AGREGAT: Jurnal Ekonomi dan Bisnis

Volume 4 (1), 2020

http://journal.uhamka.ac.id/index.php/agregat
p-ISSN: 2549-5658 e-ISSN: 2549-7243
DOI: 10.22236/agregat_vol4/is1pp8-24
Pp 8-24

THE COMPARISON OF APPLYING SINGLE INDEX MODEL AND

CAPITAL ASSET PRICING MODEL BY MEANS ACHIEVING OPTIMAL
PORTFOLIO
Siti Chanifah1, Hamdani2, Andi Gunawan3
123
Universitas Muhammadiyah Tangerang

Corresponding author: 1najahansiti57@yahoo.com, 2hamdani_82m@yahoo.com,

3
andiawan322@gmail.com

Article Info: Received: January 30, 2020; Revised: February 19, 2020; Accepted: February 30, 2020.

Abstract: The aim of this research is to analyse the comparison of applying Single Index
Model and Capital Asset Pricing Model by means of achieving the Optimal Portfolio towards
registered Issuers which are listed on the Liquid Index 45 (LQ45). The observation has been
conducted for 60 months, since February 2014 until January 2019. Quantitative approach has
been used to analyse 45 companies as the total number of population of the research. There
have been chosen 26 companies (issuers) as the sample of the research through Purposive
Sampling Technique out of 45 companies. Single Index Model and CAPM have been used as
the tools of analysis in this research. The results of the research show that portfolio is formed
by Single Index Model because it considers all aspects of the economy which cause a security
which may avoid from losses. Meanwhile, Capital Asset Pricing Model only considers
particular risk in an efficient portfolio combinations. Needless to say, it would be better for
investors to use Single Index Model in order to gain the most valueable achievement on
investment yield value.
Keywords: Optimal Portfolio, Single Index Model (SIM), and Capital Asset Pricing Model
(CAPM)

Abstrak: Tujuan dari penelitian ini adalah untuk menganalisis perbandingan penerapan Model
Indeks Tunggal dan Model Penetapan Harga Modal dengan cara mencapai Portofolio Optimal
terhadap Emiten terdaftar yang terdaftar di Liquid Index 45 (LQ45). Pengamatan telah
dilakukan selama 60 bulan, sejak Februari 2014 hingga Januari 2019. Pendekatan kuantitatif
telah digunakan untuk menganalisis 45 perusahaan sebagai jumlah total populasi penelitian.
Telah dipilih 26 perusahaan (emiten) sebagai sampel penelitian melalui Purposive Sampling
Technique dari 45 perusahaan. Model Indeks Tunggal dan CAPM telah digunakan sebagai alat
analisis dalam penelitian ini. Hasil penelitian menunjukkan bahwa portofolio dibentuk oleh
Model Indeks Tunggal karena mempertimbangkan semua aspek ekonomi yang menyebabkan
keamanan yang dapat terhindar dari kerugian. Sementara itu, Capital Priet Asset Model hanya
mempertimbangkan risiko tertentu dalam kombinasi portofolio yang efisien. Tidak perlu
dikatakan, akan lebih baik bagi investor untuk menggunakan Model Indeks Tunggal untuk
mendapatkan pencapaian yang paling bernilai pada nilai hasil investasi.
Kata kunci: Portofolio Optimal, Model Indeks Tunggal (SIM), dan Model Harga Aset Modal
(CAPM)

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AGREGAT: Jurnal Ekonomi dan Bisnis
Volume 4 (1), 2020
http://journal.uhamka.ac.id/index.php/agregat
p-ISSN: 2549-5658 e-ISSN: 2549-7243
DOI: 10.22236/agregat_vol4/is1pp8-24
Pp 8-24
INTRODUCTION
An investment decision will always be in relation to two things, returns and risks. The
rational investor invests their funds in efficient shares, it is high return with low-risk
investments (Abdilah and Rahayu, 2014). In a way to reduce investment risk, a good investor
will not only depend on only one stock. However, they will spread out by means of ditributing
their funds to more than one stocks, of course, highly preferences stocks. It could be a good
solution to suffer great losses, because if one of the stocks price falls, others will not be down.
It means that investors will save from suffering a great losses..
Investment risk can be reduced by applying concept of asset diversification through
allocating them in any types of stocks which leads to form portfolio. Of course, the rational
investor will opt optimal portfolio among the other existing portfolios (Muttaqin and Tandika,
2018).In fact, optimal portfolio can be conduted through Single Index Model and CAPM
(Yuliansyah, 2018). In this case, the thing that makes a great concern is the securities that have
been included in Liquid Market Index 45 (LQ45) which still experience price decline. This
condition seems unusual because the value of securities that have been included in Liquid
Market Index 45 (LQ45) are considered as the most profitable securities. The following is the
LQ45 movements from January 2014 until January 2019:

