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1
Nur Safitri, Indah Nur, Sudradjat Sudradjat, and Eman Lesmana. "STOCK PORTFOLIO ANALYSIS USING MARKOWITZ MODEL." International Journal of Quantitative Research and Modeling 1, no. 1 (2020): 47–58. http://dx.doi.org/10.46336/ijqrm.v1i1.6.
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A common problem that often occurs in investment is the selection of the optimal portfolio according to the wishes of investors. This thesis ueds the Markowitz Model as a basis to formed a model to choose the optimal portfolio that provided the lowest risk. Efforts to minimize risk were carried out by conducting a diversification strategy. After the selection of several companies with the criteria of capitalization value and DER (Debt Equity Ratio), a combination of stocks is formed to form a portfolio. The formed portfolio was then analyzed to determine the optimal proportion of each stock. Using the Markowitz model, which is then solved by Non Linear Programming, an optimal portfolio is obtained with the proportion of each stock minimizing risk. In general, the results of this analysis indicate that portfolios with more stocks will produce lower risks compared to portfolios with fewer stocks, thus providing optimal diversification solutions, namely portfolios with members of five stocks with optimal risk of 0.886%.
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Erwin, Dyah Astawinetu, Istiono, Hari Prastiwi Estik, and Santoso Rudy. "Optimal Portfolio Analysis on Stocks Listed in Lq45." Journal of Economics, Finance And Management Studies 07, no. 06 (2024): 3366–72. https://doi.org/10.5281/zenodo.11634966.
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The purpose of this study is to determine the optimal portfolio of stocks that are listed in the LQ-45 period (January 2023 – January 2024) and compare the return and risk in stocks that are included in the LQ-45 but not included in the optimal portfolio. The method used is the Single Index Method, which uses the ERB (Excess Return to Beta) assessment reference. The results showed that out of 45 stocks there were 10 stocks that had large ERB, which were included in the optimal portfolio were GGRM, BBTN, KLBF, EXCL, ICBP, MAPI, UNVR, CPIN, INDF, and TBIG, which provided a return of 6.61% per year and a risk of 0.08% per year. Meanwhile, the remaining thirty-five stocks were made up as well as 10 other portfolios. Each of these portfolios consists of 10 randomly selected stocks. These ten portfolios yield higher returns than optimal portfolios. However, they also have a higher risk. The results of the comparison of the coefficient of variation between the optimal portfolio and the other 10 portfolios show that the optimal portfolio is the best portfolio
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Nurhakim, Eko Sanjaya, Abdul Mukti Soma, and Irni Yunita. "Constructing Optimal Portfolios Using the Single Index Model and Markowitz Model: A Study on Cryptocurrencies." Journal of Accounting and Strategic Finance 7, no. 2 (2024): 200–218. https://doi.org/10.33005/jasf.v7i2.485.
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This study analyzes the formation of optimal portfolios on cryptocurrency assets using the single index model and the Harry Markowitz model. This study covers 79 cryptocurrencies with the largest market capitalization during the period June 2023–June 2024. We calculate the optimal portfolio using the single index model and Markowitz, and evaluate its performance using the Sharpe Ratio. The results show that the Harry Markowitz model produces better portfolio performance compared to the single index model. The Markowitz portfolio produces a positive Sharpe ratio (1.8496), a portfolio return rate of 7.678%, and lower risk (0.0415). Conversely, the single index model portfolio shows a negative Sharpe ratio (-2.0971), indicating lower returns than risk-free assets. In addition, the Markowitz model offers more efficient diversification than the single index model. However, in general, both the Single Index Model and the Markowitz Model have a significant effect on the formation of optimal portfolios, with the Sharpe Index proving to be a significant mediator in the relationship between the two models and the optimal portfolio. The R-squared value shows that the SIM variables, Markowitz Model, and Sharpe Index explain 48.4% of the variation in the optimal portfolio. This study recommends the use of the Harry Markowitz model for cryptocurrency investment because it can provide higher returns with more controlled risks. This study provides important insights for investors on the strategy of diversifying cryptocurrency asset portfolios.
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Levchenko, Valentyna, and Myroslav Ostapenko. "Formation of the optimal portfolio of insurer’s services of the voluntary types of insurance." Insurance Markets and Companies 7, no. 1 (2016): 45–51. http://dx.doi.org/10.21511/imc.7(1).2016.05.
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The article studies the possibility of using optimization modelling to form the optimal structure of insurance services’ portfolio of insurance companies. Based on the data of net insurance payments and profitability of the voluntary types of insurance in 2005-2015, the authors conducted their analysis according to the possibility to be included in the general insurance portfolio of the insurance company. The optimization model is based on the approach developed by G. Markowitz. The formation of insurance services portfolio is conducted by solving the optimization problem to maximize the portfolios’ profitability or to minimize the portfolio’s risks. The obtained results can be used in making strategic decisions by the management regarding the development of insurance companies. Keywords: insurance company, insurance service, insurance portfolio, portfolio optimization
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Yang, Hyunjun, Hyeonjun Park, and Kyungjae Lee. "A Selective Portfolio Management Algorithm with Off-Policy Reinforcement Learning Using Dirichlet Distribution." Axioms 11, no. 12 (2022): 664. http://dx.doi.org/10.3390/axioms11120664.
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Existing methods in portfolio management deterministically produce an optimal portfolio. However, according to modern portfolio theory, there exists a trade-off between a portfolio’s expected returns and risks. Therefore, the optimal portfolio does not exist definitively, but several exist, and using only one deterministic portfolio is disadvantageous for risk management. We proposed Dirichlet Distribution Trader (DDT), an algorithm that calculates multiple optimal portfolios by taking Dirichlet Distribution as a policy. The DDT algorithm makes several optimal portfolios according to risk levels. In addition, by obtaining the pi value from the distribution and applying importance sampling to off-policy learning, the sample is used efficiently. Furthermore, the architecture of our model is scalable because the feed-forward of information between portfolio stocks occurs independently. This means that even if untrained stocks are added to the portfolio, the optimal weight can be adjusted. We also conducted three experiments. In the scalability experiment, it was shown that the DDT extended model, which is trained with only three stocks, had little difference in performance from the DDT model that learned all the stocks in the portfolio. In an experiment comparing the off-policy algorithm and the on-policy algorithm, it was shown that the off-policy algorithm had good performance regardless of the stock price trend. In an experiment comparing investment results according to risk level, it was shown that a higher return or a better Sharpe ratio could be obtained through risk control.
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Gubu, La, and Muhamad Rashif Hilmi. "Pembentukan Portofolio Optimal Saham Dengan Menggunakan Model Portofolio Mean-Variance-Skewness-Kurtosis." Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika 11, no. 2 (2024): 123–33. http://dx.doi.org/10.31316/jderivat.v10i2.6218.
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This paper presents the development of Markowitz's classic Mean-Variance (MV) portfolio model, namely the Mean-Variance-Skewness-Kurtosis (MVSK) portfolio model. The MVSK portfolio model aims to overcome the fact that most stock returns in the capital market do not follow a normal distribution, and there are skewness and excessive kurtosis. The solution of the MVSK portfolio model is determined using the Newton-Raphson method. To see the advantages of the MVSK model, an empirical study was carried out on a portfolio construction using the four best stocks on the Indonesian Stock Exchange, which are included in the LQ45 index group for February-July 2023. The empirical study shows that for risk aversion the performance of portfolios formed using the MVSK model outperforms portfolios formed using the classical MV model, while for risk aversion the performance of portfolios formed using the classic MV model outperforms portfolios formed using the MVSK model. In addition, it was also found that for risk aversion , the weight and performance of the portfolio formed using the MVSK model were close to the weight and performance of the portfolio formed using the classic MV model. Keywods: portofolio, return, risk, portfolio performance, MVSK.
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Sriyono, Sriyono, Detak Prapanca, and Adelia Oktaviani. "Pengambilan Keputusan Investasi Portofolio : Pendekatan Model Indeks Tunggal Saham." Benefit: Jurnal Manajemen dan Bisnis 6, no. 2 (2021): 72–96. http://dx.doi.org/10.23917/benefit.v6i2.14489.
