Islamic Equity Investment Risk and Return Behaviour
Info: 5440 words (22 pages) Dissertation
Published: 12th Dec 2019
Tagged: FinanceRisk Management
Islamic equity investments deal with the application of Shariah in stock selection in fund management. Islamic equity investment is a new and emerging concept in fund management and posed a slow growth compared with a fast paced growth in Islamic fixed income ‘Sukuk’ markets and Islamic banking in the current decade. However Islamic equity investments contain a significant potential to generate above average risk adjusted returns than conventional equity investment as discussed in this paper. The thesis argues about the risk & returns behavior of Islamic equity investments by analyzing the risk & return behavior of Karachi Meezan Index, an Islamic index traded at Karachi stock exchange, over the period of two and a half years. Karachi Stock Exchange 100 index and Karachi Stock Exchange 30 index was used as benchmarks to find out if there are any significant differences in the returns & volatility of KMI30 and KSE 100. The complete period was also divided into bull and flat periods and each period is analyzed to further augment the research. Our findings provide strong evidence to reject the notion that Shariah Compliant investment perform poorly than conventional equity investments. In fact our finding supported the assumption that Shariah Compliant Equity Investments can deliver better returns than conventional investments given the same level of risk.
In the past few years there has been remarkable growth in the field of Islamic finance. New products are being developed on a consistent basis in capital markets which comply with the Shariah. The main distinguishing feature of Shariah Compliant Stocks is their low risk characteristics which has induced many risk averse investors into investment in Shariah complaint stocks and equity funds. According to Ernst & Young’s 2010 Islamic funds & investment report, currently there are approximately $52 billion fund assets under management in the Islamic fund industry which is still a small proportion of the total assets under global fund management which are worth $22 Trillion in 2010. Total Shariah compliant assets now exceed $1 trillion worldwide because of the fast faced growth in Islamic finance during the current decade. Currently Islamic funds only constitute about 5.5% of total Islamic finance investments which signifies the potential of growth in this industry in coming years.
From July 2007 to Nov 2009, MSCI World Islamic Index outperformed the MSCI World Index Standard Core in terms of variability of returns which shows that Shariah complaint stocks generate more returns in high volatility period compare to conventional stocks.
In an Islamic equity fund, the amounts are invested in the shares of Shariah complaint stock companies. The profits are mainly achieved through the capital gains by purchasing the shares and selling them when their prices are increased. Profits are also achieved by the dividends distributed by the relevant companies. It is obvious that if the main business of a company is not lawful in terms of Shariah, it is not allowed for an Islamic Fund to purchase, hold or sell its shares, because it will entail the direct involvement of the shareholder in that prohibited business.
In September 2008, Karachi Stock Exchange with the collaboration of Meezan Bank launched a new index called Karachi Meezan Index comprising of 30 companies. The distinguishing characteristic of this index is its Islamic nature in which selected companies will be fully Shariah-complaint. Companies will be selected in the index based on their liquidity in the stock market along with compliance with Shariah principles. These Shariah principles are formulated by the Shariah advisory council of Meezan bank which comprises distinguishing Islamic scholars. The objective of KSE-Meezan Index (KMI) is to serve as a gauge for measuring the performance of Shariah compliant equity investments. It may also act as a research tool for decisions in strategic asset allocation according to Shariah besides tracking performance of Shariah compliant equities; its construction will increase investor trust and enhance their participation.
Stock Screening Requirements for KMI-30 Index
Shariah compliance of stocks shall be done under the guidance of qualified and reputed Shariah experts. For stocks to be ‘Shariah compliant’, it must meet ALL the six key tests given below.
Business of the Investee Company: Core business of the company must be HALAL and in-line with the dictates of Shariah. Hence, investment in securities of any company dealing in conventional banking, conventional insurance, alcoholic drinks, tobacco, pork production, arms manufacturing, pornography or related un-Islamic activities is not permissible.
Debt to Total Assets: Debt to Asset ratio should be less than 40%. Debt, in this case, is classified as any interest bearing debts. Zero coupon bonds and preference shares are, both, by definition, part of debt.
Non-compliant Investments to Total Assets: The ratio of non-compliant investments to total assets should be less than 33%. Investment in any non-compliant security shall be included for the calculation of this ratio.
Non-complaint Income to total revenue – Purification of Non-compliant: income the ratio of non-compliant income to total revenue should be less than 5%. Total revenue includes Gross revenue plus any other income earned by the company. This amount is to be cleansed out as charity on a pro rata ratio of dividends issued by the company.
