Monte Carlo Simulation for Data Volatility Analysis of Stock Prices in Islamic Finance for Malaysia Composite Index

The objective of this study is to evaluate the volatility rate of sharia-company in Malaysia Stock Exchange using Monte Carlo Simulation (MCS). This study collected daily stock price form Thomson Reuters Datastream for calculating monthly return and volatility rate. In validating the findings of volatility rate, this study performed normality diagnostics test, and Monte Carlo Simulation (MCS). Result indicates the distribution of volatility rate is follows normal distribution. In addition, Monte Carlo Simulation also proved the volatility rate is 4.85% and standard deviation is 2.23. Result of process capability shows the value of volatility rate is under statistical control with implementation on Monte Carlo Simulation. The significant of this study is it provides a better understanding for investors regarding the financial environment in Malaysia Stock Exchange. This information will help investors to make proper selection of their investment portfolio. Keywords— Monte Carlo Simulation, Malaysia Stock Exchange, Volatility, Islamic Finance.


I. INTRODUCTION
Financial economists, market participants and international organizations view shariah-compliant companies as a main key in contributing capital into financial market in Malaysia. An accurate forecast of future volatility delivers important information to market participants and, consequently, there is an option to essentially bet on volatility (Kongsilp, Mateus, 2017). Various empirical investigations have been performed to analyze the volatility of shares price. Forecasting volatility of shares price plays important roles in investment market (Abu Bakar and Rosbi, 2017). Volatility is measure variation of price of financial instrument over time, and as much the market is volatile, it creates risk which is associated with the degree of dispersion of returns around the average (Siddikee and Begum, 2016). Lack of efficiency in monitoring, regulating and supervising would result with the collapse of stock market such as high volatility and bad company performance in term of revenue, dividend and etc. (Abu Bakar, et al., 2018a). Therefore, the purpose of this paper is to determine level of volatility among shariah-compliant companies on Malaysia Stock Exchange. The main important to be listed on the shariah board is that companies must be free from prohibited element in shariah law such as riba, gharar and maisir (Abu Bakar and Rosbi, 2016 In Equation (1), the parameters are described as follows: Re t : Return rate at observation monthly period t, t P : Stock price at observation monthly period t, and 1 t P  : Stock price at observation monthly period t-1.
Next, volatility in this study is represented by using standard deviation in Equation (2).
The parameters in Equation (2)  The Monte Carlo method is method for analyzing uncertainty propagation to determine variation affects the sensitivity and reliability of the system that is being modeled. Monte Carlo Simulation is defined as a sampling method because the inputs are randomly generated from probability distributions to simulate the process of sampling from an actual population. A Monte Carlo method is a technique that involves using random numbers and probability to solve problems. Monte Carlo simulation uses random sampling and statistical modeling to estimate mathematical functions and mimic the operations of complex systems. Monte Carlo simulation produces distributions of possible outcome values. Figure 1 shows Monte Carlo Simulation framework. Input variables are represented by variables X, that as independent variables for mathematical system. Next, all of input variables is transformed using mathematical function model of particular system. Finally, the outcome of study is produced and represented by Y variable.

IV. RESULT AND DISCUSSION
Main objective of this study is to develop evaluation method for volatility rate among sharia-compliant companies listed on Malaysia Stock Exchange. This study performed normality diagnostics using graphical and numerical approach. In addition, in producing a valid finding, this study implemented Monte Carlo Simulation method.

Data selection and return analysis
This study collected daily stock prices from Thomson Reuters Datastream. Then, average monthly returns are calculated for 19 companies that sharia-compliant. Table  1 indicates the companies with corresponding average monthly return.  Table 1 shows average value for monthly return is 0.442% with standard deviation is 1.248 %. The value of average return for companies is positive that is indicates all companies shows a positive gain. In addition, low value of standard deviation indicates the stock price market is stable.

Volatility analysis
The volatility of this study is calculated from return data for each of 19 companies. Figure 1 indicates histogram of data distribution for volatility rate. Figure 1 indicates data distribution of volatility close to normal distribution line (red line). Therefore, data distribution of volatility is follows normal distribution. Next, this study performed normal probability analysis. Figure 2 shows normal probability plot for volatility rate. The data distribution of volatility is close to normal straight line (red line). Therefore, data distribution of volatility follows normal distribution. Next, this study validated the normality findings using statistical test. This study implemented Shapiro-Wilk normality because sample size is less than 50. Table  indicates statistical test for normality checking of data distribution. The probability value (p-value) is 0.562 that larger than 0.05. Therefore, this study failed to reject null hypothesis. As a conclusion, data distribution of volatility rate follows normal distribution. Then, this study analyzed outlier detection using box-andwhisker plot. Figure 3 shows box-and-whisker plot for volatility rate. Figure 3 indicates there is no outlier exists in data distribution. Range Volatility rate Fig. 3: Box-and-whisker plot for volatility rate

IV.2 Monte Carlo Simulation for volatility rate
This study performed process capability analysis to inherent statistical variability which can be evaluated by statistical methods. Figure 4 shows process capability for volatility rate. Number of sample data is 19 observations. The sample mean is 4.847. Data distribution of volatility is indicated using standard deviation of within is 1.95 and overall is 2.227. Main objective of this analysis is to evaluate statistical control for volatility data. The difference value between pk C and pk P is 0.15 that indicates processes are in a state of statistical control.

International Journal of Advanced Engineering Research and Science (IJAERS)
[ Next, this study implemented Monte Carlo Simulation for simulating volatility rate in process capability method. Figure 5 shows process capability of volatility rate. This study increased number of samples to 10000 samples to attain valid and reliable findings of volatility rate. The difference value between pk C and pk P is almost zero that indicates processes are in a state of statistical control.
As conclusion, with the implementation of Monte Carlo Simulation, the level of reliability of process control is increased.
V. CONCLUSION Main purpose of this study is to analyze volatility rate of 19 sharia-compliant companies listed on Malaysia Stock Exchange. Findings of this study are listed as follows: (a) Average value for monthly return is 0.442% with standard deviation is 1.248 %. The value of average return for companies is positive that is indicates all companies shows a positive gain. In addition, low value of standard deviation indicates the stock price market is stable. (b) This study validated the normality findings using statistical test. The probability value (p-value) is 0.562 that larger than 0.05. As a conclusion, data distribution of volatility rate follows normal distribution. (c) Monte Carlo Simulation has proved that reliability of process control is increased with implementation of large data set. The important of this findings are enabling investors to gain knowledge about real financial market condition in Malaysia Stock Exchange. In the same time, Monte Carlo Simulation can be implemented to get reliable result although the real sample size is small. Future work of this study can be venture to development of determinants that contribute to dynamic behavior of volatility in Malaysia Stock Exchange.