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Abstract. This study aims to determine the composition of the optimal portfolio formation using the Single Index method on LQ-45 shares in the Indonesia Stock Exchange period 2016 - 2018. This research was conducted on the basis of the increasing number of investors who chose to invest their funds in shares, where this is indicated from the increasing positive sentiment on stock investment compared to other investments. Portfolio formation using the Single Index model is one model that can be used to form optimal portfolios, because with this model portfolios are easily formed to fit the desired investment characteristics and objectives to be achieved. The Single Index method is a method that formulates the existence of elements of return and risk in an investment, where the risk element can be minimized through diversification and combining various investment instruments into a portfolio. By using the Single Index method, investors can take advantage of all available information as the basis for maximizing portfolio formation. The sample selection technique of this study used a purposive sampling method and 19 LQ-45 Index stocks were obtained which were used as the research sample. Based on the results of research to determine the optimal portfolio of shares using the Single Index method shows that the LQ-45 Index Shares that form the optimal portfolio are INCO, BBTN, ICBP, INTP, BMRI, BBNI, BBCA, HMSP, INDF shares , GGRM and TLKM. And this study produced 55 portfolio combinations in which there is one efficient portfolio, 26 portfolios with the same funding weight (50%: 50%). Investors choose an efficient portfolio in accordance with the preferences of the level of profit and risk they bearKeywords - Single Index Model, Optimal Portfolio, Expected Return, LQ-45
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Vanti, Eka Nur, and Epha Diana Supandi. "Pembentukan Portofolio Optimal dengan Menggunakan Mean Absolute Deviation dan Conditional Mean Variance." Jurnal Fourier 9, no. 1 (2020): 25–34. http://dx.doi.org/10.14421/fourier.2020.91.25-34.
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Penelitian ini membahas tentang pembentukan portofolio optimal menggunakan model Mean Absolute Deviation (MAD) dan model Conditional Mean Variance (CMV). Pada model MAD risiko portofolio diukur menggunakan rata–rata deviasi standar sehingga portofolio optimal dapat diperoleh dengan menggunakan pemrograman linear. Sedangkan portofolio model CMV, rata–rata return diestimasi menggunakan model Autoregressive (AR) dan risiko (variansi) diestimasi menggunakan model GARCH. Selanjutnya kedua model portofolio diterapkan dalam membentuk portofolio optimal pada saham–saham yang terdaftar dalam Indeks Saham Syariah Indonesia (ISSI) periode 4 Juli 2016 sampai 4 Juli 2018. Kinerja kedua portofolio dianalisis menggunakan indeks Sortino. Hasilnya menunjukan bahwa kinerja portofolio model CMV lebih baik dibandingkan model portofolio MAD.
 [This study discusses the formation of optimal portfolios using the Mean Absolute Deviation (MAD) model and the Conditional Mean Variance (CMV) model. The MAD portfolio model measures portfolio risk by using average standard deviations so that optimal portfolios solved by using linear programming. Meanwhile the CMV portfolio model, the average return estimated by using the Autoregressive (AR) model and the risk (variance) estimated by using the GARCH model. Furthermore, both portfolio models applied in forming optimal portfolios for stocks listed in the Indonesian Syariah Stock Index (ISSI) for the period 4 July 2016 to 4 July 2018. The performance of both portfolios analyzed by using the Sortino index. The results show that the portfolio performance of the CMV model is better than MAD portfolio model.]
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Nisani, Doron. "Portfolio selection using the Riskiness Index." Studies in Economics and Finance 35, no. 2 (2018): 330–39. http://dx.doi.org/10.1108/sef-03-2017-0058.
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PurposeThe purpose of this paper is to increase the accuracy of the efficient portfolios frontier and the capital market line using the Riskiness Index.Design/methodology/approachThis paper will develop the mean-riskiness model for portfolio selection using the Riskiness Index.FindingsThis paper’s main result is establishing a mean-riskiness efficient set of portfolios. In addition, the paper presents two applications for the mean-riskiness portfolio management method: one that is based on the multi-normal distribution (which is identical to the MV model optimal portfolio) and one that is based on the multi-normal inverse Gaussian distribution (which increases the portfolio’s accuracy, as it includes the a-symmetry and tail-heaviness features in addition to the scale and diversification features of the MV model).Research limitations/implicationsThe Riskiness Index is not a coherent measurement of financial risk, and the mean-riskiness model application is based on a high-order approximation to the portfolio’s rate of return distribution.Originality/valueThe mean-riskiness model increases portfolio management accuracy using the Riskiness Index. As the approximation order increases, the portfolio’s accuracy increases as well. This result can lead to a more efficient asset allocation in the capital markets.
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Ji, Xinyue. "Comparison of Portfolio Optimizations under Markowitz Model in Technology Sector and Financial Services Sector." Highlights in Business, Economics and Management 24 (January 22, 2024): 1194–202. http://dx.doi.org/10.54097/32f00f69.
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In the period of Covid-19, different sectors received different levels of shocks, which gave investors a degree of caution when investing in various sectors. Therefore, portfolio optimization - using specific model to assign weights of stocks to achieve a higher return while reducing risk – becomes a popular strategy. This paper chooses the Markowitz model to find optimal sector-based portfolios, specifically in technology sector and financial services sector, as well as portfolios that contains stocks in both sectors. The study uses Python to do Monte Carlo simulation, finding two optimal portfolios with maximum Sharpe ratio and minimum volatility for each sector(s), and finally comparing performances to test if the sector-based portfolio works better than the inter-sector portfolio. According to results, the minimum volatility portfolio in combined sectors reaches the same return of 0.11 as the minimum volatility portfolio in technology sector, but with lower volatility. It means the inter-sectors portfolio is better off when seeking minimum volatility. On the other hand, the maximum Sharpe ratio portfolios in technology sector, financial services sector, and combined sectors have values of returns and volatility ordering from highest to lowest. As a result, with current information, without investors’ investment preference, the optimal maximum Sharpe ratio portfolio cannot be determined and needed further exploration.
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Sirait, Emmanuel Parulian, Yasir Salih, and Rizki Apriva Hidayana. "Investment Portfolio Optimization Model Using The Markowitz Model." International Journal of Quantitative Research and Modeling 3, no. 3 (2022): 124–32. http://dx.doi.org/10.46336/ijqrm.v3i3.344.
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The stock portfolio is related to how someone allocates several shares in various types of investments so that the results achieve maximum profit. By implementing a diversification system or portfolio optimization on several stocks, investors can reduce the level of risk and simultaneously optimize the expected rate of return. This study aims to determine which stocks listed on the Indonesia Stock Exchange (IDX) and included in the portfolio for the 2021-2022 period are eligible to be included in the optimal portfolio and to determine the proportion of funds for each share in the formation of the optimal portfolio. The population in this study are all shares included in the Indonesia Stock Exchange (IDX) listed on the Indonesia Stock Exchange (IDX) for the 2021-2022 period. The sample of this research is five stocks that are candidate portfolios. The sampling method uses a purposive sampling method with the criteria of 5 stocks with the highest positive ratio. The population in this study was all 30 companies included in the IDX30, while the samples were five companies. Data were analyzed using a mean-variant optimization model with a research duration between May 2021 and May 2022. Based on the results of the investment portfolio optimization analysis on the 5 (five) selected stocks, this study shows that, out of 23 stocks, five stocks are eligible to enter the optimal portfolio with their respective proportions, namely PT Adaro Energy Indonesia Tbk (ADRO) 20%, PT Astra International Tbk (ASII) 26%, PT Merdeka Copper Gold Tbk (MDKA) 10%, PT XL Axiata Tbk (EXCL) 19%, PT Bukit Asam Tbk (PTBA) 25%. The portfolio of these stocks generates an expected return of 0.00217 at a risk level of 0.00022. It is hoped that this research can be helpful to add to the literature on investment optimization models, especially the concentration of Mathematics in Finance, and serve as an additional reference for further research, as well as an alternative for investors in optimizing investment portfolios.
