Islamic Equity Investments: matching perception with the reality - an application of a Logistic Smooth Transition Autoregressive Model

Transcription

1 Islamic Equity Investments: matching perception with the reality - an application of a Logistic Smooth Transition Autoregressive Model Dawood Ashraf a*, Nazeeruddin Mohammad b a College of Business Administration, Prince Mohammad Bin Fahd University, A lkhobar, Saudi Arabia. Tel: , Fax: dashraf@pmu.edu.sa b College of Computer Engineering & Science, Prince Mohammad Bin Fahd University, Al Khobar, Saudi Arabia. Abstract The systematic failure of the global equity markets during the recent financial crisis made investors re-evaluate their portfolio constituents. It is argued that equities that comply with the Islamic investment principles perform better than conventional equities during the declining phase of capital markets. The better performance of Islamic investments can be attributed to the Shari'ah based screening criteria that specifically forbids investment in shares of those companies that are excessively leveraged and/or engaged in lending activities. This study investigates the extent to which this claim is valid by comparing the performance of global and regional Islamic equity indices (IEIs) with conventional equity indices during the past decade. The equity indices for such analysis are preferred since it does not account for transaction costs or management skills. A logistic smooth transition autoregressive (LSTAR) model is used to investigate whether the `down market' performance of IEIs differs from conventional indices. The LSTAR is superior to conventional ordinary least squares models since this allows for a smooth transition from the `down market' to the `up market' rather than an abrupt change. The empirical results indicate that IEIs, in general, perform better than conventional indices during the period 2000 to We do not find any abnormal returns associated with Islamic equity indices on a global basis however, there is evidence of positive abnormal returns in the case of regional indices from Europe and Asia. Overall, IEIs exhibit lower systematic risk as compared with their benchmark suggesting that any excess performance from Islamic investments stems from the systematic risk that each investments assumes with respect to their benchmark during the declining phase of capital markets. The findings of this study is of interest to both academics and the general investing public since it provides evidence that IEIs are comparatively less risky than their conventional counterpart and thus provide hedging opportunities during the downfall of capital markets. Keywords: Islamic equities, LSTAR, Dual Beta, Equity markets, Systematic risk JEL Classification: G11, G14, G23 * Corresponding author

2 Islamic Equity Investments: matching perception with the reality - an application of a Logistic Smooth Transition Autoregressive Model Abstract The systematic failure of the global equity markets during the recent financial crisis made investors re-evaluate their portfolio constituents. It is argued that equities that comply with the Islamic investment principles perform better than conventional equities during the declining phase of capital markets. The better performance of Islamic investments can be attributed to the Shari ah based screening criteria that specifically forbids investment in shares of those companies that are excessively leveraged and/or engaged in lending activities. This study investigates the extent to which this claim is valid by comparing the performance of global and regional Islamic equity indices (IEIs) with conventional equity indices during the past decade. The equity indices for such analysis are preferred since it does not account for transaction costs or management skills. A logistic smooth transition autoregressive (LSTAR) model is used to investigate whether the down market performance of IEIs differs from conventional indices. The LSTAR is superior to conventional ordinary least squares models since this allows for a smooth transition from the down market to the up market rather than an abrupt change. The empirical results indicate that IEIs, in general, perform better than conventional Preprint submitted to Elsevier March 12, 2013

3 indices during the period 2000 to We do not find any abnormal returns associated with Islamic equity indices on a global basis however, there is evidence of positive abnormal returns in the case of regional indices from Europe and Asia. Overall, IEIs exhibit lower systematic risk as compared with their benchmark suggesting that any excess performance from Islamic investments stems from the systematic risk that each investments assumes with respect to their benchmark during the declining phase of capital markets. The findings of this study is of interest to both academics and the general investing public since it provides evidence that IEIs are comparatively less risky than their conventional counterpart and thus provide hedging opportunities during the downfall of capital markets. Keywords: Islamic Equities, LSTAR, Dual Beta, Equity Markets, Systematic Risk 1. Introduction Islamic equity investment based on Islamic Jurisprudence (Shari ah) principles has gained considerable attention in academia as well as in the popular press during the recent global financial crisis. It is noted that speculative trading and unsafe lending practices adopted by major international banks were among the major causes for the global financial crisis (Cyree et al., 2011; Caprio, 2009; Ashraf and Goddard, 2012). Shari ah principles specifically forbids investment in any company engaged in transactions based on usury (reba), excessive risk taking such as trading in derivatives and insurance (gherar), gambling activities (meiser), trading in alcohol (khumar), and/or pork products. Shari ah principles allow 2

