JRSSEM 2023, Vol. 02 No. 8, 1884 – 1892
E-ISSN: 2807 - 6311, P-ISSN: 2807 - 6494
DOI: 10.59141/jrssem.v2i08.399 https://jrssem.publikasiindonesia.id/index.php/jrssem
OPTIMAL INVESTMENT PORTFOLIO ANALYSIS USING
THE MARKOWITZ MODEL FOR STOCK IN EACH SECTOR
IN THE INDONESIA STOCK MARKET DURING COVID 19
(2020-2021)
Fitria Ulina Meliala
1
Subiakto Sukarno
2
1.2
School of Management, Institute Teknologi Bandung, Indonesia
*
e-mail: fitria_ulina@sbm-itb.ac.id, subiaktosukarno@gmail.com
*Correspondence: fitria_ulina@sbm-itb.ac.id
Submitted
: February 20
th
2023
Revised
: March 14
th
2023
Accepted
: March 27
th
2023
Abstract: The COVID 19 pandemic in early March 2020 starting from Wuhan had a very large impact
on the global economy and the Indonesian economy, the COVID 19 pandemic forced the
government to establish a PPKM policy (Implementation of Restrictions on Community Activities)
to suppress the spread of Covid 19 in Indonesia. Indonesia's State Gross Domestic Product fell in
the second quarter 2021 amounting to -5.32% and also having an impact on the stock market in
Indonesia at January 02 2020 the JCI was recorded at 6283 fell to 3937 in March 24 2020 (minus
36.77%) in March 2020. The results of this study using 22 of the stocks representing 11 sectors in
the stock market in Indonesia obtained a maximum Sharpe ratio calculation of 31.57% with a
weekly yield of 1.48% and a standard deviation of 4.39% and a maximum yield with a Sharpe ratio
of 31.29% and a yield weekly yield of 1.37% and a standard deviation of 4.08%, the result of the
minimum standard deviation with a Sharpe ratio of 5.92% with a weekly yield of 0.24% and a
standard deviation of 2.51% and the results of Portfolio in the efficient frontier namely portfolio 6
with a Sharpe ratio of 30.94% and weekly yield of 1.3% and a standard deviation of 3.9%. For
investors who want to optimize their portfolio, they can choose stocks with optimal Sharpe ratios
that already pay attention to risk-adjusted return.
Keywords: optimum portfolio; investment; Markowitz; Sharpe ratio.
Fitria Ulina Meliala
1
Subiakto Sukarno
2
| 1885
INTRODUCTION
Pandemic Covid 19 that hit the world
since November 2019 from Wuhan China
and entered Indonesia since March 2020 is
an event that has never happened before
and was never predicted by the market and
investors. This situation had a significant
impact on the world economy. There are
many things have changed since Covid 19,
because this virus does not have the
vaccine. To avoid this virus spread fast from
people to people all the countries all over
the world do restriction in Travel, and
lockdown in some countries. The IMF has
announced that this condition has an
impact on global economic growth. The
Indonesian economy had a recession in
COVID 19. GDP decreased 2,07% overall in
2020 from a year earlier, marking the first
full-year decline since the Asian financial
crisis of 1998. This was close in the middle
of the government's predicted range of a
1,7-2,2% fall and slightly greater than the 2
percent contraction. On a yearly basis, the
GDP increased by 5% in 2019. Indonesia
has struggled to this condition and find the
way out of this recession. This condition
impact to the Indonesia stock exchange,
market response to this unpredictable
condition and fall down the Jakarta
composite index, in 24 March 2020 the
Jakarta Composite Index hit the level 3.937,
as we know in the early 2020 the JCI in level
6300. The condition of this recession
impact mostly stocks in the capital market.
