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COMPARISON ANALYSIS OF CLAYTON, GUMBEL, AND FRANK COPULA FOR MODELING THE DEPENDENCE BETWEEN BBCA CLOSING PRICE AND INDONESIA MACROECONOMIC FACTORS Hanin, Noerul; Satyahadewi, Neva; Sulistianingsih, Evy
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2405-2418

Abstract

PT. Bank Central Asia Tbk is a company in Indonesia with the biggest market capitalization. These advantages attract investors to buy PT. Bank Central Asia Tbk (BBCA) shares. However, fluctuating share prices can lead to both gains and losses, where these are not entirely caused by the company’s finances, but also by the country’s macroeconomic conditions. Therefore, this study aims to examine the dependency between BBCA closing price and macroeconomic indicators, which are limited on only three macroeconomic variables, consists of inflation, interest, and USD-IDR exchange rate. This study compares the Clayton, Gumbel, and Frank copula to analyze the dependence characteristics between two non-normally distributed variables based on the highest log-likelihood value. The data used are monthly data from 2021 to 2023, consists of inflation and interest rate from Bank Indonesia website, USD-IDR exchange rate from Satu Data Kementerian Perdagangan website, alongside BBCA closing price from yahoo finance website. Based on the analysis, the best copula models to describe the relationship between each macroeconomic factor (inflation, interest, exchange rate) and BBCA closing price respectively is Clayton copula with parameter 2.042, Frank copula with parameter 10.3, and Frank copula with parameter 5.891. These findings indicate that inflation shows a strong dependence with BBCA closing price when both variables are low, while exchange rate and interest rate exhibit strong dependence with BBCA closing price when these variables are high. It provides valuable insights into the asymmetric relationships between macroeconomic conditions and stock prices, offering practical relevance for investors and policymakers.
AN EXAMINATION OF THE GREEN STOCK PORTFOLIO IN CONNECTION WITH THE 2024 INDONESIAN REPUBLIC PRESIDENTIAL GENERAL ELECTION Sulistianingsih, Evy; Martha, Shantika; Andani, Wirda; Agustono, Hendri; Pebriyandi, Rifki; Gunawan, Risky; Maharani, Cinta Priscillia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2543-2556

Abstract

The presidential election of the Republic of Indonesia occurs on a frequency of once every five years. The present work investigated the impact of the 2024 Presidential Election on the performance of the optimal stock portfolio constructed by K-Means Clustering during the first phase of stock selection. Subsequently, the portfolio will be evaluated using two distinct approaches, namely Mean Absolute Deviation (MAD) and Mean-Variance Efficient Portfolio (MVEP). Both techniques were employed to construct several portfolios throughout three time periods: before the Presidential Election (13 August 2023 to 13 February 2024) and after the Presidential Election (15 February to 15 April 2024 and 20 April 2024 to 20 May 2024). This was done by implementing a mechanism to manage the allocation of shares in order to optimize the portfolio. The analyzed data is historical data on daily green stock closing prices indexed on the SRI-KEHATI index. A portfolio was constructed and subsequently evaluated for its performance using the Sharpe Index. The findings of this study suggest that the upcoming 2024 general election for the presidency of the Republic of Indonesia had a favorable impact on the Indonesian capital market, particularly for stocks that are indexed by SRI-KEHATI. This criterion was proposed based on the observation that the average Sharpe ratio index for Period II and Period III exceeds the average Sharpe ratio index for Period I (prior to the election day). The most optimal portfolio examined in this study was the MVEP portfolio, mostly composed of assets in the primary consumer products industry, with a Sharpe ratio of 0.53586. Furthermore, the performance of portfolios in period III (after the election result release) was far superior to that of other portfolios examined in previous periods.
INTEGRATION OF DAVIES-BOULDIN INDEX VALIDATION AND MEAN-VARIANCE EFFICIENT PORTFOLIO IN K-MEANS++ CLUSTERING FOR OPTIMIZATION OF THE LQ45 STOCK PORTFOLIO Dhandio, David Jordy; Sulistianingsih, Evy; Satyahadewi, Neva
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2609-2620