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Sadeghi, Soheila, Taimoor Marjani, Ali Hassani, and Jose Moreno. "Development of Optimal Stock Portfolio Selection Model in the Tehran Stock Exchange by Employing Markowitz Mean-Semivariance Model." Journal of Finance Issues 20, no. 1 (2022): 47–71. http://dx.doi.org/10.58886/jfi.v20i1.3061.
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In an increasingly complex financial market, selecting the optimal stock portfolio has become a subject of intense debate. This study aims to develop a model for optimal stock portfolio selection. We apply Markowitz's mean-semivariance approach to determine the downside risk of portfolios, which reflects investors' intuitive perception of risk. In the first stage, the combination of the Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) with interval data is employed to identify and rank good quality stocks according to the recommended criteria by experts. After selecting qualified stocks, in the second phase, we create portfolios, and the weight invested in each stock is determined. Then, three portfolios are created for three groups of risk-averse, neutral to risk, and risk-taker investors. The mean-semivariance optimization model is used in this phase. The proposed approach in the paper is implemented in a real case study of the Tehran stock exchange (TSE). Three portfolios for three groups of investors were evaluated and compared to the market performance using sharp criteria. All three portfolios outperformed the market portfolio both in terms of risk and return. The proposed model of this study can be utilized as a decision support tool when forming an optimal stock portfolio by considering both experts’ opinions on stock evaluation and investor risk preferences simultaneously.
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Chandra, Liliana, and Yudith Dyah Hapsari. "ANALISIS PEMBENTUKAN PORTOFO OPTIMAL DENGAN MENGGUNAKAN MODEL MARKOWITZ UNTUK SAHAM LQ 45 PERIODE 2008‐‐2012." Jurnal Manajemen 11, no. 1 (2014): 41–59. http://dx.doi.org/10.25170/jm.v11i1.832.
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The shares which are included in the LQ45 list attract investors., Make a portfolio diversification is necessary to minimize unsystematic risk. In this paper the authors wanted to construct an optimal portfolio in accordance with the theory of Markowitz.
 The data are taken from the yahoo.finance monthly data for stocks that are respectively included in LQ45 consistently in the period 2008 to 2012.. In establishing the optimal portfolio, the author uses the Linear Solver Microsoft Programming in Excel.Program.
 To determine the optimal portfolio, 17 shares which consistent listed in LQ45 in the period 2008 to 2012quired.. The Author formed 14 portfolios from the 14 stocks which have positive return. Portfolio Ewhich has the highest risk adjusted return (RAR) is selected as the optimal portfolio.
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Širůček, Martin, and Lukáš Křen. "Application of Markowitz Portfolio Theory by Building Optimal Portfolio on the US Stock Market." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 63, no. 4 (2015): 1375–86. http://dx.doi.org/10.11118/actaun201563041375.
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This paper is focused on building investment portfolios by using the Markowitz Portfolio Theory (MPT). Derivation based on the Capital Asset Pricing Model (CAPM) is used to calculate the weights of individual securities in portfolios. The calculated portfolios include a portfolio copying the benchmark made using the CAPM model, portfolio with low and high beta coefficients, and a random portfolio. Only stocks were selected for the examined sample from all the asset classes. Stocks in each portfolio are put together according to predefined criteria. All stocks were selected from Dow Jones Industrial Average (DJIA) index which serves as a benchmark, too. Portfolios were compared based on their risk and return profiles. The results of this work will provide general recommendations on the optimal approach to choose securities for an investor’s portfolio.
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Jayeola, Dare, Zulhaimy Ismail, and Suliadi Firdaus Sufahani. "Effects of diversification of assets in optimizing risk of portfolio." Malaysian Journal of Fundamental and Applied Sciences 13, no. 4 (2017): 584–87. http://dx.doi.org/10.11113/mjfas.v0n0.567.
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Diversification is a strategic option that investors use to optimize their portfolio. Diversification is investing in many assets for the purpose of minimizing risk or maximizing return of portfolio. It is an opportunity by which investors improve from his micro-firm into macro-firm. The investors’ aim is to make an optimal choice that leads to minimization of risk and maximization of return, but the platform that achieves these objectives is not at the finger tips. The purpose of this study is to propose procedures for constructing optimal portfolio for rational investors. Also, the study demonstrates the benefits of diversification of each asset in portfolio. The assets allocations divulge by Black Litterman model are used to estimate risk of both portfolios and assets. We explore DataStream (Yahoo finance) of Gold, Oil, Silver and Platinum. It is observed that diversifying in Gold minimizes higher risk and achieve more benefits than other assets in the portfolio, which made portfolio1 to be optimal portfolio. In view of these facts, it means diversifying in gold acts as hedge/safe haven for investors during economic recession.
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Elly, Susanti. "Decision to Invest Using Markowitz Model on LQ 45 Index Companies for the Period 2015 – 2019." International Journal of Business Management and Technology 4, no. 6 (2023): 145–59. https://doi.org/10.5281/zenodo.7669072.
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The purpose of this study was to find viable shares in the optimal portfolio as well as the proportion of funds from each of these stocks formed with the Markowitz Model. This research method uses literature research design. Data collection techniques are documentation. While the analysis of research data is started with the processing and preparation of data until interpreting the meaning of data. The population in this study was all companies listed in the LQ Index 45 as of December 31, 2019. While the sample is Companies that never exited the LQ 45 Index during the period 2015-2019. The results of this study showed that the shares of LQ Index 45 companies in the period 2015 – 2019 which formed an optimal portfolio based on the Markowitz model of 150 stock portfolios. From the overall weighting obtained the results of a portfolio of shares 40% ADRO & 60% BBCA, 50% ADRO & 50% BBCA and 60% ADRO & 40% BBCA are optimal portfolios for aggressive investor profiles, furthermore 40% BBCA stock portfolio & 60% UNVR, 50% AKRA & 50% BBCA, 60% BBCA & 40% GGRM are optimal portfolios for conservative investor profiles. While the stock portfolio of 40% BBCA & 60% BBTN, 50% BBCA & 50% BBTN and 60% BBCA & 40% BBTN is the optimal portfolio for the profile of moderate investors
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Abdul Gafur. "PEMBENTUKAN PORTOFOLIO OPTIMAL INVESTASI MENGGUNAKAN MODEL MARKOWITZ DAN MODEL INDEKS TUNGGAL PADA ASET BEBAS RISIKO DAN ASET BERISIKO." Journal of Management and Innovation Entrepreneurship (JMIE) 1, no. 2 (2024): 228–45. http://dx.doi.org/10.59407/jmie.v1i2.338.
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Optimal Portfolio is one way that can be used to determine stock portfolios that generate large returns with the smallest risk. The purpose of this study is to determine the optimal portfolio of risk-free assets and risk assets using the Markowitz Model, Single Index Model and portfolio performance by comparing the resulting rate of return and risk. The research sample used was LQ 45 shares listed on the Indonesia Stock Exchange from August 2014 to July 2019. The sampling technique used was purposive sampling technique, namely the selection of data based on certain criteria in order to obtain a sample of 29 listed companies. The method used is to use the Markowitz Model, the Single Index Model and portfolio performance. From the optimal portfolio formation based on the Method, there are 9 shares included in risk free assets and 20 shares included in risk assets. The results of the analysis show that by using the Single Index Model the return from the optimal portfolio produced is higher than using the Markowitz Model, as well as the risk generated on the Single Index Model is smaller than using the Markowitz Model both on risk-free assets and risk assets, this is assured with the results obtained from portfolio performance.
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Prasetyo, Irvan Fendy, and Anak Agung Gede Suarjaya. "PEMBENTUKAN PORTOFOLIO OPTIMAL DENGAN MENGGUNAKAN MODEL INDEKS TUNGGAL." E-Jurnal Manajemen Universitas Udayana 9, no. 2 (2020): 553. http://dx.doi.org/10.24843/ejmunud.2020.v09.i02.p08.