4 investments in lower leveraged companies and financial instruments linked with real assets (sukuk). The restriction on leverage 1 and trading in financial assets including derivatives may result in a very different risk adjusted performance of Islamic equity investments from that of similar conventional investments during the downturn of capital markets. Most major global commercial banks and investment firms, both in Islamic as well as in non-islamic countries, provide investors with the opportunity to invest in funds that comply with Shari ah principles of investments. All major index services providers: the Financial Times Stock Exchange (FTSE), Standard and Poor s (S&P), Dow Jones and Morgan Stanley Capital International (MSCI), now build and provide Islamic Equity Indices (IEIs) data based on independent Shari ah screening criteria at global, regional and country level. Ernst and Young (2011) estimates that there are currently more than 700 mutual funds globally investing in Shari ah compliant securities. The aggregate value of Islamic equity investments internationally has grown to USD 58 billion in 2010 from USD 3.3 billion in 2003 (Ernst and Young, 2011). Globally, assets under management (AUM) of Islamic mutual funds represent less than one percent of the USD trillion global mutual funds market. However, with the onset of the global financial crisis (GFC) in 2008, Islamic investment funds have gained popularity due to the recent empirical evidence from different countries that such funds are resilient in the downturn of the economy due to their investment in companies engaged 1 Leverage is not forbidden completely in modern day investments. Shari ah boards, consisting of Islamic scholars, have allowed up to 33% of capital finance by debt. 3

5 in businesses based on real assets and lower leverage (Alam and Rajjaque, 2010; Ashraf, in press; Hoepner et al., 2011; Merdad et al., 2010). Aside from the equity performance, managers of IMFs have more leverage on market timing and stock selection since they may not face heavy drawdowns during bearish trends as profit seeking is not the main investment objective for an investor in Islamic funds. Rather, investors seek to satisfy a broader cause of adhering to their faith (Ashraf, in press). However, Hayat and Kraeussl (2011) found that Islamic mutual funds perform worst in either a bullish or a bearish economic market as compared with conventional funds. The performance evaluation of Islamic equity investments based on mutual funds may be biased due to fund managers discretion in stock selection and market timing abilities, along with associated trading costs. Schröder (2007) suggests that index level data provides a better performance comparison of screened indices with that of conventional indices since management skills, transaction costs and/or market timing activities of funds managers or the risk profile of investors has no bearing in the performance of the index. Any abnormal return or lower volatility can be attributed to the specific screen used to isolate equities. This paper seeks to explore whether Islamic equities perform better than conventional investments during a downturn of the economy on a risk adjusted basis. For this purpose, monthly equity index level performance data for 24 indices (12 IEIs and 12 conventional indices) from global and regional equities has been collected and matched from three major equity index providers: MSCI, S&P, and Dow Jones from June 2002 to May

6 The existing literature on the performance of IEIs do not consider any performance deviation under different market conditions such as bull and bear nor does it isolate the inter temporal impacts on the performance of such indices. To the best of the authors knowledge, this is the first study that addresses both concerns using a multivariate logistic smooth autoregressive model. Aside from better empirical estimation, this paper provides more recent evidence on the performance of IEIs especially during the global financial crisis 2. We find evidence that IEIs, on average, exhibit lower risk than their conventional benchmark indices in the overall period and their performance was not statistically sensitive during the peak of the financial crisis. Overall, we do not find evidence of any abnormal returns of IEIs as compared with their benchmarks. However, regional European and Asian IEIs reflect positive abnormal returns with significant lower systematic risk. These findings are in line with the hypothesis that Islamic equity investments due to their lower leverage, linkage to real assets, and avoidance of unnecessary risk through trading in derivatives compensate investors either in the form of better returns, lower risk or both as compared with conventional indices. The findings of this paper are of interest to academics, practitioners and investors alike. The evidence of overall lower systematic risk and abnormal returns of regional indices supports the notion that a conservative approach 2 However one study Binmahfouz and Hassan (in press) measures the performance of IEIs that include the GFC period. However this study uses the standard CAPM model which assumes constant systematic risk under different market conditions over time, thus lacks the robustness in estimation. 5

