Case Of Saudi Stock Market

Published Date: 02 Nov 2017

5.1 Introduction

In this chapter, we model the stock returns and volatility and, then, assess the efficiency of SSM based on the results obtained from modeling the stock return and volatility. The behavior of stock market has been studied extensively. This is as a result of the development of theories and econometrics models that examine the stock market performance and various factors that affect it. Volatility of financial assets has been a critical subject in the finance literature. Investors and fund managers among others take in to account the returns volatility on their investment decision, where the volatility could be caused by variability in speculative prices and the shocks of the business performance (Alexander, 1998)

Volatility of Stock market is defined as fluctuations in stock prices or tradable financial instruments (derivative securities) in a certain time period. The measure of volatility is the standard deviation or the variance and it is often considered as measure of the total risk of financial assets. Measuring and understanding of stock market volatility is important for the academic and practical people that the volatility as a risk measure plays a key role in portfolio construction, risk management, hedging and pricing derivatives. In value at risk models, the measure of market risk requires the estimation or forecast of a volatility parameter (Brooks, 2008)

The stochastic behaviour of stock returns has received high attention from researchers, and this has revealed significant stylized facts- the empirical distribution of returns is shown to be leptokurtic (Fama, 1965; Mandelbrot, 1963; Nelson, 1991) Further, stock returns exhibit volatility clustering. These processes have been modelled successfully by GARCH models (Bollerslev, 1986; Engle, 1982). Moreover, Bekaert & Wu, (2000); Black (1976) and Christie (1982) show that the financial time series exhibit a “ leverage effect” which means that volatility is higher after a negative shock (bad news) than positive shocks (good news) at the same magnitude. Also, long memory in return and volatility of financial market series return are important factors for determining non-linear dependence of financial time series (S. H. Kang & Yoon, 2007).

Engle (1982) introduced the Autoregressive Conditional Heterskedasticity (ARCH) model and generalised (GARCH) by Bollerslev (1986) have became the most popular models in the financial econometrics field. ARCH models model time-varying conditional volatility as a function of past innovations in order to estimate the variance of the series while Bollerslev modelled time-varying volatility using past innovations and volatility. ARCH and GARCH models have been used widely in financial time series (for example, stock market, interest rate, and foreign exchange rate). Later and resulting from some perceived problems of standard GARCH models (such as nonnegative constraint), several types of alternative GARCH models have been developed, for example, Exponential GARCH (Nelson, 1991), GJR-GARCH (Glosten, 1993), Asymmetric Power ARCH (APARCH) (Ding, Granger, & Engle, 1993)among others.

Most of the empirical studies using these models have been carried out on developed economics and relatively few on emerging markets. With regards to GCC countries, there are only a few studies on the characteristics of stock returns, for example, (Hassan, Al-Sultan, & Al-Saleem, 2003) for Kuwait. Interest has been increased for GCC stock markets on account of their rapid growth, the monetary stability, and the reform of the stock markets. GCC are one of the main oil resources in the world especially Saudi Arabia, a member of G20 and the highest oil-exporter country. They account for approximately 54 % of world proven oil reserves and 40% of gas reserves [1] . Moreover, (Marashdeh & Shrestha, 2010)show that the GCC stock markets are not fully integrated with developed markets which give an opportunity for international investors and funds to diversify their portfolio. In this work, we consider the SSM because it is the largest stock market by market capitalisation not only in GCC but also in the Middle East and North Africa (MENA) region [2] . It is addition to that the SSM has witnessed significant events and reforms over the past decade (see chapter 3).

This work also seeks to provide more knowledge about the various stylized facts uncovered in GCC emerging markets, and thus to shed light on the risk-return trade-off. Further, this may consider the similarities and difference between SSM and its developing/developed counterparts. Finally, a study of this nature is important for policy regulators such that they could develop policies that would improve the price discovery process, improve performance and thereby contribute to growth of the economy.

The chapter makes three main contributions to existing knowledge. The first contribution derives from the application of various GARCH models with different distributional assumption to the SSM. The second contribution of the chapter is that it fills important gaps in the literature by exploring some key volatility characteristics of stock returns behaviour in SSM in different stage of its development: for example, whether or not volatility follows a process of conditional heteroscedasticity, the possibility of long-memory, and whether risk premiums exist in SSM. The final contribution is the assessment of the efficiency of SSM.

The rest of the Chapter is organised as follows; section 3.2 provides the econometrics methods employed, i.e. the ARCH model, the GARCH model and its extensions. The summary features of the Tadawul All Share Index (TASI) index and estimated results are reported in section 3.3. Section 3.4 concludes.

5.2 Methodology

Modelling stock return volatility is an important issue in modern finance. Linear models are unable to capture some feature of financial data such as leptokurtosis, volatility clustering, long memory and leverage effects. That is because the linear models assume that the variance is constant while it has long been the view that the variance (and covariance) of asset returns are time variant (See Mandelbrot (1963), and Fama (1965)). Therefore, the idea of modelling time variation in second or higher moment started in the early 1980s. The ARCH (Engle, 1982) and GARCH (Bollerslev, 1986) (see Bollerslev, Chou, & Kroner (1992)) models have found widespread application since their introduction. These models successfully capture the volatility clustering which can be observed in macroeconomic series such as inflation (Engle 1982) or financial time series such as stock returns and exchange rate.

5.2.1 Symmetric GARCH models

We use two symmetric GARCH models(GARCH(1,1) and IGARCH(1,1). Poon and Granger (2003) show that the GARCH(1,1) is the best model for capturing the performance of the financial time series. In our ARMA-GARCH(1,1) model, the mean equation of stock returns can be described as

(4.1)

, where is iid with zero mean and unit variance.

The conditional variance is

(4.2)

In equation 4.1, donates the return at time t, μ is the intercept (constant) and the is the coefficient of the lags of returns and the is the lag of the errors is the errors. In conditional variance equation (4.2), the conditional variance σ2 is a function of squared past residuals which presents the ARCH term and the past conditional variance which present the GARCH term. The sum of and indicate the degree of volatility persistence and should be less than one.

In addition to the popular GARCH (1, 1), which is equation (4.2), we also apply the IGARCH (1, 1) model. In IGARCH models, the conditional variance must be nonnegative and, hence, restrictions of and are employed.

5.2.2 Asymmetric GARCH models

In addition to GARCH (1, 1) and IGARCH (1, 1), we adopt the GJR model which was developed by Glosten, and Jagannathan and Runkle (1993) and it modifies the original GARCH specification using a dummy variable. We modelled the conditional variance equation (4.2) as

(4.3)

where if and zero otherwise. If, there is a leverage effect.

In addition, we employ the APARCH (1,1) model of Ding, Granger, and Engle (1993) as:

(5.4)

Where δ >0 and

The parameter plays the role of a Box-Cox transformation of and is the leverage effect parameter.

The APARCH model includes seven models of the GARCH family as special cases:

The ARCH model when , , and .

The GARCH model when and .

Taylor (1986)/Schwert (1990)'s GARCH when and .

The GJR model when

The TARCH when

The NARCH when and

The Log-ARCH when .

While the GARCH(1,1) and IGARCH(1,1) model are symmetric, the APARCH(1,1) and GJR(1,1) are asymmetric GARCH models .

