Analysis of the Single Index Model and Markowitz in Optimal Portfolio Selection in the Telecommunications Sub-Sector Listed on the Indonesia Stock Exchange for the Period 2020-2022

This study, which uses qualitative methodology, compares and finds the best results from two approaches, namely the Markowitz model and the single index model to build an optimal portfolio. The population of this study consists of all stocks included in the telecommunications subsector listed on the Indonesia Stock Exchange for the period 2020-2022. Purposive sampling is used in this study to select samples. There are 5 candidate company stocks that meet the requirements in the sample criteria. From the results of the research conducted, it proves that with the single index model method, 3 stocks are included in the optimal portfolio, namely PT Tower Bersama Infrastructure Tbk (TBIG) with a proportion of 50%, PT Visi Telekomunikasi Infrastruktur Tbk (GOLD) with a proportion of 15%, and PT Indosat Ooredoo Hutchison Tbk (ISAT) with a proportion of 35%. From the research results of these 3 stocks to form an optimal portfolio, the expected return is 2% and the risk borne is 18%. While for the Markowitz model, 3 stocks were obtained as optimal portfolio candidates, namely PT Telekomunikasi Indonesia Tbk (TLKM) with a proportion of 68%, PT Visi


INTRODUCTION
Investment is the activity of investing capital into assets and hoping to earn a greater return than fixed assets.The capital market is where investors want to invest in stocks and also provides them with an opportunity for diversification.Telecommunication stocks traded on the Indonesia Stock Exchange are used in this research.Investors are required to consider return and risk when making investment decisions.Both aspects are very important when making investment decisions.Yield and capital gain are the main components of investment returns (Tandelilin, 2010).Risk is defined as the probability of something unexpected happening as the definition of risk is "damage, disruption, danger of loss or accident" stated in Webster's dictionary.
Investors can use portfolios to minimize their risk.The terms "efficient portfolio" and "optimal portfolio" are used in portfolio theory.Researchers apply the Markowitz model and the single-index model to construct optimal portfolios.William Sharp created the single-index model, which is a portfolio model in which the return of a market index is used to determine the return of each asset.In addition, investors choose their portfolios based on their preferences for the expected return and risk of each portfolio option, in accordance with the Markowitz method.The main challenges faced by investors, according to (Bodie, Kene, & Marcus, 2006) is to determine which type of stocks to choose in order to create an optimal stock portfolio.
Markowitz model and single index model have been used in a number of previous studies.Research on investment analysis and the search for the best stock portfolio in the Indonesian stock market (a comparative study using a single index model and a random model on LQ-45 stocks) was conducted by (Risnawati, 2009).Based on the research findings, there is a difference in performance between choosing a portfolio randomly and using a single index model.Creating a portfolio using the single index model produces better returns than allocating portfolios randomly.According to research submitted by (Septyanto & Kertopati, 2014), there are differences between the Markowitz model and the single index model in analyzing the formation of the optimal portfolio.The investigation found that the results of Markowitz and single index calculations were different.
According to research published by (Paudel & Koirala, 2006) in "Application of Markowitz and Sharpe Model to Nepal Stock Market", the investment portfolio created by using Markowitz model becomes the best optimization.As a result, investors who want to take part in the capital market by buying and selling stocks should pay careful attention to the stock trading market.Markowitz model and single index model are the models used in this research.
The research entitled "Comparative Analysis of Optimal Portfolios with a Single Index Model Approach and the Markowitz Model in the Telecommunications Sub-Sector Listed on the Indonesia Stock Exchange for the 2020-2022 Period" was designed to be carried out based on the background above.

RESEARCH QUESTION
Based on the background information provided, the following research questions can be the main focus of the investigation of the comparative analysis of the optimal portfolio of the telecommunications subsector on the Indonesia Stock Exchange using the Markowitz model and the single index model approach: 1. How is the optimal portfolio formation using the single index model for telecommunication sector companies listed on the Indonesia Stock Exchange for the 2020-2022 period?2. How is the Markowitz model used to create an optimal portfolio for telecommunications sector companies listed on the Indonesia Stock Exchange for the period 2020-2022?3. How does the telecommunications sector companies listed on the Indonesia Stock Exchange compare in terms of optimal portfolio formation for the 2020-2022 period?

RESEARCH OBJECTIVES
Based on the problem formulation that has been presented, the following research objectives can be identified: 1. Knowing the optimal portfolio formation using a single index model for telecommunication sector companies listed on the Indonesia Stock Exchange for the 2020-2022 period.2. Knowing the Markowitz model is used to create an optimal portfolio for telecommunications sector companies listed on the Indonesia Stock Exchange for the 2020-2022 period.3. Knowing the comparison of telecommunication sector companies listed on the Indonesia Stock Exchange in terms of optimal portfolio formation for the 2020-2022 period.

