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Evaluasi Portofolio Optimal IDX30 Berbasis Safety First Criterion Menggunakan Rasio Sharpe, Sortino, dan Treynor Abdul Maulana; Yundari Yundari; Evy Sulistianingsih
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 14 Issue 2 August 2026
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v14i2.38342

Abstract

Constructing an optimal portfolio allows investors to achieve expected returns within an acceptable risk level. Unlike conventional approaches focusing on the risk--return trade--off, the Safety First Criterion (SFC) method minimizes the probability of portfolio returns falling below an investor's specified minimum threshold. This study constructs an optimal stock portfolio from the IDX30 index for the period February 5, 2024--July 28, 2025, using Roy’s, Kataoka’s, and Telser’s criteria, and evaluates performance through Sharpe, Sortino, and Treynor indices. The dataset comprises weekly closing stock prices of IDX30 constituents. The analysis calculates returns and expected returns, selects stocks with positive expected returns, constructs optimal portfolios via the Lagrange multiplier approach for each SFC criterion, and evaluates risk-adjusted performance. This study uniquely applies and compares three SFC criteria simultaneously using three distinct evaluation metrics. Results show that the Roy portfolio comprises ANTM, INDF, and PGAS; the Kataoka portfolio includes BRPT, INDF, and PGAS; and the Telser portfolio consists of ANTM, BRPT, and PGAS. The Roy portfolio generates the highest Sharpe Index (0.1453) and Treynor Index (0.00532), demonstrating superior performance against total and systematic risk compared to other portfolios. Meanwhile, the Telser portfolio achieves the highest Sortino Ratio (0.28566), showing the best capability in managing downside risk. Overall, the Roy portfolio emerges as the most optimal choice because it excels in two out of three evaluation indicators, proving that Roy's criterion produces the best risk--return balance during the study period.
OPTIMASI PORTOFOLIO SAHAM IDX30 MENGGUNAKAN HIERARCHICAL CLUSTERING METODE WARD DENGAN PEMBOBOTAN ALGORITMA GENETIKA Maria Artameivia Putri; Hendra Perdana; Evy Sulistianingsih
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 20, No 1 (2026)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v20i1.18469

Abstract

Stock portfolio is an investment consisting of stocks from different companies with the expectation that if the price of one stock decreases, the price of another stock may increase. To optimize returns and minimize risks, an investment strategy through portfolio optimization is required. This study aims to analyze the implementation of hierarchical clustering using the Ward method with genetic algorithm weighting in optimizing the IDX30 stock portfolio. The Ward method is used to group stocks based on similarities in financial ratios, while the genetic algorithm is used to determine optimal investment weights. The data used consist of 28 stocks included in the IDX30 index during the period from February 2024 to January 2025, with 6 stocks meeting the criteria of having positive expected returns and positive financial ratios. The financial ratio variables used in this analysis are Earnings per Share (EPS), Return on Equity (ROE), Debt to Equity Ratio (DER), and Price Earnings Ratio (PER). Based on the analysis results, the optimal IDX30 stock portfolio consists of PT Charoen Pokphand Indonesia Tbk (CPIN), PT Indofood Sukses Makmur Tbk (INDF), PT Perusahaan Gas Negara Tbk (PGAS), PT Bukit Asam Tbk (PTBA), and PT United Tractors Tbk (UNTR), with investment allocations of 0.23% for CPIN, 50.37% for INDF, 49.16% for PGAS, 0.12% for PTBA, and 0.13% for UNTR. The portfolio produces an expected return of 0.00112 and a portfolio risk of 0.01340. However, this study does not perform sensitivity analysis on the genetic algorithm parameters; therefore, future research may evaluate solution stability through parameter sensitivity testing.
Comparative Analysis of the Capital Asset Pricing Model and Arbitrage Pricing Theory in Estimating Expected Stock Returns in the IDX BUMN20 Index Febrant Alfariz; Evy Sulistianingsih; Neva Satyahadewi
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 14 Issue 1 April 2026
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v14i1.37760

Abstract

This study examines the comparative performance of the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT) in estimating expected stock returns within the IDX BUMN20 Index. The study is motivated by the ongoing debate regarding the empirical validity of single-factor and multifactor asset pricing models, particularly in emerging markets such as Indonesia. While prior studies provide mixed evidence, limited research has focused specifically on state-owned enterprise indices, which exhibit distinct risk characteristics. Using monthly stock price data, this study estimates expected returns under both models and evaluates their performance using Mean Absolute Deviation (MAD), which measures the average deviation between estimated and realized returns. In the APT framework, factor sensitivities are estimated using a multifactor regression approach, incorporating macroeconomic variables as systematic risk factors. This allows a more detailed assessment of how multiple sources of risk influence return estimation. The results indicate that the CAPM demonstrates relatively better estimation performance, as reflected by lower MAD values compared to the APT. However, the APT provides additional insights into the role of multiple risk factors, suggesting its relevance in capturing more complex market dynamics. These findings highlight that while simpler models may perform more consistently in certain contexts, multifactor approaches remain valuable for understanding broader sources of systematic risk. The study contributes to the asset pricing literature by providing empirical evidence from the IDX BUMN20 Index and offering a more nuanced comparison between single-factor and multifactor models in an emerging market setting.
Optimal IDX30 Stock Portfolio Construction Using a Two-Constraint Mean-Variance Model with Robust S-Estimation Anis Faiqo Tuzzainiyah; Evy Sulistianingsih; Nurfitri Imro’ah
Jambura Journal of Mathematics Vol 8, No 2: August 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i2.39603