5.2.3 Long memory model (ARFIMA-FIGARCH model)

The long memory of financial markets can be defined as the presence of dependencies among observations. In order to examine the long memory property of SSM series, we adopt the fractionally integrated autoregressive moving average (ARFIMA) of Granger & Joyeux, 1980 and Hosking (1981) and Fractional Integrated GARCH model (FIGARCH) of Baillie, Bollerslev and Mikkelsen (1996). Long memory features often exist in both the conditional mean and variance at the same time (S. H. Kang & Yoon, 2007). The ARFIMA-FIGARCH model is given by

(5.5)

(5.6)

In mean equation (5.6), the L denote the lag operator,

Where and . is a process of the innovations for the conditional variance with zero mean and serially uncorrelated. The root of and lie outside the unit root circle.

The superiority of FIGARCH model, in comparison to GARCH and IGARCH, comes from flexibility. In fact, other than modelling volatility clustering and excess kurtosis, FIGARCH process is capable of describing high volatility persistence, long memory in conditional variance, as well as leverage effect, which are features that emerging stock markets are likely to exhibit.

5.2.4 Risk return trade-off

So far, lagged returns are assumed only as explanatory variables in the mean equation (4.1). However, many asset pricing models relate expected returns to some measure of risk (e.g. the Capital Asset Pricing and Arbitrage Pricing models). It is therefore important to account for risk in the return process to be consistent with standard asset pricing theories. We account for this by using the GARCH [3] in Mean model (GARCH(1,1)-M), with an added regressor in the mean equation, which is the conditional variance or conditional standard deviation:

(4.5)

Where λ is the risk parameter.

The literature shows that the fat-tail and excess kurtosis are accepted stylised facts in financial time series data. The Student-t, GED and skewed Student distributions have fatter tails than normal distribution; therefore, we use these as well as the normal distribution. For more detail see chapter 3.

GARCH models are estimated by the maximum likelihood (ML) method using the G@RCH 5 program of Oxmetrics 5.

5.3 Data

In this study, we use daily stock closing price index data for SSM obtained from TADAWUL Company [4] . The sample period ranges from 26/01/1994 to 02/11/2011 which includes 5019 observations. The index we used in this work is the Tadawul all Share index (TASI) which is calculated as a weighted market value of all shares prices listed on SSM. (See Chapter 4 for the more detail about the Saudi Stock Market.)

Daily Closing prices of TASI are converted into daily return series as

(4.7)

Where is the return at current time, is a current closing price and is the previous price at time.

In our works, we divided the data into three samples based on the events and developments of the market. The first sample is from 1994 to 2001 which can be called a tranquil period when the market was less developed. The second period is from 2002 to 2008. We chose 2002 for the start of the second sample because of the launch of the Tadawul Company that gave significant improvements to the SSM such as the availability of the data [5] and electronic trading. This was also followed by the establishment of the Capital Authorised Market CAM, which is a milestone in the history of SSM. Moreover, in this period, the number of firms increased substantially by 87%. Also, in this period, the SSM witnessed two major events; the 2006 Correction crisis and the 2008 Global financial crisis where the TASI (Tadawul All Shares Index_General Index) dropped by 53% in 2006 and by 56% in 2008. The third sample is from 2009 to 2011 which is used to assess the significant development and events of the market in the previous sub-period (See table 4.1, for more detail see chapter 3.).

.

Table ‎0.: Features of Saudi Stock Market

Figure ‎0.: Performance of the SSM

A summary of the key statistical descriptive and unit root tests are presented in Table ‎0. and Table ‎0. respectively. Table ‎0.presents descriptive statistics of daily returns for SSM in all three sub-samples samples and the full sample. In all samples, the average return is positive and the first sample has the lower average returns (0.0139) while the average returns in the second and the last sample are (0.034) and (0.036) respectively. The standard deviation for the second sub-sample (2002-2008) is very high (1.81) indicating the high volatility in this period compared with first sub-sample (1994-2001) that is low (0.6). Also, in the third sup-period, the standard deviation is high (1.3) impling that investing in the SSM exhibits a high risk.

Table ‎0.: Descriptive Statistics

Period

26/1/1994-31/12/2001

01/01/2002-31/12/2008

03/01/2009-02/11/2011

Full Sample

No. Of Obs.

2342

1966

711

5019

Mean

0.013977

0.034654

0.036264

0.025234

Std.Dev.

0.67809

1.8174

1.3085

1.3233

Skewness

-0.26606

-0.86015

-0.57341

-0.95202

Excess Kurtosis

5.8770

7.1928

6.5129

12.754

Minimum

-4.7809

-10.328

-7.022

-10.328

Maximum

4.163

9.3907

7.0115

9.3907

Normality test

3398.0 [0.0000]*

4480.5 [0.0000]*

1295.6 [0.0000]*

34776 [0.0000]*

[0.0000]

[0.0000]

[0.0000]

[0.0000]

ARCH-LM(10)

[0.0000]

[0.0000]

[0.0000]

[0.0000]

Note: numbers in the [ ] are the P-value.

Figure ‎0.: TASI Return over the period from 1994 to 2011

In Table 1, also, the distribution of TASI returns appears to have extreme observations. The Kurtosis is high (>3) in all sub-samples as well as the whole sample. This implies that the returns have fatter tails than normal. Moreover, the returns series are negatively skewed. The Normality test rejects the normality assumptions for all samples. The null hypothesis that there is no serial correlation is rejected by results of Q test for return Q (1) and Q(10) and for squared return Q^2(1) and Q^2(10).

Figure ‎0.shows the performance of TASI index from 1994 to 2011 and Figure ‎0.: shows the returns performance. From 1994-2001, the TASI appears tranquil during this period, and later, there was a huge increase in the index level from 2002 to the early of 2006. This increase is a result of many factors such as a large number of IPOs, policy regulations, and increased oil price. It can be seen that the highest point of TASI occurred in February 25, 2006. After that, there was a sharp drop in index in early 2006 and in 2008. These drops are a result of the correction crises in 2006 and the Global crisis in 2008. The return plot, in figure 2, shows that there is high volatility in the period from 2005-2009. Moreover, the returns series look like it exhibits volatility clustering where large changes tend to be followed by large changes and small change by small change. This is a stylised fact in many financial time series.

Table ‎0.: Unit Root Tests

Figure ‎0.: The distribution plot of TASI return

Figure ‎0.: Q-Q plot of TASI Return

Figure ‎0.: Autocorrelation function of TASI return

Figure ‎0.: Autocorrelation function of squared TASI return

Figure ‎0.: Autocorrelation function of Absolute TASI return

Additionally, three unit root tests (ADF (augmented-Dickey-Fuller), PP (Phillips-Peron) and KPSS (Kwiatkowski, Phillips, Schmidt, and Shin) tests) have been applied in this study for the price and its first difference (return). These unit root tests have a different null hypothesis. The null hypothesis of the ADF and PP test is that the series contain a unit root, I(1), while the null hypothesis for KPSS test is that the series is a stationarity, I(0). Table 5.3 show the results of these unit root tests. ADF and PP test results indicate the rejection of the null hypothesis of a unit root test for all sub-samples at the 1% level of significant. Also, the KPSS result indicate that all sub-samples and the whole sample of SSM returns series are insignificant to reject the null hypothesis of stationarity which implies that the returns series are stationarity. Thus, all series are I(1), and therefore, time â€"series models can be used to test the volatility of stock returns.

