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THE EVALUATION OF MODERN PORTFOLIO
THEORY
SKRIPSI
Presented in partial fulfillment of the requirements for
The Bachelor’s Degree in Accounting
By:
Putu Chantika Putri Dhammayanti
008201500126
FACULTY OF BUSINESS
ACCOUNTING STUDY PROGRAM
PRESIDENT UNIVERSITY
CIKARANG, BEKASI
2019
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ii
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ACKNOWLEDGMENT
First of all I would like to praise God for the guidance and strength during the process of
finishing this research and also be able to finish the research on time. The research
entitled with “ The Evaluation of Modern Portfolio Theory” is established in order to
complete the requirement for me to finish the education in President University
Accounting study program. The researcher also acknowledge all people who have
contributed in fulfilling this thesis, especially to:
1. My family who supports me financially and mentally during my university life.
2. My advisor, Dr. Josep Ginting,CFA, and also my co advisor, Maria Yus Trinity
Irsan, M.Si for being patience in giving me supports and understanding so that I
could finish this thesis.
3. The Dean faculty of Business, Head of Accounting Study Program, Accounting
Study Program Lectures and Accounting Study Program Staff of President
University who already give their best assistance and guidance to support all
accounting students finish their education in President university.
4. My best friend and colleagues in President University for listening, offering me
advice and supporting me to finish this thesis.
I realize that this research is still far from perfection. Thus any recommendations and
suggestions are very welcome in order to establish a better research in the future.
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TABLE OF CONTENTS
DECLARATION OF ORIGINALITY ................................................................ i PANEL OF EXAMINER APPROVAL .......................................................................... ii
ACKNOWLEDGEMENT ............................................................................................... iii
TABLE OF CONTENTS ................................................................................................ iv
LIST OF TABLES .......................................................................................................... vi
LIST OF FIGURES ....................................................................................................... vii
ABSTRACT .................................................................................................................. viii
INTISARI ........................................................................................................................ ix
CHAPTER I - INTRODUCTION ................................................................................... 1
1.1 – Research Background ............................................................................................. 1
1.2 – Problem Identification ............................................................................................ 5
1.3 – Research Objectives ............................................................................................... 5
1.4 – Research Scope and Limitation .............................................................................. 6
1.5 – Research Benefit .................................................................................................... 7
1.6 – Thesis Organization ............................................................................................... 7
CHAPTER II – LITERATURE REVIEW .................................................................... 9
2.1 – Basic Concepts ...................................................................................................... 9
2.2.1 – Return ............................................................................................................ 9
2.2.2 – Risk ............................................................................................................. 10
2.2.3 – Covariance and Coefficient Correlation ...................................................... 11
2.2 – Portfolio Return and Risk ..................................................................................... 14
2.3 – Modern Portfolio Theory ..................................................................................... 18
2.4 – Efficient Frontier .................................................................................................. 21
2.5 – Capital Allocation Line and Separation Theorem ................................................ 23
CHAPTER III – RESEARCH METHODOLOGY ..................................................... 26
3.1 – Research Design .................................................................................................. 26
3.2 – Sampling Design .................................................................................................. 28
3.3 – Data Collection and Procedure ............................................................................ 32
CHAPTER IV – DATA ANALYSIS AND INTERPRETATION .............................. 36
4.1– Data Description ................................................................................................... 36
4.1.1 – Analysis of Individual Return and Standard Deviation of Stocks ........... 38
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4.1.2 – Analysis of Market Return .......................................................................... 40
4.1.3 – Analysis of Risk Free Rate .......................................................................... 41
4.1.4 – Analysis of Covariance and Coefficient Correlation Matrix ....................... 42
4.1.5 – Analysis of Markowitz Portfolio ................................................................. 45
4.1.6 – Analysis Passive Strategy Capital Allocation Line ..................................... 48
4.1.7 – Analysis of Efficient Frontier Curve model by using Polynomial ............. 51
4.2– Discussion and Interpretation Data ....................................................................... 55
CHAPTER V – CONCLUSION AND RECOMMENDATION ................................. 58
5.1 – Conclusion............................................................................................................ 58
5.2 – Limitation and Recommendation ......................................................................... 60
5.3 – Implications .......................................................................................................... 61
APPENDICES ................................................................................................................. 63
REFERENCES ................................................................................................................ 85
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LIST OF TABLES
TABLE 1 – REPRESENTATIVE SAMPLE CHOSEN ....................................28 TABLE 2 – LISTED OF SAMPLE COMPANIES ..........................................34
TABLE 3 – ANALYSIS OF MARKET RETURN ..........................................38
TABLE 4 – PORTFOLIO RANK BASED ON THE EXPECTED RETURN .45
TABLE 5 – RESULT OF POLYNOMIAL INTERPOLATION ......................49
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LIST OF FIGURES
FIGURE 1 – COVARIANCE AND COEFFICIENT CORRELATION MATRIX ..... 15
FIGURE 2 – PORTFOLIO RISK AND LEVEL OF DIVERSIFICATION ............... 17
FIGURE 3 – EFFICIENT FRONTIER ........................................................................ 21
FIGURE 4 – CAPITAL ALLOCATION LINE .......................................................... 22
FIGURE 5 – AVERAGE ANNUAL RETURN AND STANDARD DEVIATION ... 37
FIGURE 6 – COVARIANCE MATRIX RESULT ...................................................... 41 FIGURE 7 – COEFFICIENT CORRELATION MATRIX RESULT ....................................... 42
FIGURE 8 – FEASIBLE SET OF PORTFOLIO ...................................................................... 44
FIGURE 9 – EFFICIENT FRONTIER AND CAPITAL ALLOCATION LINE ...................... 48
FIGURE 10 – POLYNOMIAL CURVE AND EQUATION .................................................... 49
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ABSTRACT
The objective of this thesis is to discuss the strategy of asset allocation in
perspective of quantitative approach through the practical application based on the
Modern Portfolio Theory. This discussion is required in order to learn whether the
optimal portfolios constructed on the theory formulate the best allocation. In this
paper, readers will have the overall information about the role of asset allocation
and general knowledge about Modern Portfolio Theory. The outcomes of the
model and element are discussed and evaluated and will be a good source to be
referred. The empirical result show that the portfolio model can be modified so it
is useful to be used as an investment portfolio strategy under some circumstances.
Last but not least, the author will emphasize some significant improvement
suggestion at the end of the paper.
Key words : Modern Portfolio Theory, Optimal Portfolio, Efficient Frontier,
Capital Allocation Line
ix
INTISARI
Tujuan dari tesis ini adalah membahas model stategi untuk alokasi asset dengan
pendekatan kuantitatif melalui aplikasi praktis mengacu pada Teori Portofolio
Modern untuk mengetahui apakah portofolio optimal yang dibangun berdasarkan
teori merumuskan alokasi terbaik. Dalam tulisan ini, pembaca akan memiliki
informasi keseluruhan tentang peran alokasi aset dan pengetahuan umum tentang
Teori Portofolio Modern. Hasil dari model dan elemen yang dibahas dan di
evaluasi akan menjadi sumber yang baik untuk dirujuk. Hasil menunjukkan
bahwa secara garis besar model portfolio ini dapat dimodifikasi sehingga
bermanfaat untuk digunakan sebagai strategi portofolio investasi dalam beberapa
keadaan. Terakhir, penulis akan menekankan beberapa saran peningkatan yang
signifikan pada akhir penelitian.
Kata Kunci : Modern Portfolio Theory, Optimal Portfolio, Efficient Frontier,
Capital Allocation Line
1
CHAPTER I
INTRODUCTION
1.1. Research Background
Investment is highly related with the process of allocating financial
resources in variety of assets which aims to obtain certain benefit as a result of
investment. Thus, implementing a professional investment strategy is necessary
and it usually starts with determining the return requirements and the risk appetite
of the investor. This idea is the fundamental of strategic asset allocation and
diversification. These critical concepts play a key role in portfolio construction.
The first concept is asset allocation that can be defined as a specific
scheme to construct a single portfolio which involves specified target allocation of
various asset classes to provide the optimal balance between expected return and
risk. In other words, asset allocation is the most basic form for fund manager and
investor to decide how to weight financial instrument such as stocks, bonds,
treasury bills and other financial instruments. Too much investment in bonds or
cash will result in lower volatility than stocks, but may not produce optimal
returns. On the contrary, too much investment in stocks will result in higher return
but higher volatility as well.
The second concept is diversification. This concept was proposed by
(Markowitz H. , 1952). Diversification is actually a risk management technique
which reduce investment risk by investing in various financial instruments. It is
2
possible to achieve higher return and lower overall volatility, even though there
can be no guarantee that any particular yield or return will be achieved from any
investment due to sudden changes in the financial markets. But, this is the best
element to any investment plan because investment success depends on being
prepared for and being willing to take risk. The benefits of diversification could
be achieved with a portfolio consisting of several asset that have a negative or low
correlation between them (Bodie Z. a., 1980). However, even with a large number
of assets, risk cannot be reduced to zero since portfolios are affected by
macroeconomic factors which influence the market. It is called as systematic risk.
(Bodie Z. a., 2011).
Before the existence of Modern Portfolio theory, the classic portfolio
theory states that assets selection is determined by the maximization of the
expected value. But now in the existence of the modern portfolio theory, the
investment strategy must be conducted in a risk diversification perspective.
Modern Portfolio Theory had become one of the most significant and influence
theories in investment and finance. The outgrowth of Modern Portfolio Theory
(MPT) is Markowitz’s model in Portfolio selection. In his paper, he developed the
model of Efficient Frontier Curve (see figure 3), in which the development of a
plotted graph represents the set of efficient portfolio that have the maximum
expected return for any given level of risk, or the minimum level of risk for
several of risk assets combinations. Then, selecting the best portfolio from the set.
The rational investors will prefer to invest in the efficient portfolio.
3
In Modern Portfolio Theory, there is one portfolio out of the set of
efficient portfolio which have the highest returns per additional unit of risk. An
optimal portfolio is achieved where the Capital Allocation line intersects the
Efficient Frontier Curve (see figure 4). The theoretical concept of Capital
Allocation Line was introduced by (Tobin, 1958). In his paper of separation
theorem, by combining this risk-free asset with risky asset can construct portfolio
with better outcomes for risk averse investor rather than only use Efficient
Frontier Curve model.
