Co-Movement, Dependence Structure and Ethical Investment Funds under GFC

This paper extends the recent work of Mansor et al. [1] who use panel regression to measure ethics based Islamic mutual fund performance and note the various methodological issues in this respect. We attempt to capture the co-movement and dependence structure of the fund index with five major equity indices before and during the Global financial crises (GFC). Four models—CAPM, normal Copula, symmetrised Joe-Clayton Copula and Rotated Gumbel Copula—are used to analyse the co-movement and dependence structure of Islamic investment funds. Our findings show that the ethical investment funds have low dependence with the major market indices. The fluctuations in the financial markets in the U.S., the U.K., Germany and Japan are less likely to affect the Islamic investment funds than other financial assets. However, the time-varying dependence increases dramatically during the GFC indicating that the diversification merits of Islamic equity funds in the portfolio deteriorate in the bear market. Some of the empirical results drawn in this paper will raise awareness among both academicians and finan-ciers about the importance of Islamic investment funds during and out of crises periods.


Introduction
The last three decades have seen tremendous interest and growth in the field of ethical investment. For example, there are 1204 ethical retail investment funds in Europe with total size of about 136 billion Euros, with average annual growth rate of 7% [2]. UK's ethical fund "Friends Provident Stewardship Fund" is even Theoretical Economics Letters growing faster than the overall European. Though the effect of post Brexit is unknown, Latest figures show that in the USA ethical investment is over 20 times than that of the UK. Companies which are engaged in tobacco, armaments and other typically unethical investment activities are excluded by US ethical fund managers. Islamic investment fund (IMF) or Islamic Mutual fund may be more concerned with a very different set of ethical criteria from Western "green" or ethical investors, but the issues of business ethics, stock selection and screening technique are of common interest to general ethical investment and the IMF which is based on interest free settings due to religious ethics, as interest is prohibited in Islamic banking and finance (IBF) products, including IMF.
Islamic banking and finance industry is growing faster than both ethical and/or conventional banking and finance. There are more than 600 Islamic financial institutions now operate in 75 countries with an average annual growth of 15 percent and the total global size of the Islamic financial assets standing at US $1.6 trillion [3]. Takaful, Sukuks, and Islamic equity funds are the fastest growing segments of Islamic banking and finance [4] [5]. In the early 1990s, there were less than 10 Shari'ah-complaint funds in the world, mainly in the Middle East. The number was close to 400 in 2009 [6]. Over the years, the number of Islamic investment funds has grown and eventually trickled across the globe. Increasing numbers of Western financial institutions are now involved in Islamic investment funds to attract Muslim customers worldwide. The amount of finance designated as being ethically invested in the UK currently exceeds £1 billion, of which over £414 million is in the Friends Provident Stewardship Fund. In the USA over 20 times this amount is invested ethically, including finance which is invested in environmentally friendly projects and companies which are screened using moral criteria. Companies which are engaged in tobacco production or distribution or are involved in armaments are typically excluded by US ethical fund managers. Islamic investors may be concerned with a very different set of ethical criteria from Western "green" or ethical investors, but the issues of stock selection and screening technique are of mutual interest.
There is arguably much that both parties can learn from one another, especially with respect to investment techniques, even though the underlying moral value systems are very different, and there is no question of importing or exporting cultural norms or religious beliefs.
The rapid growth of Islamic investment funds raises a series of important questions: Is the growth in Islamic investment funds a result of the comparative advantages of the Islamic fund paradigm or is it largely attributable to the worldwide Islamic resurgence since the late 1960s? Do Islamic investment funds provide greater positive returns compared to the Islamic market index and the major Western market indices? And did these returns move together before and during a crisis such as the Asian and global financial crises?
The growing Islamic finance literature has attempted to answer the above questions and a few have documented that the performance of Islamic invest- Previous research has also reported some evidence on the risk and return characteristics of Islamic funds using fund level data. For instance, Abdullah et al. [16] analyse 65 Malaysian unit trusts including 14 Islamic and 51 conventional funds and conclude that both types of funds slightly underperformed the Kuala Lumpur Composite Index (KLCI) benchmark [17]. After taking risk into account, they find that Islamic mutual funds (IMFs) perform better than the conventional funds (CMFs) during the bear market, but underperform during the bull market. Hayat and Kraeussl [8] expand the sample to 145 Islamic equity funds (IEFs) and analyse the risk-return characteristics in a more rigorous manner. They argue that IEFs are underperformers compared to Islamic, as well as, to the conventional equity benchmarks, and the underperformance seems to have increased during the GFC. Hoepner et al. [18] analyse the financial performance and investment style in IMFs employing a bigger sample including 265 IEFs from 20 countries. They find that the performance of IMFs from countries with more developed Islamic financial markets is comparable to international equity benchmarks, while funds from countries with less Islamic assets, especially Western nations, tend to significantly underperform. Mansor et al. [1] follow Hayat and Kraeussl's [8] approach to measure the impact of fees on selectivity and timing for the Malaysian IMFs using panel data regression models. They observe that the fund managers lack the expertise with respect to the choice of fund selection and timing. However, they also note that the IMFs perform marginally better than the conventional funds. Lastly, their findings regarding human capital in IMFs are in line with those partially observed by Basov and Bhatti [9] who use a Mechanism approach.
Most of the studies mentioned above use the CAPM model [ [18], with the exception of Basov and Bhatti [9] to examine the financial performance of Islamic funds. However, such a setting has two limitations. First, it is empirically proven that asset returns from a wide range of markets are leptokurtic, being heavy-tailed and overly concentrated around the mean when compared to a Gaussian distribution [19]. This means that when the return distribution deviates from the elliptic class of distributions, including Gaussian, a single statistic such as the systematic risk measure (beta) estimated by Hayat and Kraeussl [8] or Mansor et al. [1] is unable to correctly assess the dependency structure between the returns. Tail dependence may also differ from dependence close to the mean [20] [21] [22]. Further, the dependence between two asset returns as the market rises may be different than the dependence as the market falls. Shaw [23] has pointed out that the linear correlation coefficient cannot capture the non-linear dependence relationships that exist between many financial series. Second, correlation coefficient estimated using CAPM or Carhart model is simply a scalar measure of dependency and it cannot embody everything one would like to know about the dependence structure. It is therefore not an appropriate dependence measure for very heavy-tailed distributions [24].
Our study contributes to the literature by providing empirical evidence of the co-movement and dependence structure of Islamic investment funds with the Islamic and the Western stock indices employing both the linear (CAPM) and non-linear (Copula) methods. Dependence structure is an important issue in measuring the co-movement of financial indices. As mentioned above, linear correlation, though it provides an easy and convenient way to describe co-movement between two random variables, is not an appropriate dependence measure and maybe highly biased in certain non-normal situations. In addition, asymmetric dependence in equity markets and foreign exchange markets is also documented in recent literature including Longin and Solnik [25], Ang and Chen [26], Patton [27], Rodriguez [28], Ahsanullah and Bhatti [29], Bhatti and Nguyen [20] and Nguyen et al. [21] [22], among others. These features can be easily captured in Copula models with tail dependence parameters. Therefore, the Copula is a more powerful and attractive tool to analyse the dependence between margins since it does not require the assumption of normality in the marginal distributions [29]. The rest of the paper is organised as follows. Section 2 provides a description of Islamic investment funds' characteristics and categories. Section 3 presents the research methodologies including the CAPM and the various Copulas namely the normal Copula, the symmetrised Joe-Clayton (SJC) Copula and the Rotated Gumbel Copula, to analyse the co-movement and dependence structure of Islamic investment fund index and the five major stock indices. The empirical results are presented in Section 4 including a detailed discussion. The final section concludes.