7 of avoiding investments in companies utilizing excessive leverage may help investors to weather falling markets better than conventional investments. The empirical evidence suggests that managers of conventional mutual funds and the general investing public can benefit by overweighting securities that comply with the Shari ah principles in their portfolios. The rest of the paper is organized as follows, section 2 provides a review of the literature. Methodology, data sources and descriptive statistics are presented in sections 3 and 4, followed by a discussion on empirical results in section 5. Section 6 concludes the paper with a brief summary of the key findings of this study. 2. Literature Review An investor in the Islamic equity market invests in equities of Shari ah compliant companies 3 or in a publicly offered portfolio consisting of these equities offered through unit trusts, mutual funds, or ETFs. The determination of Shari ah compliance rests with the judgment of Shari ah boards consisting of Islamic scholars. Early studies on the performance of Islamic equity funds (IEFs) 4 compare the performance of IEFs against selected benchmarks using several standard tools such as Sharpe ratio, Jenson s alpha and the Treynor index. Their findings, at best, are mixed. Empirical literature on the performance 3 Equities of Shari ah compliant companies include companies whose major source of revenue comes from permissible (halal) activities. All companies are excluded who are predominantly engaged in any of the following non-permissible (haram) activities: trading of alcohol, pork, pornography, gambling or from profit associated with the charging of interest on loans. 4 Includes unit trusts, mutual funds and exchange traded funds. 6

8 of IEFs suggests on the one hand that compliance cost with Shari ah may result in lower diversification, increased monitoring costs, lower efficiency and lower performance. On the other hand there is empirical evidence that IEFs perform better than conventional IEFs especially during the downturn of capital markets due to lower leverage and investment in equities with a higher proportion invested in real assets. Recent empirical literature covering different markets around the world report that IEFs, on average, perform better than conventional investment funds. The over-performance of IEFs appeared in the context of global IEFs (Hoepner et al., 2011); European (Alam and Rajjaque, 2010); Malaysian (Abdullah et al., 2007); and Saudi Arabian (Ashraf, in press; Rubio et al., 2012). However, Hayat and Kraeussl (2011) found that IEFs perform worst in either a bullish or a bearish economic market. They further suggest that managers of IEFs exhibit poor stock selection and market timing abilities. Nainggolan (2011) concurs that Shari ah compliance results in a lower performance of IEFs. But, Abderrezak (2008) found no significant performance differences between Islamic and conventional funds when comparing the performance of IEFs with conventional funds between 1997 to Elfakhani et al. (2007) suggest that the outperformance of IEFs depends on the measure, benchmark and time period used for performance evaluation. Hoepner et al. (2011) using a global dataset of 265 Islamic mutual funds found that mutual funds for countries with a Muslim majority perform better than mutual funds for countries where Muslims are the minority. The over/under-performance of IEFs may be biased due to the stock 7

9 selection and market timing abilities of fund managers and associated trading costs. To isolate the impact of Shari ah based screening of equities from that of management skills, market timing abilities and trading costs, a sample based on equity indices is more appropriate. A few studies have analysed the performance of Islamic investments using IEIs. Similar to the findings of IEFs, findings of IEI s performance is mixed. Guyot (2011) compared the performance of seven Dow Jones Islamic Market Indices with conventional indices from 1999 to The findings suggest that IEIs are as efficient as conventional indices and present diversification benefits for all investors. Hakim and Rashidian (2004) report that distinctive risk-return characteristics of IEI are not affected by broad equity market movements. Kok et al. (2009) concur with these findings when comparing Shari ah-compliant indices with mainstream or sustainability indices. Girard and Hassan (2008) had similar findings when using a sample of five FTSE Islamic indices versus conventional indices using monthly data from 1998 to 2006 and reported a high degree of cointegration between Islamic and conventional indices. They concluded that Islamic indices do not suffer higher risk - lower return and diversification loss due to the screening criteria. Albaity and Ahmad (2008) and Hassan and Girard (2011) drew similar conclusions while comparing the performance of the Kuala Lumpur Syariah Index with the Kuala Lumpur Composite Index and DJIMs respectively. However, Hussein and Omran (2005) found that the Dow Jones IEIs over the period from 1996 to 2003 yielded statistically and economically significant positive abnormal returns. Similarly, Hussein (2004) found FTSE Global Islamic Index yielded positive abnormal returns 8