Given the fact that such a large proposition of portfolio is explained by the
asset allocation decision, it could be argued that the asset allocation decision is the
most important decision in performance of portfolio. However, the process of
asset allocation has been largely split into two opposing groups: qualitative
approach and quantitative approach. In qualitative approach, fund manager prefer
to get to know a company’s management including the education and professional
background (Drachter, 2007), fund manager conducted private meeting with
companies to find the informational advantages (Barker R. H., 2012), fund
manager do the asset allocation process depends on the fund manager that had
more experienced and stock-picking abilities because the result of asset allocation
is more conservative (Lord, 2014). This could be happen because fund manager
tend to maximize their own utility of their compensation and firm’s interest rather
than that of investors (Athanassakos, 1992). Another reason, fund manager can
also find the theory is impractical to apply (Holland, 2006); (Wang, 2012);
(Coleman, 2014).
4
Though some researchers believe that process of asset allocation based on
qualitative analysis is more practical than quantitative analysis, it should be noted
that the qualitative analysis involved widespread conflict of interest and
behavioral errors within the finance industry which can be damaging to investor.
In regards with the limitation of qualitative approach, some researchers expect
that quantitative approach might also do better than qualitative approach due to
the set mathematical models that fund manager has employed to do in processing
of asset allocation. The popularity of the quantitative approach is attributed to the
belief that it has potential to be less susceptible to cognitive errors and biases.
Only a few studies address this aspect, which remains considerably
understudied. (Wermers, 2007) directly examine the differences in the
performance between fund managers that employ qualitative approaches and fund
managers that use quantitative approach in their selection process. They find that
employing quantitative models that are largely designed to take advantage of
known market which would impact to the performance of portfolio. (Jongwook
Won, et. al., 2014) shows that the quantitative approach can measuring expected
market returns with corresponding risk level.
The researcher believes that each of existing approach provided its
advantages. This raised a debate among fund manager to emphasize one approach
among quantitative approach or qualitative approach for the asset allocation
process. Based on this background, researcher have interest to examine the
process of asset allocation from the perspective of quantitative approach using
5
Markowitz’s model and whether there should be any modification that can be
done to increase the accuracy and more relevance to use in the practical world
1.2. Problem Identification and Statement
There has always been ongoing debate regarding quantitative approach
and qualitative approach for fund managers to make decision in doing asset
allocation to construct the portfolio. For quantitative oriented, fund manager will
design the asset allocation model according to the historical data of return and risk
in order to meet the overall return objectives with acceptable risk into their
quantitative model and derive a new portfolio construction whose value
characteristics make sense in the current economic (Cowell, 2002). For qualitative
oriented, the aspect of decision making to the process will use subjective in nature
and experience. Therefore, the researcher attempts to do the process of asset
allocation from the perspective of quantitative approach. Based on this research,
the question that will be answered are:
1. How do the process of asset allocation according to Markowitz ?
2. How to improve the Markowitz efficient frontier model ?
1.3.Research Objectives
Based on the research problems mentioned in the previous section, the
objective of this research is to examine the asset allocation in constructing
portfolio from the perspective of quantitative approach and whether there should
6
be any modification that can be done to increase the accuracy and relevancy to use
in the practical world. This study also provide a future recommendation for
portfolio manager in choosing several scenario within certain return and risk. To
appraise the return and risk, relevant information will be extracted from historical
company’s share price concerning the years 2015 until 2018. This research also
applies prediction, assumption, and approaches method to give a precise output.
1.4. Research Scope and Limitation
To have a common perception between reader and researcher, there are
some points should be clarified. The data used are secondary data where the data
is coming from Indonesia Stock Exchange. In terms of the accuracy of the
secondary data is beyond the control of the researcher. In this study, the selected
stocks investment is LQ-45 index without concerning the types of shares traded
throughout the research period. Three years data has been considered for the study
due to time constraints. The data used in secondary data which only included
active stocks as a representative of risky asset and Bank Certificate Indonesia
(SBI) for non-risky asset. The theories that will be examined include the portfolio
theory. The portfolio theory will be analyzed based on a literature review, such as
published books, journal and articles. The assumptions for doing the process of
asset allocation are the same assumption as (Hull, 2015) made which are no
transaction cost for trading, tax and short selling allowed. Indeed, this
assumptions not the best representation of reality, but allows to do valuable
analysis. The extent of this study is limited to the portfolio construction.
7
1.5. Significance of the Study
The result of this research is expected to give benefits to several parties, they
are :
1. Investors : the result of this research are expected to provide to the
framework of asset allocation as fundamental of investing principles
and the study will inform investors the benefit of diversification
strategy.
2. Capital Market Academician : the result of this research are expected
to enrich the field of science, particularly in the field of finance
economics. In addition, this research is also expected to provide new
insights about the portfolio construction from the perspective of
quantitative approach.
3. Researcher : this research could exercise the researcher’s skill in doing
allocation of asset to construct feasible set of efficient portfolio based
on the Markowitz modern portfolio theory. It also gains experience in
academic life, especially in surveying the case or problem in the real
world.
1.6. Thesis Organization
8
Writing system in this research are:
Chapter 1 Introduction
Discussion of research background, research question, research
objectives, significance of study, and writing systematic discuss in
introduction section.
Chapter 2 Literature Review
Discussion of the theories and concept that support research,
previous research, literature review, hypothesis development, and research
model
Chapter 3 Methodology
Discussion of the research method, variable used in the research,
research design, population and sample, instruments, and tools used in the
research, sources, and data collection method, analytical method.
Chapter 4 Analysis of data and result
Discussion of research analysis and interpretation of the result of
analysis
Chapter 5 Conclusions and Recommendations
Discussion of conclusion of the research, research limitations, and
suggestion
9
CHAPTER II
LITERATURE REVIEW
2.1 Basic Concepts
2.2.1 Return
The ultimate goals for any investors are achieving the return when they
engage in investment activity. In most cases, the investor can evaluate how
successful an investment has been by recognizing the benefit that they received in
terms of a capital gain or loss and some form of income it may generate
(dividend). This return represents how much an asset has increased or decreased
in value over a period of time.
The simple net return on share(s) will be estimated:
𝑅(𝑡0, 𝑡1) = 𝑃𝑡1−𝑃𝑡0𝑃𝑡0
or 𝑅(𝑡0, 𝑡1) = 𝑙𝑛(𝑃𝑡1𝑃𝑡0
) (2.1)
10
Here : - R is the stock return on period of time
- Pt0 is the price of stock at the beginning of the holding period
- Pt1 is the price of stock at the end of the holding period
The stock return, calculated in formula (2.1) between t0 and t1 is called
holding period return. This formula is used, if assume there are no cash-flow
(e.g., dividend) during time interval denoted by t. The holding period can be used
for any amount of time such as daily, weekly, monthly and more. Another
formula that primarily used to calculate asset price return is log returns (ln), the
concept between those formulas are similar.
2.2.2 Risk
Investment risk comes in many forms, this risk happened when there is a
difference between the expected return and the actual return. Of course, investor
will concerned if the actual return is less than the expected return. (Bodie Z. a.,
2011) talks about the characteristics of risk related of stock investment is volatile
and unstable. Obviously, it is likely to happen because our equity market is
dynamic. (Markowitz H. , 1959) introduced variance as regards to the statistical
measure to quantify risk of an asset’s expected return and cannot eliminate the
entire variance through diversification. Risk is related to the dispersion within the
uncertainty outcome and dispersion refers to variability. So, the overall risks of
investments are often measured with such common absolute measures utilized in
statistics as variance and standard deviation.
11
Variance can be estimated as the dispersion of the favorable outcome from the
expected of each investment return:
𝑉𝑎𝑟 [𝑅�𝑖] ∶= 𝐸(𝑅𝑖 − 𝑅�𝑖)2 = 𝐸[𝑅𝑖2] − [𝑅�𝑖]2 (2.2)
The variance in formula (2.2) is one measure to assess the volatility of
individual asset return. Investors have a tendency to choose the small value of
variance. Markowitz emphasized that the variance is comparable to the riskiness
of investment so that decreasing desired level of asset return. (Fabozzi FJ., 2002)
argued the limitation of variance due to this measure is the only one to describe
how the returns differ from the expected return.
Since the variance is denoted by Var [R�i] or 𝜎2 which can be interpreted
as squared units of the standard deviation, hence we can state that the standard
deviation is the square root of the variance :
𝑆𝑡𝑑 𝐷𝑒𝑣 (𝑅𝑖) = �𝑉𝑎𝑟(𝑅𝑖) (2.3)
This, imply the standard deviation can determine the likelihood of asset
return will reach on specific range. The two ideas are linear, meaning that is the
greater the investment risk indicate the larger the variance or standard deviation.
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2.2.3 Covariance and Coefficient Correlation
Covariance is statistical measure that indicate the movement of two
variables. Unlike the other statistical result that talk about how big or small the
value, but this more to emphasize the positive or negative value. There is no
limited extent of covariance, it has value from 1 to infinity. The way asset return
associated with one and another will have an impact on the portfolio risk. The
covariance between two assets X and Y may be calculated as under :
𝐶𝑜𝑣𝑥,𝑦 = ∑ [𝑅𝑥− 𝑅�𝑥] �𝑅𝑦− 𝑅�𝑦�𝑁𝑖=1
𝑁 (2.4)
Where : - 𝐶𝑜𝑣xy is covariance between x and y
- 𝑅𝑥 is return of asset x
- 𝑅�𝑥 is expected or mean return of asset x
- 𝑅𝑦 is return of asset y
- 𝑅�𝑦 is expected or mean return of asset y
- N is number of observations
Covariance does not give any detailed regarding the relationship between
the return on two assets, either both of the assets have strong or weak relation. By
using covariance, there will be three possible outcomes in analyzing the relation
of two asset returns such as positive covariance, negative covariance, and zero
covariance. Positive values of covariance have meaning that asset X and Y has
same direction. If the return of asset X is above its mean of return that represent
13
positive value as well as asset Y. Negative value of covariance indicates that if the
return of asset X is below its mean of return that represent negative value as well
as asset Y will tend to have the negative value. Otherwise, If covariance indicates
zero value is identified both of assets are independent. But in the practice, the case
of zero covariance is rare.
The coefficient correlation is beneficial to simplify the interpretation of
covariance result, since the value of covariance can never be greater than +1 or
less than -1. As mentioned earlier, covariance value can take any value; therefore
it would be harder to explain about the degree of the relationship of two variables.
