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Forecasting Islamic Stock Market Volatility: An Empirical Evidence from Pakistan Economy

Amina Rizwan1 and Ambreen Khursheed1

Abstract Islamic investment particularly, in stocks has revealed an incredible growth in the 21st century. The growing demand of Islamic finance in Pakistan has asserted the main controllers of stock market to launch Islamic index for assisting investors in buying and selling of shares in alignment to their religious beliefs. Though Pakistan is deficient in having a proper Islamic stock market but Al-Meezan and has initiated an Islamic stock market by the name of Karachi stock exchange Meezan index (KMI-30). This study uses time series analysis for the forecasting of Islamic stock index of Pakistan under the influence of volatility. The daily data of KMI-30 of five days per week starting from 1st September 2008 to 3rd May 2012 is taken. The output reveal that Muslim investors can earn substantial revenues by investing in Islamic stock indices and can also achieve their peace of mind by aligning their investments to their religious values. The results of Box-Jenkins methodology show that ARIMA model with the value of (2, 1, 0) and Generalized Autoregressive Conditional Heteroskedasticity shows that GARCH with the value of (1, 1) are the best models for forecasting of KMI-30 in Pakistan. Hence, the study assists policy makers, practitioners and investors who desire to make alignment in their financial investment and religious values.

Keywords: KSE-100 Index, Shari’ah, Stock Performance, Generalized Autoregressive Conditional Heteroskedasticity.

1. Introduction: Stock market is a place where buying and selling of financial and industrial securities take place (Hosseni, 2011). The investor may assume that he can make millions from the buying and selling of securities but unfortunately, the reality paints a different picture. Forecasting has been done in many fields but the financial markets forecasting is more complex. The different researchers proposed the different parameters to predict or forecast the trend of stock price for investors. So a trustworthy forecasting is required to predict the future of investors (Hosseni, 2011). During 1970’s a huge number of Muslims were not taking part in stock market due to the prohibition in Islam for participating in certain business activities. In the early 1990’s a revolution in religious investment took place by operating of equity investment by the operation of Islamic equity funds (Omran, 2005). According to a careful estimation there is an investment of 230 billion available to Islamic financial markets and this amount is growing by 15% annually (Rashidin, 2004).In Pakistan the Islamic banking industry is also growing by 73% during last eight years (SBP-2011). The total assets volume under Islamic banking in Pakistani market up till now is 641 Billion Rupees which capture about 8% of market share (SBP-2011). The major challenge for Islamic banking and industry is management of liquidity by investing in market securities. The Shariah compliance security only allows investing in an Islamic bank, and the interest based securities are not allowed to invest in Islamic banks. Normally Islamic banks follow two features one is to perform interest-free banking and the other is to do business in those things which are permissible in Muslims religion (El Khamlichi and Sarkar, 2013). In worldwide the eight Islamic indexes are Financial Times Islamic Index Series (FTSE), Dow Jones Islamic Index group (DJIM), Morgan Stanley Capital International Islamic Index Series MSCI, Standard and poor sharia index (S&P), HSBC Amanah Global Equity Index Fund (HSBC), American Islamic Index (AMERI) and Karachi Meezan Index i.e. KMI-30 (Murzaban, Derigs, & Sayeed, 2008). This study is about KMI30 that is Karachi Meezan Index. It is a local index of Karachi which is established for the checking of Shariah Compliance status of security. In Pakistan the three stock exchanges currently working are Lahore Stock Exchange (LSE), Islamabad Stock Index (ISE) and Karachi Stock Index (KSE). The Karachi stock index is the main index includes KSE100 index, KSE all share index and KMI30 that is Islamic stock index working in Pakistan (Naqvi, Karachi Stock Exchange, 2011).

1 Lecturer, School of Accounting and Finance, FMS, UCP [email protected] 1 Lecturer, UCP Business School, FMS, UCP. [email protected]

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The KMI 30 is established to check the status of a security before investment by IFI i.e. International Financial Institutions. The KMI-30 index is the largest free float Shariah compliant companies listed at Karachi Stock Exchange. The screening of Shariah complaint is conducted by Al Meezan Investment Management. The Shariah compliance companies are selected on the basis of free float capitalization and volume of trade. The re-composition of the KMI-30 index takes place semi-annually. The KSE Meezan index (KMI30) was launched by the alliance between Al Meezan Investment Management Ltd and with the Karachi Stock Exchange (KSE) in 2008 (Naqvi, 2011). Karachi Meezan Index is also calculated on the basis of free float market capitalization. It means at any point KMI shows free float market value of Islamic Index shares in Pakistan. The objective of the KMI-30 index is to provide a gauge for the determining the performance of Shariah Compliant equity investments. The construction of Shariah complaint will increase the participation and enhance the trust of people investing in faith-based equities. (Hanif, 2011).

The six requirements of Shari’s compliance are as follows: 1. The core business of a company should be done on Shari’s lines and must be halal. Any unlawful (haram) for example dealing in conventional bank insurance, tobacco, arms manufacturing, alcoholic drinks, pork production or anything related to non-Islamic activities are not allowed. 2. Interest-based financing should be less than 40%. In other way debt to assets ratio should be at least less than 40%. 3. The investment ratio of non-complaint to the total assets should not be more than 33%. The amount of total interest based loans should not be greater than 33% of market capitalization. 4. The Ratio of Shari’s non-complaint income to the total revenue must be lesser than 5%. 5. The share price in the market should not greater than the amount of net liquid assets per share. A liquid asset is an asset which can only be traded on par value according to Sharia’s rule. Liquid Assets include bills receivable, promissory notes and accounts receivables and preferred shares. 6. The ratio of liquid assets to the total assets should be 20% of all illiquid assets. The formula is given below

Net Liquid Assets Per share = Total Assets- Assets Illiquid - Current Liabilities – Long-Term Liabilities No of shares outstanding

The top 30 companies are included in KMI-30 index as per above criteria. The technical committee will use 15,000 points as the base value and 30th June 2008, will serve as the base period of index. The daily maintenance of index will be according to board policy framework set by stock exchange and Al Meezan Investments. They will ensure that Islamic Index will maintain their continuity while balancing between frequent replacements (Arouri et al., 2013). In the last few decades there is tremendous rise in growth and acceptability in expansion of Islamic financial products in Pakistan. Some attempts are made to assess the performance of KMI-30 with other stock indexes in Karachi from its launch in the year 2008. It was seen that KMI-30 index provided a return of 40% to investors and KSE-100 during the same situation with the 30% stocks that are most liquid provide negative results (El Khamlichi and Sarkar, 2013).