Abstract

Stock investment involves allocating funds to get returns based on the associated risks. In stock investments, returns and risks exhibit a linear correlation, meaning higher expected returns come with higher risks. Risk in stock investments can be minimized by forming portfolios using a cluster analysis approach, where the groups of stocks generated from the analysis represent the resulting portfolios. This research aims to form an optimal stock portfolio using K-Means++ Clustering, validated by the Davies Bouldin Index (DBI), the weighting of stocks in a portfolio using the Mean-Variance Efficient Portfolio (MVEP), and evaluated based on the Sharpe Index. The data used include stocks indexed in LQ45 from February 2020 to August 2024, stock closing prices from August 1, 2023, to August 1, 2024, company financial ratios as of June 2024, and the average Bank Indonesia interest rate from August 2023 to August 2024. Based on the financial ratios, K-Means++ Clustering and DBI validation identified three optimal clusters. Clusters 1 and 2, consisting of single stocks, cannot be directly utilized as portfolios due to the requirement for diversification. Each cluster’s stocks with the highest expected return were selected to form a new portfolio. According to the MVEP analysis, the investment proportion f each stock in portfolio 1 is 44.10% (BBCA.JK), 15.40% (BBNI.JK), 2.89% (BMRI.JK), 15.02% (CPIN.JK), and 22.60% (PGAS.JK). In portfolio 2, the weights are 27.68% (BBTN.JK), 36.00% (ADRO.JK), and 36.33% (BMRI.JK). Based on the Sharpe Index, portfolio 2 achieved the highest value (0.048404) compared to portfolio 1 (0.034465), indicating that portfolio 2 shows a better risk-adjusted return than portfolio 1.
The Application of Delta Gamma Normal Value at Risk to Measure the Risk in the Call Option of Stock Astuti, Ayu; Sulistianingsih, Evy; Martha, Shantika; Andani, Wirda
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.19669

Abstract

Call options of stock have a nonlinear dependence on market risk factors, thus encouraging the development of a method capable of measuring the risk of call option of stock, namely the Delta Gamma Normal Value at Risk (DGN VaR) method. The DGN VaR method can provide a more accurate VaR estimate than Delta Normal VaR (DN VaR) because of the Delta and Gamma sensitivity measures in the formula. The DGN VaR method uses the second-order Taylor Polynomial approach to approximate the return of stock price underlying the call option. This research applies the DGN VaR method to analyze the risk of call options of Atlassian Corporation (TEAM) and MicroStrategy Incorporated (MSTR). Both companies operate in the technology sector and are among the top 100 largest software companies based on market capitalization for the analysis period September 21, 2022 to September 21, 2023. The analyzed options in this research consist of in-the-money and out-of-the-money options with several strike prices (K). For in-the-money options, the strike prices are $105, $110, and $115 for TEAM, and $150, $160, and $170 for MSTR, while for out-of-the-money options, the strike prices are $190, $195, and $200 for TEAM, and $330, $340, and $350 for MSTR with varying confidence levels of 80%, 90%, 95%, and 99%. Based on the results of the analysis, the DGN VaR for the analyzed in-the-money option has a greater value than the DGN VaR for the analyzed out-of-the-money option.
Analysis of the Single Index Model Optimal Portfolio Using the Sharpe and Treynor Measurement Index Related to Covid-19 Salsabila, Yumna Hanum; Sulistianingsih, Evy; Debataraja, Naomi Nessyana; Martha, Shantika
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.21249