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The purpose of this study is to determine the stocks of the Kompas 100 Index that can form optimal portfolios and to find out the proportions of each selected stock and the level of return and risk of the resulting portfolio. Single Index Model with descriptive analysis was used. The data was obtained from the IDX, Yahoo Finance, and BI. The population in this study amounted to 77 shares. The number of samples taken was 65 company shares from the Kompas 100 Index, using the Slovin method. Based on the results of the analysis obtained from 65 shares of Kompas 100 members obtained a combination of 20 shares that can form an optimal portfolio of BUMI, MAPI, INCO, DOID, INDY, CPIN, BKSL, ACES, MEDC, ITM, UNTR, TINS, BDMN, JPFA, BBCA, BJBR, PNBN, TARA, PBRX and ANTM with portfolio expected return of 3.20 percent with a risk of 0.11 percent.
 Keywords: Compass 100 Index, Single Index Model, Optimal Portfolio
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Ta, Bao Quoc, and Thao Vuong. "The Black-Litterman Model for Portfolio Optimization on Vietnam Stock Market." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, Supp01 (2020): 99–111. http://dx.doi.org/10.1142/s0218488520400097.
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The Black-Litterman asset allocation model is an extended portfolio management model to construct optimal portfolios by combining the market equilibrium with investor views into asset allocation decisions. In this paper we apply Black-Litterman model for portfolio optimization on Vietnames stock market. We chose ARIMA methodology utilized in financial econonometrics to predict the views of investor which are used as inputs of the Black-Litterman asset allocation process to find optimal portfolio and weights.
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Saputra, Ramadhan Dwi, and Irham Alifiandipura. "Rancangan Strategi Portofolio Optimal PT. ABC dengan Metode Single Index Model." JKBM (JURNAL KONSEP BISNIS DAN MANAJEMEN) 8, no. 1 (2021): 58–69. http://dx.doi.org/10.31289/jkbm.v8i1.5627.
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As social insurance company of the Republic of Indonesia, PT ABC (Persero) has a captive market based on the provisions of Undang-undang in Indonesia. The company has managed funds from the government, and is one of the four insurance products in the company, into an investment portfolio. As one of the company’s revenue generator, PT ABC needs to put the fund into investment instruments that have higher returns to meet the needs of the company, one of which is through stock investment. The formation of stock portfolio is carried out through an optimum portfolio approach by using single index model method. This is a quantitative descriptive research using analysis tools and data processing by Microsoft Excel software. Portfolios are formed into several scenarios by considering the composition of the current portfolio in one of the company’s products and stock price movements in Indonesia. The data used in this study are historical data on daily stock movements for the five years of the 2014-2018 trading period and historical data on the investment portfolio for XYZ products in 2018. From this research, 2 strategic plans for forming company portfolios and 1 recommendation of stocks are produced that have good resilience during a pandemic. The results of the calculations are expected to be taken into consideration by the company in the formation of future company portfolios
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Anwar, Indah Lestari, Kasman Damang, and Erlina Pakki. "Comparison Analysis of Optimal Portfolio Formation on Jakarta Islamic Index 70 (JII70) (Markowitz Model and Single Index Model Approach)." Advances in Social Sciences Research Journal 9, no. 5 (2022): 224–41. http://dx.doi.org/10.14738/assrj.95.12379.
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This study analyzes the optimal portfolio formation of Islamic stocks on Jakarta Islamic Index 70 (JII70) with the Markowitz and Single Index models. The analysis then compares the proportion of funds, return, and portfolio risk. The subsequent analysis compares the two models' optimal and non-optimal returns and risks. This study uses data on stock prices, dividends, BI-7 Day Reverse Repo Rate, and Composite Stock Price Index for May 2018-September 2021. The research sample is 37 JII70 stock issuers obtained by the purposive sampling technique. The Markowitz model produces 12 combinations, a certain expected return of 0.66% and the best portfolio risk of 3.22%. In comparison, the Single Index Model produces nine stock combinations, the best-expected return of 2.28%, and a certain portfolio risk of 7.53%. Analysis with the Markowitz Model shows no significant difference between stock returns included in the optimal and non-optimal portfolio. However, there is a significant difference between stock risk. In addition, in the Single Index Model, it was found that there was a significant difference between stock returns, including optimal and non-optimal portfolios. However, there was no significant difference between stock risk. The study results can be an essential reference for JII70 investors and stakeholders before and during the Covid-19 pandemic in Indonesia.
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Nugroho, Sulistyo Adi, Tony Irawan SE MappEc, and Ir Aruddy, Msi. "Portfolio Analysis Using the Single Index Method in the COVID-19 Pandemic Period." International Journal of Research and Review 8, no. 6 (2021): 215–25. http://dx.doi.org/10.52403/ijrr.20210626.
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The COVID-19 outbreak that occurred in early 2020 put pressure on economic activity in many countries, including Indonesia. The pressure on economic activity can be seen from the index movement in the capital market. The JCI as a composite index that reflects transaction activity in the Indonesian capital market has weakened due to the impact of the COVID-19 outbreak in a number of business sectors. The decline in the index is a warning for investors to rearrange the composition of assets in their portfolios so that returns can remain optimal during a pandemic. The single index model (SIM) can be used by investors to make investment decisions, including to rearrange their investment portfolios. The share price data analyzed covers the period from 2 September 2019 to 7 December 2020, where the government confirmed the first positive case of COVID-19 in Indonesia on 3 March 2020. The Single Index Model is used to select assets to form an optimal portfolio. Portfolio performance is measured using the Sharpe, Treynor and Jensen index. The sector rotation strategy results in five selected sectors whose assets will be selected to form an optimal portfolio, namely the consumption sector (JKCONS), the basic and chemical industry sector (JKBIND), the infrastructure sector (JKINFA), the mining sector (JKMING) and the financial sector (JKFINA). The listed companies for analysis were 25 out of 184 issuers in the five sectors. The Single Index Model selects 3 issuers for the pre-COVID period and 10 issuers for the COVID period. The allocation of portfolio funds for the pre-COVID period showed BTPS of 44.94%; CPIN 47.61% and BYAN 7.46%. 2.8% allocation of portfolio funds during the COVID period to BTPS issuers; PBID 22.57%; TKIM 15.96%; BYAN 5.86%; ITMG 17.89%; MYOH 1.56%; PTBA 1.76%; ADRO 12.54% and PPRE 19.05%. The portfolio's expected return is positive, which means that the portfolio formed has the potential to generate profits. The Sharpe, Treynor and Jensen indexes are positive, which means that portfolios formed using a single index model have the potential to have good performance. Keywords: investors, IHSG, portfolio performance, single index model, optimal portfolio.
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Gopalakrishnan, M. Muthu. "Optimal Portfolio Selection Using Sharpe’s Single Index Model." Indian Journal of Applied Research 4, no. 1 (2011): 286–88. http://dx.doi.org/10.15373/2249555x/jan2014/83.
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Zheng, Jiaqi. "Markowitz Model and Index Model: A Comparative Study of Constructing Optimal Portfolios." Advances in Economics, Management and Political Sciences 99, no. 1 (2024): 23–32. http://dx.doi.org/10.54254/2754-1169/99/2024ox0198.
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In the field of investment, how to strike a balance between high returns and low risks has always been a challenge for investors. With the rise of modern portfolio theory (MPT) and index models, investors have more options for constructing optimal portfolios. This paper takes the US stock market as the research object, selects the S&P 500 index and six stocks representing different industries, uses the Markowitz model and the index model to optimize, and analyzes the optimal portfolio allocation, return, risk and Sharpe ratio of the two models under different constraints. It is found that the Markowitz model is more advantageous in risk diversification, while the index model relies more on the allocation of a single stock, especially the S&P 500 index. Both models perform similarly in terms of risk-adjusted returns, but the Markowitz model is slightly superior in terms of Sharpe ratio. In addition, there are differences in the portfolio allocation and risk-return characteristics of the two models under different constraints. The results of this study can help investors better understand the advantages and disadvantages of the two portfolio optimization models, and choose the appropriate model according to their own risk preferences and market environment to construct the optimal portfolio and achieve their investment objectives.