In this condition that has never
happened before, author want to observe
the sector in Jakarta Stock Exchange that
drag the JCI to the worst level, and during
since covid 19 in march 2020 until end of
December 2021 author want to see which
sector are impact to this condition. Through
the recession and expansion in the business
cycle phase. The author will observe the
condition of the market during business
cycle and in this condition in Covid 19
during recession and expansion, and after
weight the portfolio we can forecasted,
what sectors will perform compared to
others. As the economy moves forward
different sectors of the business tend to
perform better than the others. Sector
rotation strategy is taken advantages in
investing in the industries or sectors that
are rising and avoiding sectors that are
failing to generate superior return and how
to get the optimal portfolio during Covid
19.
Table 1. GDP Growth Indonesia
Table above is the condition of GDP
growth Indonesia from 2019-2021, the
negative GDP growth from quarter 2 and
quarter 3 in 2020, the impactful of this
pandemic take economic in Indonesia in
Quarter 4 2020 into recession.
1886 | Optimal Investment Portfolio Analysis Using The Markowitz Model For Stock In Each
Sector In The Indonesia Stock Market During Covid 19 (2020-2021)
Literature Review
a. Risk and Return
We need a definition of risk that
focuses on the fact that the outcomes of
financial and economic decisions are
almost always unknown at the time the
decision are made. The definition of Risk is
“a measure of uncertainty about the future
payoff to an investment, assessed over
some time horizon and relative to a
benchmark. The elements of this definition
are risk measure that can be quantified, risk
arises from uncertainty about the future,
risk has to do with the future payoff an
investment, which is unknown, risk refers to
an investment or group of investment, risk
must be assessed over some time horizon,
and risk must be assessed relative to a
benchmark rather than in isolation.
The two measurements of risk, the first
is based on a statistical concept called the
standard deviation and is strictly a measure
of spread, and the second called value at
risk is a measure of riskiness of the worst
case.
1. Variance and standard deviation
The variance is defined as the average
of the squared deviations of the possible
outcomes from their expected value,
weighted by the probabilities. It takes
several steps to compute the variance of an
investment, first compute the expected
value and then subtract it from each of the
possible payoffs. Then square each one of
the results, multiply by its probability and
finally add up the results.
The standard deviation is the positive
square root of the variance. The standard
deviations are more useful than the
variance because it is measured in the same
unit as the payoff: dollars, (variance is
measured in dollars squared). The more
spread out the distributions of possible
payoffs from an investment the higher
standard deviations and the bigger risk.
Standard deviation is the most common
measure of financial risk, and for most
purposes it is adequate.
The Sharpe ratio is one of the most
widely used methods for measuring risk
adjusted relative return and also described
the compensation that investor that can
take for the expected return to investment.
The Sharpe ratio can be used to evaluate a
portfolio’s risk-adjusted performance. The
greater a portfolio’s Sharpe ratio the better
risk performance. A negative Sharpe ratio
means the risk free or benchmark rate is
greater than the portfolio’s expected
return.
: Expected excess return of the
portfolio
: Rate of return on a risk-free asset
: standard deviation of the return of
the market portfolio
The higher the Sharpe ratio value, the
better because it reflects that the reward is
better per standard deviation and in other
words the portfolio will be more efficient.
Calculation by comparing return and risk is
also known as mean-variance analysis.
Sharpe with the maximum value is in the
mean-variance efficient frontier (Kourtis,
2016).
b. Markowitz Model
Modern portfolio theory uses the
Fitria Ulina Meliala
1
Subiakto Sukarno
2
| 1887
Markowitz model, commonly referred to as
the mean-variance model, as a
mathematical tool to assist investors in
maximizing expected return while lowering
portfolio risk. It was created in 1952 by
Harry Markowitz and is a crucial tenet of
contemporary financial theory. The
approach is predicated that the variation of
a portfolio's returns can be used to
investor's risk appetite. The model
presupposes that investors will aim to
minimize the variation of their portfolio
returns while still attempting to maximize
their expected return since they are risk
averse.