10 between 1996 and 2000, but from 2000 to 2003 these returns turned in to negative. Table A1 in Appendix provides a comprehensive overview of empirical studies using IEI data with their major findings. In terms of recent financial crises, there is only one study (Binmahfouz and Hassan, in press) that provides coverage of the period spanning the recent GFC. However, Binmahfouz and Hassan (in press) used standard techniques without giving any consideration to the intertemporal effects and changing market conditions. It is further evident from Table A1 that there is no study that investigates the impact of changing market conditions on the performance of IEIs in a systematic fashion. This paper investigates the performance of IEIs in a systematic manner using a LSTAR model. To our knowledge a LSTAR model has not been used in an Islamic equity context before this study Methodology The standard Constant Risk Model (CRM) is used to measure the relative risk/return payoff of IEIs within the context of the Capital Asset Pricing Model (CAPM) and has the following specifications: R it = α i + β i R jt + ɛ it, i = 1 n, j = 1 m, t = 1 T (1) where R it and R jt are the returns of i th IEI and j th benchmark. The 5 However, Woodward and Brooks (2009) used a similar model in the context of equity portfolio extracted from S&P500. 9

11 intercept α i is Jensen s alpha and measures the excess monthly returns on i th IEI once the return has been adjusted to benchmark j. β i measures the relative riskiness of i th IEI with its benchmark j at time t and is considered as systematic risk. It can be expressed as the ratio of covariance of IEI and its conventional benchmark returns with the variance of benchmark return (cov(r it, R jt )/σj 2 ). So when an IEI has β = 1 then the IEI is neutral with respect to the benchmark. Conversely, if β < 1 or β > 1 means that the IEI is relatively safe or relatively risker investment respectively. ɛ it is the error (residual) term with zero mean and assumed to be homoskedatic and serially independent. The CRM model assumes that beta coefficient is stable over the investment horizon and under different market conditions such as bull and bear markets. However, the condition for stable beta is very restrictive, Pettengill et al. (1995) provide evidence using monthly returns of the US market from Jan 1926 to Dec 1990 for varying beta under bull and bear market conditions. Further, there are several other studies (Bondt and Thaler, 1985; Lunde and Timmermann, 2004; Faff, 2001; Howton and Peterson, 1998; Hodoshima et al., 2000) that investigated the relation between market conditions and beta coefficients for different markets and provide evidence for beta variation over time under different market conditions. Most of these studies used a Dual-Beta Market (DBM) model to study the effect of a single market condition (such bull and bear market) on beta coefficient. A DBM model can be specified as: R it = α i + β i R mt + (α D i + β D i R mt )S t + ɛ it (2) 10

12 where S t is a dichotomous variable defining the two phases of the market. It takes the value of one and zero depending on whether the market state indicator (M t ) exceeds a critical value (c). If M t > c then the market is considered to be a bull market, otherwise it is considered to be a bear market. Usually the market return (R mt ) is chosen as the market state indicator and critical value is set to zero or mean/median of R mt. For our study we have chosen the moving average of monthly market returns as the market state indicator (M t ) rather that simple monthly returns. Woodward and Brooks (2009) suggest that a transition variable based on the moving average of return series of benchmark index provides support for time variation similar to the bull and bear trends in capital markets. Further the monthly observations are noisy and may not reflect the underlying cyclic characteristics (Teräsvirta, 1994). The estimation of beta in equations 1 and 2 using the ordinary least squares (OLS) is proven to be problematic. Several studies in the literature found that beta is time-varying and the error terms as heteroskedastic (Brooks et al., 1998). In such cases generalized autoregressive conditional heteroskedasticity (GARCH) models can be used to estimate the time-varying betas. The general multivariate GARCH model proposed by Bollerslev et al. (1988) can be specified as: R it = Cw t + e t (3) p q H t = s + A i vech(e t i e t i) + B j H t j (4) i=1 j=1 11

13 where R it is a n x 1 vector of dependent variables, which in our case are IEI s monthly returns. C is a n x k matrix of parameters. w t is a k x 1 vector of independent variables that contains benchmark returns and p lags of IEIs. e t = H 1/2 t v t, v t is a n x 1 vector of normal, independent, and identically distributed innovations. H t is the conditional covariance matrix of IEI returns and H 1/2 t is the Cholesky factor of H t. vech stacks the lower diagonal elements of a symmetrical matrix into a column vector. The large number of unknown parameters in the general GARCH model makes it easy to fit any financial time series, but the estimation of these parameters is too difficult. Many studies limit the number of parameters by imposing restrictions on H t. In this study we use the diagonal vech GARCH model which restricts A and B to be diagonal matrices. The diagonal-vech Garch model can be specified by replacing H t in Eq. 4 with Eq. 5 p q H t = S + A i Θvech(e t i e t i) + B j ΘH t j (5) i=1 j=1 where Θ is Hadamard product. The restriction in equation 5 implies that the variances in H t depend on past squared residuals and corresponding past ARCH terms. Such restriction ignores any cross-market dependencies in conditional volatilities. However, when low-frequency data (such as monthly returns, as in our study) is used such influences can be ignored (Santis and Gerard, 1997). To estimate the length of the autoregression model we used Akaike s information criterion (AIC) order selection criterion. We estimate AR models of different orders and the maximum lag (p) is chosen on the basis of the AIC criterion for autocorrelation. 12