Picture 1. LQ45 movements, January 2014 - January 2019

Based on the picture above, we can see that Market Index of LQ45 booked its decline in
the middle of 2015 and in the beginning of 2018, however, it was getting better in the following
month. This fact proves a thing that, although portfolio divercification has been completed by
the investors, still, risk becomes the term that can be avoided as well (Husnan, 2015). As long
as the investments do not have any coeficient correlation in relation to its negative profit value
perfectly, the level of profit fluctuation becomes the thing that cannot be ignored on it portfolio.
It is in line with the research that has been conducted by Rahmadin et al., (2014). The
conducted research result has been explained by means of achieving the portfolio becomes
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AGREGAT: Jurnal Ekonomi dan Bisnis
Volume 4 (1), 2020
http://journal.uhamka.ac.id/index.php/agregat
p-ISSN: 2549-5658 e-ISSN: 2549-7243
DOI: 10.22236/agregat_vol4/is1pp8-24
Pp 8-24
optimal which in accordance with Single Index Model to LQ45 stocks that have met the criteria
to complete optimal portfolio, there have been found 6 out of 25 stocks that could encourage
the accomplishment of optimal portfolio. They are; UNVR, TLKM, KLBF, JSMR, ASII, and
CPIN with 25,96%, 25,98%, 37,17%, 9,75%, 0,66%, and 0,48% proportion of each funds
distribution. The protfolio that has been completed by those 6 shares itself is able to contribute
an expected return with 2,30% value and 0,09% risk level. However, the result of the research
that has been conducted by Rahmadin in 2014 is a little different with the research that has
been conducted by Darmawan and Purnawati in 2015. There has been found a difference
between both. In accordance with the previous research which has been carried out by
Darmawan dan Purnawati (2015), it shows that lists of shares that has completed the optimal
portfolio of LQ45 are UNVR with 75.42% proportion of funds, JSMR with 10.17% allocation
of funds, and BBCA with 14.42% funds proportion. In addition, they also explain that the level
of expected return of the portfolio is 2.67% with 1.24% risk level.
Besides, there is a knowledge contribution which discuss about the accomplishment of
the optimality of portfolio which in line with the Single Index Model as the research that has
been conducted by Mahadwartha and Gunawan (2016). The result shows that the optimal
portfolio consists of SMGR, ASII,ICBP, KLBF, TLKM, AKRA, BMTR, JSMR, MNCN,
SSIA, WIKA, ASII, ASRI, UNVR, ICBP, and it is can be used only for 6 months period. This
optimal portfolio has booked the profit at the level of 0,242% for a week with 1,122 as beta
value. They also add that The best portfolios are mostly daily portfolios with high volatility or
aggressive portfolios.
Furthermore, Setiawan (2017) has conducted a research in relation to the optimal portfolio
with the same Model as well. The research was conducted from 2013 until 2016, with 26 shares
have been selected as sample of the research. Based on the calculation which used Single Index
Model, there have been obtained a result which shows 17 shares that have included and
categorized the fulfillment of portfoili which achieve the term of optimal, for instances; BSDE,
CPIN, UNVR, INTP, AALI, AKRA, ICBP, GGRM, LSIP, BBCA,BBRI, INDF, KLBF, JSMR,
BBNI, LPKR, and UNTR. It also proves the condition where shares that have included in the
protfolio are the share that have a higher value of ERB value than Ci their gaining values.
However, for those share which do not include in portfolio means shares which have lower
values of ERB than their obtaining values of Ci. This condition leads rational investors will use
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AGREGAT: Jurnal Ekonomi dan Bisnis
Volume 4 (1), 2020
http://journal.uhamka.ac.id/index.php/agregat
p-ISSN: 2549-5658 e-ISSN: 2549-7243
DOI: 10.22236/agregat_vol4/is1pp8-24
Pp 8-24
Single Index Model in a way to opt shares and to achieve the optimal portfolio accomplishment
in Indonesia Stock Exchange. This research also suggests that, it would be better for the
investors to figuree out through analysing the ERB and Ci value in order to opt share that would
be joining in the optimal portfolio, and would be better not to have only attention on trading
volume level for the main consideration of any investments.
In addition, the result in relation to the optimal portfolio has been contributed by Prabowo
(2013) in the form of a research as well. He has conducted a research related to shares portfolio
by using CAPM and Markowitz, where shares which have formed by using CAPM are based
on those coefficient of variation (CV). It is in line with Christiana and Fadhila (2018) who have
conducted a research in relation to implementing Single Index Model by means of achieving
the optimality of portfolio. The results shows that, both the xpected return and the Excess To
Beta (ERB) are feasible and included in the optimal portfolio.
At last, another research which used Single Index Model and CAPM has been conducted
by Yuliansyah (2018). The result shows that Single Index Model is able to create the efficient
and the optimal portfolio (ADRO, TLKM) with 21,54% fund proportion to ADRO and 78,46%
to TLKM. Add, by using CPAM method there have been found that 10 share are able to
produce the efficient portfolio (LISP, ASII, ICBP, INDE, ADRO, KLBF, TKLM, , WIKA,
UNTR, and UNVR) with greater individual return than its expected returns.
Based on the explanation above, it invites curiousity to conduct a research in relation to
figure out, which securities that would be the most optimal and efficient in Market Share Index
LQ45 by using Single Index Model and CAPM, in addition, what stocks combination that
would create the most efficient and optimal portfolio?
Theoretical Framework And Hypothesis

