The behavior of MENA oil and non-oil producing countries in international portfolio optimization

The Quarterly Review of Economics and Finance 50 (2010) 415–423

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The behavior of MENA oil and non-oil producing countries in international portfolio optimization Gholamreza Mansourfar a,∗ , Shamsher Mohamad b , Taufiq Hassan c a

Department of Accounting & Finance, Faculty of Economics and Management, Urmia University, Iran Graduate School of Management, UPM, Malaysia c Department of Accounting & Finance, Faculty of Economics and Management, UPM, Malaysia b

a r t i c l e

i n f o

Article history: Received 26 March 2010 Accepted 29 June 2010 Available online 6 July 2010 JEL classification: G11 G15 O16 Keywords: International portfolio optimization Multi-Objective Genetic Algorithm Lower Partial Moment MENA Emerging markets

a b s t r a c t It is well documented in developed economies that portfolio investment across national borders brings benefits of increasing returns and/or reducing risk. Dividing MENA stock markets into two main groups (oil producing and non-oil producing countries), this study examines the potential role of each group in providing diversification benefits for international investors. In addition, the behavior of the long and the short-run Efficient Frontiers (EFs) constructed by each of the sub-groups and the combined MENA markets is explored. Multi-objective international portfolio models are proposed under Mean-Variance and MeanLower Partial Moment frameworks, and the Multiple Fitness Function Genetic Algorithm (MFFGA) is used to find the EFs of optimal portfolios. The findings indicate that the stock markets of oil producing countries can be considered as a potential avenue for international portfolio diversification for investors not only from the same countries but also from the other MENA markets. It was also found that international portfolios constructed from the combination of MENA equity markets are more stable compared to the portfolios of sub-group markets. Further, the findings indicate that the behavior of short-term EFs in the MENA region cannot be predicted by the behavior of long-term EFs. © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.

1. Introduction Throughout the last three decades, increased financial liberalization in many emerging countries has had significant effects on portfolio selections made by international investors. Financial liberalization mainly refers to a series of deregulations which give domestic investors the right to transact in foreign equity markets and give foreign investors the opportunity to invest in domestic capital markets, and consequently it facilitates cross-border capital flows (Kim & Yoo, 2009; Park & Bae, 2002; Taskin & Muradoglu, 2003). It is a well-documented fact that portfolio investment across national borders brings more benefits of increasing returns and/or reducing risk compared to purely domestic portfolio investments (see for example: Chiou, 2008; Chiou, Lee, & Chang, 2009; De Roon, Nijman, & Werker, 2003; Dunis & Shannon, 2005; Lagoarde-Segot & Lucey, 2007; Levy & Sarnat, 1970; Li, Sarkar, & Wang, 2003; Solnik, 1974). This situation arises because of the different levels of diversity of stock markets and the low correlations between equity indices of national markets. In this

∗ Corresponding author. E-mail address: [email protected] (G. Mansourfar).

respect, empirical studies emphasize that emerging markets are highly volatile and they are less integrated with the international financial markets; therefore, emerging markets, compared to the markets of developed countries, promise higher returns and more risk reduction benefits if they are included in internationally diversified portfolios (Kabir Hassan, Maroney, Monir El-Sady, & Telfah, 2003; Naranjo & Porter, 2007). This feature of emerging markets has attracted the attention of many international fund managers who view them as potential markets to successfully exploit the benefits of diversification (Kabir Hassan et al., 2003), and it may explain the steady increase in portfolio investment which has flowed into emerging equity markets (see Fig. 1). Studies of the potential gains from international portfolio diversification (IPD) have received much attention in financial economics. However, most of the literature in this area has focused on the integration and the interaction among international stock markets and attempt to explain the ability of stock markets to provide diversification gains, but the issues of how investors should select the optimal international portfolios and what the optimal mix of equity markets would be have not received commensurate attention. Moreover, empirical studies on emerging stock markets among the equity markets of the MENA region have received less attention than other emerging regions such as the Asian or Latin American markets.