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Table 1: List of Companies Included in the Recomposed KSE-Meezan 30 Index

S-NO. SYMBOL COMPANY S-NO. SYMBOL COMPANY

01. OGDC Oil & Gas Development 10. DGKC D. G. Cement

02. FFC Fauji Fertilizer 11. MTL .

03. PPL 12. PTC P.T.C.L.A

04. POL Pakistan Oilfields 13. NRL National Refinery

05. HUBC Hub Power 14. APL Attock Petroleum Ltd

06. PSO P.S.O. 15. INDU Indus Motor

07. ULEVER Unilever Pakistan 16. ICI I.C.I. Pakistan

08. LUCK 17. ATRL Attock Refinery.

09. FFBL Fauji Bin Qasim 18. LOTPTA Lotte Pakistan PTA

19. SNGP Sui Northern 25. TRIPF Tri-Pack Films

20. PICT Pak Int. Cont. Ltd 26. MARI Mari Gas

21. SHEL . 27. ACPL Attock Cement Pak.

22. MEBL Ltd. 28. CPL Clariant Pak.

23. GLAXO Glaxo Smith Kline 29. PRL Pak Refinery

24. THALL Thal Limited 30. HABSM Habib Sugar (Karachi Stock Exchange, 2012)

Through different principles of Quran and Sunnah Muslims can easily know the right or wrong and just and unjust ways of earning money and acquisition of wealth. An important injustice in dealing with a transaction is taking monetary advantage without giving any value. Riba is a prominent source of unjustified advantage and it is prohibited in Islam. The Holy Prophet censured those who collect riba. Riba means expansion and growth without bearing hardships. While, every increase or growth is not necessarily prohibited in Islam. The riba is the premium paid to the lender by the borrower with the original amount (Chapra, 1984). (Razi, 2008) stated the true meaning of riba regarding Islam. According to him Allah swt states in Quran: ”تُ ف ِل ُحو َنَ َلعَ َّل ُك مَ ال ل َه َواتَّقُو اَ ُّم َضا َع َف ًةَ أَ ض َعا ًفا ال ِ ربَا تَأ ُكلُو اَ لَ آ َمنُو اَ ا َّل ِذي َنَ أَيُّ َها يَا“ “O you who have believed, do not consume usury, doubled and multiplied, but fear Allah that you may be successful” (ALQuran 3:130). ” َوأَ َح َّل ال ّلهُ ا ْلبَ ْي َع َو َح َّر َم ال ِّّربَا" “Allah has permitted trade and has forbidden interest” (Al Quran 2:175). The different questions rose in our minds while analyzing the performance of Islamic Indices that would the investors gain if they invest in Islamic indexes rather than conventional indexes. It is quite easy to access the Islamic indices while investing or comparing the performance because all big financial Islamic services are working like Standard and Poor FTSE, DJIM etc. Due to a larger market there are many Islamic indices available in the market by financial agencies. For example, countries like Pakistan and Iran are fully compatible according to Shariah law. In Indonesia, Malaysia, Egypt, Sudan are fully compatible Islamic as well as conventional finance (Kynas & Isaksson, 2012).

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Forecasting of volatility is very important for investors and portfolio managers. They can bear a certain level of risk. An efficient forecasting of volatility is very useful for assessing risk. Many investors have incomplete information of the difference between volatility, risk and standard deviation. In finance, volatility is used for standard deviation or variance. If an instrument enters into nonlinearity then it will construct a model for financial returns which is heteroskedastic. If volatility is found then ARCH and GARCH is the most widely accepted model for financial time series. Similarly, the implied volatility that is a market based volatility forecast can be parameterized by GARCH model (Huang Poon & Grangeri, 2003). The presence of Heteroskedasticity in time series presents a different graphical appearance as it shows the variance or volatility to time. According to Engle (1982) before ARCH model the volatility was observed by the standard deviation. The ARCH model determined the most suitable weights to forecast volatility. As ARCH models are easy to handle volatility clustering. Similarly, Bollerslev (1986) anticipated a useful extension known as the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model of ARCH model (Perelli, 2001). Stock market is a risky market and since people cannot accurately predict the next moment so measuring the risk performance and forecasting is extremely important in the field of the stock market where more challenging issues are raised. When there are reasonable predictions with less biased investor will earn a profit and it will help management to take a decision. With the emergence of artificial intelligence in recent years, the stock prediction has become more efficient (Harazdil, Chung, & Karel, 2010). Many forecast models and risk performances have measured by researchers to forecast stock prices of conventional stocks like KSE-100 index, to help investors but no attention is paid to Shariah compliance KMI-30 forecasting which is not based on interest. Due to better performance of Islamic index KMI-30 it is important to measure the risk and forecasting of stock index values of KMI-30 by using daily data of five years, which has not been done before in Pakistan. So there is a need for conducting this research. (Hussain, 2004) stated that campaigners of ethical investment argued that a corporate responsibility is in a superior position to evade social and environmental crisis that may guide to high production costs, reputation damage, advanced safety costs and lost production. A good corporate social responsibility can assist companies to have a competitive advantage. But the return on share purchased in Islamic index is doing well and also has an increasing trend due to more liquidity and less debt (Fowler and Hope 2007). It provides an investor a new guideline to make effective investment portfolio and help him to stand against market shocks. Hence, this study fills the research gap by doing a comparative analysis for forecasting Islamic Stock index. The paper aims to determine the extent to which the volatility in shares market affects Shari’ah stock in the developing . Moreover, this study provides a clear direction for the investors who are interested in investing in Islamic stocks without compromising on their religious beliefs. In this study, the Markowitz model is a theoretical framework which is used for the analysis of return and risk and the inter-relationships. The statistical analysis was used to measure the risk and it helps further in the selection of a portfolio. This study is demeanor to document the perception of the market about Shari’ah compliant equities. The objectives of our study are as follows:  To determine whether principles of Shari’ah Compliance like the prohibition of riba, less debt to equity ratio and less investment in illiquid assets are a hindrance to build a profitable portfolio.  To forecast the volatility and returns of the KMI30 index by using econometric methodology.  To determine whether Islamic index (KMI-30) benefits portfolio diversification of investors?