14 3.1. Logistic Smooth Transition Autoregressive (LSTAR) Models DBM model assumes abrupt jumps between the two market states, which is not convincing regardless of the sophistication of the logic used to define the market state. This leads to a definition of a model where the transition between the two states is smooth and continuous. Teräsvirta (1994) proposed a Smooth Transition Autoregressive (STAR) model that allows for a smooth transition and this paper considers a Logistic STAR (LSTAR) model. A LSTAR model of order p can be defined as: R it = α i + β i w t + (α D i + β D i w t )F (M t ) + u it (6) F (M t ) = 1/(1 + e [ γ i(m t c i )] ) (7) Where u it is n.i.d(0, σu) 2 and F (M t ) is a logistic smooth transition function of M t that replaces S t in equation 2. The function F (M t ) takes a value between 0 and 1 based on the magnitude of (M t c i ). The function F (M t ) approaches zero when M t << c i, thereby making equation 6 equivalent to linear CRM model. Conversely, when M t >> c i then the function F (M t ) approaches 1, thereby reducing the equation 6 to DBM model. For all other cases, the function F (M t ) smoothly varies between 0 and 1. The value of the parameter γ i defines the smoothness of the transition between two states. Figure 1 shows the transition function F (M t ) for different values of γ i. From this figure it can be noticed that DBM and CRM models are special cases of LSTAR models when γ i approaches and 0 respectively. 13

15 In our study we have chosen c i such that the sum of the square of distance is minimum for the time series M t. To account for the outliers we have take only 95 percentile of M t values. The parameter γ i is estimated such that 50% values of F (M t ) falls between 0 and 1. Before embarking with the estimation of the LSTAR model we need to justify the non-linear form, otherwise a simple linear model would be sufficient. To test for linearity against the LSTAR model we follow Woodward and Brooks s approach and form an auxiliary regression by replacing F (M t ) with a third order Taylor series approximation. The expanded equation is R it = φ 1 +φ 2 β i +φ 3 R mat +φ 4 Rmat+φ 2 5 Rmat+φ 3 6 β i R mat +φ 7 β i Rmat+φ 2 8 β i Rmat 3 (8) In this setting, the null hypothesis of linearity is H 0 : φ j = 0 for (j = 3, 8). A standard Wald test can be used to test this hypothesis (Woodward and Brooks, 2009). 4. Data sources and descriptive statistics The data used in this study is the monthly price data from June 2002 to May 2012 on global and regional Islamic equity indices and their conventional counterparts as a benchmark from where the Islamic index usually draws its equities. Data for MSCI indices is directly downloaded from their website: while the data for Standard and Poor s and Dow Jones indices are obtained from DataStream. Only those 14

16 global or regional indices that had complete price data over the entire period selected for this study. Twelve Islamic equity indices met this criterion of which two are global indices, five concentrated on Asia/Asia Pacific, two focused on Europe, one each on Americas, Eurozone, and the US. Table A2 in the Appendix provides detailed information on these indices. Table 1 reports the descriptive statistics for the U.S. dollar returns of the 12 IEIs and their respective benchmark indices. All values are calculated in excess of the return on the 3 Month U.S. T-Bill rate as reported by the U.S. Department of Treasury 6 from a continuously compounding return series for both the IEI and conventional indices calculated as the logarithmic difference between the return of month and its corresponding lag. Figure 2 illustrates the return performance of IEIs under study. There is a steep decline in the returns of all IEIs in the last quarter of 2008 which is known to be the peak of the GFC. To better capture the difference in performance, the data is further divided into three sub-periods: pre-gfc (June 2002 to August 2008), peak of the GFC (September 2008 to April 2009) and post peak of the GFC (May 2009 to May 2012). Panel A of Table 1 reports the descriptive statistics for the overall period. It is evident that all of the IEIs, on average performed better than conventional indices on nominal as well as on a risk adjusted basis except for the DJ Islamic Asia Pacific Index. On average, the excess nominal return of IEIs is about one percent higher than the conventional indices 6 U.S. T-Bill rates were downloaded from the treasury website ( 15

