeconomics
announcements which consist of news about growth, inflation, employment, Central Bank,
bonds and speeches; (ii) microeconomics announcements which contains news related to
housing, consumer survey and business survey; (iii) economics announcements which are basic
news about news about growth, inflation, employment, housing, consumer surveys, business
surveys and speeches; and (iv) financial announcements which are combined by news about
Central Bank and bonds.
This study is conducted on a sample including more than 2,200 Australian listed firms
collected from Bloomberg for the period from 1 January 2007 to 31 December 2016 is
employed. As such, the total of nearly 2 million observations has been used in this study. Using
the linear regression with panel-corrected standard errors method and Fama-Macbeth
regression across various portfolios, two fundamental findings achieved from this study are as
follows. First, there is evidence supporting the presence of systematic risk in the Australian
context. Second, the above evidence may disappear when different portfolio formations and
different definitions of macroeconomic events are adopted.
In summary, whether or not beta, or systematic risk, is alive in the Australian context
depends on how portfolios are formed and macroeconomic events are classified. These
fundamental issues are generally known as puzzles in asset pricing studies and multi factor
model has never been proven to withstand well when different markets/time/techniques are
tested.

1

An appreciation to an anonymous reviewer who provides critical comments to the previous version of the
paper which was presented at the Vietnam’s Business and Economics Research Conference on 16-18th
November 2017.


TABLE OF CONTENTS
CHAPTER 1 INTRODUCTION ............................................................................................... 1
1.1

An overview of asset pricing model ............................................................................ 1

1.2

Research questions ...................................................................................................... 3

1.3

Research objectives ..................................................................................................... 3

1.4

A choice of Australia in this study .............................................................................. 3

CHAPTER 2 LITERATURE REVIEW .................................................................................... 5
2.1

Theoretical literature ................................................................................................... 5

2.1.1

Modern Portfolio Theory ..................................................................................... 5

2.1.2

Capital Allocation Line ........................................................................................ 7

2.1.3

Capital Asset Pricing Model ................................................................................ 8

2.1.4

The Downside of the CAPM.............................................................................. 11

2.1.5

Fama-French’s Three factor Model ................................................................... 12

2.1.6

Cahart’s Four factor Model ................................................................................ 13

2.1.7

Fama-French’s Five factor Model ..................................................................... 13

2.2

Empirical literature .................................................................................................... 14

CHAPTER 3 DATA AND METHODOLOGY ...................................................................... 24
3.1

A brief description of the method ............................................................................. 24

3.2

Data requirements and data sources .......................................................................... 25

3.3

Portfolio constructions .............................................................................................. 26

3.3.1

Ten beta-sorted portfolios and Ten idiosyncratic risk-sorted portfolios ............ 26

3.3.2

The 25 Fama-French size and book-to-market portfolios.................................. 28

3.3.3

Industry portfolios .............................................................................................. 30

3.4

Calculations of portfolio’s beta and portfolio’s return .............................................. 30

3.4.1

Pooled regression ............................................................................................... 30

3.4.2

Fama-MacBeth regression ................................................................................. 31

CHAPTER 4 EMPIRICAL RESULTS ................................................................................... 32
4.1

Pooled regression’s result.......................................................................................... 32

4.2

Fama-MacBeth regression’s result ............................................................................ 36

4.3

Result’s discussion .................................................................................................... 39

CHAPTER 5 CONCLUDING REMARKS AND POLICY IMPLICATIONS ...................... 40
5.1

Concluding remarks .................................................................................................. 40

5.2

Policy implications .................................................................................................... 42


References ................................................................................................................................ 44
Appendix 1. .............................................................................................................................. 48
Appendix 2. .............................................................................................................................. 52
Appendix 3. .............................................................................................................................. 53
Appendix 4. .............................................................................................................................. 54
Appendix 5. .............................................................................................................................. 58