1.1 Research Questions 1. How volatility in shares market affects Shari’ah stock in the developing economy of Pakistan? 2. Are conditional volatilities of KMI 30 index time-varying to forecast the asset prices? 3. Does the exclusion of conventional indices impact the benefit of portfolio diversification for Pakistan Shariah investors?

The paper aims to find out the extent to which the volatility in shares market affects Shariah stock in Pakistan. Furthermore, this study provides a clear direction for the investors who are interested in investing in Islamic stocks. The theory used as the theoretical framework for this study is modern portfolio theory. As according to this theory the volatility creates risk which is linked with the degree of dispersion of returns around the average. Furthermore, this theory explains the tradeoff relationship between the risk and return. The study contributes in existing theoretical and practical research work by providing in-depth

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analysis of the volatility of the Islamic stock index for domestic and international investors. The study provides sufficient knowledge for the investors to understand that the Islamic stock index is less volatile as compared to conventional index. Furthermore, the study also explains that investors can earn more profit by having portfolio diversification that is to invest in both portfolios i.e., conventional and Islamic index. Furthermore, the knowledge of the integrations of the markets is important for domestic and international investors for portfolio diversifications. The integration of Islamic and conventional indices in Pakistan provide knowledge that the investors may not be able to benefit from diversification if they have both indices in their portfolios. However, investors may add one of the indices in their portfolios to benefit from diversification. Furthermore, investors can invest in Islamic indices which provide highest returns as compared to its conventional counterparts

2. Literature Review Contrary to existing research studies on Islamic mutual funds and banks, Islamic indices have never been considered for empirical research because of their petite histories (Hussain, 2004). Moreover, to analyze the financial cash flows with an Islamic vision is also considered as a more difficult task (Fowler and Hope, 2007). Thus, past researchers like (Naughton and Naughton, 2000) applied qualitative research methods to analyze the initial stage of Islamic indices in view of the financial framework, market principles and regulations. The Islamic economic system does not depend upon the arithmetical calculations and aptitude of production alone. Rather it is convinced in the light of a great system of principals and morals (Hannover, 2013). According to (Hussain, 2004) the development of Islamic economics highlights of destitute masses that there should be equal distribution of wealth and recompense to all participants in the market that are exposed to risk and liability. There are different studies on Islamic and conventional stock indexes. Though past research studies highlighted somehow mixed conclusions and the difference was reported mainly in terms of their sample sizes, data collection periods and performance indicators like (Ahmad & Haron, 2002) explained that in spite of the fact that the Islamic system commenced in eighties, the Malaysian customers in corporate sector had a very petite perceptiveness of Islamic financial system. They added that the market supposed an improved possibility of development of Islamic financial system if the costs of products presented by international financial institutions (IFIs) were low. (Rammal & Zurbruegg, 2007) determined the awareness of profit and loss sharing of different financial instruments. They conducted a primary research by selecting a sample of 300 Muslims in Australia for their questionnaire-based survey. The main purpose of their study was to determine that whether people in Australia were aware of Islamic financial products. The results indicated that most of the Muslim population in Australia was willing to buy Islamic banking products but they were not properly informed about the concept of profit and loss sharing. Hence their study recommended that financial institutions should invest in new products to meet the demands of customers and institutions and should inform people about new Islamic products that involve profit and loss. Same findings were reported by another study of (Abdullah and Dusuki, 2006) who recognized after surveying 203 customers in Malaysia that there was necessitate for educating customers about the products of Islamic financing. (Hussain, 2004) analyzed the performance of FTSE Global Islamic values of the index were considerably different from the FTSE All-World by analyzing a sample for the period from 1996 -2003. With a comparative study of raw and risk-adjusted performance Islamic index, he found that the performance of Islamic banks was significant and positive in the bull market and goes down in the bear market. Few research papers have also highlighted the importance of companies working in compliance with Shariah principles in view Islamic stock index. As, a study by (Kasi and Muhammad, 2016) described if the issuer company announces that its business activities and its management are directed based on the Shariah principles and it is not involved in any illegal activity then the company is considered as a Shariah Compliant Company. In the same way, a study explained that Shariah only allows common stocks to be traded. There may a difference of opinion occur regarding the permissibility of exchanging common stocks through buying and selling transactions (Ahmad et al., 2014). Furthermore, Islamic Fiqh Academy announced that investing in ordinary shares is permitted if the key business of the company is following Shariah ruling (Ahmad et al., 2014; Pradiknas and Faturohman, 2015). Similarly, past researches explain that the income of the company from non Shariah-compliant investment, which comprises of interest, should not be more than 5 percent out of its total revenue (Butt, 2014; Aljuhani & Bardesi, 2016). In view of Zakat, a study explained that if a shareholder wants to be a long-term investor then zakat will be calculated on the

