comparison study between garch and standard deviation. skripsi

R ESEARCH B ACKGROUND

R ESEARCH P ROBLEM

R ESEARCH O BJECTIVES

R ESEARCH S COPE AND L IMITATION

R ESEARCH B ENEFITS

Portfolio

Portfolio is an investment with different levels of acquisition and different levels of risk, which are combined to fulfill investment objectives and reduce risk. And investment portfolio is a collection of some investments designed to get expected return.

Stock

Sharpe Index

The data analyzed in this study is the daily closing price of the most liquid companies in Indonesia, such as the data of Astra Agro Lestari Tbk., Adhi Karya Tbk., and Adaro Energy Tbk. The tool to collect the data LQ45 is performed by obtaining the available data that was available in www.finance.yahoo.com, about the closing price data LQ45. The first step to plot the time series data to see the behavior of the data and for the second step is to check the stationary data, stationary data is checked by Augmented Dickey Fuller (ADF) test and then the white noise is checked.

If the data is non-stationary, the differentiation process and data transformation are used. To check the stationary data, we have several ways: first we look at the plot of data, we can judge the data stationary or not, secondly by statistical test ADF test. Adhi Karya Tbk is non-stationary as the data is fluctuating and confirms that the data is not constant from a certain number.

The data from ADF is also stationary, but from the graph data confirm that the data is non-stationary, and the P-value is less than 0.0001, so we can conclude that PT Adhi Karya data is non-stationary. PT Adaro Energy and PT Astra Agro Lestari are greater than the delays which means 0.3 The next step is to change the data to make the data stationary. We use differentiation with lag = 2 (d=2) respectively so that the data reach stationary time series data.

From the table we can see P values are less than 0.0001 so we can conclude that PT Adaro Energy Tbk, PT Adhi Karya Tbk and PT Astra Agro Lestari have Arch effects. The result of the analysis PT Adaro Energy Tbk using the AR(1) – GARCH (1,1) model is as follows. The result of the analysis PT Astra Agro Lestari Tbk using the AR(1) – GARCH (1,1) model is as follows.

From the analysis, we can find that the data of PT Adaro Energy Tbk, PT Adhi Karya Tbk, PT Astra Argo Lestari Tbk are non-stationary and we differentiate them with lag = 2 (d-2) and then the data is stationary. From the ARCH effect test with Q test and LM test, we conclude that all the data have ARCH effect. From the analysis, if we use Sharpe with standard deviation as the divisor, the result for PT Adhi Karya Tbk is 2.93%, PT Adaro Energy -0.48% and PT Astra Agro Lestari -3.70%.

V ARIABLES AND SAMPLE PERIODS SPECIFICATIONS

I NSTRUMENT

D ATA A NALYSIS

And last is the fourth step, to estimate and test the model of parameter and to predict the daily closing price. From the plot of data, the behavior of data can be explained, especially about stationary data, stationary data in mean and variance. Root unit is a composition of a process stochasticity that can create a problem in time series modeling.

Time series consist of uncorrelated observations and have constant variance, this is called white noise. If a time series is white noise, the distribution of sample autocorrelation coefficient at lag K in a large sample is approximately normally distributed with mean 0 and variance 1/T. Based on the comparison, we can therefore test the hypothesis of autocorrelation of lag k Ho: ρk = 0 against Ha: ρk ≠ 0 using the test statistic.

The third step is parameter estimation and testing, diagnostic and residual test, selecting the best model based on the criteria, the smallest AIC or SC value. The residuals we get from the best ARMA model are checked using the Lagrange Multiplier (LM) to check whether they have ARCH effect or not. The moving average (MA) pattern of order q is defined by MA (q) and can be written as follows:

A UTOREGRESSIVE M OVING A VERAGE (ARMA) MODEL

Homoscedasticity is the basic idea of the least squares model, assume that the expected value of the squared error term is the same at any given point. The test that can be used to detect the heteroskedasticity or ARCH effect is the ARCH-Lagrange Multiplier (ARCH-LM) (Engle, 1982; Tsay, 2005). The Lagrange Multiplier (LM) test can be used to detect the presence or existence of heteroskedasticity or ARCH effect.

Although the Lagrange multiplier is useful for detecting the ARCH effect, it is still difficult in practice to determine the order of the process. One method to determine the order of the model is to fit several competing models and then compare the AIC (Akaike Information Criterion) values of these competing models. The GARCH model is not only to see the correlation between some residuals, but also to depend on some previous residuals.

The GARCH model allows the conditional variance to depend on the conditional variance of the previous lag. Where the actual values of the conditional variance are parameterized and depend on the q-lag of the residual squares and the p-lag of the conditional variance, it is written as GARCH (p,q). So, the GARCH model if its time-varying conditional variance is heteroscedastic with both auto-regression and moving average (Wang, 2009).

Change the standard deviation to GARCH so we can get a new calculation for Sharpe and get a new result that we can use to calculate the portfolio measurement. Adaro Energy is non-stationary because the result is 0.9652 and it is not significant (Table 4.1-1), and next is the white noise test, the last part to check the stationary or non-stationary data. The standard deviation differences are significant, for PT Adhi Karya 2.9%, PT Adaro Energy -0.5% and PT Astra Agro Lestari -.3.7%.

If we use GARCH, the risk we can get is smaller rather than if we use standard deviation. Adding more period that expect the result will be better which will be generated by GARCH model.

A UTOREGRESSIVE I NTEGRATED M OVING A VERAGE (ARIMA) M ODEL . 10

C ALCULATE THE NEW F ORMULA