The Islamic Investment Fund: Characteristics and Categories
The term Islamic Investment Fund is defined by Usmani [30] as "a joint pool wherein the investors contribute their surplus money for the purpose of its investment to earn halal profits in strict conformity with the precepts of Islamic Shari'ah". The subscribers of the fund may receive a certificate of subscription which entitles them to receive pro-rata profits accruing to the fund. These certificates are subject to two sets of guidelines; sectoral guidelines and financial guidelines [31].
First, Shari'ah clearly defines business and financial activities that are prohibited for Muslims including consumption of alcohol, pork products, gambling, and porn industries. Further, the terms agreed upon must conform to the Islamic principles. This is called Shari'ah compliancy.
Second, instead of a fixed return that is tied up to their face value, these certificates must carry a pro-rata profit actually earned by the fund. Therefore, neither the principal nor the rate of profit (tied up with the principal) can be guaranteed.
The subscribers must enter into the fund with a clear understanding that the return on their subscription is tied to the actual profits earned or losses suffered by the fund. If the fund earns profits, the returns in their subscription will increase to that proportion. Similarly, in case the fund suffers a loss, that will have to be shared also, unless the loss is caused by the negligence or mismanagement in which case the management, and not the fund, will be liable to compensate it.

Islamic Equity Funds
In an equity fund, the amounts are invested in the shares of joint stock companies. The profits are mainly achieved through capital gains; by purchasing the shares and selling them when their prices have increased. Profits can also be by way of dividends distributed by the relevant companies. Dealing in equity shares is acceptable in the Shari'ah subject to the following conditions; 1) The main business of the company is not in violation of the Shari'ah; 2) If the main business of the companies is halal, but they deposit the surplus amounts in an interest-bearing account or borrow money on interest, the shareholder must express his disapproval against such dealings; 3) If some income from interest-bearing

Islamic Hedge Funds
Hedge fund is a private investment vehicle for high net worth and institutional The launch of the Dubai Shari'ah Hedge Fund index provides a benchmark for investors in Shari'ah compliant hedge funds who are looking for absolute investment returns in commodities during the periods of market volatility.