The Optimal Portfolio

The efficient protfolio do not guarantee as the optimal portfolio. The efficient portfolio
will only always consider its expected return factors or its risk level factors. On the other hand,
the optimal portfolio will always consider the combination between the expected return factors
and the best opt form its risk level (Jogiyanto, 2017: 367). The following will be value as the
knowledge as the path by means of determining required criteria of portfolio to be optimal:: a).
If the condition of Excess Return to Beta (ERB) value is ≥ than Ci, it is to say that securities

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AGREGAT: Jurnal Ekonomi dan Bisnis
Volume 4 (1), 2020
http://journal.uhamka.ac.id/index.php/agregat
p-ISSN: 2549-5658 e-ISSN: 2549-7243
DOI: 10.22236/agregat_vol4/is1pp8-24
Pp 8-24
are categirized to be included into the optimal portfolio. b).If the condition of Excess Return to
Beta (ERB) valueis < than Ci, Ci, it can be said that the securities are required to take role as
part of optimal portfolio.
Single Index Model
The Single Index Model assumes that the price of a security will be fluctuated with the
index market price. In other words, the share price tends to be increasing if the index market
price is increasing as well. Vice versa, when the index stock price falls , most stocks will
ecperience a price decline. In other words, the returns of the scurity itself has the correlation
with the climate change in the stock market, especially to the change of market value (in
Jogiyanto, 2017).
Capital Asset Pricing Model (CAPM)
CAPM believes that risks level which concernerd by the investors is only a kind of
systematic risks, because they assume that any kinds of risks cannot be avoided even by
diversification. CAPM has been mostly used to estimate the relationship between the expected
return and the risk level to a particular asset. According to Zubir (2011:197), CAPM has two
main functions, they are: a). It functions as the reference or benchmark in re-evaluating
investment, especially its rate of return. b). It can be applied to analyse value of expected return
of certain asset that is not or has not been traded in the market.
Research Hypothesis
Forming Optimal Portfolio Using Single Index Model Method
An investment decision will always be in relation to returns and risks. The rational
investors will invest their funds in efficient stocks-they are stocks which have great returns
with lower risk level. They also will invest their funds to the optimal portfolio which consists
of BBCA, SMGR, LPKR, and INDF (Abdilah and Rahayu, 2014). However, the investor
himself must have a great concern and attention to two fundamental things, they are; the level
of returns and risks level. In lowering the risk level, the investors may diversify their
investments by compiling the 38 LQ45 non-financial company shares using Single Index
Model. It leads precentage of return value becomes 0,242% per seven days and beta1,222. The
best portfolios are mostly daily portfolios with high volatility or aggressive portfolios
(Mahadwartha and Gunawan, 2016). It leads the hypothesis as the following:
H1 : The Optimal Portfolios are Formed by Single Index Model Calculation Methods.
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Volume 4 (1), 2020
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DOI: 10.22236/agregat_vol4/is1pp8-24
Pp 8-24
Forming the Optimal Portfolio Using CPAM
CAPM assumes that risks level which concernerd by the investors is only a kind of
systematic risks, because they assume that any kinds of risks cannot be avoided even by
diversification (Zubir, 2011:197). It is in line with the statement that is explained by Jogiyanto
(2017:285), who argues that risks are always related to deviation value of the received outcome