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basis of dividend per year, only one-time zakat on complete selling price at the time of selling the share (Bradford, 2015). Volatility means unpredictability and this approach is based on an autoregressive conditional heteroskedasticity model (ARCH) which was introduced by Engle (1982). In addition to this, the other method of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) is introduced by Bollerslev (1986). These models are used since they permit for heteroskedasticity in the residual series. As there exists a robust economic association between the emerging markets and the developed markets, therefore, the investor needs guidance to reduce the shocks and risks of a market and these models assist them in mitigating their investment risks (Lipe & Yang and Qiu, 2005). (Madhavan, 1992) highlighted the significance of volatility in share market by emphasizing that volatility in the terms of price should be low. As it reduces the risk which is borne by the investors who trade in the share market to liquidate their assets without paying a huge amount. Same results were confirmed by Glen (1994) who defined the volatility as the frequency and magnitude of the movements of price and compared different microstructures and concluded that efficient market have low volatility as compared to inefficient markets. A research study by (Arouri et al., 2013) examined the influence of global financial crisis (2008- 2009) on 3 Dow Jones Islamic indices to check the potential of Islamic financing banks in uplifting investors and supporting financial organizations to tackle the economic ups and downs. They developed portfolio simulation and used Granger Causality test and Multivariate Vector Autoregressive (VAR) to analyze Islamic and conventional financial systems and concluded Islamic financial systems provide more secure investment opportunities to their investors. Various studies on the global Islamic indices’ performance analysis include (Khamlichi and Sarkar, 2013; Guyot, 2011). A study by (Guyot, 2011) examines nine Dow Jones Islamic Indices (DJIM) and determined no cointegration and performance difference between non-Islamic and Islamic indices. On the similar lines, (Khamlichi and Sarkar, 2013) also confirms the findings reported by (Guyot, 2011). They also documented that Islamic financial institutes are also efficient as conventional organizations (Sadegi, 2011) investigated the influences of addition of index on the liquidity and return of shares of Shariah complaint in Jorden and Egypt. He used the data of Dow Jones Islamic index for the period from 2008 to 2009. The findings of study showed that there was positive relation between the addition in index and the return and liquidity of added shares. The Islamic index showed the same results as the conventional index. Thus, the study concludes with a positive news for investors who believed in ethics of Islamic investing of Middle East to take active part in investment. (Shabri & Yusof, 2007) endeavored to investigate the degree to which the conditional volatilities of both Islamic stock and conventional markets in Malaysia are linked to the conditional volatility of the monetary policy variables. The tested variables like interest rates, narrow money supply, exchange rate, the broad money supply and Index Industrial Production while the Rashi Hussain Berhad Islamic Index (RHBII ) and Kuala Lumpur Composite Index (KLCI) were used for measuring the conventional and Islamic stock markets, respectively. GARCH-M, GARCH (1, 1) framework with Vector Autoregressive (VAR) analysis was applied for the monthly data starting from January 1992 to December 2000. The study discovered that interest rate volatility significantly affects the conventional stock but not the Islamic stock. The results gave more support that the interest rate would have an insignificant impact on the volatility of the Islamic stock markets. A study by (Sukmana & Kholid, 2010) examined the resilience of Islamic index with its comparison index in the global financial crisis during 2008. According to them the stock indexes of developed markets had a great influence on emerging markets like Malaysia, Indonesia and different countries in South Asia. Their study provided a guideline to investors in emerging markets to make investment decisions. The risk performance of Jakarta Islamic Index (JAKISL) and its counterpart Jakarta Composite Index (JCI) was measured. To represent crisis a dummy variable was adopted. The daily data of 2185 observations, from early January 3, 2001 to December 30, 2009 was taken from Bloomberg. The daily data of closing prices of JAKISL and JCI was taken. To measure the risk the ARCH and GARCH model was employed. Their study concluded that crisis affects volatility. Risk was measured with volatility so study concluded that both the JAKISL and JCI were affected by the crisis but Islamic index was more resilient as compared to its counterpart so if an investor is a risk avoider he will select Islamic Index and even according to norms of Islam a Muslim will definitely invest in Islamic index. On the basis of these studies, we identified that Islamic stock index is an important index for research. To our knowledge this study is the first attempt of its kind to examine the forecasting trends of

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Islamic Index KMI (30) in Pakistan. The study includes KMI-30 for assisting the investors in accurate forecasting. Following hypotheses are deduced from the existing literature.

2.1 Hypothesis: H1: The principles of Shariah Compliance are a hindrance in building a profitable portfolio. H2: Proper Modeling (forecasting) of prices of Assets of Shariah index is required. H3: The return of Islamic Index (KMI 30) benefits portfolio diversification of investors.

2.2 Purpose The purpose of this study is to document the acuity of finance professionals. This study is carried out to document the theory and performance of Islamic Index KMI (30) that is doing operations in Pakistan. The paper aims to determine the extent to which the volatility in shares market affects Shariah stock in the developing economy of Pakistan. Moreover, this study provides a clear direction for the investors who are interested in investing in Islamic stocks.

3. Theoretical Framework The return on stocks and volatility is a key issue for investors, researchers and regulators. The different variables like interest rate, exchange rate, inflation, per capita income and political stability affects Pakistan equity markets. The volatility and returns, increased political stability and democratic conditions enhance the stock returns of KSE in Pakistan and the better performance of stocks market increase profitability and economic growth (Nazir, 2010). There are quite a few theoretical point of views which facilitates in accurate forecasting of Stock Index that affect the worth and liquidity of incorporated shares. The conventional finance theories are based on Efficient Markets Hypothesis (EMH) which assumes that all the securities substitute each other and the demand curve is horizontal (Malkiel B., 2003).