5.4. Empirical results

At the first stage of modelling SSM and before we can estimate the GARCH models, we fit the models with maximum and in order to capture any serial correlation on the returns. Three selection criteria for determining the best model are used; the SC information criteria of Schwartz, AIC information criteria of Akaike, and HG Hannun which are all minimised in addition to the diagnostic test and the significance of estimated parameters. Table A in Appendix 5.1 reports the information criteria of [6] models for whole period and the three sub-samples.

We find that TASI follows an ARMA(1,2) process for the whole period (1994-2011), while an ARMA(3,1), ARMA(1,1), and ARMA(1,0) is sufficient to model the sub-samples (1994-2001), (2002-2008), and (2009-2011) respectively.

In the follow section, we fit various models of the GARCH family to model the behaviour of stock returns and to capture the empirical stylized facts of volatility clustering, long memory and leverage effects in SSM.

5.4.1 Results of fitting GARCH models

Four GARCH models (two symmetric models (GARCH(1,1) and IGARCH(1,1))and (two asymmetric models (GJR(1,1) and APARCH(1,1)) are applied in this study with four distribution assumptions (Normal, student t, skewed student and GED [7] ). Estimating of the parameters is obtained by maximising the log-likelihood function over the periods under the study.

Symmetric Models

Table 5.4 presents the result of estimation for the parameter for GARCH and IGARCH models with three assumption distributions (Normal, Student-t and Skewed student-t) for the whole sample and the three sub-samples. The results show that, in the mean equation, the lags of returns are statistically significant for all the samples except the sub-sample 3 (2009-2011) which are insignificant. MA coefficients also are significant in models for the whole sample and the first two sub-samples (1994-2001) and (2002-2008). The ARMA terms can capture the effect of non-synchronous trading.

In the conditional variance equation, the coefficients of α and β are positive and statistically significant for all cases which implies the presence of strong GARCH and ARCH effect. Moreover, the sum of α and β is very close to one [8] , indicating that the volatility is highly persistent. This result is consisting with the literature that the returns series variance changes with time and the presence of volatility clustering in the stock market returns.

In Table 5.4, we used three distributions (Normal, Student-t and Skewed Student-t). The first two distributions are symmetric and the last one is asymmetric. From Table 5.4, we find that all the distributions are adequate to model all the models and the obtained results of the estimation models are quite similar. The student distribution parameter (degree of freedom) (υ) is statistically significant at a 1% level of significance and ranges between 4.29 and 4.66 for all models for the whole sample and the first two sub-samples as well. It ranges between 3.13 and 3.48 for the third sub-sample. In the case of an asymmetric distribution (skewed student-t) with symmetric models (GARCH and IGARCH), we find the asymmetric parameter (ξ) and

Table ‎5.: Symmetric GARCH models estimation

GARCH

IGARCH

0.091( 0.054 )***

0.113(0.082)

0.066(0.053)

0.093(0.054)***

0.114(0.083)

0.062(0.051)

0.996(0.003)*

0.997( 0.004)*

0.997(0.004)*

0.996( 0.003)*

0.997( 0.004)*

0.997(0.004)*

-0.850( 0.018)*

-0.868(0.017)*

-0.872(0.017)*

-0.852( 0.018)*

-0.868( 0.017)*

-0.872(0.016)*

-0.136(0.018)*

-0.119(0.016)*

-0.115(0.016)*

-0.134(0.017)*

-0.120(0.016)*

-0.115(0.016)*

0.024863

0.020525

0.020891

0.024( 0.005)*

0.021(0.004)*

0.021(0.004)*

0.173(0.017 )*

0.194(0.019)*

0.197(0.019)*

0.195(0.026)*

0.212(0.021)*

0.216(0.021)*

0.812(0.019 )*

0.793(0.021)*

0.790(0.021)*

0.804*

0.787*

0.783*

4.583(0.228)*

4.632 (0.233)*

4.374(0.223)*

4.419(0.228)*

-0.056 0.017)*

-0.058( 0.017)*

0.985

0.988

0.987

1.000

1.000

1.000

0.011(0.028)

0.043(0.031)

0.026(0.034)

0.007(0.028)

0.044(0.032)

0.026(0.034)

1.210( 0.026)*

1.216(0.025)*

1.215(0.025)*

1.203( 0.024)*

1.216(0.025)*

1.215(0.024)*

-0.275( 0.036)*

-0.292(0.032)*

-0.291(0.032)*

-0.272( 0.033)*

-0.292( 0.0319)*

-0.292(0.032)*

0.058( 0.024)**

0.070( 0.022)*

0.070(0.022)*

0.061( 0.022)*

0.070( 0.021)*

0.071(0.021)*

-0.983( 0.013)*

-0.982(0.016)*

-0.982(0.015)*

-0.982(0.012)*

-0.982(0.015)*

-0.982(0.015)*

0.050( 0.010)*

0.036( 0.006)*

0.036(0.006)*

0.043(0.010)*

0.034(0.006)*

0.035( 0.006)*

0.277(0.048)*

0.335(0.046)*

0.337(0.046)*

0.397(0.053)*

0.368(0.037)*

0.371(0.037)*

0.620(0.047)*

0.632(0.036)*

0.629(0.037)*

0.602*

0.631*

0.628*

4.662(0.473)*

4.687(0.475)*

4.403(0.368)*

4.421( 0.369)*

-0.029( 0.028)

-0.029( 0.029)

0.898

0.968

0.967

1.000

1.000

1.000

0.138(0.031)*

0.145(0.029)*

0.111(0.032)*

0.138(0.031)*

0.144(0.029)*

0.108(0.032)*

0.440(2.934)

0.928(0.031)*

0.934(0.029)*

0.421( 2.905)

0.928(0.031)*

0.933(0.028)*

-0.356( 3.080)

-0.885(0.035)*

-0.892(0.031)*

-0.336(3.042)

-0.885(0.034)*

-0.892(0.031)*

0.043924

0.038879

0.039253

0.042(0.016)*

0.041(0.012)*

0.042( 0.012)*

0.174(0.027)*

0.195(0.025)*

0.199(0.025)*

0.194(0.031)*

0.213(0.029)*

0.217(0.029)*

0.811(0.030)*

0.793(0.027)*

0.788(0.028)*

0.805*

0.786*

0.782*

4.520(0.335)*

4.584(0.350)*

4.293(0.326)*

4.354 ( 0.341)*

-0.070(0.025)*

-0.071( 0.025)*

0.986

0.988

0.988

1.000

1.000

1.000

0.054(0.040)

0.078(0.028)*

0.042(0.032)

0.068(0.035)***

0.079(0.027)*

0.042(0.032)

0.059(0.042)

0.008(0.032)

0.001(0.031)

0.054(0.040)

0.008(0.031)

0.001(0.031)

0.072(0.049)

0.035989

0.040(0.025)

0.059(0.040)

0.041(0.025)

0.040( 0.025)

0.119(0.037)*

0.105(0.028)*

0.130(0.051)**

0.167(0.042)*

0.133(0.041)*

0.134(0.041)*

0.841(0.041)*

0.872(0.037)*

0.865(0.041)*

0.832*

0.866*

0.865*

3.486(0.309)*

3.222( 0.454)*

3.132(0.306)*

3.179(0.321)*

-0.095(0.042)**

-0.094(0.043)**

0.961

0.978

0.996

1.000

1.000

1.000

Note: Numbers in ( ) are the standard error and [ ] are the p-value. is the degree freedom for the student-t and skewed student-t distributions and ξ is the symmetric parameter for the skewed student-t distribution. *, ** indicate the 1% and 5% level of significance.

degree of freedom (Ï…) are statistical significant for models for all samples except the first sub-sample (1994-2001) where the asymmetric parameter is insignificant. This result indicates that the SSM returns series are asymmetric for the period 2002-2011 and symmetric for the period from 1994-2001. This suggest that asymmetric models may be the better models for the period 2002-2011

Asymmetric Models

Table 4.5 presents the estimation results of asymmetric models (GJR(1,1) and APARCH(1,1)) for all studied samples. In the mean equation, the results are similar to the results obtained from symmetric models. That is, the lags of return and the error are significant for most of the models over the period 1994-2008, and insignificant over the period 2009-2011.