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Liu, Shirui. "Optimal Portfolio under Five Constraints in the Markowitz Model and the Index Model." BCP Business & Management 26 (September 19, 2022): 995–1006. http://dx.doi.org/10.54691/bcpbm.v26i.2062.
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Investing in stocks is an inseparable part of modern life. Besides, choosing a good investment portfolio with high return and respectively low risk is the demand and desire of most modern investors. This paper tries to obtain an optimal investment portfolio to provide accurate and professional investment suggestions to the potential investors through the Markowitz Model and the Index Model under five different constraints. It has been considered several aspects to analyse the results: minimum variance portfolio, maximal Sharpe Ratio, etc. Some findings are given, including that the options of investment portfolio available under no constraint are larger compared to portfolios without permission of short-selling and investing SPX. Besides, the influence of the former is more significant than that of the latter; and then, the corresponding impact of different constraints ---is discussed through efficient frontiers. Additionally, comparing the Sharpe Ratio under two different models, it can be found that the Markowitz Model is a better option.
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Aulina, Rahma, Khusnul Novianingsih, and Fitriani Agustina. "Optimisasi Portofolio Saham Syariah dengan Pendekatan Fuzzy Goal Programming." Interval : Jurnal Ilmiah Matematika 3, no. 2 (2024): 81–91. http://dx.doi.org/10.33751/interval.v3i2.7746.
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This study discusses about solving the problem of stock portfolio optimization. The portfolio optimization problem can be modeled as a multiobjective model with two objective functions, they are maximizing return and minimizing risk. This study uses the mean-variance Markowitz model to model the portfolio. The fuzzy goal programming approach is used to solve stock portfolio problems by converting a multi-objective model into a fuzzy mathematical programming model which is solved using a nonlinear programming method. The results of implementing the model on stocks listed on the Jakarta Islamic Index show that the best investment proportion forms an optimal portfolio according to the level of aspirations. Several different optimal portfolios can be formed using the fuzzy goal programming approach. The difference in the results of these portfolios depends on the level of aspiration of investors.
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Wulandari, Diah, Dwi Ispriyanti, and Abdul Hoyyi. "OPTIMALISASI PORTOFOLIO SAHAM MENGGUNAKAN METODE MEAN ABSOLUTE DEVIATION DAN SINGLE INDEX MODEL PADA SAHAM INDEKS LQ-45." Jurnal Gaussian 7, no. 2 (2018): 119–31. http://dx.doi.org/10.14710/j.gauss.v7i2.26643.
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Stock investment is the planting of money in a securities that indicates the ownership of a company in order to provide benefits in the future. In obtaining optimal results from stock investments, investors are expected to create a series of portfolios. The portfolio will help investors in allocating some funds in different types of investments in order to achieve optimal profitability. For selection of optimal stocks representing LQ-45 Index, used 2 methods of Mean Absolute Deviation (MAD) method and Single Index Model (SIM) method. In MAD method, 5 best stocks are BBCA with weight 23%, INDF 8%, KLBF 23%, TLKM 23%, and UNVR 23%. While the SIM method of candidate portfolio obtained is AKRA with weight 15,459%, BBCA 48,193%, BBNI 5,028%,KLBF 0,258% and TLKM 31,062%. Portfolio performance meter is used by sharpe ratio. The value of sharpe ratio is 0,36754 for optimal portfolio using MAD method and 0,40782 for optimal portfolio using SIM method, this means that optimal portfolio using SIM method has better performance than MAD. Keywords: Investment, Portfolio, Index LQ-45, Mean Absolute Deviation, Single Index Model, Sharpe Ratio
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Santosa, Santosa, Noer Azam Achsani, and Hendro Sasongko. "GUARANTEE PRODUCT PORTFOLIO: PERFORMANCE AND OPTIMAL PORTFOLIO ANALYSIS." JIMFE (Jurnal Ilmiah Manajemen Fakultas Ekonomi) 6, no. 1 (2020): 43–58. http://dx.doi.org/10.34203/jimfe.v6i1.1928.
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This study aims to analyze the performance of guarantee products and optimize guarantee portfolio at PT Penjaminan ABC. The method used in forming the optimal guarantee portfolio is the Markowitz method and the single index model. The results of the formation of optimal portfolios based on the Markowitz method show that there are five eligible guarantee products included in the optimal guarantee portfolio, namely construction financing, counter bank, general financing, micro financing, and multi-use financing. While custom bond, surety bonds, and other guarantees are not included in the optimal portfolio. In contrast to the Markowitz method, based on the single index model, all guarantee products are not eligible to be included in the optimal guarantee portfolio. Managerial implications of the optimal guarantee product portfolio is an increase in guarantee returns which will further increase company profits and increase company equity. An increase in company equity will reduce the gearing ratio in order to comply with regulations, because the gearing ratio is calculated by dividing the outstanding guarantee volume by the total equity.
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Zhu, Weixuan. "Research on Optimal Portfolio Based on the Markowitz Model." Advances in Economics, Management and Political Sciences 77, no. 1 (2024): 33–39. http://dx.doi.org/10.54254/2754-1169/77/20241786.
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This paper studies the Markowitz investment theory model. The study examined a portfolio of three companies - the Coca-Cola Company, McDonalds Corporation, and Apple Inc. This paper calculates the expected returns and the standard deviations of the Coca-Cola Company, McDonalds Corporation, and Apple Inc., respectively. In this paper, the expected return is used to measure the value of securities, and the standard deviation is used to measure the risk of securities, studying the development of three companies stocks. At the same time, the relationship between the Coca-Cola Company, McDonalds Corporation, and Apple Inc. is discussed using covariance and correlation coefficient. Next, using the Markowitz investment theory model, one can draw the effective frontier of the investment portfolio and prove that all of the risk-return portfolios on the efficient frontier are the portfolios that can get the highest return with the fixed risk. Then, combining the efficient frontier and indifference curve, simulate a rational investor with a special risk appetite and a special expected return, verify the tangential point of the indifference curve, and this tangential point is the optimal proportional portfolio for this specific rational investor of these securities.
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Uchiyama, Yusuke, and Kei Nakagawa. "TPLVM: Portfolio Construction by Student’s t-Process Latent Variable Model." Mathematics 8, no. 3 (2020): 449. http://dx.doi.org/10.3390/math8030449.
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Optimal asset allocation is a key topic in modern finance theory. To realize the optimal asset allocation on investor’s risk aversion, various portfolio construction methods have been proposed. Recently, the applications of machine learning are rapidly growing in the area of finance. In this article, we propose the Student’s t-process latent variable model (TPLVM) to describe non-Gaussian fluctuations of financial timeseries by lower dimensional latent variables. Subsequently, we apply the TPLVM to portfolio construction as an alternative of existing nonlinear factor models. To test the performance of the proposed method, we construct minimum-variance portfolios of global stock market indices based on the TPLVM or Gaussian process latent variable model. By comparing these portfolios, we confirm the proposed portfolio outperforms that of the existing Gaussian process latent variable model.
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Zhang, Xiao. "A Portfolio Study Based on the Markowitz Model - An Example of the Bitcoin Market." Highlights in Business, Economics and Management 45 (December 28, 2024): 857–66. https://doi.org/10.54097/gc71m990.
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Nowadays, financial markets are becoming more and more complex, and new portfolios need to be built to cope with them. This paper aims to build a Markowitz model for portfolio research based on new calibrations for nine different industries. Firstly, the weights and minimum variance combinations are calculated by using valid information such as mean, standard deviation, variance, and covariance. Second, this paper aims to maximize the return of the portfolio, diversify the investment risk of the selected portfolio, and finally determine the optimal portfolio. The portfolio can be adjusted to reduce risk or increase return by adjusting the percentage of Bitcoin. This paper further explores the portfolio using Bitcoin as a variable. This paper derives the volatility and return of the least risky portfolio to be 11.04% and -0.46%, respectively, when the portfolio is calibrated without Bitcoin, and the volatility and return of its Sharpe optimal portfolio are 14.61% and 7.11%, respectively. When the portfolio contains Bitcoin, the volatility and return of its risk-minimal portfolio are 9.45% and 0.6%, respectively, and the volatility and return of its Sharpe-optimal portfolio are 16.31% and 37.35%, respectively. Ultimately, it is concluded that Bitcoin has some risk-reducing and return-enhancing effects.