Illiquid Assets to Total Assets: The ratio of illiquid assets to total assets should be at least 20%. Illiquid asset, here, is defined as any asset that that Shariah permits to be traded at value other than the par.
Net Liquid Assets to Share Price: The market price per share should be greater than the net liquid assets per share calculated as: (Total Assets – Illiquid Assets – Total Liabilities) divided by number of shares.
*Courtesy of Karachi Meezan Index Brochure retrieved from Karachi Stock Exchange Website
Rationale of the Study
Islamic equity investment funds pose immense growth potential in the future mainly on account of the following reasons:
It attracts risk averse investors who previously ignore equity investments because of Islamic Equity’s low risk characteristics
It attracts new Muslim investors who previously were wary of investing in stock markets because of non-Shariah compliance
Therefore a study needs to be conducted which examines the risk & return behavior of Shariah complaint stocks so that investors and general people will have a better idea about the risks & profits which are inherent in Shariah complaint shares.
The study will help in answering the questions such as:
Is there a difference in returns of KMI30 and KSE 100 indices?
Is there a difference in the volatility of KMI30 and KSE 100 indices?
Is KMI30 index giving more or less risk adjusted returns compared to KSE 100 index?
How much variation is explained by KSE 100 index in returns of KMI30 index?
Limitations of the Study
KMI30 index represents the risk & return behavior of only 30 blue chip Shariah compliant stocks. In order to have a better comparison with the KSE 100 index, a portfolio consisting of all the stocks from KSE 100 which comply with Islamic screening principles should be constituted and the return & volatility attributes of this portfolio should be compared with KSE 100 index because a difference in returns between both indices can be because of superior judgment in the selection of stocks in KMI30.
Khan (1998) studied the modern practices in commodity, currency and corporate stock trading in the light of Islamic economic framework and stated that under Islamic principles, Mudarabah or Shirakah certificates can be traded in stock exchanges. However there is no concept of preferred equity in Islamic finance as it Riba which is forbidden under Islam. Khan stated that liability towards losses of the organization need to be met which may have accumulated over a period in order to sell or disinvest shares of that organization which implied that each shareholder has a liability for cumulative past losses as well as current losses in proportion to the capital invested. Khan (1998) proposed a model of stock valuation which incorporates the Islamic principles that intrinsic value of shares should provide the prospective investor a fair amount of information about past performance of organization.
Iv = intrinsic value of shares
Pv = par value of shares
Ri = Profits, Reserves etc
L = losses
S = No. of Share
Lewis (2010) examined the current and historic structure and performance of Islamic investment funds and found out that Islamic investments have grown quickly over the past few years and now there are approximately 650 Islamic funds operating globally. Lewis also discovered that in the past Islamic funds have focused more on negative forbidden screening principles instead of focusing on both the negative and positive screening methodologies like socially responsible funds that focus primarily more on investments in companies which play a part in human welfare. However these Socially Responsible Investments (SRI) funds performed slightly poor compared to Islamic funds because Islamic funds invested a significant portion in energy companies who enjoyed profitability because of rising oil prices, SRI funds do not invest large portions in fossil fuel energy companies primarily because of their futile side effects on environment.
Nik Maheran and Masliza (2008) analyzed the performance of Islamic mutual funds at Kuala Lumpur Stock Exchange to investigate if these funds underperform or over perform the market index using average return on mutual funds, standard deviation of weekly returns, coefficient of variation, Treynor and Sharpe index. They found out that most of the funds achieved a lower return than market from the period 2002 until 2006. However in terms of risk level Islamic mutual funds showed less risky behavior compared to the market since the betas of Islamic mutual funds was less than one.
Rennebook, Horst and Zhang (2007) critically reviewed the available literature on socially responsible investments and concluded that a primary reason for low returns from socially responsible funds could be the multi-task nature of portfolio managers who pursue both financial and social objectives. They also found out that if investors avoid investments in unethical/asocial businesses, than they may require a low rate of return than other investors who do not show any similar type of preferences.
Hussein (2007) analyzed the returns of FTSE Global Islamic index and Dow Jones Islamic Index from 1993 till 2004 and compared them with the returns of Dow jones world index and FTSE All world index. He found out that application of Shariah screening doesn’t adversely impact on Islamic indices performance as Islamic indices performed as well as their counterparts over the entire period. Hussein (2007) stated that Islamic indices yield statistically positive returns in bull market period though Islamic indices underperform the all world indices in the bear period and in the long run have a superior performance compared with counterparts in entire market period.