The use of asymmetric models (GJR and APARCH) seems to be acceptable for the period from 2002-2011 in that all the asymmetric parameter ( ) are positive and statistically significant at 1% level of significance although it is insignificant for the first sub-sample (1994-2001). These results indicate the existence of the leverage effect in return during the period 2002-2011. Also, in APARCH models, the () parameter is positive and statistically significant at the 5% level of significance. The ARCH and GARCH effect (α1 and β) are statistically significant and positive for all models.

As with the symmetric models, we also applied three alternative distributions with asymmetric GARCH models. The degree of freedom (υ) for student-t and skewed student-t are quite similar and range from 3.93 and 4.7 for all the period from 1994-2008 and range from 3.23 and 3.36 for the last sub-sample (2009-2011). The smaller the degree of freedom the fatter the tail of the return series is. The symmetric parameter (ξ) is negative and statistically significant at the 5% level of significance for the whole sample as well as for the second and the third sub-samples (2002-2008) and (2009-2011) respectively and insignificant for the first sub-sample (1994-2001). These results are similar to the results obtain from the symmetric models with asymmetric distribution.

Table ‎0.: Asymmetric GARCH models estimation

GJR

APARCH

0.030 (0.034)

0.086(0.0571)

0.029(0.040)

0.023 (0.053)

0.080(0.055 )

0.020(0.040)

0.991( 0.016)*

0.996(0.005)*

0.996(0.005)*

0.995(0.006 )*

0.996(0.005 )*

0.996(0.005)*

-0.841( 0.027)*

-0.863(0.017)*

-0.865(0.017)*

-0.854(0.020 )*

-0.867(0.018 )*

-0.870(0.017)*

-0.130( 0.023)*

-0.123(0.015)*

-0.119(0.015)*

-0.124(0.018)*

-0.119(0.015 )*

-0.115(0.015)*

0.025(0.005)*

0.020(0.004)*

0.021(0.004)*

0.031 (0.007)*

0.024( 0.005)

0.025 ( 0.005 )

0.155(0.030)*

0.213(0.029)*

0.218(0.030)*

0.211( 0.021)*

0.251( 0.026)*

0.256 ( 0.027 )*

0.795(0.022)*

0.776(0.023)*

0.772(0.023)*

0.811( 0.018)*

0.795 (0.020)*

0.792 ( 0.020 )*

0.111(0.045)**

0.086( 0.030)*

0.087(0.031)*

0.164( 0.061)*

0.101(0.032)*

0.100 ( 0.032 )*

1.358( 0.235)*

1.462(0.157)*

1.443 ( 0.15 )*

4.007( 0.254)*

4.028(0.257)*

4.023(0.255)*

4.044 (0.257)*

-0.059(0.017)*

-0.062 (0.017)*

0.000( 0.029)

0.036(0.032)

0.020( 0.035)

-0.000(0.030)

0.034( 0.033)

0.018( 0.038)

1.211( 0.026)*

1.217(0.026)*

1.217(0.025)*

1.210(0.027)*

1.213(0.024)*

1.213(0.024)*

-0.277(0.036)*

-0.292(0.032)*

-0.292( 0.032)*

-0.275(0.037)*

-0.286( 0.032)*

-0.286( 0.032)*

0.058(0.024)**

0.069(0.022)*

0.069(0.022)*

0.058(0.024)**

0.068(0.021)*

0.069( 0.021)*

-0.983(0.013)*

-0.982(0.017)*

-0.982(0.016)*

-0.983(0.014)*

-0.984( 0.013)*

-0.984( 0.013)*

0.050(0.011)*

0.036(0.006)*

0.037(0.006)*

0.054(0.013)*

0.049(0.010)*

0.050( 0.010)*

0.254(0.052)*

0.313( 0.046)*

0.316(0.047)*

0.276(0.045)*

0.321(0.038)*

0.324( 0.038)*

0.619( 0.047)*

0.629(0.037)*

0.626(0.038)*

0.627( 0.052)*

0.659( 0.036)*

0.656 ( 0.036)*

0.046( 0.058)

0.047( 0.054)

0.046( 0.053)

0.041( 0.053)

0.034( 0.043)

0.033(0.043)

1.861( 0.373)* [9] 

1.484(0.243)*

1.489(0.243)*

4.681( 0.478)*

4.702( 0.479)*

4.671(0.477)*

4.691(0.478)*

-0.029( 0.028)

-0.028( 0.029)

0.118(0.045)*

0.131(0.031)*

0.102( 0.034)*

NA

0.106( 0.032)*

0.044(0.043)

0.948(0.044)*

0.933(0.028)*

0.937(0.026)*

NA

0.929(0.028)*

0.934(0.026)*

-0.899(0.053)*

-0.883(0.032)*

-0.887( 0.030)*

NA

-0.876(0.033)*

-0.878(0.031)*

0.047923

0.042850

0.043915

NA

0.037192

0.041( 0.012)*

0.107(0.028)*

0.126(0.024)*

0.129(0.025)*

NA

0.257( 0.035)*

0.243( 0.034)*

0.809(0.026)*

0.791(0.028)*

0.788(0.028)*

NA

0.804( 0.027)*

0.808(0.026)*

0.136(0.048)*

0.138( 0.038)*

0.129(0.037)*

NA

0.223( 0.060)*

0.272( 0.075)*

NA

1.303(0.141)*

1.041(0.219)*

4.551( 0.351)*

4.661 (0.369)*

3.803(0.372)*

3.932(0.399)*

-0.059(0.025)**

-0.093(0.026)*

0.030 ( 0.040)

0.067 (0.028)**

0.030(0.033)

NA

0.067(0.028)**

0.030(0.033)

0.075(0.044)***

0.016(0.031)

0.010(0.031)

NA

0.019(0.034)

0.013(0.032)

0.069(0.051)

0.041(0.025)***

0.041(0.024)***

NA

0.034(0.019)***

0.034(0.019)***

0.043( 0.025)***

0.066(0.031)**

0.066(0.030)**

NA

0.131(0.043)*

0.131(0.042)*

0.839(0.047)*

0.860(0.042)*

0.860(0.041)*

NA

0.877(0.034)*

0.877(0.034)*

0.155(0.073)**

0.129( 0.072)***

0.127(0.070)***

NA

0.400(0.192)**

0.387(0.176)**

NA

1.363(0.586)**

1.389(0.531)*

3.237( 0.466)*

3.319( 0.476)*

3.281(0.461)*

3.360(0.469)*

-0.098(0.042)**

-0.098(0.043)**

Note: Numbers in ( ) are the standard error and [ ] are the p-value. is the degree freedom for the student-t and skewed student-t distributions and ξ is the symmetric parameter for the skewed student-t distribution. *, ** indicate the 1% and 5% level of significance.

