ANALYSIS OF OPTIMAL STOCK PORTFOLIO INVESTMENT IN LQ45 INDEX USES THE MARKOWITZ MODEL AND SINGLE INDEX MODEL

Based on the results of the optimal portfolio analysis of the Markowitz model and Single Index Model, it can be concluded as follows: Based on the optimal portfolio formation of the Markowitz Model, 4 shares form a portfolio return expectation of 0.0074, while the portfolio risk is 0.0428 and the proportion of funds formed is BBCA 50.81%, EXCL 9.83%, ICBP 30.59%, and KLBF 8.77%. Based on the formation of a single index model portfolio, 2 optimal portfolio formations were obtained with a portfolio return of 0.1486 and a risk of 0.0873, while the proportion of funds formed by ANTM was 10.5%, and BBCA was 89.5%.. Based on research results, it proves that the single index model can produce a profit of 14.86% with a risk level of 8.73% compared to the Risk-Free Asset Return Rate of 5.17%. Meanwhile, the Markowitz model can produce a portfolio return of 0.74% with a portfolio risk of 4.28%, which does not provide optimal profits because the expected return from the Markowitz model portfolio is lower than the Risk-Free Asset Return Rate.Lack of significant planning in investing by a company. This because in planning an investment project of course requires substantial funds, so if not budgeted and calculated properly, it can result in investment failure projects that can cause a company to experience large losses. This study discusses capital budgeting of a project in CV. ABC will buy a new machine. In the This study discussed how to calculate the initial investment, estimate the income that the company will get during the project, how long is the capital issued by the company for investment projects will be returned, and at most what is important is whether it is feasible or not is the investment project planning. Method used in capital budgeting calculations is the payback period, discounted payback period, Net Present Value (NPV), and Internal rate of Return (IRR). In the The results showed that CV ABC accepted the plan to purchase a corn drying machine by calculating the payback period for 5 years, the NPV and IRR are considered feasible.


INTRODUCTION
Investment is a form of managing funds by placing these funds in an allocation that is expected to provide additional profits in the future.Investment is currently the main choice for people who want to increase the value of their wealth.There are two types of markets as a place to invest, namely the money market and the capital market.One of the instruments for investing in the capital market is in the form of shares.According to data quoted from the Indonesian Stock Exchange (BEI), investors who invest in shares always experience an increase every year.It is known that the number of shares traded from 2017 to 2019 has increased.The average number of shares traded in 2019 reached 7 trillion shares, an increase of around 40% from 2017 which reached 5 trillion.The increase in the number of shares traded indicates that investors feel safe investing in shares.Meanwhile, the number of issuers registered on the Indonesian Stock Exchange experienced a trend that continued to increase during 2015-2019.At the end of 2019, the number of issuers reached 658 issuers or an increase of 137 issuers from 2015.The presence of new issuers indicates that the stock market is still an important alternative for the business world to access cheap funds and support business expansion.Investing in the stock market can provide investors with the opportunity to obtain a higher rate of return than investing in the money market.However, the higher the rate of return received, the higher the risk faced.Therefore, investing contains a fairly high element of uncertainty.Every investor wants a rate of return that can be optimized from investment activities, with risks that can be minimized, and always looks for ways to obtain higher profits than the costs that must be borne by the investor (Larasati 2013).The LQ45 index is the market capitalization value of the 45 most liquid stocks and has a large capitalization value, this is an indicator of liquidation.The LQ45 index uses 45 stocks selected based on stock trading liquidity and is adjusted every six months (at the beginning of February and August).Thus, the shares contained in the index will always change.The LQ45 index fluctuates from year to year but in general it experiences growth.This fluctuation occurs as a result of systematic risk and non-systematic risk.Systematic risk is a risk that cannot be avoided.Example of systematic riskare an increase in interest rates (interest rate risk), an increase in inflation (inflationary risk) and high market volatility (market risk).Non-systematic risk is often referred to as specific risk, company risk or un-systematic risk.Non-systematic risk can generally be managed using a portfolio.Examples of non-systematic risks are: liquidity risk, bankruptcy risk (financial / credit risk) and risk of lawsuits (operational risk).There are two models that can be used to form an optimal portfolio, namely the Markowits model and the single index model.