Abstract

The optimum portfolio is the preferred choice among investors for determining the most favorable combination of projected return and risk. This study seeks to ascertain the ideal portfolio performance of companies in the IDX30 index on the Indonesia Stock Exchange and know the value of the stock weight in each period, over three specific periods: before to the Covid-19 pandemic, at the peak of Covid-19 cases, and after a decline in Covid-19 instances. Stocks listed on IDX30 are stock companies that have high liquidity and large capitalization value on the capital market. The pre-Covid-19 era spanned from March 2019 to February 2020. The time of peak Covid-19 occurrences occurred from April 2021 to March 2022. Lastly, the period of declining Covid-19 instances extended from September 2022 to August 2023. The study employs the Single Index Model (SIM), using the Sharpe and Treynor measurement indices. The SIM will identify the relationship between the returns from each security and market returns to construct a portfolio. Meanwhile, Sharpe and Treynor Index measures the performance of portfolio. Based on the results of the analysis of optimal portfolio formation from 30 samples of IDX30 stocks, 4 stocks were obtained (ARTO, BBCA, BBRI, and BRPT) in the period before the Covid-19 pandemic, 14 stocks (ADRO, AKRA, ASII, BBCA, BBNI, BMRI, EMTK, ESSA, INCO, ITMG, MDKA, PTBA, TLKM, and UNTR) in the period when Covid-19 cases were peaking, and 7 stocks (AKRA, AMRT, BBCA, BBNI, BMRI, BRPT, and MEDC) in the period when Covid-19 cases were sloping. The Sharpe measurement index assessment had an average value in the period before the Covid-19 pandemic 1,7836; in the period when Covid-19 cases peaked it was 1,6051, and in the period when Covid-19 cases were sloping it was 0,7236. Meanwhile, the Treynor measurement index had an average value of in the period before the Covid-19 pandemic 0,8507; in the period when Covid-19 cases peaked it was 0,4095; and in the period when Covid-19 cases sloped it was 0,1317. The best period that has the highest Sharpe and Treynor index values is the period before the Covid-19 pandemic. The expected return value of the portfolio that was formed was 0,0601 in period I, 0,0509 in period II, and 0,0210 in period III. Meanwhile, the portfolio risk formed in period I was 0,1086, in period II it was 0,0150, and in period III it was 0,0089.
APPLICATION OF DELTA GAMMA (THETA) NORMAL APPROXIMATION IN RISK MEASUREMENT OF AAPL'S AND GOLD'S OPTION Sulistianingsih, Evy; Martha, Shantika; Andani, Wirda; Umiati, Wiji; Astuti, Ayu
MEDIA STATISTIKA Vol 16, No 2 (2023): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/medstat.16.2.160-169

Abstract

The option value has a nonlinear dependence relationship on risk factors existing in the capital market. Therefore, this paper considered utilizing Delta Gamma (Theta) Normal Approximation (DGTNA) as a nonlinear approach to determine the change of profit/loss of a European call option to assess the option risk. The method uses the second order of Taylor Polynomial around the stock price underlying the option to approximate the option profit/loss, which is crucial to construct the VaR based on DGTNA. VaR based on DGTNA also considered three Greeks, namely Delta, Gamma, and Theta, known as sensitivity measures in option. This research applied VaR based on DGTN approximation to analyze the European call option of Apple Inc (AAPL) and Barrick Gold Corporation (GOLD) for several strike prices. The performance of DGTN VaR analyzed by Kupiec Backtesting summarized that in this case, DGTN VaR provides the best risk assessment over different confidence levels (80, 90, 95, and 99 percent) compared to Delta Normal VaR and Delta Gamma Normal VaR.
K-Means Clustering dan Mean Variance Efficient Portfolio dalam Portofolio Saham Pratama, Yogi; Sulistianingsih, Evy; Debataraja, Naomi Nessyana; Imro’ah, Nurfitri
Jambura Journal of Probability and Statistics Vol 5, No 1 (2024): Jambura Journal Of Probability and Statistics
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjps.v5i1.20298

Abstract

K-means clustering is one of the non-hierarchical clustering algorithms that partitions n objects into k clusters. K-means clustering is used to determine which cluster an object belongs to by calculating the proximity distance between the object and the cluster center (centroid). This research aims to form a portfolio using K-means clustering and determine the weights of the portfolio using the Mean Variance Efficient Portfolio (MVEP) method. The data analyzed in this research is the closing price data of 11 stocks in the LQ45 index from January 3, 2022, to January 3, 2023. The analysis results obtained using K-means clustering reveal the formation of two portfolios. The first portfolio consists of the stocks BMRI, INCO, INDF, INTP, and SMGR. The second portfolio consists of the stocks ADRO, ANTM, BBRI, ERAA, and UNVR. Based on the MVEP method calculation, the weights of each stock in the first portfolio are 22.74\% (BMRI), 10.11\% (INCO), 49.76\% (INDF), 18.75\% (INTP), and -1.36\% (SMGR). The calculation results of stock weights show that there is a stock weight with a negative value, which is -1.36\% for SMGR, indicating a short sale in the investment. Furthermore, the weighting results for the second portfolio are 7.08\% (ADRO), 9.62\% (ANTM), 34.05\% (BBRI), 24.80\% (ERAA), and 24.45\% (UNVR).The variance values of stock portfolio 1 and stock portfolio 2 are 0.000080 and 0.000137, respectively. From the portfolio variance results, it is known that the risk of portfolio 1 is 0.008953 and the risk of portfolio 2 is 0.011706.
PENGARUH JUMLAH TENAGA KESEHATAN TERHADAP UNMET NEED PELAYANAN KESEHATAN: PENDEKATAN REGRESI LOGISTIK RIDGE Wicaksono, Juwan Prioabil Dwi; Imro’ah, Nurfitri; Sulistianingsih, Evy
BIMASTER : Buletin Ilmiah Matematika, Statistika dan Terapannya Vol 14, No 5 (2025): Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya
Publisher : FMIPA Universitas Tanjungpura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26418/bbimst.v14i5.100119