1062-9769/$ – see front matter © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.qref.2010.06.007

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G. Mansourfar et al. / The Quarterly Review of Economics and Finance 50 (2010) 415–423

Fig. 1. Portfolio in-flows to emerging markets (2000–2008). Source: International Financial Services London (IFSL, 2009) *IFSL estimate for portfolio investment.

In the view of this situation, the present study provides evidence from the MENA equity markets that they are a potential new avenue for IPD. More specifically, in this study MENA countries are divided into two groups: the first group of countries includes the world’s main oil producers which are located around the Persian Gulf; namely, Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, and the UAE. This group of countries is referred to as the Gulf Cooperating Council (GCC). The GCC aims to increase industrial and financial cooperation between the countries and to launch a customs union. In addition, there are plans to establish a monetary union with a single currency (Abed & Davoodi, 2003; Fasano & Iqbal, 2003). The second group consists of the stock markets of Tunisia, Egypt, Israel and Turkey. The segregation of the MENA capital markets from the rest of the international financial markets together with their recent improvements can be considered as a salient advantage to provide diversification benefits for international investors (see for example: Assaf, 2009; Gallegati, 2005; Maghyereh, 2006; Marashdeh, 2005; Neaime & Colton, 2005; Yu & Hassan, 2008). This study addresses the issues of optimal allocation of capital among different countries of the MENA region and the behavior of Efficient Frontiers (EFs) in long and short holding periods. These issues have not been given adequate consideration in the current literature of international portfolio investment. The objectives are investigated in the both intra- and inter-regional stages. Unlike most previous studies, which maximized return of portfolio at a given level of risk or minimized risk at a predefined level of return, in this study the international portfolio optimization problem is resolved through a multi-objective framework in which minimizing the portfolio risk and maximizing the portfolio return are taken into account simultaneously. This purpose is achieved through the Mean-Variance (M-V) and the Mean-Lower Partial Moment (MLPM) structures. To the best of our knowledge, this study is the first attempt in optimal international portfolio selection which uses a multi-objective approach within the M-LPM framework. The rest of this paper is organized as follows: Section 2 briefly reviews the theoretical background with respect to portfolio theory and evolutionary multi-objective optimization algorithms. Section 3 describes the data and the methodology, Section 4 presents the empirical results, and Section 5 concludes the paper. 2. Theoretical background 2.1. Portfolio theory Portfolio selection is one of the pertinent issues in applied finance, and refers to the selection of a combination of securities

that can optimally fulfill the investors’ objectives (Huang, 2008). Modern Portfolio Theory (MPT), proposed by Markowitz (1952), was the first mathematical formulation of the portfolio selection problem in the framework of risk-return trade-off, in which a probability distribution of the asset returns is assumed to be known (Vercher, Bermudez, & Segura, 2007). Two of the strongest assumptions made under Markowitz’ M-V approach are: (I) asset returns are normally distributed, and (II) the utility functions of investors’ preferences are quadratic. However, neither (I) nor (II) holds in practice (Coleman & Mansour, 2005; Estrada, 2006; Grootveld & Hallerbach, 1999; Konno, Waki, & Yuuki, 2002). Furthermore, in the M-V approach, the implied symmetry of the covariance-based measure of risk ignores investor risk aversion (Coleman & Mansour, 2005). In other words, other parameters being equal, investors would prefer a smaller left tail in return distributions (Cheng, 2005; Yu, Zhang, & Zhou, 2006). To overcome the weaknesses of the variance approach, researchers were led to develop other measures of risk to formulate the portfolio optimization problem. The alternative risk measures have many theoretical and practical advantages compared to the variance approach. Markowitz (1959) recognized the asymmetrical efficiencies in mean-variance analysis. Bawa and Lindenberg (1977) developed the Lower Partial Moment (LPM), which is a special approach to downside risk measures, as an alternative risk measure to variance. VaR, conditional VaR and expected shortfall are some other examples of downside risk measures which have been documented in the finance literature. The latest alternatives to risk measures are usually entered as constraints in portfolio optimization problems (Jarrow & Zhao, 2006). 2.2. Evolutionary multi-objective optimization algorithms Multi-objective problems (MOPs) have two or more objective functions that are optimized by evolutionary techniques. Mathematical programming techniques such as linear programming or gradient have some specific limitations when dealing with MOPs. For example, many of them are influenced by the continuity and/or the shape of the EFs. Another restriction of mathematical programming is that it may not work when the EF is disconnected or concave; for some mathematical programming techniques differentiability of the objective functions and the constraints are considered to be a crucial requirement (Gong & Cai, 2009). In addition, the final solution resulting from mathematical programming techniques is located relatively close to an initial point; therefore, these techniques are normally very sensitive to their initialization. Moreover, each running of a mathematical programming technique results in a single non-dominated outcome. Therefore, several runs, departing from different initial points, are required to obtain several elements of the EF (Coello Coello, 2006). Evolutionary Multi-Objective Algorithms (EMOAs) have been developed to search for EFs in multi-objective optimization problems which are too complex to be solved by mathematical programming techniques. Two main issues must be taken into account when an evolutionary algorithm is used for a multiobjective optimization (Coello Coello, 2005; Konak, Coit, & Smith, 2006; Zitzler, Deb, & Thiele, 2000): • Quality: How fitness functions and a selection process should be accomplished to guide the searching procedure towards the Efficient Frontier. • Spread: How diverse a population should be maintained to achieve a well distributed trade-off Efficient Frontier and to prevent premature convergence.