Calculation the log return of each risky
assets
: Return on individual asset period
time
: stock price period time
: stock price period time-1
Calculation Expected return of each risky
assets
: Average expected Return
: Return on individual asset period
time
: Number of Risky assets
Calculation variance and Standard
Deviation
=
Calculation co-variance stocks in the
portfolio
Cov (
)=
Calculation the weight (Wi) of each stock by
using Solver Add-in Excel
Calculation Expected Return of the
Portfolio
=
Calculation variance of the portfolio
Var
=
=
+
+ 2
Cov
This formula modified by the number of the
risky asset.
MATERIALS AND METHODS
In this paper we will evaluate stock in
the Jakarta Composite Index that related to
the sector, in Jakarta Composite Index there
are stock that classified by the sector and
there is the index that reflect to the
performance of the sectoral stock name
JASICA (Jakarta Stock Industrial
Classification), but in 25 January 2021,
Jakarta stock exchange implemented new
index sectoral name IDX-IC.
The Author will use the data of Jakarta
Composite Index (JCI) from 2020-2021 and
the sectoral index will used data from 2020-
2021. In this research we also we divine the
condition before, during and after
Pandemic COVID 19 in the stock market in
Jakarta Composite Index. Figure 3.2 and 3.3
show to us the condition of the Sectoral
Index during 2019 until 2021. In 2019-2020
1888 | Optimal Investment Portfolio Analysis Using The Markowitz Model For Stock In Each
Sector In The Indonesia Stock Market During Covid 19 (2020-2021)
the sector that get the best performance is
IDX Mining this condition related to the
trade war between US and China and in
2020-2021 the IDX Energy performance
significantly above the benchmark JCI.
Risk Free Rate
Risk free rate return is the rate of return
of an Investment with Zero Risk, this
indicates how much return that the investor
needs from the investment over a specified
period. In practice the risk-free rate of
return does not truly exist, every
investment will at least have a small
amount of risk. In Indonesia we use 10-year
government bond yield as the risk-free rate
and as the consideration that there is
default risk (for local who invest in
Indonesia assume that there is no risk for
local people, interest rate risk (assume that
we will hold the bond until it matured) and
Reinvestment risk (assume that we invest to
the bond that have zero coupon bond). In
this paper the author uses the average
historical data weekly of 10-year
Government Bond. Data in 2020-2021.
Data Analysis Method
This step is methodology that use in
this research, there are many different
methods for analysing data and which one
is best depends on the specific goals of the
analysis and the characteristics of the data.
In this final research we use quantitative
data analysis. This involves analysing data
that is in numerical form. It typically
involves using statistical techniques to
summarize and interpret the data. Some
common techniques used in quantitative
data analysis is Inferential statistics, this
involves using statistical test to make
inferences about a population based on a
sample of population and regression
analysis this involves modelling the
relationship between one or more
independent variables and a dependent
variable. This Quantitative data analysis can
be used to test hypotheses make prediction
and identify patterns and trends in the data.
RESULTS AND DISCUSSION
The analysis of the portfolio using the
Markowitz model and identify the risk and
return of each risky assets, we will define
the result of the Portfolio that we choose
and the performance of the market. We
also define the beta of each asset and from
the beta we calculate the Treynor ratio and
the Sharpe Ratio, then the result we can see
the performance of our portfolio
comparison with the market, the
comparison here is using Jakarta
Composite Index. we can see with the
Markowitz Model and diversification our
investment we can optimalization our
portfolio even the market only can give
0.09 % return weekly we still can get higher
than the market with the minimum risk.
From the yearly performance of the
portfolio, we can see a very big difference
by comparing the standard deviation which
is not too big.
In this paper the author has evaluate
the condition of the condition of the
Pandemic situation in March 2020 and the
condition after the market recovery and
market can predict the condition after
pandemic, the data identification is in 2020
and 2021. From the calculation the author
finds that even the market are recession in
the Quarter 1 2020 (March) for the first time
Fitria Ulina Meliala
1
Subiakto Sukarno
2
| 1889
case of Covid 19 are announced bring the
Jakarta Composite Index to the lower level
in but the condition is recovery bring the
Jakarta Composite Index to the lower level
in 16 March 2020 with the closed price
4194,94 but the condition recovery in the
end of year 2020 to 5879.07 and in end of
year 2021 6581.48. Even in the pandemic
that impact to the market stock in
Indonesia, the investor still need cash in
their investment and by using buy and hold
strategy in the end the market still back to
the high level.