Abdullah, Hassan and Mohammad (2007) compared the performance of Islamic and conventional mutual funds in Malaysian capital market with the help of Sharpe index, adjusted Sharpe index, Jensen Alpha, timing and selective ability and found out that Islamic funds are less risky than conventional funds and ‘both Islamic and conventional funds have diversification levels which are less than 50 per cent of the diversification level of the market portfolio’. They discovered that Islamic funds performed better than conventional funds during bearish periods while conventional funds performed better than Islamic during bullish periods and concluded that Islamic funds can be used as hedging tools.
Hussein (2005) compared the performance of Dow Jones Islamic market index and FTSE Global Islamic index and benchmarked it against their counterparts, Dow Jones World index and FTSE Global Index respectively, using parametric t-statistic and non-parametric signed rank test. Monthly returns data had been used ranged from 1996 – 2004 and the periods had been divided into bull and bear return phases to make more meaningful conclusions from results. Hussein (2005) found out that Dow Jones Islamic Index outperformed its counterpart in the entire period (1996 – 2004) and bull period. The mean monthly return of Dow Jones World Index was higher than the DJ Islamic index over the entire bull period which indicated that the Islamic index has greater volatility in comparison with DJ world index. Contrary to this, Dow Jones Islamic index fails to maintain its better performance over the bear market phase where the DJ world index gives better returns. In case of FTSE indices, FTSE Global Islamic index outperforms FTSE All world index in the entire and bull periods. However FTSE Islamic index underperforms FTSE world index over bear period. Hussein (2005) also found out that the beta of both Islamic indices is greater than one and higher than their counterparts which imply that both Islamic indices are riskier than their counterparts. Hence Hussein (2005) stated that the application of Shariah screening principles has no adverse effect on Islamic indices performance over the years and concluded that Shariah investing offer superior performance compared to unscreened portfolios.
Albaity and Ahmad (2008) examined the performance of KLSI, A Shariah Compliant Index at Bursa Malaysia, and benchmarked it against KLCI which is a conventional stock market index at Bursa Malaysia using measures of risk adjusted returns and found out that KLCI is outperforming KLSI. Albaity and Ahmed (2008) also found out that KLCI has a higher beta as evident from conventional Non-Islamic indices and that in the short run both indices move in the same direction and tend to cause each other. Hence they concluded that there is no significant difference in the returns and movements of both indices.
Hakim and Rashidian (2002) applied Islamic equity screening principles on Wilshire 5000 index and created a Shariah Compliant Portfolio and compared the return characteristics of the created Wilshire Islamic portfolio and Dow Jones Islamic market index portfolio with the parent Wilshire 5000 index and found out that the reduced diversification characteristic of newly created portfolio has not adversely affected its performance when compared with parent Wilshire 5000. Hakim and Rashidian (2002) examined the causality between the Islamic index, the Wilshire 5000 and the Tbill rate and found out that the Islamic index is influenced by factors independent from the broad market or interest rates which are contrary to the widely accepted notion that Dow Jones Islamic Index exhibits high correlation with broad market. They concluded that such correlation is temporary and false
Sauer (1997) measured and analyzed the average monthly returns and variability, Jensen Alpha and Sharpe performance of the Domini 400 Social index portfolio and benchmarked it against the performance of two unrestricted portfolios (S&P 500 and CRSP value weighted market indexes). Sauer (1997) discovered that the application of socially responsible strategy in stock selection does not impact the investment performance adversely. He concluded that the potential performance costs of implementing socially responsible criteria, as represented by the performance of Domini social index are negligible. Sauer (1997) also stated that the performance of Domini Social equity Mutual fund compares favorably to the performance of Vanguard S&P 500 index.
Bauer, Koedijik and Otten (2004) analyzed the performance of 103 German, UK and US ethical mutual funds and found no indication of substantial difference in return behavior between ethical and conventional mutual fund returns after controlling for factors like book to market and size. Bauer, Koedijik and Otten (2004) also concluded that ethical mutual funds are typically less exposed to market variability compared to conventional funds.
Hamilton, Jo and Statman (1993) studied 32 socially responsible mutual funds and compared their returns with a portfolio of 177 conventional mutual funds. They found out that market do not price social responsibility characteristics so investors can expect to lose nothing by investing in socially responsible mutual funds; social responsibility factors have no effect on expected stock returns or companies’ cost of capital.