with the expected returns. The greater deviation, it leads the greater risk that should be taken
by the investors. CPAM itself can be used as one of the technique to opt stocks and decide
which stocks are categorized as undervalued, overvalued, and fairvalued stocks. It is also can
be used as one of the methods in making investment decision in the Capital Market. There has
been found that there is a positive returns in calculating by using CAPM (Waryani, 2009). This
leads the hypothesis as the following:
H2 : The Optimal Portfolios are Formed by Capital Asset Pricing Model Calculation
Methods.
Forming the Portfolio between Single Index Model and CAPM Methods.
One of the stocks portfolios analysis perviously has been conducted by Setiawan (2010)
by using Simple Criteria for Optimal Portofolio Selection (SCOPS), which its result shows that
the selected stocks have the vlaue of Excess return to beta (ERB) > C* (cut of rate). This result
is in line with the concept of the research that has been conducted itself, which explains that
there have been found a level-up reteurns although, still, there is a small risk existed. If the
whole stocks are deversified, there will be greater returns and risk will be getting lower.
According to Firdaus, et.al (2018), risks which existed in the combination of optimal portfolio
risiko are lower than in the individual stock. It is supported by the fact which shows that the
returns value based on calculation of the combination of optimal portfolio is 0.03645 and the
value of risk level that the investors take is 0.0124. another research which used Single Index
Model and CAPM has been conducted by Yuliansyah (2018). The result shows that Single
Index Model is able to create the efficient and the optimal portfolio (ADRO, TLKM) with
21,54% fund proportion to ADRO and 78,46% to TLKM. Add, by using CPAM method there
have been found that 10 share are able to produce the efficient portfolio (ADRO, ASII, ICBP,
INDE, KLBF, LSIP, TKLM, UNTR, UNVR, and WIKA) with greater individual return than
its expected returns. This leads the hypothesis as the following:

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AGREGAT: Jurnal Ekonomi dan Bisnis
Volume 4 (1), 2020
http://journal.uhamka.ac.id/index.php/agregat
p-ISSN: 2549-5658 e-ISSN: 2549-7243
DOI: 10.22236/agregat_vol4/is1pp8-24
Pp 8-24
H3 : There Have Been Found a Difference between Applying Single Index Model and
CAPM by means of Achieving Portfolio Becomes Pptimal
METHOD
SIM or which is well known as Single Index Model and CAPM or Capital Asset Pricing
Model (CAPM) are used by means of giving an analysis in relation to which securities that
could form the optimal portfolio in Index Market Stock of Liquid 45 (ILQ45) since February
2014 until January 2019 in the Indonesia Stock Exchange. The data has been taken from the
companies which include in Index Market Stock of Liquid 45 (ILQ45) in the form of monthly
closing prices of stocks of the Composite Stock Price Index and the monthly interest rate of the
Bank of Indonesia.
The sampling technique that has been used in this research is Purposive Sampling as a
nonprobability sampling technique with certain considerations and criteria. (Sugiyono, 2016).
The sample criteria which fulfill requirements of the research are companies which registered
and legally presented on Indonesia Stocks Exchange which include in the Liquid Index Market
Stocks 45 (LQ45) and continuously analysed since February 2014 until January 2019. The data
analysis has been determined below:
1. Single Index Model
a. The calculation of securities return (Harjito and Martono, 2013):
𝑃𝑡 − 𝑃𝑡−1
𝑅𝑒𝑡𝑢𝑟𝑛 =
𝑃𝑡−1
where:
Return : the total return obtained by the investors
Pt : period of t price (selling price)
Pt-1 : period of t-1 price (purchase price)

b. Calculation of Expected Return:

𝑀

𝐸 (𝑅𝑖 ) = ∑ 𝑃𝑖𝑗 . 𝑅𝑖𝑗

𝐽=1
This formula is used when the probability can not be estimated by investors (Husnan,
2015):
∑𝑁
𝑖=1 𝑅𝑖𝑗
𝐸(𝑅𝑖 ) =
𝑁
where:
E(Ri) : amount level of expected return
M : number of cases which possibly occured
Pij : probability gaining yield in i investment
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DOI: 10.22236/agregat_vol4/is1pp8-24
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Rij : level of amount of yield in i investment
N : periods

c. The formula in calculating Market Return::

𝐼𝐻𝑆𝐺𝑡 − 𝐼𝐻𝑆𝐺𝑡−1
𝑅𝑀 =
𝐼𝐻𝑆𝐺𝑡−1
where:
RM : Market Return
IHSGt : IDX Composite in the t period.
IHSGt-1 : Previous Composite Stock Price Index (IDX Composite)

d. The calculation of Expected Market Return::

∑ 𝑅𝑀
𝐸(𝑅𝑀 ) =
𝑛
where:
E(RM) : expected market return
RM : market return
N : number of periods of market return

e. The formula in calculating the interest rate:

∑𝑛𝑗−1 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝑅𝑓 =
𝑛
where:
Rf : return of interest rate of free-risk investment
N : number of periods

f. The formula in calculating risk (Husnan, 2015):

𝑁 2
2
[𝑅𝑖𝑗 − 𝐸 (𝑅𝑖 )]
𝜎𝑖 = ∑
𝑁
𝑗=1

𝜎𝑖 = √𝜎𝑖2

where:
σi2 : variant of return of i stock
σi : deviation standard of i stock
Rij : realized return on i stock
E(Ri) : i stock value of expected return
N : periods of realized return stocks

g. The formula in calculating market return variant (Husnan, 2015):

2
∑𝑛𝑖=1[𝑅𝑀 − 𝐸(𝑅𝑀 )]2
𝜎𝑀 =
𝑛
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Volume 4 (1), 2020
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DOI: 10.22236/agregat_vol4/is1pp8-24
Pp 8-24

2
𝜎𝑀 = √𝜎𝑀
where:
σM2 : variant of market return
σM : market deviation standard
RM : realized market return
RM : expected market return
n : number of periods of realized marke return

h. Rumus untuk menilai kovarian:

CoviM = [Ri – E(Ri)].[RM – E(RM)]
where:
CoviM : kovarian antara saham i dengan pasar
Ri : realized return on i stock
RM : realized market return
E(Ri) : i stock value of its expected return
E(RM) : expected market return
i. Value of beta can be figured out with the following formula:

𝐶𝑜𝑣𝑖𝑀
𝛽𝑖 = 2
𝜎𝑀
where:
βi : value of beta of stock
σM2 : market return variant
CoviM : covariant between i stock and market

j. The formula to determine Alpha (Zubir, 2011):

αi = E(Ri) – [βi . E(RM)]

where:
αi : alpha on i stock
Βi : value of beta on i stock
E(Ri) : i stock expected return
E(RM) : value of expected return of market

k. The formula in calculating variant of residual error:

Residual error as random variable with expected value, 0 or E(e i) = 0 (Jogiyanto,
2017, on page: 409). The formula is as follows (Jogiyanto, 2017: 415):

ei = Ri – αi – βi . RM
∑(𝑒𝑖 )
𝐸(𝑒𝑖 ) =
𝑛−1
2
∑𝑛𝑖=1[𝑒𝑖 − 𝐸(𝑒𝑖 )]2
𝜎𝑒𝑖 =
𝑛−1
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where:
ei : residual error
Ri : realized return on i stock
RM : market realized return
αi : alpha on i stock
E(ei) : expected residual error
βi : beta on i stock
σei2 : residual error variant on i stock
n : number of observation periods

l. Calculating Excess Return to Beta (ERB)

Excess return to beta (ERB) is a gap of return which is expected and the return
asset which is risk-free, which means value of ERB is able to measures the excess of
relative return towards a risk unit that cannot be deiversified that measured by beta.
(Jogiyanto, 2017: 430):