LIST OF TABLES

Table 2-1 Factor classification ................................................................................................ 18
Table 2-2 Approaches to Portfolio Formations ....................................................................... 22
Table 3-1 Summary of the number of firms in 10 beta-sorted portfolios and in 10
idiosyncratic risk-sorted portfolios .......................................................................................... 27
Table 3-2 Summary of the number of firms in the 25 Fama-French size and book-to-market
portfolios .................................................................................................................................. 29
Table 3-3 Summary of the number of firms in industry portfolios ......................................... 30
Table 4-1 Regression results use linear regression with panel-corrected standard errors
method...................................................................................................................................... 33
Table 4-2 Regression results use Fama-MacBeth regression to value weighted return
manipulation. ........................................................................................................................... 37
Table 4-3 Regression results use Fama-MacBeth regression to equal weighted return
manipulation. ........................................................................................................................... 38


LIST OF FIGURES
Figure 2-1 The attainable E, V combinations ........................................................................... 6
Figure 2-2 The Capital Allocation Line .................................................................................... 8
Figure 2-3 The strategic investment of investors. ..................................................................... 9
Figure 2-4 Equilibrium in the capital market .......................................................................... 10


1

CHAPTER 1

INTRODUCTION
1.1

An overview of asset pricing model
Since the 1950s, asset pricing has seized great attention from policymakers, academics

and practitioners which pushes it to the forefront of finance. On the ground of the Modern
Portfolio Theory (MPT), Markowitz (1952) presented the efficient frontier to demonstrate the
trade-off between return and risk of an investment portfolio. Few years later, building on the
earlier work of Markowitz (1952), the Capital Asset Pricing Model (CAPM) was developed by
Sharpe (1964) and Lintner (1965).
The CAPM gained acceptance for use by academics and practitioners for an extended
period of time until the introduction of the three-factor model by Fama and French in 1992.
This three-factor model has been widely applied to explain the observed stock returns. In
addition, various empirical studies provided evidence to argue that the CAPM does
underestimate (overestimate) the return for low (high) beta asset. However, empirical evidence
has generally provided mixed evidence in relation to the validity of CAPM for the purpose of
estimating the expected equity return. Regardless of the criticism, CAPM still holds its position
of superiority of acceptance and use. 74 per cent of 392 United State Chief Financial Officer
(CFO) utilized CAPM to evaluate the cost of equity capital (Graham and Harvey, 2001).
Similarly, Brounen, Jong and Koedijk (2004) discovered that 43 per cent of 313 European
CFO’s decisions used CAPM for the same purpose. Mckenzie and Partington (2014) in their
report to the Australian Energy Regulator revealed that regulators in Australia, Germany, New
Zealand and United Kingdom employed CAPM as a primary model to estimate the cost of
equity while regulator in the United State of America utilized Dividend Discount Model
(DDM) as the first option and CAPM as the second option. Vo (2015), in his recent work,
argued that the application of the Fama-French three-factor model into public policy under the
context of Australia is not recommended. In his study, he gathered weekly data of stock returns
of all listed Australian firms and market return from 1 July 2009 to 31 May 2014 from
Bloomberg and utilized Fama-MacBeth (1973)’s two-stage regression technique. He suggested
three different scenarios to classify raw data as sub samples and five different portfolio
formations to put stock in. The portfolio formation is initiated from three fundamental ideas:
(i) formation based on a number of stocks in each group is equal; (ii) formation based on firm’s
market-capitalization; and (iii) formation based on top stock such as top 50 stocks, top 200
1