Abstract

The capital market plays an important role in the economy by providing investment instruments for investors and financing sources for companies. A capital market portfolio consists of a collection of financial assets, such as stocks, constructed to achieve an optimal return while reducing investment risk. Mean-variance portfolio construction is highly sensitive to parameter estimation errors. Therefore, a robust estimation approach is employed to obtain more stable parameter estimates by minimizing the influence of outliers. This study aims to construct an optimal stock portfolio through diversification, determine stock weights using a two-constraint mean-variance model with robust S-estimation, calculate the expected return and risk, and evaluate portfolio performance. The analysis was conducted using the closing prices of stocks included in the IDX30 Index from October 2024 to September 2025. The results identified nine stocks with positive expected returns from five different sectors. Based on the stock selection criteria, two optimal portfolios were constructed. Portfolio 1 consists of ASII, BRPT, INDF, PGAS, and TLKM, whereas Portfolio 2 consists of ASII, ANTM, INDF, PGAS, and TLKM. Portfolio 1 generates an expected return of 0.137% with a risk of 2.226%, while Portfolio 2 generates an expected return of 0.097% with a risk of 1.319%. Based on the Sharpe and Treynor ratios, Portfolio 1 demonstrates relatively better performance than Portfolio 2.
ESTIMASI VALUE AT RISK (VAR) DENGAN METODE MONTE CARLO UNTUK MENGUKUR RISIKO KERUGIAN PETANI KETIMUN DI KABUPATEN KAPUAS HULU Resti Arsanti; Evy Sulistianingsih; Anggi Septiawan
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.11433

Abstract

Measurement of an estimated loss needs to be done by every business actor. The measurement can be done by calculating the Value at Risk (VaR). VaR is an estimate of the maximum loss that is assumed to be experienced in a certain period at the confidence interval used. Three forms of calculation methods can be used in calculating VaR estimates, namely parametric methods, methods with Monte Carlo simulation approaches, and Historical Simulation Methods. The data used is the average monthly producer price data of cucumber commodities with a period range starting from January 2020 to December 2022. The VaR calculation method in this analysis is the Monte Carlo simulation approach method which has the condition that the return data from the average producer price is normally distributed. The results of the VaR calculation with the Monte Carlo simulation method show that after generating return data with repetition 1000 times for an investment of 1 rupiah, the probability that cucumber farmers in Kapuas Hulu Regency, West Kalimantan Province will experience maximum losses is 5.79% for a confidence level of 80%, 9.08% for a confidence level of 90%, 11.39% for a confidence level of 95%, and 14.81% for a confidence level of 99%.
OPTIMASI MULTI OBJEKTIF DAN ANALISIS PEMBENTUKAN PORTOFOLIO SAHAM JAKARTA ISLAMIC INDEX (JII) MENGGUNAKAN METODE NADIR COMPROMISE PROGRAMMING (NCP) Khairina Auliannisa; Evy Sulistianingsih; Neva Satyahadewi
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 1 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i1.14198

Abstract

Multi-objective problems involve multiple objective functions to solve complex problems, and the Nadir Compromise Programming (NCP) method is one way to solve these problems. These problems. Compared to other multi-objective methods, the NCP method has several advantages. Firstly, the weighting in the NCP method can utilize specific parameters to produce an effective optimal portfolio. Additionally, the optimum value of the risk coefficient can be achieved, thereby minimizing large losses. Achieved so as not to cause significant losses. When investing, several essential things need to be considered to achieve an optimal portfolio. These objectives include reducing risk, increasing potential returns, and reducing the amount of capital invested. This study aims to examine the application of the NCP method in solving multi-objective optimization problems for stock portfolios, utilizing monthly stock closing prices from May 2019 to May 2023. In this analysis, the monthly closing prices of 30 stocks that are members of the JII index are analyzed. Six stocks with positive expected returns and the highest stock ratio were selected to form the optimal portfolio. The stocks are BRIS and SIDO. The solution to this multi-objective problem indicates the proportion of funds allocated to the two stocks: BRIS, with a proportion of 0.341147, and SIDO, with a proportion of 0.658853. The analysis also shows that the optimal risk coefficient is 1, the maximum expected return is 0.014569, and the minimum investment capital is Rp.1067.
VALUE AT RISK VARIAN KOVARIAN PADA PORTOFOLIO OPTIMAL MULTI INDEX MODEL Mely Amara Putri; Evy Sulistianingsih; Nurfitri Imro'ah
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.14924