17 with a lower standard deviation of about half a percent. Overall, IEIs performed better than conventional indices on a risk adjusted basis as measured by the Shape ratio of of IEIs as compared with of conventional indices. Panel B, C and D of Table 1 report the descriptive statistics for three sub-periods: pre-peak of GFC, peak of GFC and post-peak of GFC. In each of the three sub-periods IEIs performed better than the conventional indices in terms of nominal as well as risk adjusted returns although both IEIs and benchmark indices declined in value. However, the decline in IEI is 2.48 percent lower than that of benchmark indices with a lower standard deviation of 1.52 percent on an annual basis. This suggests that IEIs on average, experienced a lower volatility during the overall period and especially a lower volatility during the peak of the financial crisis. These findings are in line with the claims that Islamic equity investments provide hedging during the an economic downturn. The last two columns in Table 1 report the estimation results of CRM model and the coefficient of determination (R 2 ). The beta coefficient as reported for all IEIs are statistically significant at 1 percent level suggesting that returns of IEIs can be explained with the return of benchmark indices. Furthermore, 7 out of the 12 indices reported a beta coefficient less than unity suggesting a lower systematic risk as compared with the benchmark index. These findings are further supported by looking at R 2 reported in the last column. These findings also clearly indicate that the majority of the variation in the IEIs returns can be explained by returns on their respective benchmark index with R 2 ranging from 0.90 to Although not reported in Table 1, the Jenson s alpha coefficient in case of all IEI is statistically not 16

18 different from zero. 5. Empirical estimations Empirical results based on a dual beta model are reported in Table 2. The estimation results are obtained using the diagonal vech type of GARCH model as suggested by Bollerslev et al. (1988). The order of the autoregressive model has been selected using the Akaike s information criterion (AIC). Column titled W aldχ 2 (3) reports a Wald test against the null hypothesis that all the coefficients on the independent variables in each equation are zero. Here the null hypothesis is rejected at all conventional levels. Column 3 reports the estimation of the beta coefficient. Beta coefficients for all IEIs are not only significant but also less than unity except in the case of two indices: AC Pacific Islamic Standard Index and DJ Islamic Asia Pacific Index, where beta coefficient is slightly higher than the unity. These results indicate that IEIs on average experience lower volatility than their respective benchmark indices. The down market differentials in IEIs are reported in column 2. The coefficient of down market differential performance of all the IEIs are statistically insignificant suggesting that IEIs do not face statistically significant diminishing marginal returns during the bearish cycle of capital markets. The dummy of the GFC is also insignificant in the case of all IEIs except for MSCI s Pacific and Asia Pacific standard indices. This suggests that the risk for returns of IEIs was not significantly different as compared with their respective benchmark returns during the peak of the GFC. Similarly, the coefficients for abnormal return due to Shari ah screening are 17

19 also insignificant for all IEIs except for AC Europe Islamic Standard Index and S&P Europe 350 Index. The significance of abnormal returns for European IEIs may be due to the screening of more stocks based on a higher number of leveraged companies in the European market. In summary, results from the dual beta model indicate a differential in performance of IEIs based on the domicile of the IEIs in terms of their sensitivity to the GFC or their ability to produce abnormal returns. However, on average, IEIs exhibit a lower risk than their conventional counterparts. This further supports our inference from the descriptive statistics that IEIs on average experience lower volatility than conventional indices. In the dual beta model, it is assumed that a change in the performance of IEIs is linear over time. However, nonlinearity arises in the model due to the transition variable M t being the moving average of the past three months of market returns. To address the nonlinearity, we performed a set of tests as mentioned in the methodology section. In the event of non-rejection of nonlinearity a LSTAR model can be applied. We provide evidence of nonlinearity in Table 3, using the linear approximation of transition variable, M t based on a standard Wald test from equation 8 for third-order Taylor series. As evidenced in Figure 2, all IEIs faced an abrupt change in return series during the GFC. To control for outliers during the peak of GFC, a separate set of test is performed by including the dummy variable GFC in all test regressions. Column 4 (T aylor SF C 3 ) of Table 3 reports the heteroskedasticity adjusted test results for non-linearity after including the dummy variable of GFC while column 3, reports the heteroskedasticity adjusted test results 18

