This research discussed the portfolio performance evaluation using the Treynor method. The portfolio performance evaluation aims to assess the established portfolio whether had a good performance and suitable to the investment goals. At the research, a portfolio was selected based on the efficient stock by taking two criteria that were, the first, (portfolio A) based on the greatest positive expected returns and the second (portfolio B) based on the smallest positive risk (beta). The result showed from the formation of the portfolio are for portfolio A was selected AKRA and PTBA stocks, as for portfolio B was selected ICBP and BBCA stocks. Of these two portfolios, both had good performance since the index Treynor acquired had positive results and portfolio B had better performance than portfolio A

Alwi, Wahidah

Anugrawati, Sri Dewi

B, Nurhafsari

Ibnas, Risnawati

Syata, Ilham

Repositori UIN Alauddin Makassar

5/8/23, 9:57 PM Turnitin - Originality Report - 28._125956479.pdfhttps://www.turnitin.com/newreport_printview.asp?eq=0&eb=1&esm=0&oid=2085080556&sid=0&n=0&m=2&svr=34&r=37.75571593929477&lang… 1/4Turnitin Originality ReportProcessed on: 05-May-2023 20:39 WIBID: 2085080556Word Count: 2495Submitted: 128._125956479.pdf ByAnonymous2% match (student papers from 17-Feb-2023)Submitted to Universitas Bung Hatta on 2023-02-172% match (Internet from 08-Sep-2021)https://enrichment.iocspublisher.org/index.php/enrichment/article/download/210/1572% match (Internet from 28-Dec-2021)http://journal.laaroiba.ac.id/index.php/alkharaj/article/download/711/657/2% match (Immas Nurhayati, Endri Endri, Titing Suharti, Renea Shinta Aminda, LenyMuniroh. "The impact of COVID-19 on formation and evaluation of portfolioperformance: A case of Indonesia", Investment Management and FinancialInnovations, 2021)Immas Nurhayati, Endri Endri, Titing Suharti, Renea Shinta Aminda, Leny Muniroh."The impact of COVID-19 on formation and evaluation of portfolio performance: Acase of Indonesia", Investment Management and Financial Innovations, 20212% match (Internet from 25-Mar-2023)http://repository.lppm.unila.ac.id/46218/1/IICIS-2021-Print-Ready_V2.pdf1% match (Adri Arisena, Lienda Noviyanti, S Achmad Zanbar. "Portfolio return usingBlack-litterman single view model with ARMA-GARCH and Treynor Black model",Journal of Physics: Conference Series, 2018)Adri Arisena, Lienda Noviyanti, S Achmad Zanbar. 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"Comparison OfSharia Performance And Conventional Mutual Funds In Forming Optimal Portfolio", Al-Kharaj : Jurnal Ekonomi, Keuangan & Bisnis Syariah, 20211% match (student papers from 10-Jan-2022)Submitted to Universitas Bangka Belitung on 2022-01-10< 1% match () Similarity Index16%Internet Sources: 9%Publications: 12%Student Papers: 7%Similarity by Source5/8/23, 9:57 PM Turnitin - Originality Report - 28._125956479.pdfhttps://www.turnitin.com/newreport_printview.asp?eq=0&eb=1&esm=0&oid=2085080556&sid=0&n=0&m=2&svr=34&r=37.75571593929477&lang… 2/4Putra, Dery Westryananda, Hasnawati, Sri, Muslimin, Muslimin. "Ramadan Effect andVolatility Risk by Garch Model: Evidence in Indonesia Stock Market", 'LembagaPenelitian dan Pengabdian kepada Masyarakat Universitas Lampung', 2021< 1% match (Internet from 08-Jul-2019)http://digilib.unila.ac.id/57510/3/3.