Abstract

The construction of an optimal portfolio aims to minimize investment risk, with the Multi-Index Model being one method that accounts for multiple factors influencing stock returns. This study analyzes the optimal portfolio allocation and estimates potential losses using the variance-covariance Value at Risk (VaR) method. The study examines seven stocks from different sectors that have consistently been part of the IDX30 index from January 2019 to June 2024. The factors considered include the Jakarta Composite Index (JCI) and the exchange rate of the Indonesian Rupiah against the US Dollar (USD). The results indicate that the optimal portfolio consists of PT Adaro Energy Tbk. (ADRO), PT Bank Central Asia Tbk. (BBCA), and PT Kalbe Farma Tbk. (KLBF), with respective weights of 18.83%, 77.12%, and 4.05%. This portfolio yields a return of 1.22% with a risk level of 4.93%. The VaR calculation at a 95% confidence level indicates a maximum potential loss of 8.11% of the initial investment value.
ANALISIS CONDITIONAL VALUE AT RISK PORTOFOLIO SAHAM DENGAN COPULA CLAYTON Sela Karlina; Evy Sulistianingsih; Neva Satyahadewi
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.13261

Abstract

Conditional Value at Risk (CVaR) is known as a risk measurement tool to estimate losses in investing. Financial data tends not to be normally distributed so that the flexible Copula method can be used to analyze financial data without requiring the assumption of normality. This study aims to analyze the CVaR of a stock portfolio with Clayton's Copula. The study began with collecting daily stock closing price data for the period October 3, 2022 to November 3, 2023. After the data was collected, the return value of the closing stock price was calculated. Furthermore, autocorrelation and heteroscedasticity tests were carried out on the closing stock price return data. Then, the Kendall's Tau correlation was calculated to obtain the Clayton Copula parameters. After that, the stock weights in the portfolio were calculated using the Mean Variance Efficient Portfolio (MVEP) method and new return data was generated using the Clayton Copula parameters. Furthermore, the portfolio return was calculated to obtain the VaR value of the formed portfolio. Then, it was repeated by generating data up to the VaR calculation 1000 times to obtain the average value of the portfolio VaR. Then, the same thing was done to CVaR. The results of the CVaR analysis of the stock portfolio with Copula Clayton on the two stocks, namely PT Aneka Tambang Tbk (ANTM) and PT Timah Tbk (TINS), obtained losses of 3.04%, 3.56%, and 4.57% with a confidence level of 90%, 95%, and 99%. This value indicates the percentage of investment risk that may be obtained in the next one-day period. This shows that the higher the level of confidence, the greater the CVaR value will be.
Remodeling and Application of Stock Option Price Based on Skewed Laplace Distribution Approach Evy Sulistianingsih; Ferdi Afrizal; Muhammad Fikri; Pitriani -
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.44222

Abstract

This paper proposed a new model to price a stock option based on the Skewed Laplace distribution approach (SLOP). The approach was considered to provide a better option price than Black Scholes Option Price (BSOP) because Skewed Laplace distribution (SL) has a shape parameter that can capture excess skewness and kurtosis frequently found in stock return underlying the option price. In this study, SL’s shape parameter was estimated using a mixture of the Moment Method and Fourth-Order Taylor Series approach. The estimator was different from the majority of prior SL’s shape parameter that was obtained by Maximum Likelihood Estimation (MLE). The proposed shape parameter was easier to obtain relative to the prior parameter because it did not require a Likelihood Function (LH) and the maximization of LH where involved a complicated numerical method. The performance of SLOP was applied to eleven different enterprises that trade stock options at several strike prices. According to the empirical results in this research, it can be summarized that the SL approach yields a better option price model rather than Black Scholes (BS).
EVALUASI KINERJA MODEL PREDIKSI RETURN SAHAM MENGGUNAKAN METODE LIGHT GRADIENT BOOSTING MACHINE Satrya, Ya’ Aditya Dian; Perdana, Hendra; Sulistianingsih, Evy
BIMASTER : Buletin Ilmiah Matematika, Statistika dan Terapannya Vol. 15 No. 2 (2026): Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya
Publisher : Faculty of Mathematics and Natural Sciences Tanjungpura University