Further, coefficient correlation formula is shown in equation (2.5)
𝜎𝑥,𝑦 = 𝜌𝑥,𝑦𝜎𝑥𝜎𝑦 and 𝜌𝑥,𝑦 = 𝜎𝑥,𝑦
𝜎𝑥𝜎𝑦 (2.5)
Here : - 𝜌𝑥,𝑦 is coefficient correlation between asset X and asset Y
- 𝜎𝑥,𝑦 is covariance between asset X and asset Y
- 𝜎𝑥 is standard deviation of asset X
- 𝜎𝑦 is standard deviation of asset Y
In the coefficient correlation framework, correlation may be positive,
negative, or zero. Positive correlation, +1.0 denoting the strong movement that
one assets going up or down, the other asset will have tendency to move in the
same direction, vice versa, Negative correlation, -1.0 denoting the strong
14
movement in opposite direction. For zero correlation, there will be no correlation
at all. However, very strong correlation being rare in the investment practices.
Most correlation fall on scale -1.0 to +1.0 The discussion of coefficient
correlation deserve to have an attention that the relationship between two
variables does not imply causation, this means that they simply are related or
associate with one and another variable.
2.2 Portfolio Return and Risk
Diversified investment portfolio is part of risk management strategy to
implement risk reduction of an investment by combining variety of assets. (Lee,
2016) assumes that investor would have a more desirable risk/return trade-off
through combined assets over a wide range of industries whose uncorrelated
return rather than investing in any single asset. According to the paper Asset
Allocation Models using the Markowitz approach (Kaplan, 2015), the investment
decision is the matter of how to allocate the funds into various of asset, not merely
which securities to own in order to achieve desired outcome.
Diversification is a well-known concept and being fundamental of portfolio
management since Markowitz introducing Modern Portfolio Theory (Markowitz
H. , 1952). In Modern portfolio theory, we assume those investors are risk averse.
In other words, if the investor faced with two scheme of investment with similar
15
return, they likely to choose return which have lower risk. There are some key
consideration to measure the expected return and risk of a portfolio.
Expected return which can defined as probability of possible return
obtained by investor. As we noted earlier, this is only consider as prediction or
estimation. Therefore, the actual return may be higher or lower than as it expected
before. The portfolio expected return is computed as the weighted average of
return on the assets held in the portfolio. The weight represent the proportion of
assets that need to be invested in portfolio and it estimated by the sample of
historical average. in spite of the fact that their estimation probably won't be the
best, it align with our purpose. The general formula of expected return on a
portfolio is :
𝐸�𝑅𝑝� = 𝑊1.𝐸(𝑅1) +𝑊2.𝐸(𝑅2) + 𝑊3.𝐸(𝑅3) + ⋯+𝑊𝑛.𝐸(𝑅𝑛) (2.6)
∑ 𝑊𝑛𝑛𝑖=1 = 1 (2.7)
Let 𝐸(𝑅1), denote the return on asset 1. Assuming the total of weight of asset in
the portfolio allocation is 1 or in term of percentage is 100% as shown in equation
(2.7). In the formula (2.6), we will allocate 𝑊𝑛 to asset 𝐸(𝑅𝑛). This formula can
be extended based on the number of assets in portfolio.
From Portfolio risk standpoint, risk can be expressed as the opportunity
for investor to carries the probability of loss. When an asset has larger
16
probabilities of loss, the asset is classified as the risky asset. The probability of
loss is occurred due to the existence of uncertainty. Mostly people who has role as
a buyer of stocks are genuinely wish trying to get as much as gain without endure
the risk even it is likely impossible. Uncertainty can be implying as the
knowledge and information were practically non-existence. Therefore, the suitable
portfolio seems become major concern for people when they get into investment
world.
The proper strategy could ensure share-owner against the risk and
meanwhile obtain the highest return, but it also requires estimating risk and return
of portfolio more accurately. Having knowledge about portfolio risk or portfolio
variance such an important matter before we do the selection of portfolio as the
main point of Markowitz study. We need to do the examination about the
potential performance (e.g., expected return) and potential magnitude of risk (e.g.,
variance) of portfolio.
The author composing portfolio of multiple assets. Therefore, the
calculation is slightly difference from the portfolio consisting of two assets. Even
so, the basic principle remains the same. Covariance and coefficient correlation
are the essential constituents of the variance of the portfolio. It is more difficult to
calculate covariance and coefficient correlation when the number of assets in
portfolio becomes large. Therefore, (Markowitz H. , 1952) has presented in the
classical mean-variance optimization framework about covariance and coefficient
correlation matrix. This method provided a convenient for us to calculate multiple
assets and depressed the error estimation (K. Chopra, 2006) and is essential to
17
deal with multi asset allocation. (John, 2017) argued that there is the downside of
the mean-variance analysis such as it is mostly identified with its affectability to
the inaccuracy estimation of the means and covariance matrix estimation of asset
return. Applying matrix notation n x n covariance matrix of returns, 𝐶𝑜𝑣𝑥,𝑦 =
𝐶𝑜𝑣(𝑅𝑥 ,𝑅𝑦) and coefficient correlation denoted by 𝝆𝒙,𝒚 as follows by figure 1
Figure (1) Covariance and Coefficient and Correlation Matrix
Thus far we have given the background and key parts to get the portfolio
variance, which are covariance and coefficient portfolio. This all elements above
are to compile the portfolio variance. The historical simulation method is one of
the most frequently method for forecasting the risk. The equations for portfolio
variances for multiple assets are the extension of portfolio risk consisting of two
assets. Further, portfolio variances is shown in equation (2.8) and (2.9)
𝜎𝑃2 = 𝑤12𝜎12 + 𝑤22𝜎22 + 𝑤32𝜎32 + 2𝑤1𝑤2𝜎12 + 2𝑤1𝑤3𝜎13 + 2𝑤2𝑤3𝜎23 (2.8)
𝜎𝑃2 = 𝑤12𝜎12 + 𝑤22𝜎22 + 𝑤32𝜎32 + 2𝑤1𝑤2𝜌12 + 2𝑤1𝑤3𝜌13 + 2𝑤2𝑤3𝜌23 (2.9)
18
In words, equation (2.8) is used covariance as the component to get
portfolio variance, on the contrary for equation (2.9) is used coefficient
correlation. But, at last those equations states the weighted total of individual
variances of the assets in the portfolio plus the weighted total of the extent to
which the asset differ from each other.
Risk related to any material loss attached to the performance of asset that
may affect the return of the asset. The types of risk can be classified under two
main groups: systematic and non-systematic risk. So, the total risk are containing
the systematic risk and unsystematic risk, see figure (2).
Figure (2) Portfolio Risk and level of diversification
The systematic risk or also known as undiversifiable risk the risk that
occur by the macroeconomic factors that affect for all risky assets, for instance
inflation risk, interest rate risk, market risk and more. The unsystematic risk is the
part of total risk that called as diversifiable risk. Systematic risk arises due to the
unique event that happen in the firm or in the industry and not have big impact for
19
entire firm and market e.g. business risk, financial risk and liquidity risk. This
type of risk can be reduce through diversification.
2.3 Modern Portfolio Theory
Modern Portfolio Theory was introduced by Markowitz (1952), the well-
known reputable ones. In its simplest form, the modern portfolio theory is about
constructing the portfolio with target to maximize the return in any given level of
risk. This theory or it can refer as mean-variance analysis figure prominently the
relationship between risk and return. Prior to Modern Portfolio Theory, it was
determined by the optimization of the real value of the possible value on the
assets. In other words, investors were just concentrating on the return and risk of
individual’s assets. His concept has been a foundation for the development of
financial economics and corporate finance. Basically, this theory focuses on the
risk of portfolio, not only risk generated by individual securities. The concept of
diversification assets or investing in much kind of assets plays a very crucial part
in the portfolio theory. Markowitz’s model concentrates on extremely complicated
statistical mathematical modelling and formulas that support the theoretical
assumption.
(Fabozzi FJ., 2002) mentioned portfolio theory is portfolio construction
framework for investment practitioners to selective in choosing portfolio depend
on the performance of expected return and level of risk. Markowitz’s model
portrays a principle of conduct about how investor should engage in building a
portfolio ( in a rational way of investing) , but in fact the majority of investors did
20
in the opposite way. Markowitz portfolio model or mean-variance formulation is
not only highly concern about the number of stock in the portfolio but finding the
small or constant variance with maximize expected return or vice versa, in the
practice this is an important point to the coefficient correlation approach.
Diversification will provides favorable set of portfolio if the portfolio consist of
companies in different industries because it can reduce the portfolio variance.
Normally, it have small covariance, which mean between one companies and
another do not affect each other.
In mean-variance approach, mean returns is a key parameters for expected
return and variance of return is a proxy for determine the risk of asset. This basic
concept were encapsulated in his journal and widely used up to now. According to
(Markowitz H. , 1952) portfolio theory was paying attention more to second stage
of the process of selection portfolio start with the relevant way of thinking about
the future performance, and continue with choosing the suitable portfolio.
Portfolio Theory explains that through diversification or holding the
enormous of assets can reduce the risk of portfolio. Therefore, (Markowitz H. ,
1987) in his model depends on the several assumptions and basics that are the
main concept whereupon it has been developed, like: the probability normal
distribution of individual asset returns, only just used the portfolio standard
deviation to measure risk, following the belief that investor are rational and risk
averse ( investor prefer for maximum risk for a given level of risk and vice versa),
there are no transaction cost for buying and selling securities, taxes is not put into
consideration while investor making an investment decision.
21
There are several assumption that he developed in his model but it raised
question and criticize by researcher. (Maehl, 2008) mentioned that investor have
strong urge to have a profit maximization, therefore it can prompt investor to do
speculative decision based on rumor and intuition (Morien, 2005). Another point
of criticism come from (Fabozzi FJ., 2002) pointed about all relevant parameters
for calculate portfolio such as predicting return, standard deviation, coefficient
correlation based on historical data are not plausible analysis to represent future
performance due to the fact that neither expected return nor risk are directly
observable. One of the principle issues when computing these estimates is
selecting a representative set of historical simulation data. The chosen set ought to
as accurately as possible represent the time horizon to be predicted. This
theoretical model about the inter-relationship between risk and return of financial
assets also led to the concept of efficient portfolio which contains all feasible
optimal portfolio.
2.4 Efficient Frontier
Investor are faced with many options about the proper asset allocation.
Generally speaking, portfolio can be referred as the variety of asset to be allocated
into a spread of investment product with purpose to fulfil the primary objective of
investment holder. What is the best one combination of asset is one of the
question which triggered the concept of asset allocation appears in the first place.