%20SKRIPSI%20FULL%20TANPA%20BAB%20PEMBAHASAN.pd< 1% match (Internet from 26-Nov-2022)https://jurnal.uii.ac.id/JSB/article/download/15211/10385/41002Proceedings of the 1st International Conference on Mathematics and MathematicsEducation (ICMMED 2020) Portfolio Performance Evaluation for LQ 45 Index in2016-2020 Periods Using the Treynor Method Wahidah Alwi1, Nurhafsari. B2,*,Ilham Syata3, Risnawati Ibnas4, Sri Dewi Anugrawati5 1,2,3,4,5 MathematicsDepartement, Faculty of Science and Technology, Univesitas Islam Negeri AlauddinMakassar * nurhafsaribahar@gmail.com ABSTRACT This research discussed theportfolio performance evaluation using the Treynor method. The portfolioperformance evaluation aims to assess the established portfolio whether had a goodperformance and suitable to the investment goals. At the research, a portfolio wasselected based on the efficient stock by taking two criteria that were, the first, (portfolio A ) based on the greatest positive expected returns and the second(portfolio B) based on the smallest positive risk (beta). The result showed from theformation of the portfolio are for portfolio A was selected AKRA and PTBA stocks, asfor portfolio B was selected ICBP and BBCA stocks. Of these two portfolios, both hadgood performance since the index Treynor acquired had positive results and portfolioB had better performance than portfolio A. Keywords: Performance evaluation,Treynor method, CAPM. 1. INTRODUCTION Everyone is faced with various choices indetermining the funds or resources they have for current and future consumption.Not a few people choose to invest to save the capital they have. Rampant stocktrading in the capital market reflects the great investment interest of the public.Investments in securities are attractive because of the sizeable returns. Besides,investment in securities has another attraction, namely the ease of investing. Wheninvesting, investors will not invest their capital in just one share, investors will investtheir shares in several different stocks to minimize the risk of loss from falling shareprices. For the right investment decision or to produce the expected return,investors need to make an initial assessment of the stocks they will choose cx. Theperformance appraisal of stock generally starts with evaluating the stock return,whether it can provide a return that exceeds (above) other stock returns andwhether the return obtained is following the level of risk that must be borne. For thisreason, investors will usually diversify by forming a portfolio, namely by investing inmany stocks so that the risk of loss on one share will be covered by the advantagesof other shares. [1] Informing a portfolio, several methods are used, one of which isthe Capital Asset Pricing Model (CAPM). Investors need to be able to estimate thereturn of a single stock. For that, CAPM can estimate stock returns. However,measuring portfolio performance is not just looking at the return. [2] However, therisks that will be borne also need attention. Following the capital market theory,three methods can be used to measure portfolio performance. In its calculation, thisperformance measure includes the risk and return factors. This method wasdeveloped by Jack Treynor, Michael Jensen, and William Sharpe. Each of thesemeasures is called the Treynor, Jensen, and Sharpe performance measure. [3]Shares listed on LQ-45 are liquid stocks, have development prospects, financialconditions, and high sales value, and have been objectively selected by theIndonesia Stock Exchange. Therefore, the researcher decided to use the Treynormethod where this method emphasizes beta fluctuations and portfolio Copyright ©2021 The Authors. Published by Atlantis Press SARL. This is an open access articledistributed under the CC BY-NC 4.0 license -http://creativecommons.org/licenses/by-nc/4.0/. 83 performance will be said to bebetter if the Treynor index value is positive, and the bigger it is. So that in thisthesis will use the data of stocks listed in LQ 45. Based on the case studies andanalyzes that have been written, the authors are interested in discussing the StockPortfolio Performance Analysis Using the Treynor Method. 