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PENGUKURAN VALUE AT RISK PADA ASET TUNGGAL DAN PORTOFOLIO DENGAN SIMULASI MONTE CARLO Maruddani, Di Asih I; Purbowati, Ari
MEDIA STATISTIKA Vol 2, No 2 (2009): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Value at Risk (VaR) is the established standard for measuring market risk. VaR measures the worst expected loss under normal market conditions over a specific time interval at a given confidence level. A VaR statistic has three components: a time period, a confidence level and a loss amount (or loss percentage). The Monte Carlo simulation method calculates the change in the value of positions by using a random sample generated by price scenarios. Instead of using the past value of risk factors, Monte Carlo simulation generates models to estimate the risk factors from past portfolio returns by specifying the distributions and their parameters. Using these distributions and parameters, we can generate thousands of hypothetical scenarios for risk factors and, finally, we can determine future prices or rates based on hypothetical scenarios. VaRs can be derived from the cumulative distribution of future prices or rates for given confidence levels. In this paper, we calculate VaR at PT Astra International Tbk., PT Telekomunikasi Tbk., and the portfolio of the two assets. PT. Astra International Tbk has higher VaR than PT. Telekomunikasi Tbk. The VaR of a portfolio has lower result than VaR of each single asset. Â Keywords : Value at Risk, Time Period, Confidence Level, MonteÂ Carlo Simulation.

UJI STASIONERITAS DATA INFLASI DENGAN PHILLIPS-PERON TEST Maruddani, Di Asih I; Tarno, Tarno; Anisah, Rokhma Al
MEDIA STATISTIKA Vol 1, No 1 (2008): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

The classical regression model was devised to handle relationships between stationary variables. It should not be applied to nonstationary series. A time series is therefore said to be stationary is its mean, variance, and covariances remain constant over time. A problem associated with nonstationary variables, and frequently faced by econometricians when dealing with time series data, is the spurious regression. An apparent indicator of such spurious regression was a particularly low level for the Durbin-Watson statistics, combined with an acceptable R2. Statistical test for stationarity have proposed by Dickey and Fuller (1979). The distribution theory supporting the Dickey-Fuller test assumes that the errors are statistically independent and have a constant variance. Phillips and Peron (1988) developed a generalization of the Dickey-Fuller procedure that the error terms are correlated and not have constant variance. In this paper, we use Phillips-Peron test for inflation data in Indonesia for the time period 1996-2003. The data showed upward trend and the error terms are correlated. The empirical results showed that the inflation data in Indonesia is a nonstationary series. Â Keywords : stationarity, non autocorrelation, Phillips-Peron Test, inflation

Perbandingan Sensitivitas Harga Obligasi Berdasarkan Durasi Macaulay dan Durasi Eksponensial dengan Pengaruh Konveksitas (Studi Empiris pada Data Obligasi Korporasi Indonesia yang Terbit Tahun 2015) Maruddani, Di Asih I; Hoyyi, Abdul
MEDIA STATISTIKA Vol 10, No 1 (2017): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Macaulay duration has often been used as a measure of the bond prices sensitivity to changes in interest rates. For a small change in interest rates, the duration provides a good approximation of the actual change in price. As the change in interest rates gets larger, the duration approximation has larger errors. The convexity of bond prices change is often used as a way to improve the accuracy of the approximation. Several authors have pointed out that the natural logarithm of bond price is a better measure of percentage changes in bond prices as interest rates change. Based on this idea, this paper derives an accurate method of estimating percentage bond price changes in response to changes in interest rates, which is called exponential duration. This paper gives new estimation of bond prices using exponential duration with convexity approach. It will be shown that the new estimation bond prices is always more accurate than by Macaulay duration with convexity approach. For empirical study, it is used corporate bond data, which is published by Indonesian Bond Pricing Agency in 2015. The result support the theory that error value of Macaulay duration with convexity is more than the error value of exponential duration with convexity.Keywords:Bond Price, Convexity, Exponential Duration, Macaulay Duration, Modified Duration