In Table 5.6, the comparison among the four GARCH models is based on the minimum of Akaike, Schwarz, and Hannan-Quinn and the estimation statistics. We find that the APARCH-Skewed student-t models are the best models for the SSM for the whole sample and the second sub-sample (2002-2008) and IGARCH-Student-t models for the first (1994-2001) and IGARCH-skewed student-t for the third sub-sample (2009-2011).

For the comparison between distributions, the results in Table ‎0. show that the skewed student-t distribution is the most appropriate distribution to the whole sample, sub-sample 2, and sub-sample 3 while the student-t distribution is appropriate for the first sample. This indicates that the SSM return is asymmetric in the whole sample and the last two sub-samples (2 and 3), while it is symmetric for the first sub-sample. Overall, the Skewed student-t distribution seems to be the more appropriated density to be used in modelling the stock market returns as it is the best densities assumption applied in this study (11 out 16 models). This is consistent with Lambert and Laurent (2001) find that the skewed student-t distribution is the more appropriate distributions in modelling NASDAQ than the symmetric ones

Therefore, we applied APARCH-skewed student-t for (1994-2011) and (2002-2008), IGARCH-student-t for (1994-2001) and IGARCH-Skewed student-t for the recent sub-sample (2009-2011). Also, for others models such as FIGARCH, the asymmetric distribution (Skewed Student-t) for the period (2002-2011) and a symmetric distribution (Student-t) for (1994-2001) is used in the further study in this work. Figure 4.8 shows the conditional variance graph and we can see there is highly significant bike in the conditional variance in 2006 (Correction crash) and in 2008 (the global financial crisis)

The diagnostic tests of all models are similar and reported in Table 5.6. The results of a Q test of the squared standardized residuals shows there is no a serial correlation in the stock return series in all samples. The ARCH-LM test also shows that there is no evidence of conditional heteroscedasticity. Therefore, all models are doing very well in modelling SSM.

Table ‎0.: Diagnostic tests and the comparison of the models and distributions

GARCH

IGARCH

GJR

APARCH

N

t

ST

N

t

ST

N

t

ST

N

t

ST

Full Sample

AIC

2.607304

2.447687

2.446113

2.605133

2.446034

2.444429

2.599416

2.443420

2.441779

2.594961

2.442040

2.440201

SC

2.615099

2.456782

2.456507

2.612928

2.455129

2.454823

2.609810

2.455113

2.454772

2.606655

2.455033

2.454493

HQ

2.610036

2.450874

2.449755

2.607864

2.449221

2.448071

2.603058

2.447518

2.446332

2.599059

2.446593

2.445209

LQ

-6537.029

-6135.471

-6130.520

-6531.580

-6131.323

-6126.294

-6515.234

-6122.763

-6117.644

-6503.056

-6118.300

-6112.684

Q2(50)

[0.9717]

[0.8997]

[ 0.8911]

[ 0.9523]

[ 0.8640]

[ 0.8524]

[ 0.9295]

[ 0.6879]

[ 0.6635]

[0.9710]

[0.8147]

[0.8014]

ARCH(10)

[0.9937]

[0.9609]

[0.9558]

[0.9867]

[0.9396]

[0.9318]

[0.9759]

[0.8009]

[0.7779]

[0.9934]

[0.9076]

[0.8975]

Sub-sample1

1994-2001

AIC

1.739688

1.631694

1.632097

1.750137

1.631294

1.631715

1.739871

1.632220

1.632644

1.740586

1.631623

1.632076

SC

1.759359

1.653825

1.656686

1.767350

1.650965

1.653845

1.762001

1.656809

1.659692

1.765175

1.658671

1.661583

HQ

1.746853

1.639755

1.641053

1.756407

1.638459

1.639776

1.747932

1.641176

1.642496

1.749543

1.641475

1.642824

LQ

-2029.175

-1901.714

-1901.185

-2042.411

-1902.245

-1901.739

-2028.389

-1901.329

-1900.826

-2028.226

-1899.631

-1899.161

Q2(50)

[0.9573]

[0.8735]

[0.8765]

[0.8712]

[0.8420]

[0.8457]

[0.9634]

[0.8886]

[0.8904]

[ 0.9659]

[ 0.9292]

[ 0.9312]

ARCH(10)

[0.9644]

[0.6577]

[0.6533]

[0.5980]

[0.5420]

[0.5342]

[0.9605]

[0.6718]

[0.6667]

[ 0.9655]

[ 0.8218]

[ 0.8175]

Sub-sample2

2002-2008

AIC

3.365868

3.226750

3.224267

3.361986

3.224119

3.221645

3.350748

3.219466

3.218034

NA

3.210726

3.206805

SC

3.380069

3.243791

3.244149

3.376187

3.241160

3.241526

3.367789

3.239347

3.240755

NA

3.233448

3.235207

HQ

3.371087

3.233012

3.231574

3.367205

3.230382

3.228951

3.357010

3.226772

3.226384

NA

3.219076

3.217243

LQ

-3303.648

-3165.895

-3162.455

-3299.833

-3163.309

-3159.877

-3287.785

-3157.735

-3155.327

NA

-3148.144

-3142.289

Q2(50)

[0.3936]

[0.3681]

[0.3684]

[0.4177]

[0.3636]

[0.3636]

[0.9850]

[0.9761]

[0.9755]

NA

[ 0.3417]

[ 0.2944]

ARCH(10)

[0.9538]

[0.9459]

[0.9468]

[0.9636]

[0.9414]

[0.9406]

[0.9645]

[0.9642]

[0.9618]

NA

[ 0.9673]

[ 0.9804]

Sub-sample3

2009-2011

AIC

3.134445

2.863620

2.861989

3.140317

2.862209

2.859201

3.111691

2.859029

2.855566

NA

2.859145

2.855674

SC

3.166560

2.895735

2.906949

3.166009

2.894323

2.897738

3.15022

2.903990

2.906949

NA

2.910528

2.913480

HQ

3.146851

2.876025

2.879356

3.150241

2.874614

2.874087

3.126577

2.876397

2.875414

NA

2.878994

2.878004

LQ

-1109.295

-1013.017

-1010.437

-1112.383

-1012.515

-1010.446

-1100.206

-1009.385

-1007.154

NA

-1008.426

-1006.192

Q2(50)

[0.7569]

[0.9861]

[0.9850]

[0.9249]

[0.9885]

[0.9862]

[0.9627]

[0.9987]

[0.9985]

NA

[0.9937]

[0.9936]

ARCH(10)

[0.9932]

[0.9991]

[0.9989]

[0.9982]

[0.9992]

[0.9990]

[0.9940]

[0.9979]

[0.9975]

NA

[0.9984]

[0.9982]

Note: AIC, SC and HQ are the Akaike, Schwarz and Hannan-Guinn information criteria respectively. LQ is the log-Likelihood value and Q^2 is the Box-Pierce statistic for squared return series for up to 10th-order serial correlation. ARCH (10) is Engle's (1982) ARCH-LM test to check the presence of ARCH effects in residuals up to lag 10. Numbers in brackets are p-values. Bold is the minimum value of information criteria among the distributions of one models (such GARCH) and the bold and underline is the minimum value among all models for one sub-samples (such 1994-2001).