Asset allocation is a broad subject especially to be implemented this subject in the
dynamic investment world. We marking boundary just to make it clear to do the
22
selection of portfolio because asset allocation consist of any number with different
asset proportion.
Assuming economic rationality, Investor are concerned with the efficient
portfolio. Having the set of efficient portfolio lead investor gain the best expected
on a given level of risk, or minimum risk for a given expected return and provides
the most satisfaction and be preferred by all investor (Bringham, 2010).
In the context of Markowitz efficient frontier curve model, when it is not
meet the criteria, then we can called as inefficient portfolio. Inefficient portfolio
has lower expected return for the amount risk taken on or they have to sacrificing
the return for reducing the risk. Therefore, this portfolio does not lie on the
efficient frontier. Meaning that, we should not invest it because the portfolio
requires too much risk and inferior. An efficient frontier is the best combination
of asset allocation that offers the highest possible return for a specific level of risk
and vice versa. Efficient frontier shows the graph of expected return (vertical axis)
and expected risk ( horizontal axis) see Figure (3).
23
Figure (3) Efficient Frontier
When choosing a portfolio, investor will choose that suit their risk
preference and the level of risk tolerance. (Girard, 2005) states that investor’s
utility functions toward are taken into consideration in the development of
efficient portfolio. The purpose of the utility theory depicts the preference by
estimating the level of gratification of decision maker. Utility approach give us an
approach to measure financial agent’s preferences for wealth and the number of
risk they will attempt in the desire for achieving greater wealth. This makes it
attainable for development portfolio theory.
2.5 Capital Allocation Line and Separation Theorem
In his essay, “ Liquidity Preference as Behavior Toward Risk”, (Tobin,
1958) extended Markowitz model efficient frontier adding the concept of risk-free
asset. This assets is one kind of asset that can be allocated in the portfolio. The
concept is also known as Tobin’s separation theorem. It clearly seen that if we
put our money to invest in stocks ( risky asset ), the size of potential loss is greater
than if we put our money to invest in separation asset i.e. risky asset and risk free
asset. In simply word, invest in one safe asset and large number of risky asset
much preferred by risk averse investor (Buitler, 2003). So, the expected risk can
be managed effectively. Forming a combination risky asset will construct efficient
frontier model that derived from mean-variance optimization, in purpose to
achieve the highest attainable return based on set of feasible portfolio. According
to (Tobin, 1958) argued that investor can build an ideal portfolio which exceed the
24
performance of portfolio on efficient frontier by adding risk-free assets and it will
create the Capital Allocation Line (CAL). Tobin was introduced the risk free asset
and this development of Tobin Separation Theorem (TSB) underpins the
framework of Markowitz’s work (Figure 4)
Figure (4) Capital Market Line (CML)
Furthermore, the tangency point where capital market line intersects with
efficient frontier indicates the best possible capital market line or as the optimal
risk portfolio on efficient frontier consisted by risky asset. Tangency Portfolio
represent the maximum Sharpe ratio. see formula (2.10)
𝑆 = ERp − Rf 𝜎𝑝
(2.10)
Where : - ERp is expected return of portfolio
25
- Rf is risk free rate of investment
- 𝜎𝑝 is standard deviation of portfolio
Since this point has the property that is has the most astounding possible
mean-standard deviation proportion, (Engels, 2014). That is the reason we called
this the tangency portfolio. It occurred because risk-free investment is present
when constructing the optimal portfolio. According to (Bodie Z. a., 2011), the
composition of optimal portfolio will be as follows:
With a proportion, x, in the risky portfolio, and 1-x in the risk free asset,
the rate return on the complete portfolio, denoted 𝐸𝑅𝑐
𝐸𝑅𝑐 = 𝑥 𝐸𝑅𝑝 + (1 − 𝑥) 𝑅𝑓 (2.11)
Where : - ERc is expected return of optimal portfolio
- Rf is risk free rate of investment
- ERp is expected return of portfolio
- x is the proportion of risky asset
- 1-x is the proportion of risk free asset
For the standard deviation of optimal portfolio will be denoted by 𝜎𝑐, the formula
is depicted as follow :
𝜎𝑐 = 𝑥 𝜎𝑝 (2.12)
26
By varying the proportion of the non-risky asset and risky asset is the beneficial
way to adjust the riskiness of portfolio.
CHAPTER III
METHODOLOGY
3.1 Research Design
In conducting the research, researchers have three types of method that can be
used: a qualitative, a quantitative and a mixed method ( combining between
qualitative and quantitative method). All of them have same purpose to capture
the wide range of phenomena and find out things of the certain area, in order to
increasing the knowledge. The distinction between quantitative and qualitative in
nature, A quantitative method is used to analyzed the phenomena, human problem
or testing a hypothesis. It contains a systematic or mathematic process which are
estimated numbers as an outcome (Creswell, 1994); (Gay, 2002). With this
approach, the researcher gather information from example database.
A qualitative method is subjective is subjective interpretation in different set
of paradigms (Hitchcock, 1995) and the type of research that develop findings that
cannot be obtained by using statistic procedure. In spite of the fact that qualitative
method is hard to define but some of issues and situation could be more
understandable when used qualitative method, also the instrument use typically
27
provides flexibility does not use rigid style. For this method, researcher gather
data in form of observation, in-depth interviews, focus group which are the data
format is more textual. Which method to use depends on the purpose of the study.
If in the end of the study, researcher want to deeper understanding find unique
details upon the phenomenon studied, then qualitative method seems a suitable
method to use. But, if researcher want to wide and direct result, then the analysis
can use quantitative method as its method.
The researcher’s input is numerical data extracted from historical data weekly
stocks price of 45 most liquid stocks included in LQ-45 index and BI rate for risk
free instrument, the analyzing process in this research also includes of various
mathematical formulas and output is a number showing the proportion of asset
allocation. Accordingly, it employs the quantitative research method as the
priority. The most valid method to use in this study is the quantitative method,
considering that the implementation of efficient frontier model and capital
allocation will be engaged in the simulation techniques and ending with
examining the model performance. In measuring the performance of the establish
portfolio, this study also requires comparative data as benchmark, therefore we
use LQ45 index.
The purpose of this study is to implement the process of asset allocation in
constructing portfolio from the perspective of quantitative approach and whether
there should be any modification that can be done to increase the accuracy and
relevancy to use in the practical world, by using the model of Markowitz because
the model is well-known especially in the investment community as a
28
fundamental for portfolio management. In fact, there are some findings that we
have known about the main characteristics and most relevant aspect of efficient
frontier, but researcher assumes more essential information is needed for
generating the theory to convince us that theory is applicable even in the changing
business environment.
3.2 Sampling Design
In this research, the author have construct a portfolio consisting stocks that
ever listed in LQ-45 index. The historical data LQ-45 performance during time
period cover years from July 2015 to July 2018. The LQ-45 index is a stock
market index for Indonesia Stock Exchange (Jakarta Stock Exchange). The
Liquid-45 index (LQ-45) is the national benchmark index that was established in
February 1997 that represents 45 of the most liquid stocks , this index is one of
indicator of stocks in the capital market in Indonesia. The LQ-45 consist of 45
common stocks that have been chosen through the following criteria that have to
be fulfilled by firms which are being among the Top 60 common stocks with the
highest transaction value over the past 12 months , being among Top 60 common
stocks with the highest market capitalization in regular market over the past 12
months, having listed on the Indonesia Stock Exchange for at least 3 months,
having good financial condition and the prospect of future growth.
These stocks will be evaluated and monitored by Indonesia Stock
Exchange every six months, included in the calculation LQ-45 index. The stock
29
will be replaced on the next cycle of stock selection, if a stock does not fulfil the
criteria that have been set. This replacement occurs every six months, and
effective in early February and August. The stock used in LQ45 index is common
stocks, meaning that the investor who hold this stock will have voting rights and
right to receive dividends under certain condition, if the corporation able to make
profit. Company usually choose this strategy by issuing common stocks with
purpose to seek funds in the equity market (e.g., Indonesia Stock Exchange).
Stock that listed on LQ-45 are attractive stocks for investor to buy and sell due to
their high liquidity assets criteria. However, it does not mean that the performance
of LQ-45 index is the best performing major index because this index also heavily
reliance on the global market.
This research is limited using the LQ45 index because researcher were
trying to capture the phenomena that efficient frontier curve model that have been
made based on modern portfolio theory. MPT have an assumptions that investor
are risk averse, they prefer to hold stocks which gives maximizes return and
minimizes risk. Theoretically, all set of portfolio that lies on the curve are
efficient portfolio indicates the portfolio offer the minimum risk and greater
return. According to the purpose of construct portfolio based on EFC model,
researcher assumes that LQ-45 index is suitable to be used as a sample in this
study because stocks that listed on LQ-45 index are traded actively in Indonesia
Stock Exchange. In this regards, these stock have been proven to have a strong
fundamental analysis for investor to follow the rules of selecting stocks. With a
shortlist of companies, an investor might to examine the capabilities of the
30
company and potential for future growth. In simple word, investor have to choose
which company is good to be an investment choice.
The concept of Capital Allocation Line is involving the combination
between risky assets and non- risky asset. Another instrument was involved in
forming portfolio is non-risky asset e.g. Bank Indonesia Certificate (BI Rate). The
data used in this study is weekly historical data for three years period, so the
interest rate taken is the interest rate during the study period. For the comparison
performance portfolio and marked index, we used historical weekly data of LQ-45
index as our benchmark.
In constructing optimal portfolio of stocks, The selection of data samples
is done by purposive sampling, which is the selection of data based on specific
criteria. The criteria of shares listed is actively traded companies on the Indonesia
Stock Exchange which consistently appears in the index with a certain period.
This limitation is implemented to avoid the extreme changes in stock prices
during the observation period, average prices and incomplete data. This criterion
is used in order to prevent any research bias caused by the inclusion of
inconsistent stocks in the LQ45 index. Based on screening and the
implementation of Modern portfolio theory, there are nine stocks were selected as
candidates for building portfolio. Below is the list, appeared alphabetically: (table
1)
31
Code Company
1. AKRA AKR Corporation, Tbk.
2. BSDE Bumi Serpong Damai, Tbk.
3. JSMR Jasa Marga ( Persero ), Tbk.
4. KLBF Kalbe Farma, Tbk.
5. LPKR Lippo Karawaci, Tbk.
6. LPPF Matahari Department Store, Tbk.
7. PGAS Perusahaan Gas Negara ( Persero), Tbk.
8. PTPP PP ( Persero ) Tbk
9. WIKA Wijaya Karya ( Persero ) Tbk
Table 1 Representative Sample Chosen
Source : data processed, 2018
The estimation period in this study is three years. Researcher assumes that
three years is adequate to do this research because of the consideration about
macroeconomics in Indonesia. As part of emerging market, Indonesia has faced
challenging times for the world ’s developing economies. In recent weeks, money
has been flowing out of emerging markets and into the US as international
investors repositioned their portfolios in anticipation of a fed rate hike by the
Federal Reserve. This indicates that the impact of the macroeconomic situation
reflects the changes in the stock market.