4. Modern Portfolio Theory The most relevant theory to this study is modern portfolio theory. According to this theory, the volatility creates risk which is linked with degree of dispersion of returns around the average. In other way greater the chance of lower than the expected returns (Merdad, 2010).The Modern Portfolio Theory (MPT) is a theory of investment which endeavors to maximize the expected return of a portfolio for the given portfolio risk or minimizes risk for the given expected return level by choosing the various proportions of assets. The MPT theory is a different approach to investment decision that helps the investor to control, categorize and estimate both kinds of expected risk and return. This theory is also called the portfolio management theory. Furthermore, this theory explains the tradeoff relationship between the risk and return.

5. Research Methodology The research methodology included the entire procedure and methods through which the research objectives of our study can be achieved.

5.1 Target Population The Karachi stock exchange (KSE) is our population. KSE includes KSE all Share index includes KSE-100 index, KSE-30 index, KMI-30 index. KMI-30 index is our target population. The sample of six years daily data is taken from target population to present the Islamic Index. KMI 30 is selected as target population of our study as it is the single Shariah compliance index in Pakistan. The study uses secondary data to examine the risk performance of KMI-30 index SPSS and E-views are used for the analysis of econometric results.

5.2 Data The various volatility models are estimated using daily data of the KMI-30 index to represent the Shariah index. Islamic stock index is an important index for research. To our knowledge, this study is the first attempt of its kind to forecast by focusing on only the Islamic Index KMI (30) in Pakistan. Therefore, the study includes KMI-30 for accurate forecasting and for providing a clear view of stock market to the investors who believe in Ethics and morals of Islamic financing. The data of Islamic stock index comprises of 1000 entries taken on a daily basis from 1st September 2008 to 2nd May 2012 from Karachi stock

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exchange. We have taken data for six years as we want to analyze the performance of Islamic stock index specifically during the period of Global Financial Crisis that began in 2008. The first time period is in “sample period” that is from 1st September 2008 to 2nd may 2012. The second time period is “out of sample” is from 3rd May 2012 to 3rd August 2012.

5.3 Data Analysis The univariate method is used in forecasting of Karachi Meezan Index on the basis of past data. At first, stationary is checked by using the most widely accepted Augmented Dickey-Fuller unit root test. In order to achieve the objectives of our study i.e., whether principles of Shari’ah Compliance are a hindrance to build a profitable portfolio, to forecast the volatility and returns of KMI30 index and to determine whether Islamic index (KMI-30) benefits portfolio diversification of investors we have used ARIMA modeling, ARCH and GARCH models. The volatility is checked by ARCH effects and the risk performance measurement and forecasting are done by applying Generalized Autoregressive conditional heteroskedasticity GARCH model. An augmented Dickey-Fuller test is a version of the Dickey-Fuller test which is used for a larger and more complicated set of time series models. After applying the ADF test if unit root is identified and then differencing will be used in order to make data stationary. This study consists of time series approaches to estimate and forecast KMI-30 index prices by using ARIMA and GARCH model. These approaches are used to estimate the latest data and to forecast the data in future. The volatility is tested by ARCH model. If volatility clustering is identified in data, then Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model will be applied for forecasting and comparing risk. It is a univariate study in which the volatility of Shariah index (KMI-30) is measured and lastly forecasting of the index is done for assisting the investors.

5.4 KMI-30 Time Series A line graph is plotted for a sample period of index prices from 1st September 2008 to 2nd May 2012 shown in graph 1. The line graph depicts a downward trend from 31st Jan 2008 to December 12th, 2008, a continuous decrease in stock prices and there is a significant upward trend on 4th February 2015. The variability is greater when the series takes high values from June 2010 to November 2010 (values from 451 to 551) than when it takes low ones in year from values 16th April 2009 to 26th June 2009 (values from 151 to 201). The series clearly shows periodic behavior and non-constant mean. However, the ARIMA model with correlogram is shown in table 2 which shows that autocorrelation and partial correlation is present in the data. The figure shows the ACF of KMI index series: a slow linear decay of the coefficients can be observed, which indicates the need to differentiate.

Graph 1: Line graph of KMI-30

Source: Author’s Calculations

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Table 2: ARIMA MODEL Identification-Correlogram at level

Source: Author’s Calculations

5.5 Histogram and Normality Tests For evaluating the normality in the data, histogram and normality tests are performed which are shown in figure 1. The mean is 15958.13 and the standard deviation is 4612.141 respectively. The histogram is slightly negatively skewed that -.098 and Kurtosis is 1.920 that is not too much. The results obtained from Jarque-Bera tests reveal that we cannot reject hypothesis of data’s normal distribution at 5% significance level. The original series is not suitable for estimating and forecasting. Hence, our data is following a normal distribution.

Figure 1: Histograms and Normality tests 80 Series: KMI30 70 Sample 9/01/2008 5/03/2012 Observations 910 60 Mean 15958.13 50 Median 15417.33 Maximum 24868.74 40 Minimum 6322.230 Std. Dev. 4612.141 30 Skewness -0.098033 Kurtosis 1.920758 20

10 Jarque-Bera 45.62153 Probability 0.000000 0 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 Source: Author’s Calculations

At level Augmented Dickey-Fuller test and Phillips person test uses parametric autoregression to estimate errors and to check the stationary of the data. The statistics in table 3 and 4 respectively shows that its value is greater than critical values at 1%, 5% and 10% level and the p value is 0.9 which is not acceptable, which means the data is not stationary. Hence, we cannot reject hypothesis that KMI-30 has root.

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Table 3: Augmented Dickey Fuller Test Augmented Dickey-Fuller test statistic Null Hypothesis: KMI30 has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, max lag=20) t-Statistic Prob.*

Augmented Dickey-Fuller test statistic 0.349363 0.9807 Test critical values: 1% level -3.437330 5% level -2.864510 10% level -2.568405

Source: Author’s Calculations

Table 4: Phillips-Perron Test Phillips-Perron Test Null Hypothesis: KMI30 has a unit root Exogenous: Constant Bandwidth: 10 (Newey-West automatic) using Bartlett kernel

Adj. t-Stat Prob.*

Phillips-Perron test statistic 0.198911 0.9725 Test critical values: 1% level -3.437322 5% level -2.864507 10% level -2.568403

Source: Author’s Calculations

The value of PP test is greater than the critical values at 1%,5% and 10% at level and the probability of PP test is greater than 0.05 so we accept the null hypothesis that KMI series has a unit root at level. So we need to take values at first differencing.