The calculation of the efficient frontier
is the simulation to find the maximum
return of the risky assets and get the
minimum standard deviation. The efficient
frontier is the set of the optimal portfolio.
Successful optimization of the return versus
risk should place the portfolio along the
efficient frontier line. Markowitz also makes
several other assumptions in his theory,
including the notions that investors are
rational and seek to minimize risk, that
there are insufficient investors to have an
impact on market prices, and that investors
have unrestricted access to borrowing and
lending money at the risk-free interest rate.
The market, however, includes irrational
and risk-taking investors, there are sizable
market participants who could affect
market pricing, and there are investors who
do not have unrestricted access to
borrowing and lending money. These facts
demonstrate that the market is not
completely rational.
This are the solver parameters to find the
efficient frontier:
1. Open Excel, Data Solver and set the
objective the Standard Deviation
and setting to the minimum
2. The changing value is the weight of
the portfolio of the risky assets
3. Make some constraints, the total of
portfolio must be 1 or 100%
4. The weight of risky assets is >=0
5. Set the expected return = the
expected that the author has
decided
In the table we can see the solver
parameters and constrained
Capital Allocation Line
The Capital Allocation Line (CAL) is a
graphical presentation of the efficient
frontier for two or many assets portfolio,
this CAL showing us the expected return
and the risk of risky assets. The CAL is the
straight line that starts from the risk-free
asset and extend to the risky portfolio. the
portfolio can be created by combining the
risk-free assets and the risky portfolio.
Positive slope of CAL will occur if the risky
portfolio has less risk than the risk-free
asset, but if the risky portfolio has more risk
than the risk-free asset, the CAL will have a
negative slope. This CAL uses in investment
to help the investor to choose the optimum
portfolio in investment based on their risk
appetite.
1890 | Optimal Investment Portfolio Analysis Using The Markowitz Model For Stock In Each
Sector In The Indonesia Stock Market During Covid 19 (2020-2021)
Table 2. Capital Allocation Line
Capital Allocation Line
Risk-free Rate
0,09%
Portfolio 6 Return
1,300%
Portfolio 6 Variance
3,904%
CML Slope/Sharpe Ratio
30,938%
Variance (X)
0,00000
0,08085
CAL (Y)
0,09%
2,59%
Figure 1. Efficient Frontier and Capital Allocation Line
From the calculation above we can see
the capital allocation line of this asset
is the portfolio that intersects with the
risk-free asset, we find the portfolio in
the capital allocation line and more left
of the assets higher expected return
with minimum of risk.
Table 2. Portfolio 6 in the efficient frontier
Table 3. Portfolio 6 Risk and Return
TBIG EMTK ASSA MTDL MIKA UNTR BBCA ADRO
24,74% 24,13% 18,71% 13,39% 11,38% 4,77% 2,18% 0,70% 1,30% 3,90% 0,86 30,94%
0,09% 2,92% 1 -0,07%
Weight of stock
Return
Risk (SD)
Beta
Sharpe
0.00%
1.00%
2.00%
3.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00%
Expected Return
Risk (Standard Deviation)
Efiicient Frontier & Capital Allocation Line
TBIG EMTK ASSA MTDL MIKA UNTR BBCA ADRO
Portfolio 6 24,74% 24,13% 18,71% 13,39% 11,38% 4,77% 2,18% 0,70% 1,30% 3,90% 96% 28,15%
JCI 0,09% 2,92% 4,8% 21,07%
Investment
Weight of stock
Return
(weekly
Risk
(SD)
Return
(yearly)
Risk
(SD)
Fitria Ulina Meliala
1
Subiakto Sukarno
2
| 1891
Table 4. Stock Selection
Table 5. Risk and return of risky asset
Stock calculation of the return by
calculating stock from the data weekly from
