Abstract

In the current study, we assess the risk from conventional and Islamic stock indices under CAPM downside risk. We apply the DCC-GARCH and the BEKK-GARCH models to create the time-varying betas for the conventional and Islamic stock indices of 7 countries: Malaysia, Bahrain, Kuwait, Oman, Qatar, the United Arab Emirates and Indonesia. We use daily data, from 10 August 2006 to 26 November 2015. We examined how the restrictions imposed by Islamic law affect the risk. The results show no remarkable difference between the two classes of stock indices. This can be explained by the contradictory effect of filtering criteria on risk. Also, the results showed that the measures Downside risk are more appropriate than traditional measures for both Islamic and conventional stock indices.

1. Introduction

Traditional risk measures used have been widely criticized in the literature. Specifically, in the mean-variance CAPM, the constant variance over time was long regarded as a proxy for risk calculation. This measure identifies the extreme gains and extreme losses in the same way ¹. Thus, the variance of returns is not considered an appropriate measure of risk when the return distribution is symmetrical according to the normal law.

Financial theories postulate that investors observe the gains and losses in different ways. They are generally more concerned and attach great importance to losses than gains ². The use of the traditional mean-variance CAPM framework leads to poor risk assessment because of the asymmetric nature of returns. Therefore, new models have emerged as alternative to standard conventional models.

A number of studies, including ^{3, 4, 5, 6, 7, 8, 9, 10} provided analytical and empirical evidence to support the use of downside risk measures. This is a risk measure that focuses only on the downside part. Indeed, the concept of "downside" was discussed for the first time in the fifties by ¹¹ and then by ¹ who also recognized the importance of this concept. Thus, the downside risk measures are considered as a major improvement over the traditional portfolio theory. These measures help investors to take appropriate decisions to face non-normal distributions of asset returns ³. Many researchers, such as ^{12, 13, 14} suggested that the capital asset pricing model CAPM- lower partial moments is more relevant for assessing the risk of assets than the traditional mean-variance CAPM. Researches ^{7, 15, 16} also provided evidence of the importance of considering the downside risk measure beta. These researches have confirmed that the beta downside is empirically different from traditional beta when asset returns are distributed asymmetrically.

The aim of this paper is to assess the risk from conventional and Islamic stock indices under CAPM downside risk. To our knowledge, no previous research has studied the CAPM Downside risk in the context of Islamic stock index. Our analysis is important for international investors and portfolio managers, and has policy implications in stock markets.

The paper is organized as follows. Section 2 gives an overview of Islamic finance. Section 3 presents the empirical methodology. Section 3 describes the data. Section 4 reports the empirical results and section 5 concludes the article.

2. Theoritical Baground

Islamic equity indices have attracted the attention of investors willing to invest in portfolios that comply with their beliefs and religious principles. Indeed, in the build framework of Islamic indices, each index goes through a conventional Islamic filtering to detect if the securities that composed the Index, are in line with Islamic law. Therefore, a financial security can be regarded as Islamic if it goes through two main stages namely the qualitative assessment regarding the main activity of the company and the quantitative assessment regarding its secondary activity. The qualitative filter examines the nature of the company's core business. It implies the prohibition to invest in illegal activities and thus excludes all sectors deemed incompatible with the principles of Islamic investment. Indeed, to determine the conformity of business sectors with Islamic law, two sectoral classifications can be used namely Industry Classification Benchmark (ICB) and Global Industry Classification Standard (GICS). After passing through the qualitative filter, financial securities must go through the quantitative criterion which has four levels: Leverage Compliance (debt), Cash Compliance (Account Receivable + cash), Cash and Interest Bearing Items, Revenue from NonComplaint Activities and Total Interest.

In an Islamic context, risk-taking is legitimate when it is necessary and indispensable to the creation of value. Otherwise it is a form of gambling ^{17, 18}. Islamic law provides for the prevention of excessive risk and pure risk trade that threaten the instability of the financial and economic system ^{17, 18, 19}. Previous studies suggest that the risk cannot be completely eliminated. ²⁰ evokes the principle of sharing profits and losses as well as the partnership concepts in Islamic contracts require that an element of risk is supported by all partners. Similarly, ²¹ suggest that all economic activity is associated with a degree of risk. The risk cannot be completely eliminated. In this sense, ²² distinguishes two types of risk. Firstly, the risk associated with business operations and activities of creating wealth and value. This risk encourages the preservation and development of wealth. This type of risk is strongly encouraged. Secondly, the risk associated to game and activities where no zero-sum additional wealth is created. It is the most common form gharar. This type of risk is clearly forbidden in the Islamic context. Indeed, Muslim scholars have mentioned three conditions for the risk to be tolerated is the risk must be inevitable, insignificant and involuntary ^{22, 23}.