5.6 Stationary at First Differencing The series clearly shows periodic behavior and non-constant mean. So initially the study took differencing at first level as shown in model described in graph 2. The figure shows the first difference of the KMI-30 series and we can see that it contains very noticeable variations in its value on a monthly basis.

Graph 2: Line Graph at First Difference

Source: Author’s Calculations

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The correlogram at first differencing is shown in table 5 which reveals the data is stationary at first differencing now. The spikes of ACF and PACF within brackets indicates that data is stationary at first difference. Table 5: Correlograms at First Differencing

Source: Author’s Calculations

ADF and PP test is applied to check the stationary at first difference. Results are shown in table 6 and 7 respectively. Thus, the data is stationary now. This test reveals that the value of ADF is much lesser than critical values and value of p with the value of 0.000 is significant. The value of the PP test is - 27.82199, which is much lesser than critical values of 1%, 5% and 10% and value of p with 0.000 is significant. Hence, we reject the null hypothesis that KMI 30 series has a unit root at first difference.

Table 6: ADF Test for the First Differencing Null Hypothesis: D(KMI30) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=20)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -27.46654 0.0000 Test critical values: 1% level -3.437330 5% level -2.864510 10% level -2.568405

Source: Author’s Calculations

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Table 7: PP Test for the First Differencing of KMI-30 Null Hypothesis: D(KMI30) has a unit root Exogenous: Constant Bandwidth: 10 (Newey-West automatic) using Bartlett kernel

Adj. t-Stat Prob.*

Phillips-Perron test statistic -27.82199 0.0000 Test critical values: 1% level -3.437330 5% level -2.864510 10% level -2.568405 Source: Author’s Calculations

The t- statistics for the coefficient variables AR (p) and MA (q) is represented in table 8. It rejects the hypothesis that MA is zero. The estimated parameter coefficients by ARIMA (2, 1, 1) model gives α1=0.937741, α2=-0.040012and β1=-0.0863388. The value of R2 is 0.004223 which shows that the dependency on estimated value by the series is not strong enough. The DW statistics is approximately equal to 2 due to the existence of a positive serial correlation in the residuals. Thus the model equation is formed as:

Yt= 0.937741t-1+0.040012t-2+0.085451t-1+µt Time series forecasting is used to predict the expected values of a series given its preceding values of an error term. If the scale of the most recent error has a tendency to be constantly larger than preceding errors, it is better to reexamine the model.

Table 8: ARIMA MODELS ARIMA MODELS (0, 1, 1) (1,1,1) (1,1,0) (2,1,0) (2,1,1) (2,1,2) Best model MA(1) AR(1) AR(1) AR(2) AR(2) AR(2) Variable MA(1) MA(0) MA(1) MA(2) AR(1)=0.937741 AR(2)=-0.040012 MA(1)=- Coefficient 0.0863388 R-squared 0.005982 0.008315 0.006288 0.00091 0.004223 0.009402 RMSE 127.950 127.018 127.727 127.446 127.013 127.076 Adjusted R- squared 0.005000 0.004864 0.005306 -0.00007 0.002353 0.005472 S.E. of regression 188.5260 188.4903 188.5895 189.188 188.5721 188.6638 Sum squared resid 36004111 35992807 361860 35879488 35878764 Durbin-Watson 1.84458 stat 1.993094 1.956797 2.000983 1.996417 1.996876 Akaike info criterion 13.31832 13.31892 13.31899 13.3213 13.32078 13.32273 Schwarz criterion 13.32802 13.33349 13.32870 13.3359 13.34021 13.34702 Hannan-Quinn riter. 13.32200 13.32445 13.32268 13.3268 13.32816 13.33196

Inverted AR Roots .80 .80 .08 .20 .89 .75 .86 Source: Author’s Calculations Even ARIMA models involve differences; the forecast for the original series can be always calculated from fitted models. Forecasting in this study is done for three months’ period. The graph 3 reveals stationary in volatility pattern represented by spikes in the graph.

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Graph 3: Volatility Pattern DKMI30

400

200

0

-200

-400

-600 III IV I II III IV I II III IV I II III IV I II 2008 2009 2010 2011 2012 Source: Author’s Calculations

5.7 Diagnostic Checks The following diagnostic checks have been used for checking the accuracy and adequacy of the estimated ARIMA model.  The Individual significance of parameters  ARCH- LM test  ARIMA structure of the estimated model  Overall significance of the model  Durbin Watson d test  AIC and SIC  Q-stat and Correlogram of standardized squared residuals.  Normality of residuals

5.8 Heteroscedasticity Test To check the heteroskedasticity in daily stock prices before estimating the GARCH model this test is mandatory to perform. The daily stock prices data used in this study contains volatility periods. Hence, heteroskedasticity test is important to measure when conditional variance is not constant all over the time period. For this purpose, following tests are applied on the data.

5.9 ARCH-LM Test The study applies ARCH Lagrange Multiplier test to determine the occurrence of ARCH effect in the residuals. Therefore, to find out whether arch effect is present or not we estimated arch model and univariate modelling. The results of ARCH-LM test for ARIMA (0, 1, 1) and figure are shown in table 9 and figure 2 which shows that arch effects are present in the data and our data is suitable to apply GARCH.

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Table 9: Estimating an ARCH Model Dependent Variable: DKMI Method: ML - ARCH (Marquardt) - Normal distribution Included observations: 909 after adjustments Convergence achieved after 14 iterations Presample variance: unconditional GARCH = C(2) + C(3)*RESID(-1)^2

Variable Coefficient Std. Error z-Statistic Prob.