32
The condition of the capital market has strongly influenced by
macroeconomic variables such as rupiah exchange rate, inflation, interest rate,
gross domestic product. From the point of view of our current economic
condition, it can be ascertained that Indonesia cannot be separated from the
positive and negative sentiments brought by developed countries. For instance, a
significant slowdown in economic activity resulting a decrease in GDP. The
strong decline of the Rupiah, the interest rate hikes, these will burden demand
sides and the economy. Economic actors may decide to invest or sell an
investments. If we see the GDP growth rate from 2015 until 2018 is relatively
stable rather than GDP growth rate in 2013 and 2014 during Jokowi’s era, see
figure (A.1). For this reason, researcher have an intention to limit the time
period with assumption the data taken is stable and not heavily rely on economic
condition.
3.3 Data Collection and Procedure
Sources of information are divided into two types: primary sources and
secondary sources. Secondary data are data gathered and recorded by someone
else prior to the current needs of the researcher. Secondary data are usually
historical, already assembled, and do not require access to respondents or subjects
and researchers are able to build on past research a body of business knowledge.
The primary advantage of secondary data is the obtaining secondary data is almost
always less expensive than acquiring primary data. In addition, secondary data
33
can generally be obtained rapidly and may include information that not available
in primary data.
Researcher using weekly stock price data of listed company in LQ-45
index over period 2015 – 2018. Historical data of stocks and LQ-45 index were
taken by from yahoo finance, from starting period of July 30th, 2015 until the last
week of July 2018. Meanwhile, to obtain Bank Indonesia (BI) rate as a proxy to
non-risky rate, researcher gather data through the website of Bank Indonesia (The
type of data used in this study can be categorized as secondary data. As far as we
all know, there is no study that allows us to understand what is the best period of
time horizon to get reliable input data ( average return, standard deviation and
covariance ). Thus, we have a consideration a period between three years may
sufficient to produce final result. Researcher also need to employ Microsoft excel
for data processing because this software has the function and features needed for
analysis the data. The advantages of using Microsoft excel as tools to do the
portfolio calculation based on Markowitz approach is because this software is
easy to use and very popular in our community.
In order to attain the final result of this analysis, there are some steps
appear in this research conducted by researcher and according to reference on
chapter 2: (1) Calculate the return, standard deviation, and variance of each stocks
listed in LQ-45 index. The price that is used to calculate those variables is
adjusted closing price of each week. This is useful for researcher to do screening
with an intention to select stock that have higher mean and lower standard
deviation. This screening refers to mean-variance framework The first step of this
34
process generate nine stocks that match with the criteria (2) Determine the
proportion of possible funds from each share; This research used Excel software
and its random number. In this study, random number used as representative of
probability. Basically, we apply the additional requirement, which is the
proportion of each asset is more than zero and with the constraints 𝑤𝑖 = 100%, the
consideration of this assumption is the total portion of asset must be equal to
100%. In addition, this indicates that researcher will allocate fund for all asset.
(3) Calculating the covariance and correlation matrix of portfolio which consist of
nine stocks. Due to the difficulty of calculate the covariance and correlation more
than two assets. Thus, researcher use this matrix in order to make it in easier way.
(4) Determining the efficient portfolio return and risk based on the scheme
proportion of possible funds. Each of respective portfolio will present different
level of return and risk. (5) Making chart and comparing all the efficient portfolio
which has been formed and constructing the efficient frontier of all the
probability. From this steps, as a result of many probabilities. Researcher obtain
the result that some of portfolio have different return but the same level of risk or
have the same return but different level of risk. From that finding, researcher will
choose that given a higher return or lower risk. This assumption is supported by
Modern Portfolio Theory (MPT). (6) Establish a Capital Allocation Line (CAL).
From an efficient set of portfolios, an optimal portfolio can be formed with the
help of the Capital Allocation Line (CAL). To make Capital Allocation Line, we
need put another kind of asset, which is non-risky assets. Therefore, researcher
used Bank Indonesia Certificate ( BI rate ) that represent non-risky asset. (6)
35
From the steps before, the optimal portfolio will be obtain from the measurement
index that has the highest value, which is the maximum Sharpe Ratio. The
tangency portfolio or the optimal portfolio can be measure using Sharpe Ratio.
This measurement is used to help investor understand about risk adjusted return.
This result will support the final result to generalize the conclusion of this
research.
Validity relates to the thesis’s ability to look at what's meant to be
researched, notice association between theory and empirical findings (Kumar,
2011). (Brown, 2003) states that the information collected should be precise and
correct with the set purpose, this to form the correct interpretations and to provide
a plausible analysis. Researcher follow the steps that often used and recommended
by some previous researcher and the efficient frontier model has examined by
mathematical programming model using Matlab software.
In order to verify the efficient frontier model is coded by Matlab 16
software. To identify whether the model can be used to accurately predict the
standard deviation where the value of expected return has been known.
36
CHAPTER IV
DATA ANALYSIS AND INTERPRETATION
4.1 Data Description
The research used the secondary data taken from LQ-45 index of the
companies listed in Indonesia Stock Exchange from the year of 2015 – 2018. LQ-
45 consist of 45 most liquid companies. There are several considerations that
underlying the selection of stocks, the criteria by using purposive sampling as
follows: first, the companies have already been listed on Indonesia Stock
Exchange for period July 2015 – July 2018. Second, the companies that have been
listed on LQ-45 index during the research period consistently and stocks are
37
qualified active. This research will take companies that listed in LQ-45 index for 3
consecutive years and fulfilled the criteria that set by researcher.
The table below shows the list of companies that used as samples :
Code Company Mean Std. Dev Variance
1. AKRA AKR Corporation 5,37% 31,86% 10,2%
2. BSDE Bumi Serpong Damai 4,88% 31,84% 10,1%
3. JSMR Jasa Marga 0,39% 29,11% 8,5%
4. KLBF Kalbe Farma 6,03% 28,61% 8,2%
5. LPKR Lippo Karawaci 38,78% 33,94% 11,5%
6. LPPF Matahari Department
Store
24,30% 41,09% 16,9%
7. PGAS Perusahaan Gas Negara 18,39% 46,73% 21,8%
8. PTPP Perusahaan
Pembangunan
18,15% 36,60% 13,4%
9. WIKA Wijaya Karya 12,78% 33,77% 11,4%
Table 2 Listed of Sample Companies
Source : Processed by researcher (2018)
38
Based on the criteria above, only thirty one companies that fulfilled the
criteria. In addition, researcher attempts to add additional requirement, which is
screening the stock selection based on MPT framework. Thus, this process
generate nine stocks that match with the all the criteria, see table (2). From the list
of LQ-45 shares taken from historical data, researcher has to calculate average
rate of return, standard deviation and variance from each of shares. Calculation of
returns and standard deviation are calculated using weekly observation from
closing price. Thus, researcher calculates the performance of the stock. The most
effective way of expressing investment returns is on an annual basis. For a weekly
investment return, the researcher will be presented in value per annum.
Annualized return is obtained by:
𝑅𝑦 = (𝑅𝑤 + 1)52 – 1. (4.1)
Where :
-𝑅𝑦 is the annual return
- 𝑅𝑤 is the weekly return.
For standard deviation of the average weekly return, multiply it by the square root
of the number of weeks in a year. so: 𝜎𝑤 × √52. We got the result of the average
annual return and standard deviation for the research considered periods (table
4.1)
4.1.1 Analysis of individual Return and Standard Deviation of Stocks
39
Allocation for Institutional portfolios, postulated by (Kritzman, 1990),
analysis of investment return start from calculation of return for each asset. The
return of individual shares is the amount of real profits received by investors when
investing in stocks . Stock returns can be calculated by comparing the closing
price of the stock this week which is denoted by the week t minus the closing
price of the stock last week denoted by the week t-1 then divided by the closing
price of the stock week t-1. The calculation return of individual shares from nine
shares of the LQ-45 Index which are used as research samples, (can be seen in
full in appendix 3).
Processing data in this study using an average formula, where the
calculation is the cells that contain the weekly return of each share. As for the
calculation of the risk or standard deviation of each stock, it uses the formula
standard deviation where the calculation is the cells that contain weekly return
data during the analysis period. The larger standard deviation for an expected
return, the larger the dispersion of expected returns and the greater the risk of the
investment. Stock price can wildly fluctuate every day because of supply and
demand for various industries making the author difficult to estimate the
probability distribution of each stock. Therefore, for calculation expected return or
mean return, researcher assumed that the data has normal distribution of return,
which mean the denominator is the total data of return samples is 156 data
adjusting closing price per week on each stocks during the study period.
40
Figure 5 Average annual return and standard deviation on each stock
Source : Processed by researcher (2018)
The figure shows it can be seen that shares that have the highest average
return are shares of Lippo Karawaci, Tbk (LPKR) with average returns of 38,78%
and risk of 33,94%, whereas, the lowest return is shares of Jasa Marga, Tbk
(JSMR) with average return of 0,39% and standard deviation of 29,11%. The
LPKR is the highest return among other stocks sampled. This is also estimated
that LPKR is able to provides the largest return in the constructed portfolio, but it
does not mean LPKR provides the highest risk too.
4.1.2 Analysis of Market Return
41
Stock market index return provides a great outlook for the movement
stock price due to the volatility. It is calculated from the prices of several stocks as
guidance for investor and financial market to predict the condition of market and
also as a benchmark towards the return on particular stocks. To determine its price
usually an index used weighted average.
In this study, LQ-45 is an index to represent the stock market return. This
indicates that if the movement of stock market is positive and investor do the
passive strategy, it is more likely the return is equivalent to the index followed.