Derigs and Marzban (2009) analyzed S&P, DJIM, FTSE, MSCI and HSBC Shariah Complaint indices and stated that current Shariah compliant strategies result in much lower portfolio performance than portfolios without considering Shariah Compliance. They suggested that the return from Shariah complaint strategies can be increased by making Shariah compliance an attribute of portfolio constructed rather than measuring compliance on as asset level. Derigs and Marzban (2009) argued, ‘Funds are investment vehicles, which are financially independent of the institutions that establish them.’ Therefore, a fund takes the form of an independent company, such as a limited liability company (Norman, 2004), in which investors act as shareholders. So they proposed that with respect to compliance a fund which itself invests in multiple companies has to be evaluated in the same way as a conventional independent company.
Hassan and Antoniou (2006) examined the potential impact of Islamic screening restrictions on investment performance by comparing the performance characteristics of a diversified of Islamic screened stock indices with conventional benchmarks (Data stream Global Index) and the degree of correlation and volatility in price movements between both indices. Hassan and Antoniou (2006) concluded that the impact of stock screens is closely related to the performance of stock markets and further stated that any argument that Islamic equity investments are less profitable than conventional types of investments is questionable which is supported by relatively major differences between Sharpe and Treynor measures and significant positive Alpha over the positive returns period when the Dow Jones Islamic Market Index outperformed the Data stream Global Index.
This section emphasizes the research methodology and the type of data that has been used in this research. The research is quantitative in nature as statistical and financial models are being used to test the STOCK INDEX time series for volatility and return. The data which is going to be used in the research is secondary in nature and in the form of time series. Daily index values of Karachi Meezan Index (KMI-30), KSE-30 index and KSE-100 index from Karachi stock exchange are being used as secondary data from December 15, 2008 till March 11, 2011.
Daily logarithmic returns of all indices are being calculated such that:
Where is the raw return for index i for the time t, refers to the price of index i at time t, and is the price of index i at time t-1.
A descriptive statistical analysis was performed on the calculated daily logarithmic returns using to calculate mean, standard deviation, standard error, median, variance, kurtosis, skewness, maximum and minimum values of all three indices for the whole period from December 15, 2008 to march 11, 2011. Also Geometric mean for all three indices was also calculated as it contains the effect of compounding. Coefficient of variation is calculated to measure the variation in each index given its return. A correlation matrix was being calculated using excel spreadsheet to find the degree of correlation between KMI-30, KSE-30 and KSE-100 indices. A linear regression analysis has been performed using the returns of KMI-30 index as dependent variable and returns from KSE-100 as the independent variable to estimate the coefficient of determination (R-Square) and beta of KMI-30. Another linear regression was performed using KSE-30 as the dependent variable and KSE-100 as the market independent variable to estimate the beta of KSE-30 and coefficient of determination.
The regression equations were as follows:
Where is the intercept, is the beta of the stock index, and are the returns on KMI30 and KSE30 indices respectively and is the return on KSE100 regarded as the return on the stock market.
Risk ratios which are used in the analysis to compare the risk reward profile of KMI30 with KSE 30 and KSE 100 are Alpha, Beta, Standard Deviation, R-Squared, Sharpe Ratio and Treynor ratio.
A paired t-test was performed to check the hypothesis of difference in means of KMI30 and KSE 100 index because nearly all of the stocks of KMI30 are part of KSE 100 hence dependent. Also F-test was performed to check the difference in variances of KMI30 and KSE 100 indices assuming that the returns from both indices are normally distributed.
The whole period from December 15, 2008 to March 11, 2011 is than divided into two bull periods and one relatively flat period to find out the risk-return profile of KMI30 and KSE 100 in these periods. The first bull period is from January 15, 2009 till October 15, 2009 while the flat period is from October 15, 2009 till October 15, 2010. The second bull period is considered from October 15, 2010 to January 15, 2011.
A descriptive analysis was again performed on these bull and flat periods along with similar paired t-tests, F-tests, linear regression and correlation matrices. Sharpe ratio, Treynor ratio, Jensen Alpha, Beta and S. Deviation were also calculated for these bull and flat periods.