C 17.71323 6.096114 2.905659 0.0037

Variance Equation

C 28618.33 1220.103 23.45567 0.0000 RESID(-1)^2 0.178895 0.047428 3.771901 0.0002

R-squared -0.000204 Mean dependent var 15.04815 Adjusted R-squared -0.000204 S.D. dependent var 186.8016 S.E. of regression 186.8207 Akaike info criterion 13.26657 Sum squared resid 31690982 Schwarz criterion 13.28245 Log likelihood -6026.656 Hannan-Quinn criter. 13.27263 Durbin-Watson stat 1.818037 Source: Author’s Calculations

Figure 2: Univariate Modeling and Forecasting of GARCH (1, 1) 200 Series: DKMI Sample 9/01/2008 5/03/2012 160 Observations 909

Mean 15.04815 120 Median 1.750000 Maximum 672.7200 Minimum -796.3900 80 Std. Dev. 186.8016 Skewness -0.183588 Kurtosis 4.499210 40 Jarque-Bera 90.23527 Probability 0.000000 0 -800 -600 -400 -200 0 200 400 600 Source: Author’s Calculations

5.10 Testing for ARCH Effects The regression residuals are obtained from the mean equation. As heteroskedasticity makes the standard errors biased so in order to remove it we applied heteroskedasticity tests and its output shows the regression of differenced series on a constant term in table 9. Since the LM statistic (30.81513) is significant as results are shown in table 10, we reject the null hypothesis that there are no first-order ARCH effects. Note that the LM statistic in Views is calculated as LM=T x _=908 x 0.033937 = 30.8148. Furthermore, the F- and t- Statistics (31.82739=5.641577) corroborate the ARCH effects.

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Table 10: Heteroskedasticity Test: ARCH Heteroskedasticity Test: ARCH

F-statistic 31.82739 Prob. F(1,906) 0.0000 Obs*R-squared 30.81513 Prob. Chi-Square(1) 0.0000

Variable Coefficient Std. Error t-Statistic Prob.

C 28486.29 2413.950 11.80069 0.0000 RESID^2(-1) 0.184684 0.032736 5.641577 0.0000

R-squared 0.033937 Mean dependent var 34894.58 Adjusted R-squared 0.032871 S.D. dependent var 65264.84 S.E. of regression 64183.21 Akaike info criterion 24.97907 Sum squared resid 3.73E+12 Schwarz criterion 24.98967 Log likelihood -11338.50 Hannan-Quinn criter. 24.98312 F-statistic 31.82739 Durbin-Watson stat 2.077447 Prob(F-statistic) 0.000000 Source: Author’s Calculations

The top section in table 10 is the mean equation. It shows that the average return is 17.71323. The lower section is the variance equation that gives the results of the ARCH model, namely that the time- varying volatility includes a constant component (28618.33) plus a component which depends on past errors 0.178895_. The shaded line in graph 4 highlights the significant ARCH effects in the form of spikes with an upward pattern.

Graph 4: ARCH Effects (Upward Pattern)

GARCH01

160,000

140,000

120,000

100,000

80,000

60,000

40,000

20,000 III IV I II III IV I II III IV I II III IV I II 2008 2009 2010 2011 2012 Source: Author’s Calculations

After removing the problem of heteroskedasticity from data, we again tested the arch effects and then finally GARCH model was applied on it and the results depicted in table 11 and 12 proves the significance with p value of 0.01 and 0.000. Thus, the objectives of our study are achieved.

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Table 11: Testing for ARCH Effects

Variable Coefficient Std. Error t-Statistic Prob.

C 15.04815 6.195819 2.428759 0.0153

R-squared 0.000000 Mean dependent var 15.04815 Adjusted R-squared 0.000000 S.D. dependent var 186.8016 S.E. of regression 186.8016 Akaike info criterion 13.29907 Sum squared resid 31684526 Schwarz criterion 13.30437 Log likelihood -6043.428 Hannan-Quinn criter. 13.30109 Durbin-Watson stat 1.818408

Source: Author’s Calculations

The GARCH (1, 1) model is of the form: + + Results of GARCH model are shown in table 12.

Table 12: Generalized ARCH Dependent Variable: DKMI Method: ML – ARCH Included observations: 909 after adjustments Convergence achieved after 28 iterations Presample variance: backcast (parameter = 0.7) GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*GARCH(-1)

Variable Coefficient Std. Error z-Statistic Prob.

C 19.44703 5.642095 3.446775 0.0006

Variance Equation

C 1345.868 216.8455 6.206574 0.0000 RESID(-1)^2 0.114744 0.018692 6.138546 0.0000 GARCH(-1) 0.852232 0.021156 40.28310 0.0000

R-squared -0.000555 Mean dependent var 15.04815 Adjusted R-squared -0.000555 S.D. dependent var 186.8016 S.E. of regression 186.8535 Akaike info criterion 13.17131 Sum squared resid 31702115 Schwarz criterion 13.19248 Log likelihood -5982.359 Hannan-Quinn criterion 13.17939 Durbin-Watson stat 1.817399 Source: Author’s Calculations

Now the value of =0.114744 and the value of =0.852232 thus we can write GARCH (1, 1) model as:

+ +

Sample forecast is done for the period of 3 months before forecasting so we have to resize the KMI-30 series. The in-sample forecast is depicted in graph 5 and the results of out of sample forecast are shown in graph 6 and both sample forecast reveals an upward trend of Islamic stock index which reveals that it is profitable for investors to invest in Islamic stock index.