Therefore, for investor, the movement of stock market return is taking into
consideration. Market return is calculated by measuring the difference in the
Market Index (Rmt) current week with the previous week (Rmt-1) then divided
with the market index the previous week. The results of the calculation of market
return can be seen in the table 3
E(Rm) 0,087420988
𝝈m 0,178960976
Table 3 Analysis of market return and standard deviation Index LQ-45
Source : Processed by researcher (2018)
The table shows that average return market (Rm) has a positive value,
which is 0,087420988 (8,74%) per annum, standard deviation of 0,178960976
42
( 17,90%), Risk free rate is 6,19% per annum. Aligned with the theoretical
concept of CAPM, market returns return can also be used as a basis for measuring
stock investment performance. If the market return is greater than the risk-free
rate of return, we conclude that investment performance is good.
4.1.3 Analysis of Risk-free rate
After calculating the return and risk each stock, the next step is calculation
of risk free rate, it can be defined as the return on investment with standard
deviation of zero (Hull, 2015). Generally, return and risk is two distinction
concept that correlate with each other. Therefore, as an investor have required to
be aware about the risk return trade off because the potential of return, the greater
probability of risk. But, this kind of asset is offering no loss because a couple of
reasons. First, the instruments is issued by government that has never defaulted on
its debt obligation. Second, this instrument has short term maturities in one year
or less, thereby this instruments is more safety, very liquid and practically no risk
attached such as interest rate risk.
In this study, we use BI 7 day repo rate (BI 7 RR) for analysis risk free
rate. We assume that Bank Indonesia certificates are type of investment without
risk for investor. BI rate 7 day repo rate is used as an interest rate for Bank
Indonesia Certificate ( SBI ) within a period of one year. The average of risk free
rate return for period August 2015 – August 2018 is 6,19% per year. From the
appendix A.4 shows that for period 31 July 2015 until 8 January 2016 is 7,5% per
43
year. Then, for period 15 January 2016 until 12 February 2016 had decreased 25
bps from 7,5% become 7,25%. After that, for period 19 February 2016 until 11
March 2016 is 7,00%. Then, it had decreased 25 bps from 7,00% become 6,75%
for period 18 March 2016 until 15 April 2016. During the period above, Bank
Indonesia using BI rate as their benchmark interest rate.
Bank Indonesia introduced new policy rate which is BI 7 days repo rate
and effective from 19th august 2016 in order to strengthened monetary operations.
Therefore, starting period 19 August 2016 until the latest period 15 August 2018,
the range of BI 7 days repo rate, which is 4,25% until 5,50%. ( see appendix A.4)
4.1.4 Analysis of Covariance and Coefficient Correlation Matrix
From the discussion above, we first select nine stocks from the 45
component of stocks from Index-LQ45. Before we construct the efficient portfolio
for the case of nine stocks, it is necessary to calculate covariance and coefficient
correlation between the chosen individual assets because the portfolio risk will be
influenced by the relationship of the assets in the portfolio. However, the
covariance only determine whether the assets are positively related or inversely
related, while the coefficient correlation explained more profoundly about the
degree to which the assets move together. Covariance and coefficient correlation
between two assets are calculated with the statistical function covar and
correl .The result of covariance can be seen in the figure 6
44
Figure 6 Covariance Matrix Result
Source : Processed by researcher (2018)
Covariance can be positive, negative, or zero value. Positive covariance value
means the tendency of two securities to move in the same direction, this indicates
that if stock returns rise then the market return will also rise and vice versa.
Covariance value of zero indicates that the movement of two securities is
independent of one another which shows stock returns and market returns do not
move towards the same or opposite.
From the covariance matrix (figure 6) in this study, the covariance of each
stock has a positive value, meaning that each of stocks are positively correlated to
each other and tend to move together in the same direction. By knowing
covariance and coefficient correlation among each of asset, so investors can find
out the composition of several assets to get an optimal portfolio with minimum
risk and maximum returns.
45
Figure 7 Coefficient Correlation Matrix Result
Source : Processed by researcher (2018)
The next step is to calculate the correlation between each stock, the
researcher build [9x9] correlation matrix representing the correlation between the
nine stocks. The figure 7 shows that the correlation between each stock result has
positive value and weak correlation since the amounts is relatively small, that is
almost near to zero. It implies that each stock has small affects to one and another,
or in other word, the responses of the investor concerning to these stocks are not
impacted by one and another.
According to the result of coefficient correlation matrix, we did not obtain
the negative value. The biggest coefficient correlation value is shares between
PTPP and WIKA, which is 0,56 and for the coefficient correlation between shares
of LPKR and AKRA is relatively small with 0,08. Investor gain diversification
benefit of effective risk reduction when the portfolio consists of stocks whose
correlation is getting smaller or the same as negative one. In Modern Portfolio
46
Theory, this is the character of coefficient correlation. So, between each stock is
independent and does not affected each other.
4.1.5 Analysis of Markowitz Portfolio
After we calculate the annual returns and standard deviation of individual
stock, the next step is calculating the expected return, covariance, and standard
deviation from each stock to construct Markowitz Portfolio. Forming the optimal
portfolio can be interpreted as set up the component of assets that produce the
most favorable expected return in any given level of risk. Therefore the expected
return and variance of portfolio are the areas that investor need to take into
consideration before make investing decisions.
The expected return can be defined as weighted average of expected
individual stock return. Asset allocation is the main concept to generate the
expected return of portfolio. We made numerous probability to produce the
optimum asset allocation ( five hundred in the example, Appendix 5). However,
we put some constraints for asset allocation, the total weight must also be equal to
1 and no negative or zero weightage. So, there would be no asset without fund
allocation. Then, to have the value of the expected return of portfolio, it simply by
multiplying the equally weighted asset with the average return each stock. (more
detail in the appendix A.5)
Portfolio Variance is to measure the risk of portfolio in any given level of
return. The role coefficient correlation and covariance are crucial to calculate the
47
portfolio variance. The more portfolio’s return vary from the average portfolio
returns, the volatile of portfolio is greater. Portfolio that have combination of
small correlation among all assets will have minimum variance portfolio.
Therefore, we use this strategy to combine risky assets (stocks) and non-risky
asset (BI rate) to accomplish the principle of diversification.
The quadratic function is used to generate for five hundred feasible set of
portfolios, the function produces the expected return, variance and composition of
each asset. Each X-point produced with a combination of standard deviations and
expected returns is a point ((𝜎𝑥,𝐸(𝑅)𝑥) The appendix A.5 clearly explains the
result of portfolio return and variance.
Figure 8 Feasible Set of Portfolio (EFC model)
Source : Processed by researcher (2018)
𝐸(𝑅)
48
Efficient Frontier Curve model is the best measurement to ensure these
combination of nine assets are presenting the optimal combination. From Figure
8 shows that only several set of portfolios whose succeeded in forming the
efficient frontier curve. The point in the graph represent the set of portfolio, thus
we only choose the point at the surface of the efficient frontier curve because
these represent the most optimal combination among the other portfolios. In this
study, we build five hundred the combination of asset, but we only select eight set
of portfolio from the total number of portfolio that we have constructed. The eight
set of portfolio can be seen from this table below.
Table 4 Portfolio Rank Based on The Expected Return
Source : Processed by researcher (2018)
The weight of asset is taking part to maximize the expected return of
portfolio. From table 4 shows that Portfolio 1 represent the portfolio with the
highest expected return, while Portfolio 6 provides the lowest risk. The result of
portfolio 1 and portfolio 6, we can concluded that the risk return trade-off still
remain in the optimal portfolio. It can likewise be seen that the more assets
49
comprised in a portfolio, the more expanded the risk are, yet the lower expected
return on portfolio.
4.1.6 Analysis Passive Strategy Capital Allocation Line
Previously, in determining portfolio, all instrument used for build portfolio
is part of risky asset. If we put one kind of asset such as risk free asset e.g. Bank
Indonesia Certificate ( SBI – Surat Berharga Indonesia), then it will obtain the
new portfolio allocation. To find the optimal portfolio, we forming capital
allocation line by connecting the point on risk free asset with the point that lies on
the efficient frontier curve and determine the optimal portfolio, the straight line is
denoted by CAL(P).
The point on risk free asset (Rf) is represent the instrument with a
combination of standard deviation and expected return of an investment with zero
risk, it can be interpreted that the value of expected return and actual return are
likely to be about the same. Bank Indonesia Certificate is considered as the
instrument for risk free asset, we obtained the average of risk free rate return for
period August 2015 – August 2018 is 6,19% per year. As a result, for risk free
instruments, we get the points at coordinates (0;6,19%).
Therefore, CAL (P) is in the form of an equation of a straight line where
the capital allocation line is tangent to the efficient frontier curve. This point will
represents the optimal portfolio indicate this portfolio provides the highest returns
per additional unit of risk. In the figure below shows that the efficient frontier
50
curve intersect with capital allocation line (CAL) at the third portfolio point
indicates the optimal portfolio. The optimal portfolio has an ERp (Expected Return
portfolio) of 18,2% with the 𝜎 ( Standard deviation) of 20,34% and Rf ( Risk Free
Rate) of 6,19%. Thus, the risk premium on the risky asset is ERp - Rf = 12,01%.
With a proportion, x, in the risky portfolio, and 1-x in the risk free asset,
the rate return on the complete portfolio, denoted ERc , where
ERc = x ERp + (1- x) Rf
= Rf + x [ ERp - Rf ] = 6,19 + x(18,2 – 6,19)
Because the standard deviation of the risky portfolio is 𝜎𝑝 = 20,34%
𝝈𝒄 = 𝒙𝝈𝒑 = 𝟐𝟎,𝟑𝟒𝒙
In sum, the rate of return of the complete portfolio will have expected value ERc =
6,19 + 12,01x and standard deviation 𝜎𝑐 = 20,34𝑥
However, in relation with the type of investment and allocation of investor’s fund,
there are some possible risk and excepted return that will be obtained in capital
allocation line, which are:
51
1. For investor who invest all their funds into risk-free assets, then the yield
of optimal portfolio that investor obtained will equally with the point of
Rf.
2. For investor who invest all their funds into risky asset, then the yield and
risk level of optimal portfolio that investor obtained will equally with the
point of P.
3. For Investor who invest in some percentage of their fund on risk free asset
and (1-x)% of their funds on risky assets, then then the yield and risk level
of optimal portfolio that investor obtained will graph on the straight line
connecting points Rf and P.
Thus the expected return of the complete portfolio as a function of its standard
deviation is a straight line, with intercept Rf and slope.
S = ERp − Rf 𝜎𝑝
= 12,0120,34
= 0,59
The slope of the CAL, denoted S, equals the increase in the expected return of the
complete portfolio per unit of additional standard deviation.