stocks. Particularly, for each scenario, he adopted five approaches to portfolio formation. For
each approach, he applied the Fama-MacBeth (1973)’s two-stage regression technique to
determine risky factor’s risk premium. Finally, his finding showed that the value risk factor is
well priced while the size risk factor is not under the context of Australian firms. Therefore,
the application of Fama-French three-factor model is not appropriate. This result is also
consistent with Brailsford, Gaunt and O’Brien (2012) and Faff (2004)’s findings.
The central piece of the CAPM is its beta. A recent work by Savor and Wilson (2014)
presented that beta is after all an important measure of systematic risk. They found that beta is
strongly as well as positively related to average excess return on days when inflation,
employment, or Federal Open Market Committee interest rate decisions, which are generally
considered sources of systematic risk, are announced. Overall, the key contribution of this
Savor and Wilson (2014) study is that beta is still alive. This simply means that CAPM is still
alive at least in the US market. From a status quo, our preferred approach is that CAPM and
Fama-French three factor model are equally treated. Fama-French three-factor model has been
proven to work well in the US market. However, it has equally been proven to not work well
in the Australian context (Vo, 2015). Equally, beta is still alive in the US market. A similar
question is that whether or not beta is still alive in Australia? We are not aware of any study on
the issue which has been conducted recently. This study is conducted to fill in the gap.
Due to the foregoing dedicated research, probably, a pattern is observed to have emerged
that different asset pricing models are suitable to different countries. Therefore, this research
raise up a hypothesis that whether the single factor asset pricing model-CAPM is usable or not
in calculation of a return on equity in Asia-Pacific in general or in Australia in particular.
To shed light on the controversy about Sharpe-Lintner version of CAPM in the context
of Australia, this study bases on the pioneering work by Savor and Wilson (2014) for the US.
This research utilizes daily data for more than 2,200 Australian listed firms are collected from
Bloomberg for the period from 1 January 2007 to 31 December 2016. Days with
announcements (the a-day) in relation to growth, inflation, employment, central bank
announcements, bonds, housing, consumer surveys, business surveys and speeches from the
Prime Minister or the Governor of the Reserve Bank of Australia scheduled to be announced
are allocated into the group which is separated from the n-day (non-announcement days) group.
Moreover, various portfolios are considered in this study including: (i) 10 beta-sorted
portfolios; (ii) 10 idiosyncratic risk-sorted portfolios (iii) 25 Fama-French size and book-tomarket portfolios; and (iv) industry portfolios. Portfolio’s return is considered in two

2


dimensions: value-weight and equal-weight based direction. In relation to methodology, the
linear regression with panel-corrected standard errors method and Fama-MacBeth regression
are both employed. The structure of thesis is represented as follow: Chapter 2 is about
Literature Review. Data and methodology are discussed in the Chapter 3. Chapter 4 considers
emperical results. Concluding remarks and policy implications are put in the Chapter 5.
1.2

Research questions
It is noted that different asset pricing models have been applied to different countries or

regions and empirical findings are generally mixed. It is generally agreed that estimating return
on equity is still a puzzle regardless of a number of Nobel prizes have been awarded. This
observation leads to following research question:


Is Beta still alive in Australia using Savor and Wilson (2014) approach using similar
definition of macroeconomic events?



Do the findings above still hold when macroeconomic events are classified into various
groups, including (i) macro event-related group; (ii) micro event-related group; (iii)
financial event-related group; and (iv) economic event-related group?

1.3

Research objectives
This study is conducted to achieve the following research objectives:


A confirmation of the validity/non-validity of employing the Capital Asset Pricing
Model (CAPM) in Australia on the ground of its Beta following Savor and Wilson
(2014) approach.



The robustness of empirical findings in relation to the validity of the CAPM using Savor
and Wilson (2014) approach when various portfolio formations and detailed
classification of macroeconomic events are considered.

1.4

A choice of Australia in this study
It is optimal if this study is conducted using data from Vietnam. However, a preliminary

analysis indicates that a substantially large volume of data is required for this type of study. In
addition, one of the key cornerstones of this empirical study is the availability of various
announcements in relation to macroeconomic issues such as economic growth, money supply,
unemployment and the others. Unfortunately, this type of data is not publicly and substantially
available in Vietnam.
From 30 countries including in the Asia Pacific region, Australia is the best candidate at
least on the following aspects: (i) a substantially large volume of data for listed firms are
3


available (more than 2,200 listed firms for more than 20 years of data); (ii) announcements of
macroeconomic issues are publicly available and they are transparently recorded; (iii) Australia
is by all means a small, open, and advanced economy in the region; and (iv) support from the
access of data is available and confirmed. As such, Australia is selected for the purpose of this
study.