2. PORTFOLIO & ASSETPRICING 2.1. Portfolio A portfolio is a collection of securities (securities). In 1956Prof. Harry Markowitz first developed portfolio theory. This theory explains how toform an optimal portfolio from the many choices of efficient portfolios. [4] 2.2.Return The general formula for total return between period t-1 to t is as follows 𝑅𝑡 =5/8/23, 9:57 PM Turnitin - Originality Report - 28._125956479.pdfhttps://www.turnitin.com/newreport_printview.asp?eq=0&eb=1&esm=0&oid=2085080556&sid=0&n=0&m=2&svr=34&r=37.75571593929477&lang… 3/4𝑃𝑡𝑃−𝑡𝑃−𝑡1−1 (1) 𝑅𝑡 : total return 𝑃𝑡 : the investment price at time 𝑡 𝑃𝑡−1 : theinvestment price at time 𝑡 − 1 The market return is a cumulative profit thatdescribes all shares listed on the exchange [2] 𝑅𝑚 = 𝐺𝐺𝑅𝐺𝐺𝐺𝑡−𝑅𝐺𝐺𝐺𝑡−𝑅1𝐺𝑡−1 (2) 𝑅𝑚: market return 𝐺𝐺𝑅𝐺𝑡 : IHSG price at time 𝑡 𝐺𝐺𝑅𝐺𝑡−1 : IHSG price at time 𝑡 − 1The expected return is the weighted average of the returns of each stock in theportfolio. [5] The mathematically expected return is formulated as follows: (𝐸(𝑅𝑚))= 𝐸(∑𝑚𝑖=1 𝑤𝑖𝑅𝑖) (3) (𝐸(𝑅𝑚) : expected return portfolio 𝑤𝑖 : the individual stockweight (𝐸(𝑅𝑖) : the individual value of expectation of return from the stock 2.3. Risk(Beta) Beta is a measure of risk that comes from the relationship between the rateof return of a stock and the market rate of return, or in other words, beta is thequotient between stock covariance and market variance. [5] Find the beta value ofeach stock using the equation 𝛽𝑖 = 𝜎𝜎𝑖𝑚2𝑚 (4) 𝛽 𝑖 : estimation of the stock betacoefficient value 𝜎𝑖𝑚 : covariance of the stock return with the market return 𝜎 𝑚 2 :variance of the stock market 2.4. Model of Capital Asset Pricing The CAPM model isa balance model that describes the relationship between return and risk to besimpler because it only uses a variable (also called a beta variable) to describe risk.Sharpe, Litner, and Mossin in the mid-1960s, introduced the CAPM. Markowitz putforward a portfolio theory called CAPM. Following the Markowitz model, it is assumedthat each investor will diversify his portfolio and choose the optimal portfolioaccording to his preference for risk and return. The portfolio chosen by investors isthe portfolio points that are on all efficient portfolio lines. [1] The expected rate ofreturn is the return desired by investors on investments made based on beta riskpreference. Calculating the Expected Return of Shares using the equation. 𝐸(𝑅𝑖) = 𝑅𝑓+ (𝐸(𝑅𝑚) − 𝑅𝑓) 𝛽𝑖 (5) 𝐸(𝑅𝑖) : return equilibrium stock 𝑅 𝑓 : risk-free return value 𝛽 𝑖: estimation of the stock beta coefficient value (𝐸(𝑅𝑚): value of expectation ofreturn from the market 2.4 Treynor Performance Measures This performancemeasure is measured by comparing the portfolio risk premium (the differencebetween the average portfolio return and the risk-free return) with the portfolio riskexpressed by β (market risk or systematic risk). [6] Portfolio performance is said tobe good if the slope of the line is getting bigger that forms the line. The Treynorindex can be systematically written as follows: 𝑅𝑚𝑖 = 𝑅𝑝𝛽𝑖−𝑝𝑅𝑖𝑓 𝑅𝑚𝑖 𝑅𝑚𝑖 𝑅𝑓 𝛽𝑚𝑖 (6) :Treynor performance index : portfolio return value : risk free return value :𝑐𝑚𝑣(𝑅𝑖,𝑅𝑚) = portfolio beta i 𝑣𝑎𝑟(𝑅𝑚) 3. RESULT AND DISCUSSION The data used inthis study are monthly stock return data from companies listed on LQ-45 that havebeen registered from 2016 to 2020 3.1. Individual Monthly Share Rate of Return andMarket Return By using equation (1) we get monthly stock returns and equation (2)we get market returns. 