Results & Analysis
Descriptive Statistical Analysis
Descriptive analysis shows that KMI30 index showed very good daily mean returns of 0.1014% since Dec 15, 2008 till March 11, 2011. KMI30 index started in September 2008 and considering the mean returns, it is a very good performance by a stock exchange index especially when comparing with geometric mean of KSE 30 returns of 0.0227% and KSE 100 daily returns of 0.0451% in the same period. The standard deviation of KMI30 index daily returns was 1.5051% which is considerably less than its counterpart KSE 30 index however more than the S. Deviation of KSE 100 index as expected because of large diversification effects of stock returns in KSE 100. The coefficient of variation for KMI30 index is 15.97 compared to 33.36 for KSE 100 and 74.593 for KSE 30 which clearly indicates that KMI30 is less risky when compared to both other indices per unit of return. The excess kurtosis for KMI30 for the complete period is 2.58 compared to 2.13 for KSE 100 and 2.29 for KSE 30 which shows that all three indices are more peaked than normal distribution and are leptokurtic. All three indices are negatively skewed which shows that most of the returns are negative.
As indicated by higher standard deviations of KSE 30 index, its maximum and minimum return are greater than KMI30 maximum and minimum returns. The maximum one day return for KMI30 during the whole period was 5.3% while the minimum return was -5.19%.
From January 15, 2009 to October 15, 2009, KSE showed a bullish trend. The geometric mean of KMI30 index daily returns during this first bullish period was around 0.31% much higher than 0.24% of KSE 100 and 0.28% of KSE 30. However the standard deviation of KMI30 index is 1.93% less than 1.88% of KSE 100 and 2.35% for KSE 30. This shows that not only KMI30 beat KSE 100 and KSE 30 in returns but also remained less volatile over the bullish period when compared to KSE 100 and KSE 30. The kurtosis of all three indices is slightly over 3 (Excel displays Excess Kurtosis) which shows that all three indices are mesokurtic and have a kurtosis equal to that of normal distribution. KMI30 showed a slight negative skewness of -0.0195, while KSE 100 showed positive skewness of 0.04058 in this bullish period.
From October 15, 2009 to October 15, 2010, KSE showed a relatively flat period of returns with KMI30 index showing a mean geometric return of 0.0498% while KSE 100 and KSE 30 showed a geometric return of 0.017% and –0.0249% respectively. The KMI30 again outperformed KSE 100 and KSE 30 in returns over this flat period. KSE 30 had negative mean returns in this period. KMI30 also showed low standard deviation of 1.088% compared to 1.1049% of KSE 100 and 1.3866% of KSE 30. Hence KMI30 again outperformed KSE 30 and KSE 100 index in this relatively flat period in terms of returns and low volatility. KMI30 had an excess kurtosis of 2.18 more than 1.79 for KSE 100 but less than 2.26 of KSE 30. Hence all three indices have leptokurtic distribution with high peaks than normal distribution. KMI30, KSE 100 and KSE 30 all showed negative skewness in this flat period.
From October 15, 2010 till January 15, 2011, KSE showed a relatively bullish trend with KMI30 showing a daily return geometric mean of 0.36% against 0.3% by KSE 100 and 0.33% by KSE 30 index. However KMI30 index showed a higher daily standard deviation of 0.86% compared to 0.73% of KSE 100. KMI30 also showed a more leptokurtic distribution compared to KSE 100 as the excess kurtosis of KMI30 was around 0.497 compared to 0.262 for KSE 100. During this bullish period all three indices showed a positive skewness with impressive returns in a short span of time.
Over the whole period, from December 15, 2008 to march 11, 2011, KMI30 showed impressive annualized returns of 28.825% compared with KSE 100 and KSE 30 which showed annualized returns of 11.9367% and 5.85% respectively. The annualized standard deviation for KMI30 index was a little higher than KSE 100 but lower than that of KSE 30. Also the total return over this two and a half year period by KMI30 was quite impressive and 2.5 times more of KSE 100. KMI30 had a total return of 75.11% from Dec 15, 2008 to March 11, 2011. Sharpe ratio is only positive for the KMI30 because the other two indices had returns less than 12 month Treasury bill rate. Jensen’s alpha for KMI30 was 16.8687 which indicated the average return on KMI30 over and above the CAPM predicted return of 11.9566%. KMI30 also had a beta lower than one which shows that KMI30 is less volatile than the overall market. KSE 30 had a beta of greater than one showing that it’s more volatile than the market KSE 100 index.