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Graph 5: In-Sample Forecast

30,000 Forecast: KMI30F Actual: KMI30 25,000 Forecast sample: 1 1016 Adjusted sample: 2 1016 20,000 Included observations: 1015 Root Mean Squared Error 188.9663 15,000 Mean Absolute Error 136.1786 Mean Abs. Percent Error 0.894854 10,000 Theil Inequality Coefficient 0.005326 Bias Proportion 0.000638 5,000 Variance Proportion 0.001841 250 500 750 1000 Covariance Proportion 0.997521

KMI30F ± 2 S.E.

160,000

120,000

80,000

40,000

0 250 500 750 1000 Forecast of Variance Source: Author’s Calculations

Graph 6: Out of Sample Forecast

50,000 Forecast: KMI30F Actual: KMI30 40,000 Forecast sample: 1 1107 Adjusted sample: 2 1107 30,000 Included observations: 1015 Root Mean Squared Error 5284.687 20,000 Mean Absolute Error 5011.700 Mean Abs. Percent Error 31.73208 10,000 Theil Inequality Coefficient 0.130309 Bias Proportion 0.899245 Variance Proportion 0.033414 0 250 500 750 1000 Covariance Proportion 0.067341

KMI30F ± 2 S.E.

50,000

40,000

30,000

20,000

10,000

0 250 500 750 1000 Forecast of Variance Source: Author’s Calculations

The output of out of the sample and in sample forecast reveals that there is an increasing trend in the values of KMI-30 index for the next three months. When KMI-30 was launched there was a financial crisis in the world which also influenced Pakistani markets but Pakistani Stock index KSE-100 and KSE-30 outperformed by 42% and 60% respectively. The final ARIMA (Best Fit Model) is depicted in graph 7 and 8 which confirms the upward trend.

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Graph 7: ARIMA Model Graph 8: ARIMA Model (Best Fit Model) (Upward Trend)

24,000 Forecast: KMIF Actual: KMI 20,000 Forecast sample: 9/21/2008 5/03/2012 Adjusted sample: 9/23/2008 5/03/2012 16,000 Included observations: 1319

Root Mean Squared Error 5999.800 12,000 Mean Absolute Error 4890.610 Mean Abs. Percent Error 28.26540 8,000 Theil Inequality Coefficient 0.213073 Bias Proportion 0.484417 Variance Proportion 0.512988 4,000 Covariance Proportion 0.002595

0 2009 2010 2011

KMIF ± 2 S.E.

Source: Author’s Calculations

5.11 Comparison of ARIMA and GARCH Model

ARIMA Model (2,1,1) GARCH (1,1)

RMSE 127.013 188.963 MAE 135.503 130.0211

MAPE .887 0.854725

Akaike info criterion 13.29752 13.32078

Schwarz criterion 13.30282 13.34021

Variance proportion 0.025072 0.997681

Covariance proportion 0.175317 0.997681

As for selecting the best model a comparison of models in terms of its root mean square error (RMSE) , Akaike info criterion and Schwarz criterion is required. Therefore, the comparison between ARIMA and GARCH in table 5.11 shows that ARIMA model is the best model for forecasting of Islamic stock index as its values of RMSE is 127.013 which lower than GARCH value of RMSE and its values of Akaike info criterion(13.29752) and Schwarz criterion (13.30282) is also lower than the values of GARCH model.

6. Conclusions, Discussion and Research Implications With the help of key performance indicators, this research paper determined the hypothesis that Islamic stock indices provide a vital opportunity of investment to those who believe in following Islamic values by using Generalized Autoregressive Conditional Heteroskedastic in the mean (GARCH-M) model. A few numbers of academic experts still argue that the economic stability of ethical investment is facing risk due to limited diversification, small investment scale and increasing operating costs. Hence, emphasizing the difficulty involved in ethical Islamic investment. However, experts of socially efficient investment argue that with focusing on ethical corporate Islamic practices one can achieve a competitive edge in investment. So we reject our H1 that the principles of Shariah Compliance are a hindrance to build a profitable portfolio as there is an upward trend of KMI-30 stock return. So, shariah compliance is not a hindrance to developing a profitable portfolio. However, the existing literature is limited to some extent and

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mixed results are reported by past researches. The results are consistent with the findings of (Saiti, Bacha, & Masih, 2014; Miniaoui et al. 2015; and Majdoub & Mansour, 2014). Financial risk management has a dominant role and proper modeling (and forecasting) of volatility is compulsory risk management exercise for financial institutions around the world. As high volatility is found in the graphical representation of (KMI- 30) index. Hence market estimates of volatility that can serve as a measure for the vulnerability of financial markets and economy help the policymakers in designing appropriate policies. So, we accept our H2 that proper modeling of Shariah index is required and this result is also supported by (Saadaoui & Boujelbene, 2015) and (Nazlioglu, Hammoudeh, & Gupta, 2015) findings. As risk is imperative in investment as risk is a feature that shapes an individual’s decisions to make an investment. Thus one of our objectives is to evaluate the performance of model ARIMA and GARCH in view of risk and volatility and the output reveals that GARCH model has less value of AIC and SIC. Therefore, the findings reveal that Muslim investors can earn substantial revenues by investing in Islamic stock indices and can also achieve their peace of mind by aligning their investments to their religious values and this finding is also supported by past research findings of (Arshad and Rizvi, 2013; Abbes & Trichilli 2015) who revealed that KMI stocks generate a higher average return and lower risk as compared to KSE 100 index. Moreover, KMI-30 index shows a higher risk-adjusted return of Treynor ratio as compared to its conventional counterpart. Thus, we accept H3 that the return of Islamic Index (KMI 30) does benefit portfolio diversification of investors. The study also facilitates policymakers, practitioners and specifically those investors who desire to make an alignment in their financial investment and religious values. Future research can be done by focusing on other vital macroeconomic determinants, like GDP and inflation rates on the volatility of KMI-30. Therefore, we conclude that GARCH (1, 1) is a better model for the forecasting of daily prices and it has a strong ability to capture the volatility by non-constant of conditional variance. The forecast results showed an upward increasing pattern that may increase in future.

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