𝐸(𝑅𝑖 ) − 𝑅𝐵𝑅
𝐸𝑅𝐵𝑖 =
𝛽𝑖

where:
ERBi : value of i stock on its Excess Return to Beta
E(Ri) : expected return on i stock
RBR : risk free rate
βi : value of beta on i stock

m. The Formula in Determining Cut Off Rate (Ci)

Cut off rate or cut off point (Ci) can be measured based on characteristics of
return and risk from those stock which include in the optimal portfolio (Zubir, 2011).
Cut off rate becomes the limit point merupakan titikwhich used to measure value of
stocks which can encourage the optimal portfolio. (Jogiyanto, 2017:430). Measuring
the value of Ai and Bi for each security should be conducted first, then, calculating C i
(cut off point), by using the following formula (Jogiyanto (2017):

[𝐸(𝑅𝑖 ) − 𝑅𝐵𝑅 ] . 𝛽𝑖
𝐴𝑖 = 2
𝜎𝑒𝑖
𝛽𝑖2
𝐵𝑖 = 2
𝜎𝑒𝑖
2 ∑𝑖
𝜎𝑀 . 𝑗=1 𝐴𝑖
𝐶𝑖 = 2 ∑𝑖
1 + 𝜎𝑀 . 𝑗=1 𝐵𝑖

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2 ∑𝑖 [𝐸(𝑅𝑖 ) − 𝑅𝐵𝑅 ] . 𝛽𝑖
𝜎𝑀 𝑗=1 2
𝜎𝑒𝑖
𝐶𝑖 =
2 ∑𝑖 𝛽𝑖2
1 + 𝜎𝑀 𝑗=1 𝜎 2
𝑒𝑖
where:
E(Ri) : value of i security return which is expected
RBR : value of rate ofn risk-free
βi : i security value of beta
σei2 : residual error variant of i security
Ci : Cut off point
σM 2
: variant of market index return

n. The formula in Determining funds proportion on stocks:

Funds proportion is the amount of funds which belongs to investor that will be
invested in any securities. (Jogiyanto, 2017:434):

𝑍𝑖
𝑤𝑖 = 𝑘
∑𝑗=1 𝑍𝑖

In order to obtain the value of Zi can be determined by using the following formula:

𝛽𝑖
𝑍𝑖 = (
2 𝐸𝑅𝐵𝑖 − 𝐶𝑖
)
𝜎𝑒𝑖

where:
wi : proportion of funds on i security
Zi : scale of proportion on i stock
βi : beta i security
σei2
: residual error variant i security
ERBi : i security of excess return to beta
Ci : greatest value of point which is cut off

o. The formula in calculating alpha and beta of the portfolio:

p.
𝑛

𝛽𝑝 = ∑ 𝑤𝑖 𝛽𝑖
𝑖=1
𝑛

𝛼𝑝 = ∑ 𝑤𝑖 𝛼𝑖
𝑖=1

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where:
αi : value of alpha of securities
αp : value of alpha of portfolio
βi : value of beta of securities
βp : value of beta of portfolio
wi : funds proportion of securities

2. Capital Asset Pricing Model

The analysis by using CPAM method is actually almost the same as the Single Index
Model method. The main difference is that CAPM todes not calculate the ERB and the cut
off rate, and proportion of funds that should be considered and calculated by the investors.
The technique in analysing data by using CPAM is as follows (Jogiyanto, 2017:575:
Ri,t = RBR,t + βi [RM,t – RBR,t] + ei,t
where:
Ri,t : monthly realized return realisasi on i security
RBR,t : monthly risk-free return
Βi : beta on i stock
RM,t : monthly market return
ei,t : monthly residual error on i security