ANALISIS DATA PANEL UNTUK MENGUJI PENGARUH RISIKO TERHADAP RETURN SAHAM SEKTOR FARMASI DENGAN LEAST SQUARE DUMMY VARIABLE Astuti, Tutut Dewi; Maruddani, Di Asih I
MEDIA STATISTIKA Vol 2, No 2 (2009): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Panel data analysis is a method of studying pooling observations on a cross-section of subjects over several time periods. There are several types of panel data analytic models, constant coefficients models, fixed effects models, and random effects models. Fixed effects models would have constant slopes but intercepts that differ according to the cross-sectional (group) unit. While the intercept is cross-section (group) specific, it may or may not differ over time. To show how to test for the presence of statistically significant group and/or time effects, i-1 dummy variables are used to designate the particular group, so we use Least Squares Dummy Variable method. In this paper, we use this method for testing the relationship between risk and stock return at farmation sector data in Indonesia for the time period 2007-2008. The empirical results showed that the model is statistically significant time effects. Â Keywords : Risk, Stock Return, Panel Data, Least Square Dummy Variable

PENGARUH SKEWNESS DAN KURTOSIS DALAM MODEL VALUASI OBLIGASI Abdurakhman, Abdurakhman; Maruddani, Di Asih I
MEDIA STATISTIKA Vol 11, No 1 (2018): Media Statistika
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

The Gram-Charlier expansion, where skewness and kurtosis directly appear as parameters, has become popular in finance as a generalization of the normal density. Non-normal skewness and kurtosis of underlying asset of bond issuer company are significantly contributes to the phenomenon of volatility smile. Hermite polynomial is used to get an expansion of the probability distribution. In this paper, Gram-Charlier model is applied to BTPN Bond which is issued in 2017. The result showed that Gram-Charlier model is more consistent than Black-Scholes model when the skewness and kurtosis are taken into account.Keywords:Â Skewness, Kurtosis, Gram-Charlier, Hermite polynomialÂ

PENGGUNAAN SIMULASI MONTE CARLO UNTUK PENGUKURAN VALUE AT RISK ASET TUNGGAL DAN PORTOFOLIO DENGAN PENDEKATAN CAPITAL ASSET PRICING MODEL SEBAGAI PENENTU PORTOFOLIO OPTIMAL (Studi Kasus: Index Saham Kelompok SMinfra18) Pradana, Danang Chandra; Maruddani, Di Asih I; Yasin, Hasbi
Jurnal Gaussian Vol 4, No 4 (2015): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

In financial markets, a stock is a unit of account for various investments. It often means the stock of a corporation, but also used for collective investments such as mutual funds, limited partnerships, and real estate investment trusts. In this era, most investors establish a stock portfolio as one way to reduce the risk of loss or risk which may be obtained when investing in stocks. Formation of portfolio in this research, investors is used to calculate the weight of the investment using the Capital Asset Pricing Model (CAPM). Risks of investing often called Value at Risk (VaR), calculate the VaR using Monte Carlo simulation. From the results and analysis conducted on a group of SMInfra18 stocks, there are two stocks into the portfolio with an allocation of the largest given to the ISAT (PT. Indosat, Tbk) and the allocation of funds smallest given to stock TBIG (PT. Tower Bersama Infrastructure Tbk). While the losses or the estimated risk of the portfolio at 95% confidence level is IDR 18,860,237.00 of the initial capital of IDR 1,000,000,000.00 during the holding period 1 day after portfolio formation. Keywords: Stock, Portfolio, SMInfra18, CAPM, Monte Carlo

ANALISIS FAKTOR-FAKTOR YANG MEMPENGARUHI PERSENTASE PENDUDUK MISKIN DI JAWA TENGAH DENGAN METODE GEOGRAPHICALLY WEIGHTED PRINCIPAL COMPONENTS ANALYSIS (GWPCA) ADAPTIVE BANDWIDTH Mas'ad, Mas'ad; Yasin, Hasbi; Maruddani, Di Asih I
Jurnal Gaussian Vol 5, No 3 (2016): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Poverty is one of the fundamental problems that is faced by developing country such as Indonesia. One of provinces with high poverty in Java is Central Java. The factors affecting poverty in the districts/cities in Central Java are Human Development Index, pre-prosperous family, population density, Labor Force Participation Rate, and Regional Minimum Wage. Variables which is affecting poverty percentage are multivariate data that have spatial effect and are correlated to each other. Therefore, Geographically Weighted Principal Components Analysis (GWPCA) Adaptive Bandwidth is suitable to analyze what dominant factor that effects poverty percentage in the districts/cities in Central Java. GWPCA Adaptive Bandwidth is a multivariate analysis method that is used to remove the correlation in multivariate data that have spatial effects with the distance weighting measure and the extent of location influence relative to each other location conforming to the variance size of data density. The result of this research the variables affecting poverty percentage each region can be replaced by new variables called principal components which can explain 82% of the original variables. This research also found five regional groups that have different poverty-percentage-affecting characterics. Keywords : poverty, multivariate, correlation, spatial effect, GWPCA adaptive bandwidth.