52
𝒇(𝒙) = 𝟏,𝟏𝟑 ∙ 𝟏𝟎𝟖𝒙𝟕 − 𝟏,𝟏𝟗 ∙ 𝟏𝟎𝟖𝒙𝟔 + 𝟓,𝟑𝟎 ∙ 𝟏𝟎𝟕𝒙𝟓 − 𝟏,𝟐𝟕 ∙ 𝟏𝟎𝟕𝒙𝟒 + 𝟏,𝟖𝟎 ∙ 𝟏𝟎𝟔𝒙𝟑 − 𝟏,𝟒𝟗
∙ 𝟏𝟎𝟓𝒙𝟐 − 𝟔𝟕𝟓𝟔,𝟖𝟕𝒙 + 𝟏𝟐𝟕,𝟐𝟕
Figure 9 Efficient Frontier and Capital Allocation Line
Source : Processed by researcher (2018)
4.1.7 Analysis of Efficient Frontier Curve model by using Polynomial
Equation
We make polynomial equation derived from the Efficient Frontier Curve model
using mathematical support as we see in the figure 10. From this figure, we can
state that the standard deviation is an independent variable and the expected return
𝐸(𝑅)
𝜎
53
is an dependent variable. In mathematics, we generally found y = f(x) with x as
dependent variable and y as the independent variable. Therefore, we can construct
a curve with polynomial interpolation function (Friedman, 1994). The purpose of
interpolation is to figure out the value of missing data either within the range of
existing data or outside the experienced of data. We forming the polynomial
equation as we seen below and an expected return is denoted by x :
𝝈 = 𝒇(𝒙) = 𝟏,𝟏𝟑 ∙ 𝟏𝟎𝟖𝒙𝟕 − 𝟏,𝟏𝟗 ∙ 𝟏𝟎𝟖𝒙𝟔 + 𝟓,𝟑𝟎 ∙ 𝟏𝟎𝟕𝒙𝟓 − 𝟏,𝟐𝟕 ∙ 𝟏𝟎𝟕𝒙𝟒 + 𝟏,𝟖𝟎 ∙ 𝟏𝟎𝟔𝒙𝟑
− 𝟏,𝟒𝟗 ∙ 𝟏𝟎𝟓𝒙𝟐 − 𝟔𝟕𝟓𝟔,𝟖𝟕𝒙 + 𝟏𝟐𝟕,𝟐𝟕
Figure 10 Polynomial Curve and Equation
Source : Processed by researcher (2018)
54
The polynomial equation generates the function that has degree of seven which
indicates the best fit of the series data point. From figure 10, we conclude that the
equation can be employed to predict the value because all the data used to form
the equation lies on red line. The limitation of the equation is we have to do the
long computation. This equation is practical to determine the value and forecast
the value of expected return of portfolio equal to the level of the risk.
Polynomial Interpolation : to determine the value of portfolio risk within
the range of 0,0829 ≤ x≤ 0,2335 . We obtained the range value based on the
numerous probability of the asset allocation. This indicates that the portfolio has
minimum potential to deliver the return is 0,0829 (8,29%) and the maximum
return is 0,2174 (21,74%).
Polynomial interpolation can be used in cases, for example:
- Suppose fund manager has required to estimate the potential of loss if
investors are seeking the return in the range of 10% until 15%.
𝝈 = 𝒇(𝒙) = 𝟏,𝟏𝟑 ∙ 𝟏𝟎𝟖𝒙𝟕 − 𝟏,𝟏𝟗 ∙ 𝟏𝟎𝟖𝒙𝟔 + 𝟓,𝟑𝟎 ∙ 𝟏𝟎𝟕𝒙𝟓 − 𝟏,𝟐𝟕 ∙ 𝟏𝟎𝟕𝒙𝟒 + 𝟏,𝟖𝟎 ∙ 𝟏𝟎𝟔𝒙𝟑
− 𝟏,𝟒𝟗 ∙ 𝟏𝟎𝟓𝒙𝟐 − 𝟔𝟕𝟓𝟔,𝟖𝟕𝒙 + 𝟏𝟐𝟕,𝟐𝟕
By substituting the value of x based on investor’s expected return , we can
obtained 𝝈 data using the polynomial equation as shown in the table 5:
55
Actual data Forecast
Expected
Return (x)
Std.Dev (𝝈) Expected
Return (x)
Std.Dev (𝝈)
10,64% 20,42% 10,6% 19,73%
11,24% 20,64% 11,2% 20,63%
12,80% 20,87% 12,8% 23,83%
13,50% 20,60% 13,5% 24,12%
14,70% 22,45% 14,7% 22,49%
Table 5 Result of Polynomial Interpolation
Source : Processed by researcher (2018)
We can conclude that this polynomial interpolation can be used to estimate the
value of standard deviation because three of five experimental result have precise
results. In addition, investor will have the potential loss in the range of minimum
20,23% until maximum 20,96% , with the level of expected return around 10%
until 15% for period 2015 until 2018.
Polynomial extrapolation : to approximating the future value of expected
return within short term period by relying on the existing scenario data of asset
56
allocation. The differences is x value is not among the range Min (0,0829) ≤ x≤
Max (0,2174).
Polynomial interpolation can be used in cases, for example:
- During this period, fund manager has achieved the best of level portfolio
return around 21,74%. Then, investors request to fund manager to generate
the return of portfolio around 22,5% and forecast the approximately value of
potential loss with given level of return in the next three years.
𝝈 = 𝒇(𝒙) = 𝟏,𝟏𝟑 ∙ 𝟏𝟎𝟖𝒙𝟕 − 𝟏,𝟏𝟗 ∙ 𝟏𝟎𝟖𝒙𝟔 + 𝟓,𝟑𝟎 ∙ 𝟏𝟎𝟕𝒙𝟓 − 𝟏,𝟐𝟕 ∙ 𝟏𝟎𝟕𝒙𝟒 + 𝟏,𝟖𝟎 ∙ 𝟏𝟎𝟔𝒙𝟑
− 𝟏,𝟒𝟗 ∙ 𝟏𝟎𝟓𝒙𝟐 − 𝟔𝟕𝟓𝟔,𝟖𝟕𝒙 + 𝟏𝟐𝟕,𝟐𝟕
By substituting the value of x based on investor’s expected return , we can
obtained 𝝈 data using the polynomial equation. If the fund manager build a
scenario in order to generate the return portfolio around 22,5%, then the potential
loss that investor have to compensate is around 33,01%.
4.2. Discussion and Interpretation Data
There are several empirical findings and result obtained through the
research of this study:
57
First, by composing portfolio, it makes investor bear a small risk rather
than invest in a single stocks. It is the main reason why investor needs to do
understand diversification concept.
Second, in order to obtain the efficient portfolio, we apply portfolio
optimization method based on Markowitz Modern Portfolio Theory in which
selecting stocks that have minimum risk (standard deviation) and maximum
return, also considering non-correlated asset.
Third, find the optimal portfolio is part of investor’s goal but still
considering investor risk preferences. We construct the set of portfolio consisted
risky asset using efficient frontier curve model for investor risk taker, it means
they are willing to have higher return with higher risk. Then, continued by using
concept of capital allocation line, where the portfolio does not only contain risky
asset but also consist of risk free asset.
Fourth, to build an optimal portfolio, BI rate have been chosen as the
proxy for risk free investment rate and the benchmark rate that reflect the
macroeconomic condition in a country. In period 2015 -2018, the average BI rate
was relatively stable but low around 6% indicates that the research was conducted
in the relatively stable macroeconomic condition. Indonesian Bank use BI rate as
an instrument to control the level of inflation so that it will be consistent with the
inflation target established by government. Therefore, in case of the country fails
to meet economic stability, it will affect the BI rate and inflation, respectively. In
this study, one of the variable for constructing optimal portfolio is BI rate.
58
Although, we find the optimal portfolio (expected return of 18,2% with the risk
level of 20,34%) from the set of efficient portfolio, it may change under these
circumstances.
Fifth, after we build the efficient frontier curve, we examined the model
and converted into mathematical function, namely polynomial equation. We
called this model as the modification of Efficient Frontier Markowitz. The
advantages using the model are fund manager can determine the value of potential
loss with a given level of expected return within certain period and fund manager
also can forecast the future value of potential loss with a given level of expected
return within next short term period. While the Markowitz portfolio model has
focused on constructing the feasible set of efficient portfolio, this model can be
used to measure how much the rate of change in expected return can affect the
rate of change in portfolio risk.
59
CHAPTER V
CONCLUSION
5.1. Conclusion
The concept of asset allocation plays a key role in portfolio management.
Through clear understanding of asset allocation, investor can develop appropriate
investment strategy in selecting several investment assets into portfolio with the
purpose of seeking profit and limiting the odds of devastating loss. It has
meaningful contribution in term of literal study.
The main goal of this research is to implement the asset allocation using
Markowitz portfolio model and whether there should be any modification that can
be done to increase the accuracy and relevancy to use in the practical world. We
used the Markowitz Efficient Frontier model consist of risky asset that
represented by common stocks. The common stock have been chosen due to the
fact that common stocks are more desirable investments than other kind of assets.
Aligned with the concept of diversification. The result of coefficient correlation
and covariance among these assets has small value indicates that the assets are
independent and does not affect one and another.
In order to construct the optimal portfolio, the alteration in weight
allocation of each asset in portfolio have considered in this study. We believe that
the numerous probability that we had would produce the optimum asset
60
allocation. From the result of efficient frontier curve, we have eight set of
portfolio that precisely lies on the surface of efficient frontier indicates the
efficient portfolio offers the highest expected return for a given level of risk, or
one with the lowest level of risk for a given expected return. For the portfolios
that lies below efficient frontier model is an in-efficient portfolio because they
don’t provide enough return for given level of risk.
However, the EFC model is not good enough for investor categorized as
risk-aversion who have tendency to avoid risky asset. Therefore, we have to find
the optimal one from all the set of the optimal portfolio. By using the Capital
Allocation Model, the optimal one is known as the tangency portfolio, it is an
intercept point of efficient frontier and capital allocation line. The CAL model is
required us to put one kind of non-risky asset. In this study, The optimal portfolio
has expected return of 18,2% and the risk level of 20,34%. After that, we examine
the performance of portfolio by using Shape ratio.