RESULTS
This research has opted 26 companies as sample of the research out of 45 existed
companies. They are: ADHI (Adhi Karya (Persero) Tbk, ADRO (Adaro Energy Tbk), AKRA
(AKR Corporindo Tbk), ASII (Astra International Tbk), BBCA (Bank Central Asia Tbk),
BBNI (Bank Negara Indonesia (Persero) Tbk), BBRI (Bank Rakyat Indonesia (Persero) Tbk),
BSDE (Bank Mandiri (Persero) Tbk), GGRM (Gudang Garam Tbk), ICBP (Gudang Garam
Tbk), INDF (Indofood Sukses Makmur Tbk), INTP (Indocement Tunggal Prakarsa Tbk),
JSMR (Jasa Marga (Persero) Tbk), KLBF (Kalbe Farma Tbk), LPKR (Lippo Karawaci Tbk),
MNCN (Media Nusantara Citra Tbk), PGAS (Perusahaan Gas Negara Tbk), PTBA (Bukit
Asam Tbk), PTPP (PP (Persero) Tbk), SMGR (Semen Indonesia (Persero) Tbk), TLKM
(Semen Indonesia (Persero) Tbk), UNTR (United Tractors Tbk), UNVR (Unilever Indonesia
Tbk), WIKA (Wijaya Karya (Persero) Tbk), and WSKT (Wijaya Karya (Persero) Tbk).
In fact, based on the process of data analysis, there have been found that, there only 5
companies (issuers) out of 26 companies which are able to encourage achievement portfolio
becomes optimal. In order to determine the weight scale, there should be a consideration on
proportion of funds (capital) that is planned to be invested in the most valuable securities.
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AGREGAT: Jurnal Ekonomi dan Bisnis
Volume 4 (1), 2020
http://journal.uhamka.ac.id/index.php/agregat
p-ISSN: 2549-5658 e-ISSN: 2549-7243
DOI: 10.22236/agregat_vol4/is1pp8-24
Pp 8-24
Based on the process of analysis and calculation that have been conducted using Single Index
Model,through considering the weight scale of funds proportion which equals to calculation of
beta value, residual error variant, value of beta on its excess return, and calculating rate of cut
off. There have been found proportion of funds on 5 securities as the following table:
Tabel 1. Funds Proportion, Expected Return, and Risk on Portfolio Combination
No. Kode Saham wi E(Rp) σp
1 PTPP 5.90% 0.000584 0.000048
2 BBCA 63.55% 0.011875 0.007863
3 WSKT 12.37% 0.003654 0.001063
4 GGRM 12.27% 0.001671 0.000156
5 UNVR 5.90% 0.000654 0.000035
Jumlah 100.00% 0.018438 0.009164

Source: the data has been processed by researchers, 2019

Based on the above table, there have been found that the proportion of funds from several
securities are less than 10%. This condition will not give a significant effect to the combination
of portfolio itself. It can be seen that because the funds proportion proporsi are considered less
and they will not gain a satisfying gain of yield. It is to say that there should be a combination
of securities which can encourage achievemnt as expected by investors, it is great return value
with lower risk
Tabel 3. Funds Proportion, Expected Return, and Risk in Portfolio Combinations.

Source: the data has been processed by researchers, 2019

Tabel 4. Funds Proportion, Expected Return, and Risk in Portfolio Combinations.

Source: the data has been processed by researchers, 2019

Based on the calculation on securities that has been conducted, the results shows that:
First, there are 5 combinations of securities that can encourage optimal portfolio because thos
securities reach 0.018438 value or (1.84%) on expected return with 0.009164 atau (0.91%)
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AGREGAT: Jurnal Ekonomi dan Bisnis
Volume 4 (1), 2020
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DOI: 10.22236/agregat_vol4/is1pp8-24
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value of risk level. Second, the combinations of 3 securities value 0.016113 or (1.61%) on the
expected return with 0.008974 or (0.9%) risk level. Third, the combinations of 3 securities
values 0.017201 or (1.72%) expected return value with 0.009081 or (0.91%) risk level.
The portfolio which formed by 3 securities has a different expected return value and, of
course, has different risk level as well. It is because different ccombinations of each securities
that support the form of portfolio itself. The Portfolio combination as has been shown on table
4.3, has been formed by the highest value of excees return to beta (ERB). Meanwhile, the
portfolio combination as has been shown on table 4.4 has been formed based on several
considerations, like: funds proportion which can be allocated more, by means of gaining the
greatest return yield. The fewer securities opted, the lower return that will be obtained as well.
This result is in line with Halim (2005), who argues that the more number of securities in a
combination in the portfolio, the lower risk existed.
The analysis by using CAPM compares the expected rate of return (E(R i)) and the
realized return (Ri).The level or rate expected return (E(Ri)) itself is becomes yield that will be
obtained by the investors as the result of securities investments conducted. CAPM method has
been applied by means of calculating rate of expected return using risk-free variable (Rf),
average market return (E (Rm)) and systematic risk (β) which cannot be eliminated even by
diversification.
The criteria in selecting securities that can support to be an efficient portfolioare the
securities that have greater realized return than its return value which is expected (R i > E(Ri)),
meanwhile, for those securities that have lower realized return than its expected return (R i <
E(Ri)) are actegorized as the unefficient securities, and of course, they should be eliminated.
The obtaining value of return which is expected of securities can be seen on the following table:
Tabel 5. The Calculation of Securities Expected Return Compared by Its Realized
Return