4


2

CHAPTER 2

LITERATURE REVIEW
2.1

Theoretical literature

2.1.1 Modern Portfolio Theory
Markowitz (1952) suggested Modern Portfolio Theory (MPT) which is one of the two
standard asset pricing theories as an explanation of investment behavior. The MPT is
constructed from the rule (so-called expected returns-variance of returns rule or E-V rule) that
the investor probably does consider expected returns a desirable thing and variance of returns
an undesirable thing and focuses on the stage of originating the relevant beliefs and ending
with the choice of portfolio.2 In his interesting note, he stated that this rule has some advantages
to shed light on risk-averse investor’s behavior (i.e. minimizing variance of returns for given
expected returns and maximizing expected returns for given variance of returns) and to imply
diversification.
Followed by E-V rule, a rational investor, instead of allocating all his funds in a security
with the greatest discounted value, he would diversify his fund among all those securities with
give maximum expected returns. However, the return, by itself, is not a constant number
overtime and always influenced by specific-firm characteristics and nonspecific-firm
characteristics. Thus, as a matter of fact, investors have to bear risk. Moreover, the portfolio
with maximum expected return is not necessarily the one with minimum risk. That is, there is
a rate at which investors would make a trade-off between expected return and risk. To a riskaverse investor, he would minimize risk for given expected return and maximize expected
return for given risk. Graphically, his best selection of risk-expected return combination is
demonstrated by the curve which begins from A and ends at B in the following figure. The risk
factor is plotted on vertical line while the expected return plotted on the horizontal line.

2

A belief includes a set of expected returns of securities and covariance between two any returns’ securities.

5


Figure 2-1 The attainable E, V combinations

Source: Markowitz (1952)
The expected return (E) and risk (V) are calculated as follows:
𝐸 = ∑𝑁
𝑖=1 µ𝑖 𝑋𝑖

(1)

𝑁
𝑉 = ∑𝑁
𝑖=1 ∑𝑗=1 𝜎𝑖𝑗 𝑋𝑖 𝑋𝑗

(2)

Where:


E:

Expected return of portfolio.



V:

Variance of portfolio.



µi:

Expected return of security i.



Xi:

The fraction of the investor's funds invested in security i.



σij:

Covariance between security i and j.

In terms of diversification, the E-V rule also suggests a guide to the right kind of
diversification. The diversification process is not as simple as increasing the number of
securities in the portfolio. One direction of diversification of a set of sixty different railway
securities is different from the same size one with railroad, public utility, mining,
manufacturing, construction and real estate,…One plausible reason is that securities in the
same industry probably tends to move together greater than those in different industry. Another
explanation is that from equation (2), the bigger covariance is, the larger the variance of
portfolio is. That is, the latter is better than the former. Finally, Markowitz concluded that a
risk-averse investor probably follows the strategy of minimizing risk for given expected return
6


and maximizing expected return for given risk and, after all, right kind of diversification is
better.
2.1.2 Capital Allocation Line
Tobin (1958), in his attractive paper, developed his Separation Theorem to investigate
the operation of the capital market. While Markowitz focused on the risky assets and
diversification, he took one step back for a broader view. His idea, through Separation
Theorem, stated that an investor allocates his wealth not only on the risky assets but also the
riskless one. It is said that the risky asset features for the equity market and riskless assets does
for the bond market so his finding is probably one of the connections between the stock market
and bond market. For the graphical relationship, the Capital Allocation Line (CAL) was
introduced as an appropriate nominator.
Given the expected return of the risky assets and riskless assets are E(Rp) and Rf while
their risks are measured by standard deviation denoted by σp and σf, respectively. It is could be
inferred that the σf is zero because by definition, the riskless assets produces a certain future
return and their covariance – cov(p, f) - is zero, too.3 Suppose that an investor places a
proportion of his wealth (α) in the risky assets the remainder (1 – α) in the riskless assets.
According to Markowitz, his expected return and risk are yielded:
𝐸(𝑅𝑐 ) = 𝛼𝐸(𝑅𝑝 ) + (1 − 𝛼)𝑅𝑓
𝜎𝑐 = √𝛼 2 σ2𝑝 + (1 − α)2 σ𝑓2 + 2α(1 − α)cov(p, f) = 𝛼𝜎𝑝

(3)
(4)

Where:


E(Rc):

Expected return of the combination.