Figure 5.: Conditional variance graphs

5.4.2 Long memory in SSM

In this section, we apply the ARFIMA-FIGARCH model to examine the long memory properties of SSM series. Long memory in financial time series can be defined as a presence of dependencies among distant observations. The literature shows that financial asset returns exhibit a long memory property where the autocorrelation of the absolute and squared returns of time series slowly decay (Kang et al., 2010).

In the literature, The ARFIMA model is used to investigate the long memory in returns. ARFIMA allows the integration process of the conventional ARMA models to take non-integer value between 0 and one. The results of empirical studies applying ARFIMA have revealed mixed results. Some studies of developed markets show that there is no long memory (see for examples (Cheung & Lai, 1995; Lo, 1991; Tolvi, 2003). However, a number of studies on emerging markets have found the existence of long memory (see for example, (Cavalcante & Assaf, 2004; Henry, 2002; Kiliĉ, 2004) [10] .

To investigate the long memory in volatility, FIGARCH models are proposed by Baillie et al. (1996) these are an extension of the IGARCH model (that are themselves a special case of the GARCH model). The IGARCH model captures the long memory effect but it has two drawbacks which are: 1; the shock of this model impacts upon future volatility over infinite horizon, and; 2; the unconditional variance does not exist in this model. Thus, the FIGARCH model performs better in capturing the long memory effect (Poon & Granger, 2003). FIGARCH model captures the long memory in volatility by adding flexibility.

It is well-known that the shocks to financial time series can influence return and volatility at the same time (S. Kang & Yoon, 2012). Thus, the dual long memory properties in return and volatility could be a feature of the financial time series. In this context, empirical studies have examined the long memory feature of returns and volatility using a joint ARFIMA-FIGARCH model (Arouri, Hammoudeh, Lahiani, & Nguyen, 2012; Conrad & Karanasos, 2005; S. Kang & Nguyen, 2007; S. Kang & Yoon, 2012)among other)

Most of the empirical works that examine long memory have been applied in developed markets. However, there is an in studies in developing markets (Floros, Jaffry, & Lima, (2007); Kiliĉ (2004) among others). In this section, we aim to examine the long memory feature of the GCC market using SSM market as a case study. This study, to the best of our knowledge, is the first full investigation of the long memory property, in return and volatility, in SSM returns series over the period from 2002-2011. However, the first study to test the long memory properties in eight Arab markets (including Saudi Arabia) is Limam (2003) This study used weekly data over the period from 1994 to 2002 and finds there is a long memory property in return in the SSM and other developing markets.

Sourial (2002) also finds existence of long memory properties for returns in the Egyptian stock market.

We test the long memory in mean and conditional variance separately and simultaneously, In Table ‎5.: Long Memory models estimation, the results of estimating five models of long memory for all samples are reported and the models are ARFIMA-GARCH(1,0,1), ARFIMA-IGARCH(1,1,1), ARMA-FIGARCH(1,d,1), ARFIMA-FIGARCH(1,d,1) and ARFIMA-FIGARCH(1,d,0). We compare the results of ARFIMA-GARCH and ARFIMA-IGARCH with ARFIMA-FIGARCH models in term of their performance of capture the long memory feature of returns and volatility simultaneously. ARMA-FIGARCH (1,d,1) is used to test the long memory of the volatility only and we can consider the ARFIMA-GARCH models as a model tests the long memory feature of returns. The results of dual long memory properties confirm the existence of the long memory in the return and volatility in all models for the whole sample (1994-2011) and the first two sub-samples (1994-2001) and (2002-2008). These results retrieve from the highly statistically significant of the d-ARFIMA and d-FIGARCH coefficients at 1% level of significant.

However, the results for the recent sub-sample (2009-2011) show that there is a long memory property only in the volatility that the d-FIGARCH coefficients are statistically significant at 5% level of significant (less significant than ones in others sub-samples) while the d-ARFIMA coefficient is insignificant indicate that there is no long memory in the return in SSM over the period 2009-2011.

The results of estimation ARMA-FIGARCH models confirm the presence of the long memory of the volatility in SSM for all models. The d-ARFIMA parameter is statistically significant at 1% in whole samples and the first two sub-samples and statistically significant at 5% for the third sub-sample. Moreover, the ARFIMA-GARCH estimation results confirm the existence of the long memory in the return in all samples except the third subsample. These results are consistent with the results obtained from testing the dual long memory in the return and volatility simultaneously.

We applied the ARFIMA-FIGARCH(1,d,0) models to test the dual long memory because it is shown that the ARCH term in the conditional variance equation is insignificant in most of the ARFIMA-FIGARCH(1,d,1)models. The results of estimation of the ARFIMA-FIGARCH(1,d,0) model are quite similar to those obtained from other models.

These results show that the FIGARCH models where d is statistically significant and positive for all models are performed and doing better that the GARCH modes which assume and the IGARCH models which assume . This results are similar to finding of previous works ((Aloui & Mabrouk, 2010; S. Kang & Yoon, 2012); Kang et al.,2009 and Kang and Yoon, 2012).

The diagnostic test of the long memory models are reported in Table 5.7. the Akaike information criterion (AIC) Schwarz criterion (SC) and the Hannanâ€"Quinn criterion(HQ) are reported in order to be used to choose the best specification model among the long memory given models in Table 5.7. The diagnostic tests show that the all models perform well.

Additionally, the lowest values of three selection information criteria (AIC, SC and HQ) indicate the ARFIMA-FIGARCH(1,d,0) is the appropriate long memory model for the whole period (1994-2011) and the third sub sample (2009-2011) whereas the ARFIMA-FIGARCH(1,d,1) and ARMA-FIGARCH(1,d,1) are the appropriate models for the second sub-sample (2002-2008) and the first sub sample (1994-2001) respectively. Thus, the ARFIMAâ€"FIGARCH models best capture the long-memory dynamics and this model modelled the long memory feature of both returns and volatility simultaneously. However, we find the ARMA-FIGARCH model is the best model to capture the long memory for the data for 1994-2001. We conclude, in general, the dual long memory model is the more appropriate model for capturing long memory and separately modelling the long memory for return and volatility.