This first criterion implies that the value cannot be created without using risk of loss or bankruptcy. Thus, the risk is inseparable from the actual financial transaction and value creation. In the Islamic context, separation of risk in the actual transactions will create more risk and lead to greater instability in the economy. All derivatives, whose structure is based on separation of proprietary risk and operating activities, are prohibited in Islamic finance.

Also, the risk must be insignificant: This second criterion is the degree of risk. According to Islamic law, the risk is acceptable when the probability of failure is sufficiently small compared to the probability of winning. Thus, the game that is based on a strong possibility of loss is forbidden by Islamic law.

The risk must be involuntary: This criterion combines the first two criteria. Indeed, the aim of all economic activity is the creation of added value. Thus, the decision of an economic agent should not be based on a strong possibility of loss. It must be motivated by intent to success. This done, the risk is only allowed to create wealth and value.

3. Empirical Methodology

The conditional CAPM may be expressed as follows:

(1)

, are excess returns over the risk free asset return, is the conditional expectation on the information available for investor at time (t-1)

(2)

In order to calculate conditional variances and covariances, we refer to the BEKK – GARCH model, introduced by ²⁴ and DCC – GARCH model introduced by ²⁵.

The conditional covariance matrix of bivariate BKKK-GARCH (1, 1) is parameterized as:

(3)

(4)

(5)

C is a lower triangular matrix with intercept parameters, and A and B are 2 X 2 square matrices of parameters. The bivariate version is written as :

(6)

²⁵ introduced the model dynamic conditional correlation (DCC) to enable the conditional correlation matrix varies over time. The conditional covariance matrix () is decomposed into conditional correlation matrix () and diagonal matrices conditional standard deviations .

(7)

(8)

(9)

is a symmetric positive definite matrix

(10)

The GARCH (1,1) is written as follows:

(11)

DCC model parameters’ are estimated by the maximum likelihood method. Engel ²⁵ expressed the log likelihood function as follows:

(12)

(13)

(14)

The empirical literature provides two suggestions to measure the downside risk that is a semi-variance calculated from the average return and a semi-variance calculated from a target yield as the risk free rate. Both semi variance measures calculate a variance using only yields below an average yield or target return. Three models of asset pricing in the downside risk framework have been discussed in the literature: Hogan and Warren ¹³ model, Harlow and Rao ¹⁴ model and the Estrada ²⁶ model.

Under Hogan and Warren ¹³ model, the risk was measured by bearish partial moments calculated relative to the risk free rate.

(15)

: is the systematic risk measure beta downside Hogan and Warren (1974) which is equal to:

(16)

(17)

(18)

is the co-semivariance between the market portfolio returns below the risk-free return with the title of the performance i. is the semi variance of market return.

Harlow and Rao ¹⁴ proposed that the target rate of return is estimated by the average rate of return. In this context, CAPM downside risk of Harlow and Rao ¹⁴ is written:

(19)

Where : is the average returns on assets i

(20)

(21)

(22)

In its analysis, Estrada ²⁶ has developed a new measure of co-semivariance and proposed a new model CAPM downside risk. CAPM downside risk Estrada ²⁶ becomes:

(23)

Systematic risk, measured by Estrada ²⁶, as part of downside risk represented by

(24)

(25)

(26)

4. Data

The data used are conventional and Islamic stock indices from 7 countries: Malaysia, Bahrain, Kuwait, Oman, Qatar, the United Arab Emirates and Indonesia. These indices are extracted from the MSCI database. The market index is represented by the MSCI World global stock index. All these indexes are taken into USD.  The data are daily, covers the period from 10 August 2006 to 26 November 2015 including 2425 cases for each market. The good treasure of 3months rate is used to calculate the return on risk-free rate in the conventional framework obtained by Federal Reserve Economic Data (FRED). In the Islamic context, Dow Jones Sukuk total return index (ex-reinvestment) is used to calculate sukuk.

The Daily returns were calculated as the first difference of the natural logarithm of each index and expressed as percentages:

(27)

The excess returns are expressed as follows:

(28)

Table 1 lists the statistics describing the daily returns of the conventional indices. All returns exhibit negative skewness. The series are characterized by distributions spread to the left. This suggests a greater likelihood of suffering losses as gains for the period of time taken in the sample. The excess kurtosis shows a strong presence of extremes. The distribution has leptokurtic tail. The values of the test Jarque Bera are very high. This test rejects the normal distribution. Thus, skewness values, kurtosis and Jarque Bera indicate that daily returns for conventional stock indexes are asymmetrical, thick tail and do not follow the normal distribution.