RESEARCH METHODS 1. Types and Sources of Research Data
The type of data used in this research is descriptive research with quantitative data analysis techniques and is secondary data, namely data that has been published and previously processed.The data collected in this research includes monthly closing stock price data for companies that have gone public on the Indonesia Stock Exchange, monthly IHSG, and interest rates on Bank Indonesia Certificates (SBI).This data was obtained from IDX Statistics for 2017 -2020, the Indonesian Stock Exchange website.

Population
The population in this study are all issuers included in the LQ45 calculation for the period February 2018 -July 2020.Based on observations of the population on the LQ45 Index on the Indonesian stock exchange from February 20218 -July 2020, there are 59 shares.

Sample
In this research, the author will use a purpsive sampling method by considering the following criteria: a) The company is on the LQ 45 Index b) The company did not carry out corporate actions during the observation period that directly affected share prices on the IDX.c) Companies that are consecutively listed in 5 periods of the LQ 45 index, namely in period https://jaruda.orgVolumes 2 No. 2 (2023) Journal of Accounting Research, Utility Finance and Digital Assets

Single Index Model Portfolio Analysis
The Single Index Model is based on the observation that the price of a share fluctuates in the same direction as the market price index.In particular, it can be observed that most shares tend to experience an increase in price if the market share price index rises and vice versa.The calculation of the single index will be explained in seven parts as follows.

Return Value & Market Risk
Determining the value of return and market risk in this research is based on the closing price of the LQ 45 Index on the Indonesia Stock Exchange with an observation period from February 2018 to July 2020, in calculating the market index using market realized return (Rm), market expected return E(R( m)) as well as market risk (σ2) with the market price index at LQ 45 Index as the input variable, the calculation results are in Table 2 as follows.Based on the research results in Table 4.1 between realized market returns and Market Expectations on the LQ 45 Index for the period February 2018 to July 2020.Meanwhile, regarding the relationship between market expectations and market risk, according to Jogiyanto (2017: 322), return expectations and risk have a positive relationship, the greater the risk of a security or market, the greater the expected return and vice versa, this positive relationship only applies to returns that have not yet occurred.However, in this study this positive relationship did not occur so that the market expectation value in the LQ 45 Index in Table 4.1 shows a low value for market risk, which means that a positive relationship does not always occur.

Calculating ChangeStock Prices Against the Market and Contrary Price Changes and Calculating Unsystematic Risk
After obtaining the values of return and market risk which have been described in the previous section, the next step is to look for the values of beta, alpha and variance residual error.In this calculation, apart from return and market risk, you also need the value of the return and individual risk of each stock which has also been calculated.described in the results of the optimal portfolio analysis of the Markowitz Model, beta which is the sensitivity of a security's return to returns from the market and beta is used to calculate excess return to beta (ERB) and (Bi), this (Bi) value is also used to calculate (Ci), Beta calculations are carried out using the Excel program with the slope formula, namely calculating the realized return of a stock and calculating the realized return of the market index in a certain period.Alphawhich is the change in market price of a security, is used to find the value (Ai) needed in the calculation (Ci), the alpha value calculation is carried out using the Excel program with the intercept formula, while the residual error variance is used in the calculation to find the value (Ai=Aj), (Bi=Bj) and proportion of funds.Beta, alpha and variance residual error values can be seen in Table 3 below.-0.010 0.286 0.008 The research results in Table 3 show that the alpha value () in Table 4.2 ranges from -0.0349 to 0.1383.If the alpha value is positive, it indicates that the stock performance is better compared to the market index.The higher it is of course the better, if the alpha value negative means that the stock performance is worse compared to the market index and the lower it is, the worse it is.beta () for each stock ranges from 0.2081 to 2.2886.If the stock has a beta value equal to or more than -0.009 then the stock's sensitivity is the same as the market sensitivity.In other words, if the market index falls by -0.009 or 1% then the stock also fell by 1%.In the context of this research, the highest beta value was obtained by PP (Persero) Tbk (PTPP) of 2,Risk (2) in Table 4.2 is the variance of the residual error of the stock (i) which is also a unique or unsystematic risk.The greater the value of variance ei, the greater the unsystematic risk that will be borne by investors and vice versa.Unsystematic risk is a risk that can be eliminated by diversifying, factors related to this risk such as capital structure, asset structure, level of liquidity, level of profit and so on.