3.2. Risk-Free Return Rate The risk-free rate of return isused by investors to determine the rate of return on their investment. The BankIndonesia interest rate (SBI) is the risk-free rate of return used. The calculation ofthe risk-free return is as follows: 0.050815 𝑅𝑓 = 12 = 0.004 = 0.04% 3.3.Calculation of the Systematic Risk of Shares By using equation (4), the beta valuecan be obtained which can be seen in Table 1. Table 1. The result of the stock betacalculation N 1 Stock Code AKRA 𝜷𝒊 1.52468 2 ASII 2.29988 3 BBCA 1.04799 4BBNI 1.8153 5 BBRI 1.3386 6 BBTN 1.77083 7 BMRI 1.14977 8 BSDE 1.46837 9GGRM 0.98903 10 ICBP 0.59402 11 INCO 1.81879 12 INDF 0.99649 13 JSMR1.04107 14 KLBF 1.34008 15 LPPF 1.89284 16 MNCN 1.72322 17 PGAS 2.00083 18PTBA 2.03793 19 PTPP 2.74179 20 SMGR 1.75454 21 SRIL 0.64032 22 UNTR1.0149 23 UNVR -4.1601 24 WIKA 2.17519 From the results obtained, the share ofthe company that has the largest beta is PP Persero Tbk (PPTP) shares with a valueof 2.74179. This shows that PTPP's share is aggressive stock because it has morethan one beta (β> 1). On the other hand, the one with the smallest beta is UnileverIndonesia Tbk (UNVR) with a value of -4.1601. 3.4. Level of Expected Return ofShares Using CAPM To find the expected return, equation (5) is used so that theexpected return can be seen in Table 2. Table 2. The result of expectation returnfrom the stock N 1 Stock Code AKRA 𝑬(𝑹𝒊) 0.00654 2 ASII 0.00783 3 BBCA 0.005744 BBNI 0.00702 5 BBRI 0.00623 6 BBTN 0.00695 7 BMRI 0.00591 8 BSDE 0.006449 GGRM 0.00565 10 ICBP 0.00499 11 INCO 0.00703 12 INDF 0.00566 13 JSMR0.00573 14 KLBF 0.00623 15 LPPF 0.00715 16 MNCN 0.00687 17 PGAS 0.00733 18PTBA 0.00739 19 PTPP 0.00856 20 SMGR 0.00692 21 SRIL 0.00506 22 UNTR0.00569 23 UNVR -0.0029 24 WSKT 0.00762 Based on Table 2 above, shares of thecompany PP Perseo Tbk (PTPP) have the largest expected return of 0.00856% whileUnilever Indonesia Tbk (UNVR) is the company stock with the lowest expectedreturn with a value – 0.0029%. this means that the size of the expected return 𝐸(𝑅𝑖)depends on the size of the risk (beta) of the stock, in other words, the expectedreturn 𝐸(𝑅𝑖) and risk (beta) have a positive relationship. 3.5. Portfolio FormationThis selection is based on the highest value of expected return and 4 companieswere selected, namely PTPP, ASII, PTPP, and WSKT. Of the four stocks that areincluded in the efficient portfolio candidate, an opportunity is formed from the four5/8/23, 9:57 PM Turnitin - Originality Report - 28._125956479.pdfhttps://www.turnitin.com/newreport_printview.asp?eq=0&eb=1&esm=0&oid=2085080556&sid=0&n=0&m=2&svr=34&r=37.75571593929477&lang… 4/4stocks that will be used as an efficient portfolio. The stocks that are formed are asfollows: Table 3. Stocks that make up an efficient portfolio N Portfolio 1 PTPP ASII 23 PTPP WIKA PTPP PTBA 4 ASII WIKA 5 ASII PTBA 6 WIKA PTBA 3.6 CalculatingPortfolio Weights Calculating the portfolio weight using the equation: 𝑤𝑖 = ∑𝑖𝑚=1 𝑧𝑖 𝑧𝑖 Table 4. Portfolio weighting result N Portfolio Weight 1 PTPP ASII 0.321 0.679 2PTPP WIKA 0.971 0.083 3 PTPP PTBA 0.260 0.740 4 ASII 0.716 WIKA 0.284 5 ASIIPTBA 0.364 0.636 6 WIKA PTBA 0.175 0.825 Based on Table 4 above, the largestshare weight is in the 2nd portfolio, namely shares of the company PP (Persero) Tbk(PTPP) amounting to 91.7% 3.7 Calculation of Expected Return and Portfolio RiskCalculating the expected return and beta of the portfolio is necessary to determinethe rate of return of the portfolio, how much return will be obtained on the selectedportfolio, and the risk of the portfolio using the equation (3) and 𝛽𝑚 = ∑𝑖𝑚=1 𝑤𝑖𝛽𝑖Table 5. The result of expectation from the stock and portfolio beta N Portfolio E(Rp)Βp 1 PTPP ASII 0.00718 1.91522 2 PTPP WIKA 0.0081 2.69452 3 PTPP PTBA 0.00762.2204 4 ASII WIKA 0.0068 1.709 5 ASII PTBA 0.00708 1.8511 6 WIKA PTBA0.0074 2.0618 From the results of Table 5 above, the efficient portfolio is the secondportfolio with an expected return of 0.81% and a beta of 2.69452 because it has thelargest expected return compared to other portfolios, although the risk it has is notthe smallest. 