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Meng, Yue. "Portfolio Selection Based on the Application of CAPM and FF3F Model." BCP Business & Management 35 (December 31, 2022): 694–700. http://dx.doi.org/10.54691/bcpbm.v35i.3372.
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Portfolio optimization is the selection of the optimal portfolio from all the portfolios considered. This paper uses diversified data, including technology, medicine, real estate and so on, to make the data more referential. In the process, five stocks with better performance in the corresponding fields were selected. In this paper, the CAPM and FF3F model are used to select the optimal portfolio. This paper also uses Sharpe ratio and weight to measure whether the portfolio can achieve the optimal. The results show that except for ‘VLO’, the covariance of other assets is below 0.01, which can perform better in the minimization of variance. And ‘MDT’ has the highest weight in the CAPM model, followed by ‘JLL’, which can maximize the Sharpe ratio. But in the FF3F model, ‘JLL’ has the highest weight and ‘WMT’ has zero weight to maximize the Sharpe ratio. The results of this paper will enable investors in related industries to get a better portfolio paradigm.
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Anugrahayu, Mella, and Ulil Azmi. "Stock Portfolio Optimization Using Mean-Variance and Mean Absolute Deviation Model Based On K-Medoids Clustering by Dynamic Time Warping." Jurnal Matematika, Statistika dan Komputasi 20, no. 1 (2023): 164–83. http://dx.doi.org/10.20956/j.v20i1.27755.
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The tendency of investors to choose investments with maximum return and minimal risk causes the need for diversification in a portfolio to form an optimal portfolio. A lot of research on stock portfolio optimization has been conducted extensively, but not many have tried to apply machine learning concepts such as clustering analysis to accelerate the establishment of a model that can have a positive effect on the time and cost efficiency of portfolio management. However, clustering is only limited to determining the optimal stock candidate, so it is necessary to add another optimization model to calculate the portfolio weight. Based on these problems, this study carried out portfolio optimization using Mean-Variance (MV) and Mean Absolute Deviation (MAD) model based on K-Medoids Clustering by Dynamic Time Warping approach using Monte Carlo-Expected Tail Loss for risk analysis. Based on the analysis results, the MAD portfolio is more optimal than the MV portfolio by the MAD portfolio consists of five stocks, namely BMRI shares with a weight of 0.06243, UNTR shares of 0.08658, BBRI shares of 0.10285, BBCA of 0.53623, and KLBF shares of 0.21191 are the best optimal portfolios. The optimal portfolio of the MAD model has a rate of return of 87.836% in May 2017 - December 2022 with a portfolio performance of 0.03704, while the resulting risk level based on Carlo-Expected Tail Loss is 2.2416%.
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Rahmawati, Septi, Dwi Susanti, and Riaman Riaman. "Determination of Optimal Stock Portfolio Return by Single Index Model (Case Study on Banking Sector Stocks in Indonesia)." International Journal of Business, Economics, and Social Development 5, no. 1 (2024): 72–77. http://dx.doi.org/10.46336/ijbesd.v5i1.585.
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The optimal portfolio is a portfolio chosen by investors from the many options available in the collection of efficient portfolios. To get the optimal proportion, which is the maximum return and minimum risk, it is necessary to analyze the stocks to be selected in the investment model. The research objective is to determine the optimal return, risk, and proportion for each banking stock portfolio in Indonesia in the period February - July 2023. The method used is the Single Index Model. The process of determining the optimal proportion of stocks with the Single Index Model requires stock and market return data as the main basis for applying this method. This study involves the formation of an optimal portfolio of daily closing prices of 46 banking stocks. As a result of this research, there are 5 optimal stocks that meet the criteria for optimal portfolio formation with each fund proportion of 21.43% (BNII), 13.52% (BDMN), 35.02% (BBRI), 23.69% (BTPN), and 6.34% (BBCA). Expected return from optimal stocks is 0.152% and the risk that will be borne by investors is 0.0011% per day.
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Faqihatun, Fihha, Euis Bandawaty, Sunaryo Sunaryo, and Gunardi Gunardi. "Investment Efficiency in Indonesia's Construction Sub-Sector: An Optimal Portfolio Approach Using the Markowitz Model." Jurnal Ilmu Keuangan dan Perbankan (JIKA) 14, no. 1 (2025): 177–90. https://doi.org/10.34010/jika.v14i1.15149.
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Investment is an activity aimed at generating future profits but is inherently accompanied by uncertainty risks. To minimize such risks, investors need to construct an optimal portfolio. This study uses the Markowitz Model approach to analyze the allocation of returns and risks in forming an optimal portfolio of construction sub-sector stocks listed on the Indonesia Stock Exchange (IDX) from January to December 2021 as well as identifies the stocks selected as part of the optimal portfolio. The research employs a descriptive quantitative approach, with a population of 29 stocks and a sample of 18 stocks meeting the selection criteria. The results reveal that applying the Markowitz Model results in an optimal portfolio with a risk level of 0.47% and an expected return of 4.12%. The four stocks selected for the optimal portfolio include DGIK (44.4%), IDPR (2.2%), PPRE (30.9%), and RONY (18%). This study contributes new insights by highlighting investment efficiency in the construction sub-sector in Indonesia, which plays a vital role in national development. Moreover, it compares various portfolio scenarios to identify the best efficiency point, a method rarely applied in the context of the construction sector within the Indonesian market. This research is expected to serve as a reference for investors and scholars in understanding the formation of optimal portfolios and to encourage further. Keywords: Investment Efficiency; Optimal Portfolio; Markowitz Model; Return and Risk; Construction Sub-Sector
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Hartono, Nuralfira Putri, Onoy Rohaeni, and Eti Kurniati. "Menentukan Portofolio Optimal Menggunakan Model Markowitz." Jurnal Riset Matematika 1, no. 1 (2021): 57–64. http://dx.doi.org/10.29313/jrm.v1i1.162.
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The provider company on the covid-19 pandemic became an interest in investors to invest. Investing certainly has a risk then investors must have an analysis to know what to bear during investing is like making a portfolio. In determining the optimal portfolio there are several models that one of them can use is the Markowitz model. Specifies an optimal portfolio with Markowitz models only reserved for investors who want the smallest risk outcome with a particular profit. The results earned for the investor's optimal portfolio could instill its funds on each provider's shares, on W shares with a fund proportion of 0.48%, on X shares with a fund proportion of 50%, on Y shares with a fund proportion of 49.5% and on Z shares with a fund proportion of 0.11%. The optimal portfolio formed gives a portfolio return expectation of 7.53% with a portfolio risk or risk that investors will bear is as much as 9.95%.
 Perusahaan provider pada pandemi covid-19 menjadi ketertarikan para investor untuk berinvestasi. Berinvestasi tentunya memiliki risiko maka investor harus memiliki analisis untuk mengetahui apa yang akan ditanggung selama berinvestasi seperti membuat suatu portfolio. Dalam menentukan portfolio optimal ada beberapa model yang dapat digunakan salah satunya adalah model Markowitz. Menentukan portfolio optimal dengan model Markowitz hanya diperuntukan untuk investor yang menginginkan hasil risiko terkecil dengan keuntungan tertentu. Hasil yang diperoleh untuk portfolio optimal investor dapat menanamkan dananya pada masing-masing saham provider, pada saham W dengan proporsi dana sebesar 0,48%, pada saham X dengan proporsi dana sebesar 50%, pada saham Y dengan proporsi dana sebesar 49,5% dan pada saham Z dengan proporsi dana sebesar 0,11%. Portofolio optimal yang terbentuk memberikan return ekspektasi portfolio sebesar 7,53% dengan risiko portfolio atau risiko yang akan ditanggung oleh investor adalah sebesar 9,95%.