ReturnRisk-Free Assets
AssetsRisk-free is an asset that has a certain expected return with a risk equal to zero (Jogiyanto: 2008: 301), meaning that if an investor invests his funds in a type of asset, he can know the amount of profit that will be obtained in the future.In this research, risk-free asset returns are sourced from Bank Indonesia for the period February 2018 to July 2020, the average monthly risk-free asset return value will be used as the value (Rf) for calculations for optimal portfolio formation, as for the calculation of risk-free asset returns in Table 4 is as follows.Based on the research results in Table 4.4, the average growth in risk-free assets from 2018 to 2020 increased with a decrease of 0.45%.
Meanwhile, for the research results in Table 4.3, the average growth in risk-free assets from 2019 to 2020 decreased by a difference of 1.16%.

Optimal Portfolio Forming Stocks
The shares selected in the optimal portfolio are shares that have a high excess return to beta (ERB) value, shares with a low excess return to beta (ERB) value will not be included in the optimal portfolio, so a limiting point is needed that determines the excess return value high to beta (ERB), which is meant by excess return to beta (ERB) is defined as the difference between the expected return and the return on risk-free assets, the cut off point (C*) is obtained from the largest value (Ci), which is meant by (Ci) is the value (C) for security I which is calculated by accumulating the values (A1) to (Ai) and also the values (B1) to (Bi), the shares forming the optimal portfolio are those that have a value (ERB) of more is large or equal to the limiting point value (C*),Shares whose value (ERB) is smaller than the limiting point (C*) will not be included in the optimal portfolio, while the shares selected in the optimal portfolio are in Table 4.5 as follows.Based on the research results in Table 5, Aneka Tambang Tbk obtained the highest (ERB) value of0.0426The highest (Ci) value obtained by Bank Central Asia Tbk was 0.0039 which will be used as the limiting point (C*) because it has the highest (Ci) value.The criteria for determining the inclusion of a security in the optimal portfolio is if the value (ERB) of a share is equal to or greater than the limiting point value (C*) so that the shares included in the optimal portfolio are Aneka Tambang Tbk and Bank Central Asia Tbk.Shares that are included in the optimal portfolio have a positive value, which means that each individual's expected return is greater than the return on risk-free assets.This illustrates that shares that are included in the optimal portfolio of the Single Index Model are companies that have a high level of return.higher than investing in risk-free securities or assets, namely Bank Indonesia Certification (SBI), excess return to beta (ERB) is used to measure stock premium returns relative to a unit of risk that cannot be diversified which is measured by beta.(ERB) shows the relationship between return and risk which is a determining factor in investment.

Proportion of Funds in Securities for Optimal Portfolio Formation
After determining the selected securities in forming an optimal portfolio as in Table 4.4, the next step is to determine the proportion of funds that will be invested by investors in each selected security in the optimal portfolio using a single index model.The proportion of funds for each security that will be invested can be seen in Table 4.6 as following.Before calculating the return and risk of a single index model portfolio, the beta and alpha values of the portfolio must first be known.The beta and alpha of the portfolio are input in calculating the return and risk of the portfolio.The beta value is also called the sensitivity of changes in securities to the market, while the beta of the portfolio is the beta of the individual shares.included in the formation of an optimal portfolio with the proportion of funds invested, while the portfolio alpha is the individual alpha of the securities selected in the optimal portfolio with the proportion of funds invested, the Beta and Alpha values of the portfolio in Table 7 are as follows.

Table 1
shows that the development of sectoral shares fluctuates from year to year.Several sectors experienced positive and negative growth.In 2019, there were 6 groups of shares that experienced depreciation, namely the agriculture sector, mining sector, miscellaneous industrial sector, industrial consumer goods sector, trade services & investment sector, and manufacturing sector.In the consumer goods industrial sector, share price depreciation was quite high, around -20.11% and the highest share price appreciation in 2017 was in the finance sector at 15.22%.