E(Rp):

Expected return of risky assets.



Rf:

Expected return of riskless assets.



σc :

Standard deviation of the combination.

Extracting α from equation (4) and substituting for it in equation (3). That yields:
𝐸(𝑅𝑐 ) = 𝑅𝑓 + (

3

𝐸(𝑅𝑝 )− 𝑅𝑓
σ𝑝

)𝜎𝑐

(5)

The numerator is zero.

7


From the equation (5), it is inferred that there is a linear line is drawn in the σ c, E(Rc)
space.
Figure 2-2 The Capital Allocation Line

Source: Tobin (1958)
2.1.3 Capital Asset Pricing Model
Sharpe (1964) re-employed the hypothesis of E-V rule of risk-averse investor and
portfolio’s expected return and its risk manipulation (Markowitz, 1952) and Tobin (1958)’s
finding of wealth allocation of an investor into risky asset and riskless one in order to examine
further the operation of capital market as investors physical interact. His interesting note
probably could be divided into three sub sections: (i) the optimal investment policy; (ii) the
equilibrium of the capital market and (iii) the capital assets’ price.
In relation to the optimal investment policy, basing on E-V rule, he pointed out that a
rational investor is likely to pick up efficient portfolios which are X, B, A, θ and Y in the
following figure. Remarkably, all those points lie on the same line – the investment opportunity
curve.4

4

Markowitz (1952) named it efficient E, V combinations.

8


Figure 2-3 The strategic investment of investors.

Source: Sharpe (1964)

Moreover, in combination with wealth allocation of risky asset and riskless one, he
demonstrated that there is a linear relationship between portfolio’s expected return and its risk
in the σR, ER plane.5 This relation is graphically represented by PB, PA and Pθ line in the
foregoing figure. He argued that although an investor has three options, the one whose slope is
lowest would be chosen.6 As such, Pθ is the answer. Intuitively, this decision could be
explained by the E-V rule. From the vertical axis, draw a horizontal line which intersects PB,
PA and Pθ at C, D and F, respectively. The C, D and F portfolio all offer the same risk but their
expected returns are not equal. That of F portfolio is higher than that of D and that of D is
higher than that of C. Thus, F is chosen or investor’s portfolio is reflected by Pθ.
Next, in terms of the equilibrium of the capital market, Sharpe (1964) stated that it is a
consequence of investors’ optimal investment policy and their physical interaction.
Particularly, to an investor, a combination of stocks in the portfolio F is likely to bring attractive
expected return as compared to portfolio C, D. Therefore, each investor wants to own that such
portfolio F and reject portfolio C, D. As a matter of fact, to stocks in the portfolio F, higher

5
6

𝐸(𝑅𝑝 )− 𝑅𝑓

This linear relationship is expressed as follow: E(Rc) = Rf + (

σ𝑝

) σc.

The slope is the derivative of σR with respect to ER.

9


demand at any given current price leads to less stocks’ expected return. Due to lower stocks’
expected returns, expected return of the F portfolio is lower too. This leads to portfolio F
become inefficient or its position shifts to the left while its risk does not vary. Similarly, by the
same arguments, portfolio C, D become efficient or its position shifts the right while its risk
does not vary. Consequently, the movement of those portfolios makes the investment
opportunity curve to be flatter. This result is represented in the following figure.

Figure 2-4 Equilibrium in the capital market

Source: Sharpe (1964)

Finally, regarding to the capital assets’ price, the researcher proposed the terminology of
systematic risk denoted by β which is defined as the response of stock’s return with respect to
return of efficient portfolio in order to explain expected stock return in equilibrium. It is also
inferred that β, by itself, is a component of the asset’s total risk. On the ground of the idea of
slope of the tangent line of investment opportunity curve at θ equal to the slope of Pθ yields
the following equation:

10


𝐸(𝑅𝑖 ) = 𝑃 + (𝐸(𝑅𝑔 ) − 𝑃)𝛽𝑖𝑔

(6)

Where:


E(Ri): Expected return of stock i



P:



E(Rg): Expected return of efficient portfolio g.