Abstract

Regresi Logistik Ridge merupakan pengembangan dari Regresi Logistik yang dilengkapi dengan penalti ridge, dan bertujuan untuk mengatasi multikolinearitas serta meningkatkan kestabilan estimasi parameter. Dalam penelitian ini, multikolinearitas teridentifikasi pada variabel prediktor, sehingga metode Regresi Logistik Ridge digunakan. Variabel dependen adalah tingkat unmet need pelayanan kesehatan, yaitu persentase penduduk yang mengalami keluhan kesehatan dan terganggu aktivitasnya namun tidak melakukan pengobatan rawat jalan. Untuk keperluan analisis, variabel tersebut dikategorikan menjadi dua kelas, yaitu provinsi dengan nilai unmet need di atas dan di bawah rata-rata nasional, sehingga pendekatan klasifikasi logistik menjadi sesuai. Penelitian ini bertujuan menganalisis faktor-faktor yang mempengaruhi tingkat unmet need serta merumuskan langkah strategis yang dapat dilakukan pemerintah. Data unmet need bersumber dari Survei Sosial Ekonomi Nasional (Susenas) bulan Maret 2023, sedangkan data jumlah tenaga kesehatan dari Badan Pusat Statistik (BPS) tahun 2023 mencakup enam profesi di tingkat provinsi. Pemodelan dilakukan dengan Regresi Logistik Ridge, dilanjutkan dengan uji signifikansi parameter secara parsial dan serentak, serta interpretasi menggunakan odds ratio. Hasil menunjukkan bahwa terdapat dua faktor, yaitu jumlah tenaga perawat dan tenaga farmasi, berpengaruh signifikan secara negatif terhadap tingkat unmet need. Artinya, peningkatan ketersediaan kedua jenis tenaga kesehatan tersebut berpotensi menurunkan tingkat unmet need pelayanan kesehatan di Indonesia.
PENGELOMPOKAN DAERAH DI KALIMANTAN BARAT BERDASARKAN INDIKATOR TINGKAT PENGANGGURAN DENGAN HIERARCHICAL CLUSTERING MULTISCALE BOOTSTRAP Hafifah, Nanda; Perdana, Hendra; Sulistianingsih, Evy
BIMASTER : Buletin Ilmiah Matematika, Statistika dan Terapannya Vol 14, No 3 (2025): Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya
Publisher : FMIPA Universitas Tanjungpura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26418/bbimst.v14i3.95740

Abstract

Pengangguran merupakan masalah umum yang ditemui di negara-negara berkembang, termasuk Indonesia. Kondisi ini dipengaruhi oleh beberapa faktor seperti pertumbuhan penduduk, ekonomi, ketersediaan lapangan kerja, tingkat pendidikan, serta besaran upah. Tingginya populasi di Indonesia menjadi tantangan dalam menekan angka pengangguran. Untuk mengukur dampaknya dalam suatu wilayah, digunakan indikator tingkat pengangguran, yaitu persentase jumlah pengangguran dibandingkan dengan total angkatan kerja. Berdasarkan data BPS tahun 2023, Kalimantan Barat mencatat tingkat pengangguran sebesar 5,05% yang masih tergolong tinggi. Penelitian ini bertujuan untuk mengelompokkan Kabupaten/Kota di Kalimantan Barat berdasarkan indikator tingkat pengangguran dengan hierarchical clustering multiscale bootstrap serta mengevaluasi validitas setiap cluster. Dalam analisis multivariat, Analisis cluster digunakan untuk mengelompokkan objek berdasarkan kesamaan karakteristik. Metode Ward, yang meminimalkan varians internal dalam cluster merupakan salah satu metode hierarki yang digunakan. Validasi dilakukan dengan metode resampling multiscale bootstrap, yang menghasilkan dua nilai, yaitu bootstrap probability (BP) dan approximately unbiased (AU). Nilai BP menunjukkan seberapa sering suatu cluster terbentuk saat data diulang, sedangkan AU dianggap lebih akurat dalam menilai keandalan cluster. Sebuah cluster dianggap stabil jika nilai AU ≥ 0,95. Namun, dalam penelitian ini digunakan batas minimal AU ≥ 0,75 sebagai ukuran stabilitas. Hasilnya, diperoleh dua cluster yang stabil yaitu cluster 1 dengan tingkat pengangguran rendah terdiri dari Mempawah, Kayong Utara, Sanggau, Kota Singkawang, Landak, Sambas, Sintang, Bengkayang, Kapuas Hulu, Sekadau, dan Melawi. Cluster 3 dengan tingkat pengangguran tinggi yaitu Kabupaten Kubu Raya dan Kota Pontianak, Serta cluster 2 dengan tingkat pengangguran sedang yaitu Ketapang, namun memiliki nilai AU sebesar 0,72.
PENERAPAN MODEL SELF-EXCITING THRESHOLD AUTOREGRESSIVE (SETAR) DALAM MEMODELKAN DATA HARGA PEMBUKAAN SAHAM APLN Meilandra, Irvan; Imro’ah, Nurfitri; Sulistianingsih, Evy
BIMASTER : Buletin Ilmiah Matematika, Statistika dan Terapannya Vol 14, No 5 (2025): Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya
Publisher : FMIPA Universitas Tanjungpura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26418/bbimst.v14i5.100120