3.8 Portfolio Performance Calculation Using the Treynor MethodPortfolio performance is calculated by comparing the portfolio risk premium (thedifference between the average portfolio return and the risk-free return) with β(market risk or systematic risk) representing portfolio risk. Where the portfolioperformance will be said to be getting better if the index value is getting bigger.Treynor index value for each portfolio. Table 6. Index Treynor value N PortfolioE(Rp)-Rf Βp Treynor 1 TLKM UNVR 0.003187 1.91522 0.001664259 2 TLKM ASII0.004484 2.69452 0.001664453 3 TLKM INDF 0.003695 2.2204 0.00166436 4UNVR ASII 0.002845 1.709 0.001664468 5 UNVR INDF 0.003081 1.85110.001664468 6 ASII INDF 0.003431 2.0618 0.001664429 Based on Table 6 above,shows that the portfolio performance selected using the Treynor method has apositive Treynor index value. This shows that based on the Trenor method allselected portfolios have good performance. 4. CONCLUSION Based on thecalculations and discussion described in the previous chapter, it can be concludedthat there are six combinations of stocks that make up a portfolio taken from thefour stocks that have the highest expected return value. The four stocks that makeup an efficient portfolio are PTPP, ASII, WIKA, and PTBA Of the six portfolios formed,namely the 1st portfolio (PTPP and ASII), 2nd portfolio (PTPP and WIKA), 3rdportfolio (PTPP and PTBA), 4th portfolio (ASII and WIKA), 5th portfolio (ASII andPTBA), the 6th portfolio (WIKA and PTBA) has good performance because it has apositive Treynor index value. In this study, the authors provide suggestions, namelythat further researchers can use different methods in portfolio formation such as theSingle Index Model or use other methods of calculating portfolio performance suchas the Jensen method and the Sharpe method. REFERENCES [1] Guerard, J. B,Portfolio Construction, Measurement, and Efficiency. Springer Nature, USA, 2017, p275. [2] Treynor, J. L, Treynor on Institutional Investing, Simultaneously, Canada.2007, p 87. [3] Hubner, G, The Generalized Treynor Ratio. EDHEC Business School,University of Liege, 2003. [4] Jozef, G, Time-Varying CAPM And Its Applicability InCost Of Equity Determination, vol 32. Elsevier, Slovak Republic, 2015, p 62. [5]Bodie, K.M, Investment, McGraw-Hill Education, 2014 p 164. [6] Suriyani, A., TheAnalysis Of Risk-Adjusted Return Portfolio Performance Share for LQ 45 Index inIndonesia Stock Exchange In 2010-2014 Periods, vol 211, Elsevier, Bali, 2015, p639. Advances in Social Science, Education and Humanities Research, volume 550Advances in Social Science, Education and Humanities Research, volume 550Advances in Social Science, Education and Humanities Research, volume 550Advances in Social Science, Education and Humanities Research, volume 550Advances in Social Science, Education and Humanities Research, volume 550Advances in Social Science, Education and Humanities Research, volume 550 84 8586 87 88

Portfolio Performance Evaluation for LQ 45 Index in 2016-2020 Periods Using the Treynor Method

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Portfolio Performance Evaluation for LQ 45 Index in 2016-2020 Periods Using the Treynor Method

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