No. Code of Stocks E(Ri) Stocks Evaluation Ri

1 WSKT 0,008383 Efficient 0,027874
2 BBCA 0,007104 Efficient 0,018686
3 PTPP 0,008422 Efficient 0,016554
4 BBNI 0,00857 Efficient 0,015526
5 GGRM 0,006542 Efficient 0,013616
6 ADRO 0,008277 Efficient 0,012058
7 UNVR 0,006443 Efficient 0,01078
8 TLKM 0,006183 Efficient 0,01068
9 ADHI 0,008123 Efficient 0,009243
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AGREGAT: Jurnal Ekonomi dan Bisnis
Volume 4 (1), 2020
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DOI: 10.22236/agregat_vol4/is1pp8-24
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No. Code of Stocks E(Ri) Stocks Evaluation Ri
10 UNTR 0,006525 Efficient 0,007584
11 PTBA 0,006596 Efficient 0,007507
12 ASII 0,00803 Not Efficient 0,006652
13 AKRA 0,006482 Not Efficient 0,006427
14 WIKA 0,008838 Not Efficient 0,006288
15 ICBP 0,006144 Not Efficient 0,0045
16 INDF 0,007262 Not Efficient 0,00392
17 KLBF 0,007253 Not Efficient 0,003839
18 BBRI 0,008641 Not Efficient 0,002738
19 INTP 0,008169 Not Efficient 0,002233
20 BMRI 0,007744 Not Efficient 0,002024
21 SMGR 0,0081 Not Efficient 0,00182
22 JSMR 0,007467 Not Efficient 0,001813
23 BSDE 0,008184 Not Efficient 0,001771
Source: data has been processed by researchers, 2019
Based on the claculation by using CPAM method, there have been found that there are
11 securities that suitable for portfolio, and, which efficiently can be categorized as the
candidates for investment. However, based on the table above, there have been found that 12
securities which are not efficient, because, those securities are not able to provide realized
returns above the expected returns of investors. In fact, securities which categorized as efficient
securities if the condition of the securities themselves have greater individual realized return
value compares with return value which is expected (R i > E(Ri)). The statement is in accordance
with data that has been analsed that can be seen clearly on the above table. The table shows
that security that has the highest individual realized return than the expected return value (Ri >
E(Ri)), can be found on WSKT with 0.019491752 atau (1.95%) difference value between its
realized return value and the expected return value. In addition, the security that has the lowest
difference between realized return value and its expected return value is PTBA with
0.000910959 or (0.09%).

CONCLUSION
The analysis by using each method leads to securities combination which different
between each other, and it leads difference to the amount of return as well. It occurs because
there have been found steps differences in each method, one of the difference comes from
CAPM menthod which assumes that diversification becomes the way of investors to reduce
the risk. However, even deversification itself carries out perfectly, still, there will be systemic
risk which is macro. Portfolio can be achieved opimally can be formed through appling Single

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AGREGAT: Jurnal Ekonomi dan Bisnis
Volume 4 (1), 2020
http://journal.uhamka.ac.id/index.php/agregat
p-ISSN: 2549-5658 e-ISSN: 2549-7243
DOI: 10.22236/agregat_vol4/is1pp8-24
Pp 8-24
Index Model, its applied encourages considering whole aspects in economics which may lead
a security to suffer losses. Meanwhile, the CAPM method only moves through considering
certain risks in an efficient combination of portfolio. It would be better for investors to consider
internal and external factors in their investments in order to avoid fatal mistakes which leads
to suffer losses. As the information, this research has ignored companies that conduct kind of
right issue activity, which leads different significant result at the end of each method applied,
because of complexity on its method itself.
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