βig:

The pure interest rate.
The response of stock’s return with respect to return of efficient portfolio

According to the above equation, given the pure interest rate and expected return of
efficient portfolio g, low β asset is probably to associate with low expected return and vice
versa. This finding is also consistent with risk-return trade off regime reflected through
Markowitz (1952)’s efficient E-V combination curve.
2.1.4 The Downside of the CAPM
In 2002, Estrada, following Bawa and Lindenberg (1977) and Hogan and Warren
(1974)’s finding, criticized that probably CAPM is not an appropriate model to manipulate
assets return due to the fact that variance of return employed as a measure of risk. He pointed
out that, in practice, it is probably not all assets returns follow the property of symmetry and
normality which CAPM relies on. Therefore, he suggested downside beta as an alternative
outlet for risk. In his research, the downside beta is defined as the ratio of co-semi-variance
between assets return and market return to the market’s semi-variance of return. The key point
differentiates his approach in calculation of beta from that mostly mentioned in textbook is that
the former one only takes care of returns below sample mean in contrast to the latter one does
both. The reason behind originated from the fact that investors do not worry about returns
jumps above the sample mean. In order to demonstrate convincible justification, he utilized
Morgan Stanley Capital Indices database of emerging markets including monthly return of 27
countries. One of the regression analysis is made in which mean return is the regressand while
four risk variables beta, downside beta, semi-deviation and standard deviation are regressors.
As a matter of fact, the result showed that only downside beta is the only significant one. Put
it differently, downside beta is better than beta in terms of assets return explanation. To deepen
this finding, the researcher also divided 27 countries into three equal-member groups ranked
from highest beta to the lowest beta. The result also reaffirms the foregoing regression’s result
that downside beta dominates beta in terms of assets return explanation.

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2.1.5 Fama-French’s Three factor Model
Fama and French (1992), in their remarkable paper, showed a voice that the market ß as
employed alone probably has no ability to describe stock return of nonfinancial firms listed on
the NYSE, AMEX and NASDAQ in the period of 1963-1990. This study attracts academics’
and practitioners’ attention at that time because its finding contradicts traditional wisdom about
the role of market ß. Indeed, following Bhandari (1988) and Banz (1981)’s study, they stated
that the existing negative relationship between size (ME-equals to stock prices times number
of share) and average stock return. Moreover, they also found that a robust positive relationship
between book-to-market equity (BE/ME) and average stock return (Stattman 1980; Rosenberg,
Reid and Lanstein 1985; Chan, Hamao and Lakonishok 1991). On that basic, in 1993, Fama
and French argued that there are three variables make stock return deviate around its mean: (i)
Rm-Rf: the excess return between market portfolio and risk-free rate, called market risk
premium; (ii) HML: the return of high book-to-market ratio portfolio less low book-to-market
ratio portfolio, called value premium and (iii) SMB: the difference in return between small
capitalization portfolio and big capitalization portfolio, called size premium. All of them play
as a risk factor in the sense that they capture variation in stock return. Put it differently, the
expected stock return is explained by market risk premium, high minus low and small minus
big. Based on the following argument, Fama and French suggested another asset pricing model
called Fama-French three-factor model or FF3F, for short. The model is expressed as follow:
E(Ri) = Rf + (E(Rm) – Rf)βmkt + E(SMB)βsmb + E(HML)βhml
Where:


E(Ri):

Expected return of stock i.



Rf:

The risk-free rate.



βmkt:

The response of stock’s return with respect to return of market portfolio.



βsmb:

The factor loading of stock on SMB factor.



βhml:

The factor loading of stock on HML factor.



E(Rm):

Expected return of market portfolio.



E(SMB):

The difference in expected return between small capitalization portfolio
and big capitalization portfolio.