Table 2 lists the statistics describing the daily returns of the Islamic indices. The results show that, over the entire period, no remarkable difference between the average of the Islamic and conventional return. The standard deviation of Islamic countries indices is higher than that of conventional country indexes except for the global market where the risk is lower. The skewness always takes negative values which mean that the series are characterized by distributions spread to the left. The kurtosis statistics greatly exceed three showing that the tails of the distributions are leptokurtic. Jarque Bera test values are very high indicating that distributions are not normally distributed. In conclusion, the results indicate that daily returns of Islamic equity indices are asymmetrical, leptokurtic and don’t conform to the normal distribution. Similarly, we find that the Islamic market indices capture the same stylized facts that conventional stock indexes in terms of asymmetry, kurtosis and non normality of distributions.

5. Estimation Results

Figure 1 depicts only the four types of time-varying DCC betas of seven countries of the sample. The graphs show that measures based on the downside risk are more important. A notable difference between the and . This observed difference between the two models can be attributed to the asymmetry of the distributions of returns and investor perceptions for downside risk that cannot be captured by traditional CAPM.

Table 3 shows the mean of the time-varying betas of conventional indices during the entire period. As expected, downside systematic risks were once again higher than the systematic risks calculated from the CAPM. Indeed, during portfolio construction, international investors should be concerned about the systematic downside risks that are poorly captured by traditional models ^{27, 28}.

Figure 2 shows the time-varying betas of Islamic indices. Table 4 summarizes the means of time varying betas of Islamic indices. The results for Islamic equity indices are consistent with results of conventional stock indices. The results indicate that systematic risk calculated by the CAPM mean - variance show low betas for all indices taken in the sample. This for, the results based on the CAPM downside risk of Hogan and Warren ¹³ and CAPM downside risk of Harlow and Rao ¹⁴ provide evidence of high systematic risk.

However, measure of Downside risk of Estrada ²⁶ shows the betas close to those calculated by the CAPM mean-variance. The results show that the betas calculated from the CAPM mean-variance and CAPM downside risk of Estrada ²⁶ are not suitable for assessing the risk associated with the Islamic market indices. These empirical results are of great importance for investors in decision making process to assess and identify an appropriate measure of risk.

Islamic systematic risk estimates are not very different than conventional (see Table 3 and Table 4). Indeed, no remarkable difference between the systematic risks varying times of the two indices. Results show that Islamic betas are slightly lower than conventional betas for some countries like Malaysia, Oman, Indonesia; and slightly superior to conventional betas in other countries such as Kuwait and Emirate. One might well conclude that Islamic market indices do not provide real opportunities for investors. The superiority of Islamic indices, led to a lower beta, can be explained by the selection criteria of the securities index components. Indeed, the Islamic market indices filtering process excludes companies incompatible with Islamic law directives. Islamic finance eliminates investments in illicit sectors such as alcohol, tobacco, gambling.... Also, it eliminates all speculative financial transactions based on derivatives. Indeed, conventional stock markets are exposed at a higher risk due to excessive risk-taking and short selling positions that are not permitted by Islamic law ²⁹. However, stock selection Islamic stock index components augment investor risk due to reduced diversification opportunities. ³⁰ point out that Islamic fund managers tend to eliminate the assets of large companies for the assets of small businesses. Indeed, the assets of small companies tend to be riskier and more volatile. What makes them riskier Islamic markets that conventional market. Financial theorists argue that ethical investment leads to lower returns over the long term as ethical portfolios are subsets of the market portfolio lacks sufficient diversification. Similarly, ethical filters can be a costly practice that may ultimately have a negative impact on portfolio performance.

6. Conclusion

Using daily index returns for seven markets over the period August 2006 to 26 November 2015, we empirically computed time-varying downside betas by means of the BEKK - GARCH model and DCC – GARCH model. We examined how the restrictions imposed by Islamic law affect the risk. Many conclusions can be drawn from the empirical results, which are somewhat mixed. Results show that no remarkable difference between the two classes of stock indices. This can be explained by the contradictory effect of filtering criteria on risk. Indeed, the selection of the Islamic index component securities declines, firstly, the risk through the elimination of excessive risk-taking and derivatives that are totally prohibited by Islamic law. And secondly, increases the risk due to the decrease of portfolio diversification opportunities.

References