Correlation matrix shows a strong correlation of 92.933% of KMI30 and KSE 100 over the whole period from December 15, 2008 to March 11, 2011. KSE 30 showed a less strong correlation of 87.48% in the same period with KSE 100. In the first bullish period, KMI30 however had a rather less strong correlation with KSE 100 compared to the whole period correlation described above. In the flat period from Oct 15, 2009 till Oct 15, 2010, KMI30 had a very strong correlation with KSE 100 index. In second bullish period, from Oct 15, 2010 to Jan 15, 2011, KMI30 again had a relatively less strong correlation with KSE 100 as already happened in first bullish period. It looks like KMI30 is showing less strong correlation with KSE 100 in bull markets and very strong correlation with KSE 100 in relatively flat periods which shows that KMI30 shows returns which are less correlated with market in bull periods and give more correlated returns in flat market periods.
In both bull periods, Jan 15, 2009 – Oct 15, 2009 and Oct 15, 2010 – January 15, 2011, KMI30 outperformed KSE 100 and KSE 30 index with impressive margins. KMI30 gave a total return of 81.68% in the first bull period, 13.24% in the flat period and 23.67% in the second bull period. KSE 100 gave total returns of 57.3%, 4.34% and 19.92% in the same periods. KMI30 also showed a relatively same standard deviation as the KSE 100 except for the second bull period when there was a large difference in S. Deviation of KMI30 and KSE 100 returns. What this means is that KMI30 is giving higher returns than KSE 100 while having the same risk as KSE 100 also evident by Sharpe ratio. In first bull period, KMI30 had a beta of 0.927 compare to 1.077 of KSE 30. In the flat period, KMI30 had a beta of 0.948 while KSE 30 had a beta of 1.06. In the second bull period, KMI30 and KSE 30 showed an irregular trend when the beta for KMI30 increased over 1 while beta for KSE 30 dropped less than one.
A regression analysis was performed on the daily returns of KMI30, KSE 30 and KSE 100 for the complete period to explain the variation in the returns of KMI30 and KSE 30 index by using KSE 100 as the independent market index. The regression equations are as follows:
—— Equation 1
—– Equation 2
The R-Square for the first model of KMI30 returns come out to be 86.366% which tells us that 86% of the variation in KMI30 index is caused by KSE 100 index. The R-square for the second KSE 30 model was 77% which shows that KSE 100 causes more variation in returns of KMI30 than KSE 30 index. The intercept of first equation is 0.000523179 which shows that when the daily market return is zero, than KMI30 has a daily return of 0.0523179%. The slope of the first equation, beta of KMI30 index, tells us that a one percentage change return in KSE 100 index causes a 0.9752 percentage change return in KMI30 index which shows low volatility in KMI30 compared to KSE 100. The slope and intercept for the KSE 30 model are 1.1018 and -0.0216% respectively which indicates that KSE 30 is more volatile than KSE 100 (has a beta higher than 1) and that a zero return from market will causes a -0.0216% daily return fall in KSE 30 index.
The first hypothesis was to test that whether there are any significant differences in daily returns of KMI30 and KSE 100 indices for the whole period from December 15, 2008 to March 11, 2011. Since all the stocks which are part of KMI30 index are also a part of KSE 100 index which indicates that both samples are dependent hence paired t-test was employed to test the differences between returns of both indices. The null and alternative hypotheses are given as:
Ho: The difference in mean daily returns of KMI30 and KSE 100 index for the period from December 15, 2008 to March 11, 2011 is equal to zero
H1: The difference in mean daily returns of KMI30 and KSE 100 index for the period from December 15, 2008 to March 11, 2011 is not equal to zero
The paired t –test was performed on a 5% level of significance with 552 degrees of freedom. The calculated t statistic was 2.310548072 which was greater than the critical value of 1.96. Hence the null hypothesis was rejected and the conclusion was that the difference in mean daily returns of KMI30 and KSE 100 returns is different from zero.
The second hypothesis tested whether there are any significant statistical differences in returns of KMI30 and KSE 100 indices during the first bullish period from January 15, 2009 to October 15, 2009. The same paired t test was employed to test the difference in returns in this bullish period using a significance level of 5%. The null and alternative hypotheses are given as:
Ho: the difference in mean daily returns of KMI30 and KSE 100 index for the bullish period from January 15, 2009 to October 15, 2009 is equal to zero
H1: the difference in mean daily returns of KMI30 and KSE 100 index for the bullish period from January 15, 2009 to October 15, 2009 is not equal to zero
The calculated t-statistic was 1.2773207 less than the critical value of 1.972 at 5% level of significance with 187 degrees of freedom. Hence the null hypothesis was failed to reject and it was concluded that there is no difference in the returns of KMI30 and KSE 100 indices during the first bullish period from January 15, 2009 to October 15, 2009.