LITERATURE REVIEW Investment Management
Investment management, according to (Alhidayatullah, et al., 2021), is the process of organizing, implementing, and monitoring decision-making related to any investment activity.On the other hand, investors are individuals or organizations that have money to invest with the aim of making more money in the future.On the other hand, according to (Wef, 2020) Investment management is the management of various securities, such as investments in stocks, bonds, and other assets, including real estate, in an effort to meet financial goals that will make money for investors.Based on both definitions, investment management is the process of organizing, implementing, and regulating decision-making on every aspect of investment with the aim of achieving financial goals that provide profits for investors.

Investment
Investment is the process of allocating money into companies, stocks, or other assets with the aim of making a profit in the future.Jogiyanto said in (Ayuningsih, 2016).The investment process shows the process in which an investor makes decisions.Investment according to (Tandelilin, 2010) is a financial or resource commitment made now in the hope of receiving beneficial returns at a later date.Investment as defined by (Hartono, 2015) is a delay in the use of current consumption to be used in productive activities over a certain period of time.This definition leads to the conclusion that investment is a method of using present funds to generate future profits.
According to (Tandelilin E. , 2012) there are several aspects that become the basis for people in making investment decisions.First is the return on investment which is the main motivation behind investment activity.Risk comes second.The greater the risk involved in an investment, the greater the expected return.Thirdly there is a one-way or linear relationship between the return and the predicted rate of return.Whether parallel or inversely proportional.(Oktaviana, 2019) states that the investment decision-making process continues until the optimal choice.

Shares
Ownership of shares in a limited liability company is evidence of participation in its operations, according to (Riyanto, 2008).On the other hand, shares as stated by (Mingka & Lubis, 2023), are proof of ownership of the company and shareholders are entitled to a portion of the income with the amount varying based on the number of shares owned in the company.Whatever percentage or number of shares a company issues, a share is a piece of paper that represents its owner.Thus, it can be said that shares in a corporation or limited liability business serve as proof of ownership of the company's assets.Buying shares entitles the buyer to a portion of the business's profits, which are then paid out as dividends.There are three categories of shares, according to (Kieso & Weygandt, 2008) treasury stock, preferred stock and common stock.

Stock Return
Investments are made by investors to obtain various benefits in the future, according to (Hartono, 2015).The amount of profit from an investment is known as a return.One of the things that attracts investors to invest is return.According to Brigham in (Dewi, 2019), stock returns or also known as stock returns are calculated by dividing the total amount invested by the total amount received.According to (Tandelilin E. , 2012) one of the things that encourages investors to invest and rewards them for their courage to bear risk is stock returns.
The two main components of investment returns are yield and capital gains.The yield portion known as yield represents the consistent cash flow or income generated by an investment.The increase or decrease in the price of assets, including stocks and long-term debt instruments is referred to as capital gains (losses).This is the part of the yield that results in profit or loss for the investor.Capital gain is the difference between the current price of an investment and its previous price.A gain is realized when the selling price of a stock exceeds its purchase price.Conversely, a capital loss occurs when the selling price of a stock is less than its purchase price.Portofolio Optimal (Tandelilin E. , 2010) states that the portfolio that investors choose from the various options in the efficient portfolio group is the optimal portfolio.There is no doubt that each investor's choice with regard to return expectations and risk tolerance is reflected in the portfolio they choose.An optimal portfolio according to (Hartono, 2014) is a portfolio designed to offer the maximum rate of return with the lowest risk.The actions required to create an optimal portfolio are as follows: 1

Single Index Model
One way to determine the optimal portfolio is to use William Sharpe's single index model, which was developed in 1963.The Markowitz model's very complicated covariance calculation is one of its weaknesses.The Markowitz model has been simplified into a single index model (Oktaviana, 2019).Based on the finding that security prices fluctuate in line with the stock market price index, the single index model predicts that most stocks will increase in value when the stock price index increases (Hartono, 2015).On the other hand, most stocks will decline in price if the stock index declines.This suggests the correlation of security returns may result from a collective response to shifts in market value.
The premise that stock prices will move in the same direction as the market price index is the basis of the single index concept.One method to determine the optimal portfolio is the single index approach.The single index model describes the correlation between the return of each investment and the market return.According to (Bawasir & Sitanggang, 1994).Using the single index approach, the optimal portfolio is sought by comparing the cut-off-rate (Ci) and excess-return-to-beta (ERB).ERB is the return on a stock above the risk-free rate of return or risk return premium determined by beta.The cut-off rate (Ci) is the final sum of the market variance, the return premium, the stock variance error with the market variance and the susceptibility of each stock to the stock variance error.The concept of this calculation is based on a system to rank stocks based on their ERB, from high to low (Elton & Gruber, 1995).Finding the excess return of a stock over the risk-free return per unit of risk is the purpose of ranking.Therefore, stocks with an ERB comparable to or greater than C* are the best way to construct a portfolio.