Table ‎5.: Long Memory models estimation

0.025 0.031)

0.021 (0.033)

0.054 (0.046)

0.020 (0.031)

0.020 (0.031)

0.465 (0.147)*

0.468 (0.142)*

0.996 (0.005)*

0.476(0.139)*

0.476 (0.139)*

-0.536 ( 0.181)*

-0.541 (0.177)*

-0.864 (0.017)*

-0.544 (0.174)*

-0.544 (0.174)*

-0.064 (0.025)**

-0.064 (0.025)**

-0.122 (0.016)*

-0.068 (0.024)*

-0.069 (0.024)*

d-ARFIMA

0.195(0.051)*

0.198(0.051)*

0.200(0.051)*

0.200(0.051)*

0.021

0.022(0.004)*

0.033(0.008)*

0.035 (0.009)*

0.035 (0.008)*

0.197 (0.019)*

0.216 (0.022)*

0.016 (0.085)

0.007 (0.088)

-

0.790 (0.021)*

0.783*

0.324 (0.100)*

0.312(0.102)*

0.304(0.044)*

4.589(0.229)*

4.373(0.22)*

4.568(0.245)*

4.522(0.241)*

4.523(0.240)*

-0.063(0.017)*

-0.065(0.017)*

-0.061(0.017)*

-0.067(0.017)*

-0.067(0.017)*

0.554(0.039)*

0.551(0.038)*

0.549(0.036)*

0.026 (0.025)

0.027 (0.025)

0.047 (0.033)

0.030 (0.025)

0.029 (0.025)

0.164 (0.297)

0.176 (0.302)

1.219 (0.027)*

0.154 (0.280)

0.146 (0.286)

-0.117 (0.037)*

-0.118 (0.037)*

-0.296 (0.032)*

-0.117 (0.036)*

-0.115 (0.036)*

-0.038 (0.038)

-0.037 (0.039)

0.071 (0.022)*

-0.040 (0.037)

-0.040 (0.037)

-0.087 (0.306)

-0.100 (0.310)

-0.981 (0.020)*

-0.076 (0.287)

-0.067 (0.293)

d-ARFIMA

0.156(0.038)*

0.157 (0.037)*

0.158(0.037)*

0.156(0.037)*

0.036 (0.006)*

0.034 (0.006)*

0.048 (0.011)*

0.049 (0.012)*

0.042 (0.009)*

0.325 (0.045)*

0.362 (0.038)*

-0.112 (0.097)

-0.112 (0.098)

-

0.638 (0.037)*

0.637*

0.254 (0.116)**

0.241(0.116)**

0.341(0.079)*

4.630(0.468)*

4.343(0.365)*

4.648(0.420)*

4.604(0.419)*

4.586(0.415)*

0.676(0.090)*

0.659(0.089)*

0.667(0.087)*

0.063 (0.064)

0.055 (0.065)

0.102 (0.032)*

0.046 (0.067)

0.049 (0.069)

0.481 (0.078)*

0.481 (0.077)*

0.933 (0.028)*

0.487 (0.076)*

0.497 (0.075)*

-0.668 (0.089)*

-0.670 (0.086)*

-0.891 (0.030)*

-0.678 (0.086)*

-0.690 (0.079)*

d-ARFIMA

0.235(0.084)*

0.237(0.083)*

0.241(0.084)*

0.247(0.087)*

0.0385

0.041(0.012)*

0.016(0.004)*

0.015 (0.004)*

0.073 (0.021)*

0.201 (0.026)*

0.219 (0.030)*

-0.066 (0.081)

-0.077 (0.081)

-

0.787 (0.028)*

0.780*

0.928 (0.020)*

0.930(0.020)*

0.480(0.273)*

4.636(0.361)*

4.404(0.351)*

4.330(0.337)*

4.376(0.346)*

4.437(0.352)*

-0.089(0.026)*

-0.091(0.026)*

-0.079(0.026)*

-0.098(0.026)*

-0.095(0.027)*

1.287(0.095)*

1.299(0.095)*

0.725(0.230)*

0.042 (0.028)

0.042 (0.028)*

0.040 (0.032)

0.040 (0.028)

0.041 (0.028)

0.026 (0.059)

0.027 (0.059)*

-0.000 (0.031)

0.023 (0.059)

0.023 (0.059)

d-ARFIMA

-0.025(0.052)

-0.026(0.051)

-0.024(0.051)

-0.024(0.051)

0.039 (0.024)

0.040(0.025)

0.103 (0.081)

0.102 (0.080)

0.087 (0.054)

0.131 (0.051)**

0.134 (0.040)*

-0.049 (0.153)

-0.049 (0.151)

-

0.865 (0.041)*

0.865*

0.474 (0.345)

0.480(0.353)

0.524(0.237)**

3.217(0.459)*

3.183(0.323)*

3.255(0.362)*

3.255(0.362)*

3.268(0.350)*

-0.096(0.042)**

-0.095(0.042)**

-0.095(0.044)**

-0.096(0.043)**

-0.096(0.043)**

0.583(0.282)**

0.589(0.293)**

0.590(0.245)**

Note: Numbers in ( ) are the standard error and [ ] are the p-value. is the degree of freedom parameter of student-t and skewed student-t distributions and is the symmetric parameter of skewed student-t distribution. *, ** indicate the 1% and 5% level of significance.

The presence of long memory in the volatility of SSM return implies dependencies between distant observations. These results can be used to predict future volatility.

The existence of the long memory feature in the volatility of SSM can be explained by the mixture of distribution hypothesis (MDH) that is due to a large amount of heterogeneous information arrival process (Andersen and Bollerslev, 1997).

Table ‎5.: Diagnostic tests of long memory models estimation

AIC

2.446293

2.444572

2.433794

2.433767

2.433370

SC

2.457987

2.456266

2.446787

2.448059

2.446362

HQ

2.450391

2.448670

2.438347

2.438775

2.437923

LQ

-6129.973

-6125.655

-6097.606

-6096.538

-6096.541

Q2(10)

[0.8946]

[0.8570]

[0.9399]

[0.9400]

[0.9678]

ARCH(10)

[0.9580]

[0.9351]

[0.9808]

[0.9811]

[0.9810]

AIC

1.633529

1.633242

1.628922

1.630588

1.630144

SC

1.658118

1.655372

1.653511

1.657636

1.654733

HQ

1.642486

1.641303

1.637878

1.640440

1.639101

LQ

-1902.862

-1903.527

-1897.467

-1898.418

-1898.899

Q2(10)

[0.5666]

[0.4579]

[0.7283]

[0.7355]

[0.8132]

ARCH(10)

[0.6825]

[0.5538]

[0.8393]

[0.8509]

[0.8455]

AIC

3.220990

3.218187

3.218612

3.215114

3.220571

SC

3.243711

3.240908

3.244174

3.243515

3.246133

HQ

3.229340

3.226537

3.228006

3.225551

3.229965

LQ

-3158.233

-3155.478

-3154.896

-3150.457

-3156.822

Q2(10)

[0.8846]

[0.8765]

[0.8682]

[0.8976]

[0.8117]

ARCH(10)

[0.9631]

[0.9581]

[0.9505]

[0.9643]

[0.8768]

AIC

2.864237

2.861472

2.862550

2.861077

2.858748

SC

2.922043

2.912855

2.920356

2.925306

2.916554

HQ

2.886567

2.881320

2.884879

2.885888

2.881078

LQ

-1009.236

-1009.253

-1008.636

-1007.113

-1007.285

Q2(10)

[0.9912]

[0.9916]

[0.9977]

[0.9974]

[0.9992]

ARCH(10)

[0.9988]

[0.9988]

[0.9998]

[0.9997]

[0.9998]

Note: AIC, SC and HQ are the Akaike, Schwarz and Hannan-Guinn information criteria respectively. LQ is the log-Likelihood value and Q^2 is the Box-Pierce statistic for squared return series for up to 10th-order serial correlation. ARCH (10) is Engle's (1982) ARCH-LM test to check the presence of ARCH effects in residuals up to lag 10. Numbers in brackets are p-values. Bold is the minimum value of information criteria among all models for one sub-samples (such 1994-2001).