VALUASI COMPOUND OPTION PUT ON PUT TIPE EROPA Sutarno, Yulia Agnis; Maruddani, Di Asih I; Sugito, Sugito
Jurnal Gaussian Vol 3, No 3 (2014): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Options are one of the form of investment which a contract that gives the right (not obligation) to the option holder to buy (call options) or sell (put options) the underlying asset by a certain date for a certain price. Option price is a reflection of the intrinsic value of the option and any additional amount over intrinsic value. One type of options that are traded is compound options. Compound option model is introduced by Robert Geske in 1979. Compound options are options on options. Compound option put on a put is put option where the underlying assets are another put option. The compound option put on put will be exercised on the first exercise date only if the value of the put option on that date is less than the first stike price. An empirical study using compound option put on a put stocks of Apple Inc which is strike price compound option US$ 560, strike price put option US$ 585, with the first exercise date on March 28, 2014 and the second exercise date on May 17, 2014. The theoritical price of compound option put on put on stocks of Apple Inc is US$ 501.4566.

AUTOREGRESSIVE FRACTIONAL INTEGRATED MOVING AVERAGE (ARFIMA) MODEL TO PREDICT COVID-19 PANDEMIC CASES IN INDONESIA Kartikasari, Puspita; Yasin, Hasbi; Maruddani, Di Asih I
MEDIA STATISTIKA Vol 14, No 1 (2021): 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.14.1.44-55

Currently the emergence of the novel coronavirus (Sars-Cov-2), which causes the COVID-19 pandemic and has become a serious health problem because of the high risk causes of death. Therefore, fast and appropriate action is needed to reduce the spread of the COVID-19 pandemic. One of the way is to build a prediction model so that it can be a reference in taking steps to overcome them. Because of the nature of transmission of this disease which is so fast and massive cause extreme data fluctuations and between objects whose observational distances are far enough correlated with each other (long memory). The result of this determination is the best ARFIMA model obtained to predict additional of recovering cases of COVID-19 is (1,0,489.0) with an SMAPE value of 12,44%, while the case of death is (1.0.429.0) with SMAPE value of 13,52%. This shows that the ARFIMA model can accommodate well the long memory effect, resulting in a small bias. Also in estimating model parameters, it is also simpler. For cases of recovery and death, the number is increasing even though the case of death is still very high compared to cases of recovery.

RISK ASSESSMENT OF STOCKS PORTFOLIO THROUGH ENSEMBLE ARMA-GARCH AND VALUE AT RISK (CASE STUDY: INDF.JK AND ICBP.JK STOCK PRICE) Tarno, Tarno; Trimono, Trimono; Maruddani, Di Asih I; Wilandari, Yuciana; Utami, Rianti Siswi
MEDIA STATISTIKA Vol 14, No 2 (2021): 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.14.2.125-136

Stocks portfolio is a form of investment that can be used to minimize the risk of loss. In a stock portfolio, the Value at Risk (VaR) can be predicted through the portfolio return. If portfolio return variance is heteroskedastic risk prediction can be done by using VaR with ARIMA-GARCH or Ensemble ARIMA-GARCH model approach. Furthermore, the accuracy of VaR is tested through Backtesting test. In this study, the portfolio is formed from PT Indofood CBP Sukses Makmur (ICBP.JK) and PT Indofood Sukses Makmur Tbk (INDF.JK) stocks from 01/01/2018 to 07/30/2021. The results showed that the best model isÂ Ensemble ARMA-GARCH with MSE 1.3231Ã—10-6. At confidence level of 95% and 1 day holding period, the VaR of the Ensemble ARMA-GARCH was -0.0213. Based on the Backtesting test, it is proven to be very accurate to predict the value of loss risk because the value of the Violation Ratio (VR) is equal to 0.

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