E(HML):

The expected return of high book-to-market ratio portfolio less low
book-to-market ratio portfolio.

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2.1.6 Cahart’s Four factor Model
Jegadeesh and Titman (1993) investigated firms with significant profits listed on NYSE
and AMEX from 1965 to 1989 for the explanation of stock return. Based on the examination,
they suggested a strategy for holding stock is that purchase stocks performed well and selling
those did poorly in the last 6-month will generate a significant return in the next 6-month. As
a matter of fact, this strategy originated from delayed price reactions to firm-specific
information instead of being implied by stocks’ systematic risk or their delayed reaction to
common risk factor. Four year later, their work in combination with FF3F was inherited by
Carhart (1997). He constructed a model in order to describe the return of mutual fund equity
named after him called Cahart four-factor model or C4F, for short. The model is expressed as
follows:
E(Ri) = Rf + (E(Rm) – Rf)βmkt + E(SMB)βsmb + E(HML)βhml + E(WML)βwml
Where:


E(WML): The difference in expected return between diversified winner portfolio
and looser portfolio. Other factors are defined similarly in the FF3F
model.

2.1.7 Fama-French’s Five factor Model
Fama and French (2015) based on the dividend-discount model (DDM) to argue that
some other factors are able to explain the share price. With a bit of manipulation, they express
the relation between expected return and expected investment, book to market ratio and
expected investment as follows:

𝑀𝑡 = ∑∞
𝜏=1

𝐸(𝑌𝑡+𝜏 −𝑑𝐵𝑡+𝜏 )
(1+𝑟)𝜏

(7)

Where:


Mt :



Yt + τ: The total equity earnings.



dBt + τ: Change in the total book equity.



r:

The long-term average expected stock return.



t, τ:

Indicator of time period.

The total market value of the firm’s stock.

Dividing both side of the foregoing equation by book equity. That yields:
𝑀𝑡
𝐵𝑡

=

𝐸(𝑌𝑡+𝜏 −𝑑𝐵𝑡+𝜏 )
(1+𝑟)𝜏

∑∞
𝜏=1

𝐵𝑡

(8)

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Fama and French stated that the above equation produces three implication about
expected returns: (i) keep other things constant, a higher book-to-market equity ratio pertains
to higher expected return; (ii) keep other things constant, a higher expected earnings yields a
higher expected return and (iii) keep other things constant, a higher expected growth in book
equity related to lower expected return. Due to those implications, the authors concluded that
investment and profitability are likely able to describe expected stock return. Their finding is
also consistent with the previous findings such as Novy-Marx (2013); Haugen and Baker
(1996); Fairfield, Whisenant and Yohn (2003); Titman, Wei and Xie (2004). The work of Fama
and French (2015) probably could be expressed by the following equations:
Rit– Rft= αi+ bi(Rmt– Rft) + siSMBt+ hiHMLt+ riRMWt+ ciCMAt
Where:


Rit:

The time-series return of stock or portfolio i.



Rft:

The risk-free rate return.



Rmt:

The return on the value-weighted market portfolio.



SMBt:

The difference in return between small capitalization portfolio and big
capitalization portfolio.



HMLt:

The return of high book-to-market ratio portfolio less low book-tomarket ratio portfolio.



RMWt:

The difference between return on the diversified portfolios of stocks
with robust and weak profitability.



CMAt:

The difference between the return on diversified portfolios of stocks of
low and high investment firms.

2.2

Empirical literature
In the empirical studies focusing on capital asset pricing model, undoubtedly, some of

the most well-known are the work of Fama and MacBeth (1973) and Jensen, Black, & Scholes
(1972). In relation to Fama and MacBeth’s study, in order to examine the validity of CAPM
on practice, they verified the risk-return tradeoff on the New York Stock Exchange. They
observes that, on average, a linear positive relation between the two. Moreover, they also
confirmed CAPM’s hypothesis that except for beta, there is no measure of risk which possibly
could systematically influence the return. In addition, Shapiro and Lakonishok (1984), in an
effort to revive CAPM, spilt their data on market excess return. That is, they classified the

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