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Yasmin, Arla Aglia, Riaman Riaman, and Sukono Sukono. "Investment Portfolio Optimization In Infrastructure Stocks Using The Mean-VaR Risk Tolerance Model." International Journal of Quantitative Research and Modeling 5, no. 1 (2024): 74–82. http://dx.doi.org/10.46336/ijqrm.v5i1.602.
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Infrastructure a crucial role in economic development and the achievement of Sustainable Development Goals (SDGs), with investment being a key activity supporting this. Investment involves the allocation of assets with the expectation of gaining profit with minimal risk, making the selection of optimal investment portfolios crucial for investors. Therefore, the aim of this research is to identify the optimal portfolio in infrastructure stocks using the Mean-VaR model. Through portfolio analysis, this study addresses two main issues: determining the optimal allocation for each infrastructure stock and formulating an optimal stock investment portfolio while minimizing risk and maximizing return. The methodology employed in this research is the Mean-VaR approach, which combines the advantages of Value at Risk (VaR) in risk measurement with consideration of return expectations. The findings indicate that eight infrastructure stocks meet the criteria for forming an optimal portfolio. The proportion of each stock in the optimal portfolio is as follows: ISAT (2.74%), TLKM (33.894%), JSMR (3.343%), BALI (0.102%), IPCC (5.044%), KEEN (14.792%), PTPW (25.863%), and AKRA (14.219%). The results of this study can serve as a foundation for better investment decision-making.
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Rong, Runsheng, and Fu Haifeng. "CAPM Model and Optimal Risky Portfolio for American Stock Market." Journal of Investment, Banking and Finance 2, no. 1 (2024): 01–09. http://dx.doi.org/10.33140/jibf.02.01.12.
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The stock market has high risks. The purpose of this project is to calculate the beta coefficients and build the optimal risky portfolio consisting of eight different stocks each representing different significant industries (which includes information technology, electric cars etc.) to diversify risk and gain a high return. Putting more stocks into the portfolio can help analysts carry out comprehensive analysis on different situations, periods, and types of investment portfolio, so as to disperse risks and obtain high returns, also, ensure the diversity of portfolio and a lower risk. The empirical results in this paper shows that by allocating their money appropriately in different stocks, investors can gain returns multiple times higher than putting all of them in merely one single stock, which proves the validity of this paper
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Yusup, Adi Kurniawan. "Mean-Variance and Single-Index Model Portfolio Optimisation:Case in the Indonesian Stock Market." Asian Journal of Business and Accounting 15, no. 2 (2022): 79–109. http://dx.doi.org/10.22452/ajba.vol15no2.3.
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Manuscript type: Research paper Research aims: This study aims to compare the performance of meanvariance and single-index models in creating the optimal portfolio. Design/Methodology/Approach: This study creates optimal portfolios using the mean-variance and single-index models with daily stock return data of 38 companies listed on the LQ45 index, IDX Composite index and Bank Indonesia’s 7-Day (Reverse) Repo Rate from January 1, 2012 to December 31, 2019. The two models are compared using the Sharpe ratio. Research findings: The result shows that the single-index model dominates the Indonesian Stock Exchange (IDX), more so than the meanvariance model. BBCA has the highest proportion for both mean-variance and single-index portfolios. Theoretical contribution/Originality: This study compares two popular portfolio models in the Indonesian stock market. Practitioner/Policy implication: This study helps investors to create optimal portfolios using a model that is more suited to the IDX. Research limitation/Implication: This study creates the optimal portfolio without differentiating risk preferences (i.e., risk averse, risk moderate and risk taker). In addition, this research only uses daily return data and does not compare it with weekly and monthly data.
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Pandey, Manas. "Application of Markowitz model in analysing risk and return a case study of BSE stock." Risk Governance and Control: Financial Markets and Institutions 2, no. 1 (2012): 7–15. http://dx.doi.org/10.22495/rgcv2i1art1.
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In this paper the optimal portfolio formation using real life data subject to two different constraint sets is attempted. It is a theoretical framework for the analysis of risk return choices. Decisions are based on the concept of efficient portfolios. Markowitz portfolio analysis gives as output an efficient frontier on which each portfolio is the highest return earning portfolio for a specified level of risk. The investors can reduce their risks and can maximize their return from the investment, The Markowitz portfolio selections were obtained by solving the portfolio optimization problems to get maximum total returns, constrained by minimum allowable risk level. Investors can get lot of information knowledge about how to invest when to invest and why to invest in the particular portfolio. It basically calculates the standard deviation and returns for each of the feasible portfolios and identifies the efficient frontier, the boundary of the feasible portfolios of increasing returns.
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Xiao, Yao. "Optimization Model of Financial Market Portfolio Using Artificial Fish Swarm Model and Uniform Distribution." Computational Intelligence and Neuroscience 2022 (June 15, 2022): 1–9. http://dx.doi.org/10.1155/2022/7483454.
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The central issue in finance is how to select a portfolio in the financial market. The traditional artificial fish swarm algorithm (AFSA) is optimized in this paper, and the improved AFSA is used to solve the portfolio model. This model generates a uniform distribution operator using uniform distribution and combines it with the basic fish swarm algorithm. Uniform variation occurs when the variance of the optimal value of continuous convergence is within the allowable error. In this manner, the fish can escape the trap of the local extremum, obtaining the global optimal state. To validate the feasibility of improving AFSA, this paper conducts simulation experiments on portfolio problems using MATLAB tools. Experiments show that this model has an accuracy of 93.56 percent, which is 8.43 percent higher than that of the NSGA-II model and 3.76 percent higher than that of the multiobjective optimization model. The experiment shows that the algorithm in this paper can solve these types of problems well and that, using this model, the optimal portfolio investment decision scheme satisfying investors can be obtained. The optimized AFSA presented in this paper can serve as an important reference for investment portfolios and has a wide range of application possibilities in the investment market.
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Jayeola, Dare, and Peter O. Olatunji. "Optimizing Portfolio Risk through Diversification: Application of The Black-Litterman Model." Journal of Economics, Management and Trade 31, no. 4 (2025): 13–19. https://doi.org/10.9734/jemt/2025/v31i41280.
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Aim: The study investigates how the risk reduction strength of different assets and their impact on minimizing portfolio risk. It seeks to recommend an optimal investment strategy using the Black-Litterman model to balance risk and return, helping investors make informed decisions to enhance portfolio stability and financial resilience. Study Design: We adopt a quantitative approach, by employing the Black-Litterman model to analyze portfolio risk reduction. Monthly financial data from 2018 to 2022 is used to evaluate the impact of asset allocation on risk minimization, focusing on assessing various asset combinations to determine the most effective diversification strategy. Place and Duration of Study: The study took place at the Department of Mathematical Sciences, Adekunle Ajasin University, Akungba Akoko, Nigeria, where we explored data from Yahoo finance of Gold, Oil and Gas which span from 2018 to 2022. Methodology: Data from Yahoo Finance (2018-2022) covering Gold, Oil, and Natural Gas was analyzed. The Black-Litterman model was used to compute portfolio risk. The Augmented Dickey Fuller test verified stationary conditions of time series data before the model implementation. Mean-variance optimization techniques determined asset allocation. Various portfolios were compared to identify those with the lowest risk levels. Results: Gold exhibited the highest risk reduction strength (8.7%), followed by oil (8.37%) and natural gas (0.47%). Portfolios containing gold had significantly lower risk levels. The benchmark portfolio had 0.0038 risk, while portfolios excluding gold had higher risks, confirming gold’s effectiveness in minimizing overall portfolio risk. Conclusion: The study confirms that diversification alone does not guarantee risk minimization unless optimal asset selection is applied. Portfolios with high-risk reduction assets like gold significantly lower overall risk. Investors should prioritize assets with strong risk reduction capabilities to enhance portfolio stability, particularly during economic downturns or financial crises.
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Zhang, Peng, and Hui Li Wang. "The Optimization on the Expected Utility Portfolio Selection Model without Short Sales." Advanced Materials Research 225-226 (April 2011): 1071–74. http://dx.doi.org/10.4028/www.scientific.net/amr.225-226.1071.