Copula Models
As a dependency measure, the correlation coefficient estimated using CAPM contains a number of pitfalls as mentioned previously. Copula models, on the other hand, represent a way of trying to extract the dependence structure from the joint distribution and to extricate dependence and marginal behaviour. This allows for the decomposition of a joint distribution into its marginal distributions and its dependence function 1 , i.e., the Copula function [34]. We may construct the Copula function by transforming the random variables 1 Y and 2 Y with the joint distribution function ( ) ( ) Nelsen [34] and Patton [27] provide complete discussions on Copula and conditional Copula theory. We follow their methods for the normal (Gaussian) and Generalized Joe-Clayton (GJC) Copula. The former is a good model to measure general dependence and the latter is good at modeling both upper and lower tail dependencies. These two types of Copula models will give us a fuller picture of dependence structures for the indices.
Gaussian Copula has the dependence function associated with bivariate normality and can be expressed as: captures the variation effect on independence.
The second Copula used in our study is the symmetrised Joe-Clayton (SJC) Copula that is a slight modification of the original Joe-Clayton Copula. Joe-Clayton Copula proposed by Joe [35] itself is a Laplace transformation of the Clayton's Copula. It is defined as: Unlike the Gaussian Copula, there are two tail dependence parameters, U τ and L τ , in this Copula function [20]. The upper tail dependence is defined as: If this limit exists, the Copula shows lower tail dependence when ( ] 0,1 L τ ∈ and no tail dependence when 0 L τ = . By construction, the Joe-Clayton Copula always gives asymmetric tail dependence even if the two tail dependence measures are in fact equal. In order to overcome this shortcoming we will use the SJC Copula proposed by Patton [27] in the present study, given by

Data Description
We examine the interaction between the Europe Open-end Islamic Shari'ah Equity fund and the five major stock indices. These are labelled as, "ISE" for the Is-   We find that, in Panel A of Table 1, the average return of ISE is lower than most of the major stock market indices except NIK with the Japanese stock market reporting the worst performance in recent times considering the negative average returns between 1997 and 2009. According to the standard deviations, the most volatile index is the DAX while the least volatile index is the FTS. The volatility of the ISE, measured by the standard deviation, is in the middle. All five major market indices, including the DJIM, exhibit negative skewness while the ISE shows positive skewness. All of these results indicate that the empirical distributions of weekly returns of the ISE and the five major market indices exhibit a non-normal pattern. We also find significant kurtosis in each series. ISE displays extremely high kurtosis indicating that more of the variance is due to infrequent extreme deviations.
In Panel B of Table 1 Table 2.
As expected, the returns are leptokurtic with all the normality tests rejecting the null hypothesis of Gaussian distributed returns. In such a situation, a single statistic such as beta estimated in the CAPM model is not able to correctly assess the dependency structure between the returns and the tail dependence may differ from dependence close to the mean. As mentioned earlier, the correlation coefficient estimated using CAPM is a scalar measure of dependency, and is unable to embody the required information about the dependence structure.    The asterisks, (*), (**), and (***) indicate a rejection of the null hypothesis at the 1%, 5%, and 10% levels, respectively. P-values are reported in parentheses. Theoretical Economics Letters and the adjusted R-squared statistics are much higher than those in Table 3.

CAPM and Copula Results
This result implies that the Islamic Equity Funds provide good diversification benefits to the investors, even when compared to the Islamic market index.
The time path of dependence parameters are presented in Figure 2 to Figure   6. We report the Gaussian Copula parameter estimates for both constant and

Concluding Remarks
Dependence structure is an important issue in understanding the individual financial asset's return against a market benchmark. Linear measures, such as alpha and beta estimated by the traditional CAPM model and the Carhart model, provide an easy and convenient way to describe the performance and co-movement of Islamic funds. However, they are not the appropriate dependence measures and may be highly biased in certain non-normal situations.
In this study, we use both the traditional CAPM model and the time-varying conditional Copula models to study the co-movement and dependence struc- Third, normal Copula parameter estimates suggest that the Islamic investment funds have low dependence with the major Western market indices before the GFC. The fluctuation in the financial markets in the U.S., U.K., Germany and Japan is less likely to affect the Islamic investment funds relative to other financial assets. One of the implications is that Islamic investment funds are not only attractive for Muslim investors, but also a good alternative for the fund managers to diversify their portfolios.
Last, the time-varying dependence between Islamic Shari'ah Equity index and Dow Jones Islamic Market index and the four major Western market indices increases dramatically during the GFC. This finding is supported by the SJC Copula results. SJC Copula lower-tail dependence is slightly higher than the upper-tail dependence indicating that there is a higher probability of joint extreme events during the bear market than during the bull market. The implication here is that diversification benefits of including the Islamic equity funds in the portfolio seem to deteriorate in the financial crisis.