January 2020-December 2021. We can see
the from the data chart that the Stock ASSA
that give highest return does not stock with
highest standard deviation. The highest
standard deviation of the stock BRPT (Basic
Materials) which the Standard Deviation is
10.89 % and the return is 0.151%
CONCLUSIONS
The strategy of individual investment is
based on risk appetite to investor, if we can
see from table above the minimum
expected return, we can get is 13.32% with
standard deviation is 18.09 % and Sharpe
ratio is 5.92 %, and the second is the equal
weight of each stock of portfolio with
expected return 17.25% with standard
deviation 25.83% and the Sharpe Ratio
5.98%. We can see that the portfolio 6 and
the maximum expected return have almost
the same number of calculations for
Maximum expected return the expected
Return is 102.79 % and standard deviation
29.42 % with Sharpe ratio 31.29 % and for
The Portfolio 6 the Expected return 95.75%,
Kode Saham Saham
PGAS Perusahaan Gas Negara
ADRO Adaro Energy
TPIA Chandra Asri Petrochemical
BRPT Barito Pacific
ASII Astra International
UNTR United Tracktors
UNVR Unilever
HMSP HM Sampoerna
SCMA Surya Citra Media
ACES Ace Hardware Indonesia
KLBF Kalbe Farma
MIKA Mitra Keluarga Karyasehat
BBCA Bank BCA
BBRI Bank BRI
PWON Pakuwon Jati
BSDE Bumi Serpong Damai
EMTK Elang Mahkota Teknologi
MTDL Metrodata Electronics
TLKM Telkom Indonesia
TBIG Tower Bersama Infrastructure
ASSA Adi Sarana Armada
BIRD Blue Bird
Transportation and Logistic
11
5
Consumer Cyclicals
9
10
6
Healthcare
7
Financials
8
Properties and Real Estate
Technology
Infrastructure
Basic Materials
2
3
Industrials
4
Consumer Non Cyclicals
No
Sector
2020-2021
1
Energy
1892 | Optimal Investment Portfolio Analysis Using The Markowitz Model For Stock In Each
Sector In The Indonesia Stock Market During Covid 19 (2020-2021)
standard deviation 28.15 % and the Sharpe
ratio 30.94%. The aggressive investor can
choose the portfolio Maximum Sharpe
Ratio with Expected Return 114.615,
standard deviation 31.69 % and Sharpe
Ratio 31.57%. however, investors must
know that this is a historical calculation that
can be applied in making investments.
However, as investors, we must also look at
other aspects, such as top-down analysis,
fundamental analysis, technical analysis for
the selection of stocks used from each
sector. In this calculation it can be
concluded that the Markowitz model can
be used in every business cycle.
Investor can use this Markowitz Model
to do their investment in doing
diversification, the investor can use this
strategy in any kind of business cycle and
the investor can get the maximum return. A
higher Sharpe ratio indicates that an
investment has a higher return relative to
its risk. The Sharpe ratio is widely used
measure of risk adjusted return. It is
calculated by dividing the excess return of
an investment (the return in excess of the
risk-free rate)
REFERENCES
Kourtis, A. (2016). The Sharpe ratio of
estimated efficient portfolios.
Finance
Research Letters
,
17
, 72–78.
McLaney, E.J. (2017)
Business finance:
Theory and practice
. Harlow, England:
Pearson.
Berwick, D. M., Nolan T. W., & Whittington,
J. (2008). The triple aim: care, health
and cost. Health affairs.
Bodie, Z., Kane, A, and Marcus, A, J. (2011),
Investments. 10th edition, New York:
McGraw-Hill/Irwin
Fama, EF. (1970). Efficient capital markets.
A review of theory and empirical work.
Journal of Finance
Ivanova, M., & Dospatliev,L. . Application of
Markowitz Porfolio Optimization
© 2023 by the authors. Submitted
for possible open access
publication
under the terms and conditions of the Creative
Commons Attribution (CC BY SA) license
(https://creativecommons.org/licenses/by-sa/4.0/).