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A new expected utility (EU) portfolio selection model without short sales is proposed. In the model, the expected utility function is quadratic. The model is solved by the pivoting algorithm. The paper showed in the EU portfolio selection model without the short sales, the relationship between the risk preference coefficient and the expected return is not linear but more complex. The risk preference coefficient could just reflect the investors’ preference in some intervals. We wrote program to calculate the optimal portfolios with the different coefficient. Investors could choose the optimal investment strategy according to both their own risk preference and the expected return of the portfolio.
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Aminah, Siti. "Markowitz Model for Forming an Optimum Stocks Portfolio in The January Effect." International Student Conference on Business, Education, Economics, Accounting, and Management (ISC-BEAM) 3, no. 1 (2025): 61–74. https://doi.org/10.21009/isc-beam.013.05.
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This research aims to analyze the formation of an optimal portfolio using the Markowitz model for stocks listed in the LQ45 Index during the period from December 2022 to Jan 2024. The population of this research includes all 45 stocks in the LQ45 over this timeframe, with a sample of 5 stocks selected through purposive sampling and January Effect criteria. Data collection was carried out through documentation, and the analysis followed the steps of the Markowitz model, starting from gathering closing stock prices to determining the optimal portfolio. The findings reveal that four stocks are part of the optimal portfolio: BBTN 32.4%, BMRI 22.7%, ICBP 39.4%, and MEDC 5.5%. The portfolio’s expected return is 4.8 percent, with a portfolio risk of 3.6 percent, which is lower than the individual risk of any of the stocks in the sample
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Salam, Abd Muhni, and Augustina Kurniasih. "Optimal Portfolio of Liquid 45 Stocks: Single Index Model Approach." International Journal of Science and Society 3, no. 3 (2021): 69–84. http://dx.doi.org/10.54783/ijsoc.v3i3.354.
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The purpose of this study is to analyze the return, risk, and optimal portfolio performance of LQ45 stocks formed by a single index model in the period August 2017-January 2020. This research is a descriptive study with a quantitative approach. The data collection technique used is documentation study. Based on the results of the calculation, it is found that out of 33 stocks that met the sample criteria, 3 stocks were selected to compile the optimal portfolio, namely BRPT, ICBP, and BBCA stocks. The stock had expected returns of 5.50%, 1.34%, and 2.02%, respectively, whit a risk of 12.87%, 4.75%, and 4.08%, respectively. The optimal portfolio formed has expected return of 2.60% and risk of 4.05%. After measuring performance with the Sharpe, Treynor, & Jensen approach, it is found that the performance of the portfolios that is formed is better than market performance.
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Gusliana, Shindi Adha, and Yasir Salih. "MEAN-VARIANCE INVESTMENT PORTFOLIO OPTIMIZATION MODEL WITHOUT RISK-FREE ASSETS IN JII70 SHARE." International Journal of Business, Economics, and Social Development 3, no. 4 (2022): 168–73. http://dx.doi.org/10.46336/ijbesd.v3i4.352.
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In investing, investors will try to limit all the risks in managing their investments. Investor strategies to minimize investment risk are diversification by forming investment portfolios, one of which is the Mean-Variance without risk-free assets. The calculation results will show the composition of the optimum portfolio return for each stock that forms the portfolio. Optimum portfolio obtained with wT = (0.39853, 0.25519, 0.13644, 0.09788, 0.11196) sequential weight composition for TLKM, KLBF, INCO, HRUM, and FILM stocks. The composition of this optimal portfolio return is ???? 0.04 with a return of 0.00209 and a portfolio variance of 0.00015. The formation of this portfolio optimization model is expected to be additional literature in optimizing the investment portfolio with the Mean-Variance.
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Gubu, La, Dedi Rosadi, and Abdurakhman Abdurakhman. "Pembentukan Portofolio Saham Menggunakan Klastering Time Series K-Medoid dengan Ukuran Jarak Dynamic Time Warping." Jurnal Aplikasi Statistika & Komputasi Statistik 13, no. 2 (2021): 35–46. http://dx.doi.org/10.34123/jurnalasks.v13i2.295.
Full textAbstract:
This research will present the formation of stock portfolios by preprocessing data using time series clustering with a distance measure of Dynamic Time Warping (DTW). First, stocks are grouped into several clusters using the Partitioning Around Medoids (PAM) time series cluster based on the DTW distance measure. After the clustering process, stocks are selected to represent each cluster to build the optimum portfolio. The stock selected from each cluster is the one with the highest Sharpe ratio. The optimal portfolio is determined using three portfolio models, namely: the classic MV portfolio model, the FMCD robust MV portfolio model and the S robust portfolio model. Using this procedure, an optimum portfolio can be obtained efficiently if there are many stocks involved in the portfolio formation process. Sharpe ratio is used to measure the performance of the portfolios. The results of the empirical study show that the portfolio performance generated using the PAM time series clustering with DWT distance dissimilarity measure combined with the classic MV portfolio model outperforms the resulting portfolio performance in combination with other models.
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Li, Heqing, and Ting Liu. "Portfolio Optimization Based on the LSTM Forecasting Model." Advances in Economics, Management and Political Sciences 48, no. 1 (2023): 97–106. http://dx.doi.org/10.54254/2754-1169/48/20230431.
Full textAbstract:
The prediction of stock performance is a crucial component in formulating investment portfolios and optimizing portfolios within the realm of quantitative trading. However, the inherent unpredictability and volatility of the stock market pose significant obstacles for investors in accurately predicting stock performance. To build an optimal portfolio, the LSTM model is selected as a forecasting technique. Subsequently, data sourced from Yahoo Finance is acquired for training and testing purposes. Based on the prediction data, the paper applies the maximum Sharpe ratio model and the minimum variance model to reach portfolio optimization. Finally, the paper uses the S&P 500 index as a standard to evaluate the constructed portfolio. The results indicate that the LSTM prediction model has effective functionality and exhibits superior performance in the domain of data forecasting. In addition, the minimum-variance optimization and the maximum Sharpe ratio models explore optimized return and minimized risk in portfolio construction. The constructed portfolio outperforms the S&P 500 in terms of risks and returns. Therefore, the results in the paper are good for investors to reduce risk and increase return in portfolio construction.
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Elahi, Younes, and Mohd Ismail Abd Aziz. "Mean-Variance-CvaR Model of Multiportfolio Optimization via Linear Weighted Sum Method." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/104064.
Full textAbstract:
We propose a new approach to optimizing portfolios to mean-variance-CVaR (MVC) model. Although of several researches have studied the optimal MVC model of portfolio, the linear weighted sum method (LWSM) was not implemented in the area. The aim of this paper is to investigate the optimal portfolio model based on MVC via LWSM. With this method, the solution of the MVC model of portfolio as the multiobjective problem is presented. In data analysis section, this approach in investing on two assets is investigated. An MVC model of the multiportfolio was implemented in MATLAB and tested on the presented problem. It is shown that, by using three objective functions, it helps the investors to manage their portfolio better and thereby minimize the risk and maximize the return of the portfolio. The main goal of this study is to modify the current models and simplify it by using LWSM to obtain better results.
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Gusliana, Shindi Adha, and Yasir Salih. "Mean-Variance Investment Portfolio Optimization Model Without Risk-Free Assets in Jii70 Share." Operations Research: International Conference Series 3, no. 3 (2022): 101–6. http://dx.doi.org/10.47194/orics.v3i3.185.
Full textAbstract:
In investing, investors will try to limit all the risks in managing their investments. Investor strategies to minimize investment risk are diversification by forming investment portfolios, one of which is the Mean-Variance without risk-free assets. The calculation results will show the composition of the optimum portfolio return for each stock that forms the portfolio. Optimum portfolio obtained with wT = (0.39853, 0.25519, 0.13644, 0.09788, 0.11196) sequential weight composition for TLKM, KLBF, INCO, HRUM, and FILM stocks. The composition of this optimal portfolio return is 𝜏 0.04 with a return of 0.00209 and a portfolio variance of 0.00015. The formation of this portfolio optimization model is expected to be additional literature in optimizing the investment portfolio with the Mean-Variance.