Markowitz Model
During the 1950s, Markowitz created a new theory of optimal portfolio theory with the Markowitz model.Markowitz's theory uses several fundamental statistical markers, such as expected returns or correlations, portfolio and security standard deviations, and correlations of returns, to create a portfolio plan.Harry Markowitz inspired the saying "Don't put your eggs in one basket, but put them in several baskets" (Fahmi, 2015).This statement states that the foundation of the Markowitz portfolio model is to advise investors on how to minimize risk and maximize returns from each investment decision."The foundation of the Markowitz portfolio concept aims to provide investors with targeted knowledge and guidance to minimize risk and offer maximum returns when they make investment choices."According to this idea, an investment has a return and risk component.The risk component can be minimized by diversifying investment holdings and building a portfolio of investment instruments in the portfolio.
Markowitz's portfolio theory suggests investing in different directions by dividing the investor's funds to be allocated as an investment.The purpose of segregating funds is to lower the investor's risk exposure in the future.During the evaluation or valuation stage, investors evaluate the performance of their portfolio in terms of the risk taken and the amount of profit generated.(Husnan, 2009) provides the assumption that a portfolio with greater returns is always superior to other portfolios.The following are the assumptions made by the Markowitz model, according to (Hartono, 2015): 1.Only one time period is applied.2. There is no transaction fee.
3. The projected return and risk of the portfolio are the only factors that influence investor preferences.4. No risk-free savings and loans.
The Markowitz technique determines the optimal risk based on investor preferences determined by both risk-taking and risk-averse investors.The maximum predicted expected return with a certain desired risk based on each investor's risk preference is the notion of optimal measurement used.

CONCEPTUAL FRAMEWORK
Two aspects that will be encountered when doing investment activities are return and risk.Therefore, determining stocks before making an investment needs to be done by an investor.Of course, an investor wants stocks that offer the highest return with the highest risk, or stocks that provide the lowest risk but the highest return.Investment risk can be reduced by creating an optimal portfolio with a diversity of stocks.
Both the single index model and the Markowitz model can be used to create an optimal portfolio.The Markowitz model outlines the steps an investor should take when constructing a portfolio and determines how much weight should be given to a particular stock when allocating funds.There is a weakness in the Markowitz model that requires calculating the complete covariance.

RESEARCH METHODS
Qualitative data or non-numerical data is used in this study to support a qualitative descriptive approach.In this study, stock market data, the composite stock index, and interest rates were used during the 2020-2022 research period.This study analyzes the telecommunications subsector listed on the Indonesia Stock Exchange from 2020 to 2022.In the telecommunications subsector there are 18 companies listed on the Indonesia Stock Exchange during the research period.This study uses a purposive sample method based on criteria that are in accordance with the research objectives.These criteria are as follows: 1.) Listed on the Indonesia Stock Exchange during the period 2020-2022.2.) Telecommunication subsector companies engaged in telecommunication services that have been listed on the Indonesia stock exchange.3.) Has had an IPO for more than five years.
Five telecommunications companies listed on the Indonesia Stock Exchange were selected as research samples based on predetermined criteria.The following steps should be followed to form an optimal portfolio using the single index model, namely: 1) Determining stock returns (Hartono, 2010) 2) Determine the expected return with the formula: (Hakim & Waluyo, 2023) 3) Return of each stock (Hakim & Waluyo, 2023) 4) Calculating Beta β (Hakim & Waluyo, 2023) αi = E(i) − i.(m) To find the optimal portfolio in this model, follow these steps: 1) Using the formulas below, determine the stock return for each stock of the sample company (Hartono, 2010) 2) Use the formula below to calculate the expected return for each sample (Husnan, 2009) 3) Use the formula below to calculate the variance of each stock (Tandelilin E. , 2010) 4) Use the formula below to calculate the covariance value of the stocks in the portfolio (Hartono, 2010) 5) Use the formula to calculate the expected return of the portfolio that has been created (Tandelilin E. , 2010) 6) Use the formula below to determine the portfolio variance (Hartono, 2010) 7) Minimize the objective function to determine the investment proportion (Wi).(Hartono, 2010) The main parameter to be used is Wi with constraints ∑ =1    = 1, Wi ≥ 0 for 1= 1,2,..,n, dan ∑ =1    .  = Rp 8) To find the optimal portfolio, construct an efficient frontier curve and a global minimum variance (GMV) curve.9) Repeat the fifth step and get the optimal expected return of the portfolio.

Management Finance
to get the value of Bi.The result will be used to determine the value of Ci(Hakim & Waluyo, 2023) 10) Calculate fund proportion (Xi), percentage of fund proportion (Wi) Subsequently, the single index portfolio model was developed, a model developed from the Markowitz portfolio model and first proposed by William Sharpe in 1963.The calculation of the Markowitz model becomes easier with this model.The calculation of Markowitz portfolio risk, which was previously quite complicated, can then be calculated simply by applying the single index model.Investors can use whichever portfolio model will generate the highest returns.
FINANCE P-ISSN 3026-6734 | E-ISSN 3026-6742 76 The samples of this study are: Apply the same procedure to calculate the portfolio variance, but add the final proportion determined earlier using the following formula to get the optimal portfolio variance.