Abstract

Model Self-Exciting Threshold Autoregressive (SETAR) merupakan salah satu model nonlinier dalam analisis runtun waktu yang memiliki keistimewaan dapat menangkap loncatan data yang tidak dapat ditangkap oleh model runtun waktu linier. Karena keistimewaannya tersebut, SETAR dapat digunakan untuk data yang berfluktuasi seperti saham agar hasil yang diperoleh memiliki akurasi yang baik. Tujuan penelitian ini adalah untuk memodelkan harga pembukaan saham APLN dengan model SETAR. Saham APLN milik PT Agung Podomoro Land Tbk merupakan perusahaan yang bergerak di bidang properti. Penelitian ini menggunakan 153 data harga pembukaan bulanan saham APLN dalam periode Januari 2012 sampai dengan September 2024. Tahapan pemodelannya yaitu uji stasioneritas dalam rata-rata dan varians, uji Terasvirta, identifikasi model SETAR, pendugaan dan uji signifikansi parameter, kemudian uji diagnostik. Hasil penelitian menunjukkan bahwa data menggunakan 1 threshold dengan embedding dimension 4 dan jarak waktu 1. Model SETAR yang didapatkan merupakan model 2-regime SETAR (2,1,2) dengan threshold 5,463832.
Co-Authors ., Putri Agustono, Hendri Alsa Muarti Amalia, Disya Recita Ananda, Adelia Andani, Wirda Anisa Shafarianti Ardhitha, Tiffany Arsanti, Resti 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 Febryanti, Winda Fiqriani, Rizha Aynul Fransiska Fransiska Gristia Aldilla Gunawan, Risky Hafifah, Nanda Hanin, Noerul Hendra Perdana Imanni, Rahmania Andarini Hatti Imro'ah, Nurfitri IMRO’AH, NURFITRI Kamila, Diva Rahma Karlina, Sela Laksono Trisnantoro Lisa Lestari Maga, Fahmi Giovani Maharani, Cinta Priscillia Maresha Widya Muliadiasti Martha, Shantika Matius Robi Meilandra, Irvan Meliana Pasaribu Melvin, Melvin Misno Misno Mutiara Nurisma Rahmadhani Nabilah, Niken Aushaf Nanda Shalsadilla Naomi Nessyana Debataraja Natalia, Desa Ayu Neva Satyahadewi Nurfitri Imro’ah Oktaviani, Indah Oktitannia, Dea Panawaristia, Brigitha Pebriyandi, Rifki Perangin Angin, Christi Alemsa Pratama, Aditya Nugraha Pratama, Yogi Priani, Wina Putra, Fajar Rahmana Radinasari, Nur Ismi Rahmah, Mhaulia Rahmania Andarini Hatti Imanni Rifqi, Bhima Fairul Risma Junian Salsabila, Hana Salsabila, Yumna Hanum Septiawan, Anggi 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 Yundari, Yundari Yustosio, Darwis Zakiah, Ainun Zaria, Della