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Investasi saham memiliki risiko yang sebanding dengan potensi keuntungannya akibat volatilitas harga pasar yang dinamis. Ketidakpastian pergerakan harga yang fluktuatif ini menjadi tantangan utama bagi investor dalam menentukan momentum investasi yang tepat. Penelitian ini bertujuan untuk mengevaluasi kinerja model prediksi return saham PT Bank Negara Indonesia Tbk (BBNI.JK) serta mengidentifikasi indikator teknikal yang memiliki pengaruh terbesar menggunakan metode Light Gradient Boosting Machine (LightGBM). Data yang digunakan dalam penelitian ini adalah data historis harian periode 18 September 2023 hingga 18 September 2025. Variabel target yang ditetapkan adalah log return harian, sedangkan variabel prediktor terdiri dari Indeks Harga Saham Gabungan (IHSG) dan indikator teknikal yaitu Simple Moving Average ( ), Exponential Moving Average ( ), Moving Average Convergence Divergence (MACD), Relative Strength Index (RSI). Proses pembentukan model dilakukan dengan skema pembagian 80% data training dan 20% data testing. Berdasarkan evaluasi kinerja pada data testing, diperoleh nilai Root Mean Squared Error (RMSE) sebesar 0,024667 dan Mean Absolute Error (MAE) sebesar 0,019465. Hasil analisis tingkat kepentingan fitur menunjukkan bahwa indikator MACD memberikan kontribusi paling dominan dengan nilai gain 0,3235, diikuti oleh . Hal ini mengindikasikan bahwa model LightGBM secara dominan memanfaatkan sinyal momentum dan tren jangka menengah dalam memprediksi variabel target.
Co-Authors ., Putri Abdul Maulana Agustono, Hendri Alqadri, Syarifah Putri Tasya Vahira Alsa Muarti Amalia, Disya Recita Ananda, Adelia Andani, Wirda Anggi Septiawan Anis Faiqo Tuzzainiyah Anisa Shafarianti Annisa Auliarahmi Ardhitha, Tiffany Atlantic, Virginnia AYU ASTUTI, AYU Banu, Syarifah Syahr Dadan Kusnandar Debataraja, Naomi Nessyana Desdianti, Maycandra Deva Kurnia Aristi Dhandio, David Jordy Dinanti, Rahila Dara Eka Lestari Eka Wahyuning Dhewanty Elga Fitaloka Fadhilah Rizky Aulia Febrant Alfariz Febryanti, Winda Ferdi Afrizal Fiqriani, Rizha Aynul Fransiska Fransiska Gristia Aldilla Gunawan, Risky Hadi, Muhammad Silmi Hafifah, Nanda Hanin, Noerul Hazwani Dhiya' Atiq Viatmaja Hendra Perdana Imanni, Rahmania Andarini Hatti Immy, Immy Imro'ah, Nurfitri IMRO’AH, NURFITRI Imro’ah, Nurfitri Jessica Audrey Valeria Kamila, Diva Rahma Khairina Auliannisa Laksono Trisnantoro Lisa Lestari Louis Putra Jaya Maga, Fahmi Giovani Maharani, Cinta Priscillia Maresha Widya Muliadiasti Maria Artameivia Putri Martha, Shantika Matius Robi Meilandra, Irvan Meliana Pasaribu Melvin, Melvin Mely Amara Putri Misno Misno Muhammad Fikri Mutiara Nurisma Rahmadhani Nabilah, Niken Aushaf Nanda Shalsadilla Naomi Nessyana Debataraja Natalia, Desa Ayu Nazwa Nursyifa Neva Satyahadewi Nurfitri Imro'ah Nurfitri Imro’ah Oktaviani, Indah Oktitannia, Dea Panawaristia, Brigitha Pebriyandi, Rifki Pendra, Yunus Eduard Perangin Angin, Christi Alemsa Pitriani Pitriani - Pratama, Aditya Nugraha Pratama, Yogi Priani, Wina Putra, Fajar Rahmana Radinasari, Nur Ismi Rahmah, Mhaulia Rahmania Andarini Hatti Imanni Resti Arsanti Rifqi, Bhima Fairul Risma Junian Salsabila, Hana Salsabila, Yumna Hanum Satrya, Ya’ Aditya Dian Savitri, Dini Dwi Sela Karlina Setyo Wir Rizki Setyo Wira Rizki Shantika Martha Siti Aprizkiyandari, Nurul Qomariyah, Shantika Martha, Sriyana Sriyana Sulya Hikma Yulandari Supandi Supandi Susanti Susanti Syafitri Wulandari Tamtama, Ray Tiara, Dinda Umiati, Wiji Wahyu Kurniasari Wati, Setio Kusumo Westi Widiyatari Wicaksono, Juwan Prioabil Dwi Wirda Andani Wulandari, Afrilia Putri Yohanna Gabriel Richsita Yundari, Yundari Yundari, Yundari Yustosio, Darwis Yuyun Eka Pratiwi Zakiah, Ainun Zaria, Della