20 without the dummy of GFC. In case of column 3, null hypothesis of nonlinearity is rejected at 15 percent significance level for all IEIs with 6 at 1 percent, 5 at 10 percent and one remaining at 15 percent. T aylor SF C 3 results show some differences, however the qualitative conclusion are quite similar. Both sets of test results of p-values indicate the existence of time varying returns and supports the application of nonlinear method for estimations. Based on the evidence of nonlinearity as reported in Table 3, we estimate the time varying return model for IEIs as a logistic smooth transition autoregressive (LSTAR) model. The LSTAR model allows for a smooth transition between the up and down market rather than abrupt change based on the dummy variable in case of a dual beta model as reported above. We estimate the transition function F (M t ) by joint estimation of γ i and c i using the transition variable M t. The parameter estimates for γ i and c i are reported in the last two columns of Table 3. The values of γ i and c i indicates a smooth transition between a narrow range of γ from 160 to 233. This range is sufficient to support for smooth transition of transition variable from down market to up market and vice versa. In our case the transition function takes a minimum of and maximum of with the mean and a standard deviation of The order of the autoregressive model has been selected using the AIC and is reported in Table 4 along with estimation results for the LSTAR model. Since we are interested in the performance differential of IEIs with conventional indices during the down markets we used the difference of transition function from unity as a variable in the regression model along with the dummy variable of extreme market movement GFC 19

21 during the peak of the GFC. The estimation results for beta coefficient for all IEIs are below unity and are statistically significant at 1 percent level suggesting that on average, IEIs exhibit a lower risk than that of the benchmark index. These lower beta coefficients further suggest that IEIs provide hedging opportunities during an economic downturn. The differential beta coefficients are very similar to the DBM model with the exception of the AC Europe Islamic Standard Index and the AC Far East Islamic index. These two indices show a positive significance relationship suggesting that the beta coefficient of IEIs increases during the downturn of capital markets. Similarly, the GFC peak dummy is also significant in case of the DJ Islamic market index and the AC Europe Islamic Standard Index. The above differences in estimation results indicate that IEIs performance is not only dependent on the Shari ah screen but also on the market from where these indices normally draw their securities. The coefficient on abnormal return is positive and statistically significant for four of the indices: AC Asia Islamic Standard Index, AC Europe Islamic Standard Index, AC Far East Islamic Standard Index and S&P Europe 350 Index. This result indicates that IEIs focusing on regional investments especially in Asia and Europe, during the period under study produced on average, better returns than that of their conventional indices. The global IEIs on the other hand exhibit similar return patterns with lower risk as the conventional counterpart indices. In total, we can conclude that the LSTAR model provides more robust evidence that IEIs provide hedging opportunities to the general investing public by exhibiting a lower volatility without any 20

22 significant loss of returns. 6. Summary and Conclusion Islamic equity investment based on Shari ah principles is one of the fastest growing segments of international capital markets. Recent empirical evidence suggests that Islamic mutual funds perform better than conventional mutual funds during economic downturns. However, it is not clear whether such over-performance is attributed to the Shari ah based screening criteria, market timing, and/or stock selection abilities of fund managers. In contrast to other studies focusing on Islamic mutual funds, this study concentrates on Islamic equities indices representing a portfolio of equities based on Shari ah principles. The performance of IEIs is comparable with Islamic mutual funds in the sense that both apply similar screening criteria for selection of equities. However, the use of IEIs for performance comparison has a clear advantage since this isolates the effects of screening criteria on the risk/return performance from that of management skills and trading costs. The assumption of constant risk (stable beta coefficient) under the standard CAPM model makes the empirical estimation flawed since the market goes through up and down phases and the sensitivity of an IEI return may change considerably from that of the benchmark index from one phase to the other. This study applies an LSTAR model which incorporates a smooth transition between the two extreme phases of the capital markets by utilizing a transition function based on three months moving average of the benchmark index. We also estimated our results based on the dual beta 21