5.4.3 Risk-Return relationship

This section deals with the relationship between risk and return in the SSM. GARCH-M models are employed in this section because they provide a convenient measure of the risk premium, and they connect conditional volatility and return in the mean equation (equation 4.2). The volatility variable in mean, in equation 4.2 is used as a proxy for the risk premium.

We used daily data to capture the relationship between the SSM returns and its own conditional volatility. Based on the GARCH models and distributions selection in the previous chapter, we applied APARCH-M with skewed distribution for the whole sample (1994-2011) and the second sub-samples (2002-2008), and the IGARCH-M with student-t and IGARCH-M with skewed student-t distributions for the first (1994-2001) and the third sub-samples (2009-2011). Our study differs from previous works in two ways. First we applied the long span data cover all the development in SSM and also divided it into three sub-samples based on the stages of development of SSM. Second, we apply GARCHâ€"M models with different distributions which have been chosen as the best models for the SSM returns series.

Abdulla (2012) investigates the risk-return trade-off in emerging markets using a daily data of Saudi and Egyptian stock markets over the period from January1, 2007 to December 30, 2011. He employs two GARCH models (GARCH-M and EGARCH-M) and finds that the risk-return relationship is insignificant in both markets. However, the insignificance of the risk coefficients in the models applied imply that there is no meaning for the sign and the magnitude of the coefficients..

Error: Reference source not found presents the results of estimation GARCH-M for all samples and the results indicate that the coefficients of the risk premium are insignificant in all models. These results suggest that investors in SSM may consider other risk measure than the conditional standard deviation (variance) of portfolio returns. This result is consistent with the results of Abdalla (2012) and Abdmoulah (2010).

Table ‎5.: Estimation the GARCH-M models

Full Sample

1994-2011

APARCH-M(SK)

Sub-sample 1

1994-2001

IGARCH-M(t)

Sub-sample 2

2002-2008

APARCH-M(sk)

Sup-sample 3

2009-2011

IGARCH-M (sk)

Mean Equation

ð"Š

0.019

( 0.068)

0.024

(0.049)

0.073

( 0.048)

-0.015

( 0.093)

AR(1)

0.997

( 0.013)*

1.214

(0.026)*

0.069

(0.024)*

0.001

(0.031)

AR(2)

-0.290

( 0.032)*

AR(3)

0.070

( 0.021)*

MA(1)

-0.871

(0.025)*

-0.980

(0.019)*

MA(2)

-0.116

(0.019)*

Risk parameter

-0.014

(0.166)

0.064

(0.082)

0.023

(0.045)

0.062

(0.093)

Variance Equation

0.025

(0.005)*

0.035

(0.006)*

0.043

(0.013)*

0.043

(0.029)

0.256

(0.027)*

0.372

( 0.037)*

0.259

(0.037)*

0.139

(0.046)*

0.792

(0.021)*

0.627*

0.795

( 0.029)*

0.860*

0.103

( 0.042)**

0.158

( 0.056)*

1.435

(0.190)*

1.148

(0.210)*

Skewed distribution:

Asymmetry:

Tail:

-0.063(0.021)*

4.043(0.259)*

-0.078(0.027)*

3.996( 0.415)*

-0.084(0.047)***

3.156(0.323)*

Student-t distribution:

Student(DF)

4.400

(0.368)*

LL

-6112.649

-1901.819

-3154.198

-1010.187

Akaike

Schwarz

2.440585

2.456177

1.631784

1.653914

3.218919

3.247321

2.861287

2.906247

Hannan-Quinn

2.446049

1.639845

3.229357

2.878654

Q2(50)

[0.0268]**

[0.8357]

[0.4820]

[0.9804]

ARCH-LM(10)

[0.8996]

[0.5309]

[0.9820]

[0.9987]

Note: Numbers in ( ) are the standard error and [ ] are the p-value. *, ** indicate the 1% and 5% level of significance. Q^2 is the Q-Statistics on Squared Standardized Residuals.

5.5. Efficiency of Stock Markets

The Efficient Market Hypothesis (EMH) indicates that current asset prices fully reflect all publicly available information. EMH holds when the asset prices are determined by the outcome of supply and demand in a competitive market, traded by rational investors. These investors rapidly assimilate any information that is relevant to the determination of asset prices, so that current prices fully reflect all available information (Fama, 1970). The concept that the current prices fully reflect all available information implies two things: (1) successive price changes (returns) are independent; (2) successive price changes are identically distributed. These constitute the cornerstone of the random walk model (Fama, 1970).

However, efficient markets do not allow investors to earn abnormal returns without accepting above-average risks (Malkiel, 2003). It is, therefore, important to determine whether a market is efficient or not. As a consequence a large amount of research has been carried out to examine market efficiency.

A weak form market efficiency indicates that all available information are fully reflected in current asset prices, so any change in the prices should require a new arrival information, which is unpredictable. This returns of assets should be unpredictable as well. Unpredictable returns means that it follows a random walk and hence considered to have a unit root (Hasanov & Omay, 2007).

This section assesses empirically the validity of the efficient market hypothesis in an emerging GCC market particularly the SSM. Butler and Malaikah (1992) evaluate the weak form efficiency of Saudi Arabia and Kuwait stock exchanges over the period from 1985-1989, using serial correlation and runs tests and find that SSM is inefficient. Onour (2009) examine the Saudi stock market using daily data from first 1st march, 2003 to 30th June, 2006. He applies a unit root test and variance ratio test and concludes that the SSM is inefficient during the period under the study. Simpson (2004) examines the efficiency of all GCC stock markets using daily data over the period from 1st January 2000 to the 10th November 2003. He finds the GCC markets are not efficient. Also, Elango and Hussein (2008) test whether GCC markets followed a random walk stock during 2001 to 2006. Their results conclude that all GCC markets are weak-form inefficient. Recently, Ibnrubbian (2012) test the weak-form of market efficiency in Saudi Arabia over the period from 2002 to 2008 using daily data of 50 individual companies from five different sectors. He employs serial correlation and Ljung-Box tests, run test, filter rule test and variance ratio test. Generally, the results indicate that the SSM is inefficient. Abdmoulah (2010) investigates the efficiency of Arab stock markets (including Saudi Arabia) using GARCH-M(1,1) models over the period from 2003 to March 2009. The results show that all markets are sensitive to past shocks and are weak-form inefficient. Moreover, the results show that the largest Arab markets shows some improvment in efficiency over time..

In cases of regional markets, Abraham, Seyyed, and Alsakran (2002) examine the random walk hypothesis and market efficiency for the Kuwait stock markets by applying runs and variance ratio tests. They find weak form market efficiency, but no random walk. Also, Al-Jafari and Abdulkadhim (2012) and Jaradat and Al-zeaud (2011) examine the random walk hypothesis in Bahrain and Amman stock markets (Jordan) respectively. Unit root tests and serial correlation tests are used in the Jaradat and Al-Zeaud study while unit root tests, runs test and he variance ratio test are used in the study of Al-Jafari and Abdukadhim and they find that the both markets are not weak form efficient. While Oskooe, Li, and Shamsavari, (2010) examine the random walk hypothesis in the Iran stock market using unit root tests and the results show that the Iranian stock market follows the random walk process which means that the marke