Moreover, we also presented the model derived from Markowitz curve
that converted into mathematical function as polynomial equation. We called this
model as the modification of Efficient Frontier Markowitz. The advantages using
the model are fund manager can determine the value of potential loss with a given
level of expected return within certain period and fund manager also can forecast
the future value of potential loss with a given level of expected return within next
short term period. While the Markowitz portfolio model has focused on construct
the efficient portfolio, this model can be used to measure how much the rate of
change in expected return can affect the rate of change in portfolio risk.
61
Therefore, the modification of efficient frontier Markowitz is adding the
relevancy in the practical world.
We also conclude that applying quantitative approach provide more
robust portfolios in terms of return and relative to the risk incurred than
qualitative approach because these processes involves use of mathematical models
that aiding investors to achieve more efficient and appropriate investment
outcomes.
5.2. Limitation and Recommendation
In this study, the researcher meets some limitations about the time and
information gathered. First, the research period for observation is quite short, so it
cannot show the all the possibilities that would happen in case of longer period.
The limitation in the number of stocks selected in portfolio due to the short time
period. Second, we limit the data sample on purpose to period of stable economic
condition in order to avoid unprecedented interventions related to the frequency of
the data. If the conditions allowed, the result generating from doing stock listed on
Indonesia stock exchange from various industries and 260 historical periods
instead of stocks listed on LQ-45 index and 156 historical period will be more
convinced. Third, the methodology is not intended to fully capture about the
systematic risk that influence on stock price leading to the formation of optimal
portfolio. Fourth, the formulation has an inherent instability once the mean and
variance are replaced by their sample counterparts.
62
According to the result of calculation and conclusions, some suggestion
are needed for future research:
- For further research, we suggest using another kind of asset that
represented of market such as instrument of future, options, bonds and
longer time intervals, so the result of the study are more accurate.
- Another suggestion is determine the accuracy of the Polynomial
interpolation in estimating the data in comparison to other models to
find out which produce better results.
5.3. Implications
This research contains the information of stocks performance listed on
LQ-45 index for period 2015 – 2018. This research is expected to be used as
consideration for investor and market participants to invest in financial asset
through the diversification strategy based on the model has explained in this
research. The stocks listed in LQ-45 can be selected as an alternative investment
option. The result of this study also test of Markowitz modern portfolio theory to
individual stock performance and portfolio performance with the result that this
research not only determines the set of efficient portfolio, but also select the
optimal portfolio of the efficient portfolio and modified the Markowitz model of
modern portfolio theory.
In addition, Investor should pay attention regarding the level of risk
preferences such as risk averse, risk neutral and risk seeker. This research also
stated the possible proportion of funds to invest through these stocks in order to
63
achieve the optimal portfolio. For the modification of Markowitz Efficient
Frontier model, the model offers the advantages for fund manager in the real life
applications. So, investor can find out the percentage of stock funds that will be
invested.
64
APPENDICES
LIST OF FIGURE
Figure 1 Covariance and Coefficient Correlation Matrix
Figure 2 Portfolio Risk and Level of diversification
65
Figure 3 Efficient Frontier
Figure 4 Capital Allocation Line
66
Figure 5 Average annual return and standard deviation on each stocks
Figure 6 Covariance Matrix Result
Figure 7 Coefficient Correlation matrix
67
Figure 8 Feasible of Portfolio ( Efficient Frontier Curve Model )
Figure 9 Efficient Frontier and Capital Allocation Line
68
Figure 10 The Polynomial Curve
69
LIST OF TABLES
Table 1 Representative Sample Chosen
Table 2 Listed of Sample Companies ( Return and Risk )
Code Company Mean Std. Dev Variance
10. AKRA AKR Corporation 5,37% 31,86% 10,2%
11. BSDE Bumi Serpong Damai 4,88% 31,84% 10,1%
12. JSMR Jasa Marga 0,39% 29,11% 8,5%
13. KLBF Kalbe Farma 6,03% 28,61% 8,2%
Code Company
10. AKRA AKR Corporation, Tbk.
11. BSDE Bumi Serpong Damai, Tbk.
12. JSMR Jasa Marga ( Persero ), Tbk.
13. KLBF Kalbe Farma, Tbk.
14. LPKR Lippo Karawaci, Tbk.
15. LPPF Matahari Department Store, Tbk.
16. PGAS Perusahaan Gas Negara ( Persero), Tbk.
17. PTPP PP ( Persero ) Tbk
18. WIKA Wijaya Karya ( Persero ) Tbk
70
14. LPKR Lippo Karawaci 38,78% 33,94% 11,5%
15. LPPF Matahari Department
Store
24,30% 41,09% 16,9%
16. PGAS Perusahaan Gas Negara 18,39% 46,73% 21,8%
17. PTPP Perusahaan
Pembangunan
18,15% 36,60% 13,4%
18. WIKA Wijaya Karya 12,78% 33,77% 11,4%
Table 3 Analysis of market return and standard deviation Index LQ-45
E(Rm) 0,087420988
𝝈m 0,178960976
Table 4 Portfolio Rank Based on The Expected Return
71
Table 5 Result of Polynomial Interpolation
Expected Return (x) Standard Deviation (𝝈)
10,6% 19,73%
11,2% 20,63%
12,8% 23,83%
13,5% 24,12%
14,7% 22,49%
Appendix 1 Indonesia Quarterly GDP Growth for period 2009 until 2018
72
Appendix 2 Company have been listed on LQ-45 index consistently for period 2015 – 2018
73
Appendix 3 Historical Data Stock Return LQ-45 for Research Sample
74
75
76
77
Appendix 4 BI 7 days RR as Risk Free Rate
78
79
Appendix 5 Feasible set of Markowitz Portfolio
80
81
82
83
84
85
86
References Athanassakos, G. (1992). Portfolio rebalancing and the January effect in Canada.
Financial Analysts Journal, 67-68.
Barker, R. H. (2012). Can company fund manager meetings convey informational
benefits? Exploring the rationalisation of equity investment decision
making by UK fund managers. Accounting, Organizations and Society,
207-220.
Bodie, Z. a. (1980). Risk and Rturn in Commodity Futures. Financial Analyst
Journal.
Bodie, Z. a. (2011). Investment and Portfolio Management. New York: The
McGraw-Hill Companies,Inc.
Boyle, P. U. (2003). Ambiguity aversion and the puzzle of own-company stock in
pension plans. IFA Working Paper.
Buitler, W. (2003). An appreciation of his contribution to economics. Royal
Economic Society .
Buffet, W. (1999). Mr. Buffet on the Stock Market. Fortune.
Bringham, E. a. (2010). Intermediate Financial Management. Cengage Learning.
Brown, J. a. (2003). Towards a Second Order Research Methodology. Electronic
Journal of Business Research Methods.
Coleman, L. (2014). Why finance theory fails to survive contact with the real
world: a fund manager perspective. Critical Perspectives on Accounting,
226-236.
Cowell, F. (2002). Quantitative Asset Allocation Models. In: Practical
Quantitative Investment Management with Derivatives. Finance and
Capital Markets Series. Palgrave Macmillan, London.
Creswell, J. W. (1994). Research Design: qualitative and quantitative
approaches. Thousand Oaks, Sage.
Drachter, K. K. (2007). Decision processes in German mutual fund companies:
evidenfrom a telephone survey". 46-49.
Engels, M. (2014). Portfolio Optimization: Beyond Markowitz. Leiden University,
Netherlands: Master's thesis.
87
Fabozzi FJ., G. F. (2002). The legacy of Modern Portfolio Theory, Journal of
Investing.
Friedman, M. K. (1994). Fundamental of Computer Numerical Analysis .
Amerika: CRC Press, Inc.
Gay, L. a. (2002). Educational Research: Competencies Analysis and Application
. Upper Saddle River, Prentice Hall .
Girard, E. a. (2005). A n-assets efficient frontier guideline for investment courses
. Journal of College Teaching and Learning , 53-56.
Grant, J. a. (2001). Equity Portfolio Management.
Hagstrom, R. G. (1999). The Warren Buffet Way. Wiley.
Hitchcock, G. a. (1995). Research and the teacher: a qualitative introduction to
school-based research. London: Routledge.
Holland, J. (2006). Fund management, intellectual capital, intangibles and private
disclosure. Managerial Finance, 277-316.
Hull, J. C. (2015). Risk Management and Financial Institution. WILEY.
John, A. L.-P. (2017). Portfolio Optimization using Matrix Approach: A case of
some stocks on the Ghana Stock Exchange.
Jongwook Won, et. al. (2014). Quantitative approach vs Qualitative decision
making in Asset Allocation of National Pention Fund of Korea.
K. Chopra, V. &. (2006). The Effect of Errors in Means, Variances, and
Covariances on Optimal Portfolio Choice.
Kaplan, P. (2015). Asset-Allocation Models using the Markowitz approach.
Frontiers of Modern Asset Allocation, 267-274.
Kumar, R. (2011). Research methodology: A step-by-step guide for beginners.
Los Angeles: SAGE.
Kritzman, e. a. (1990). Asset Allocation for Institutional Portfolio. New York :
The McGraw-Hill Companies, Inc.
Lee, H. S. (2016). Markowitz Portfolio Theory and Capital Asset Pricing Model
for Kuala Lumpur Stock Exchnge: A case revisited. . International
Journal of Economics and Finance.
88
Lord, M. (2014). Smaller University Endowments: Team Characteristics,
Portfolio Composition and Performance. Qualitative Research in
Financial Markets , 4-32.
Maehl, M. (2008). Can Modern Portfolio Theory Survive in the 21st Century?
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance.
Markowitz, H. (1959). Portfolio Selection : Efficient Diversification of
Investment. New York: John Wiley and Sons.
Markowitz, H. (1987). Mean-Variance Analysis in Portfolio Choice and Capital
Markets. Basil Blackwell Ltd. Oxford .
Morien, T. (2005). Modern Portfolio Theory Cirticism. Journal of Sustainable
Finance and Investment.
Peter Bryne, S. L. (1994). Real Estate Portfolio Analysis using a spreadsheet
Optimizer. Journal of Property Finance, 19-31.
Sharpe, W. (1964). Capital Asset Prices: A theory of market equilibrium under
conditions of risk . Journal of Finance , 425-442.
Tobin, J. (1958). Liquidity Preference as Behavior Toward Risk . Review of
Economic Studies , 65-86.
Wermers, R. Y. (2007). The investment value of mutual fund portfolio disclosure .
Working Paper, University of Maryland .
Wang, J. a. (2012). Private information acquisition and stock evaluation by
Chinese Financial Analysts. International Journal of Management, 117-
132.