23 model that allows for abrupt movement between the market phases. Using a monthly price dataset of 12 world and regional IEIs and their conventional counterparts as a benchmark from June 2002 to May 2012, we find strong evidence that IEIs on average exhibit lower volatility as compared with their benchmark index during the sample period. This implies that changes in conventional benchmark returns translate into a smaller change in IEI returns. We do not find any significant change in the relative riskiness of IEIs during the downturn of the economy. These findings support the popular view that IEIs provide hedging opportunities during a downturn of the capital markets. We did not find any evidence of abnormal returns on global basis. However, we did find positive abnormal returns associated with the European and Asian regions suggesting that investors can achieve better returns by diversifying into Islamic equity investments. Our results provide important policy implications. The evidence of overall lower systematic risk of IEIs as compared with conventional indices highlights the importance of sound business practices and the dangers of excessive risk taking whether in the form of debt leverage or trading in derivatives. Based on the empirical evidence, the managers of conventional mutual funds and ordinary investors can benefit from overweighting securities in their portfolios that comply with Shari ah principles. The advantage could be bigger for fund managers in the socially responsible investing horizon where adding a negative screen on leverage and derivative trading may result in lower risk and possibly positive abnormal return. The positive abnormal return in the case of specific indices warrants further investigation on country level data to identify the specific markets causing abnormal returns. Further research is 22

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30 Figure 1: Transition function F (M t ). This figure plots F (M t ) = 1/(1 + e [ γ i(m t c i )] ) for six different values of γ. 29

31 Figure 2: The return performance of IEIs from June 2002 to May

32 Table 1: Descriptive statistics of Islamic equity indices versus conventional benchmark indices. This table provides the descriptive statistics on the sample of indices separated into IEIs and conventional benchmark indices. Return is calculated by ln(rt Rt 1). The data is pooled over period of 06/2002 to 05/2012. Panel A, Panel B, Panel C and Panel D report the descriptive statistics for all IEIs versus their benchmarks for the entire period, pre-peak of the GFC (Jun 2002 to Aug 2008), peak of the GFC, (Sept 2008 to Apr 2009) and post-peak of the GFC (May 2009 to May 2012) respectively. The last two columns represent β coefficient of CRM and R 2. Panel A Panel B Panel C Overall period Pre-peak GFC Peak GFC Panel D Post-Peak GFC IEI Benchmark IEI Benchmark IEI Benchmark IEI Benchmark CRM beta R 2 mean sd mean sd mean sd mean sd mean sd mean sd mean sd mean sd MS *** 0.95 MS *** 0.97 DJ *** 0.95 MS *** 0.98 DJ *** 0.94 DJ *** 0.90 MS *** 0.96 MS *** 0.97 MS *** 0.98 DJ *** 0.95 DJ *** 0.97 MS *** 0.97 Total Annualized 1.59% 18.57% 0.63% 19.13% -1.89% 18.38% -2.60% 18.99% % 36.46% % 37.98% 9.63% 18.83% 7.95% 19.25% Sharp Ratio

33 Table 2: Empirical Estimations based on the Dual Beta Model. This table reports the coefficients R it = α i + β i R mt + (αi D + βi D R mt )S t + ɛ it for 12 IEIs with an international and regional focus from 06:2002 to 05:2012 period. The regression results are based on the Multivariate GARCH model. The coefficients α i and β i reflects the Jenson s alpha and systematic risk of index i with respect to the overall market. αi D + βi D reflect the down market differentials. GFC reports the performance differential of IEIs with respect to the conventional benchmarks during the peak of the GFC, W aldχ 2 (3) report the standard Wald test for all coefficient equal to zero. L(p)ARCH reflects the coefficient of the ARCH term based on lags selected using the AIC criteria. Asterisks *** denotes statistically different from zero, 1% level, two tail test, **5% level, *10. ID GFC Lag(p) L(p).ARCH Wald (3) MS *** *** ( ) ( ) ( ) ( ) ( ) MS *** *** ( ) ( ) ( ) ( ) ( ) DJ *** *** ( ) ( ) ( ) ( ) ( ) MS *** ** *** ( ) ( ) ( ) ( ) ( ) DJ *** *** ( ) ( ) ( ) ( ) ( ) DJ * *** *** *** ( ) ( ) ( ) ( ) ( ) MS * *** * *** ( ) ( ) ( ) ( ) ( ) MS *** *** ( ) ( ) ( ) ( ) ( ) MS *** ** *** ( ) ( ) ( ) ( ) ( ) DJ *** *** *** ( ) ( ) ( ) ( ) ( ) DJ *** *** ( ) ( ) ( ) ( ) ( ) MS *** *** *** ( ) ( ) ( ) ( ) ( ) 32