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Table 1 Annualized return and risk for MENA stock markets.

Panel A First group Return Risk (SD) Risk (LPM)

Panel B Second group Return Risk (SD) Risk (LPM)

Bahrain

Kuwait

Oman

Qatar

Saudi

UAE

Average

15.15% 15.84% 7.86%

23.84% 27.20% 12.98%

25.55% 24.84% 11.25%

31.79% 35.62% 14.87%

23.36% 53.22% 24.13%

24.34% 38.24% 16.12%

23.46% 30.31% 13.71%

Egypt

Israel

Tunisia

Turkey

Average

41.00% 64.82% 30.91%

10.00% 26.74% 11.93%

12.00% 16.10% 6.39%

15.00% 46.04% 21.72%

19.50% 38.43% 17.74%

Coello Coello (2005) categorized EMO algorithms as aggregating functions, Pareto-based approaches, and population-based approaches. This classification is based on the selection mechanism. Aggregating functions, in which all objectives are aggregated into a single scalar value (e.g., adding them together) are the most basic approaches to deal with MOPs; therefore, the multi-objective problem changes to a single objective one. The most popular examples of aggregating approaches are: Weighted Sum Approach, Goal Attainment, Goal Programming, and The ␧-Constrained Method. Under Pareto-based approaches, the selection mechanism must deal with the concept of Pareto optimality. The idea is that a set of strings should be found that are non-dominated by the rest of the population. In the last few years many algorithms based on the Pareto approach have been developed. All these models are extensions of Genetic Algorithms (GA) that have been implemented to solve the MOPs. Coello Coello (2003) and Konak et al. (2006) have mentioned some examples of these algorithms, including: Multi-Objective Genetic Algorithm (MOGA), Niched Pareto Genetic Algorithm (NPGA), Non-dominated Sorting Genetic Algorithm (NSGA-I and NSGA-II), Pareto Archived Evolution Strategy (PAES) and Strength Pareto Evolutionary Algorithm (SPEA-I and SPEA-II). In population-based approaches, the population of an EA is used to diversify the search, but the concept of Pareto dominance is not directly incorporated into the selection process. The classical example of this sort of approach is the Vector Evaluated Genetic Algorithm (VEGA). Lexicographic Ordering, Use of Game Theory and Weighted Min-Max Approach are some other well-known examples of Population-based Approaches in EMOAs. Our proposed mathematical model of an international portfolio looks for the optimal allocation of capital among a set of countries to maximize the expected return and minimize the risk. Therefore, it is a multi-objective problem for which the Multiple Fitness Functions Genetic Algorithm (MFFGA) developed by Solimanpur, Vrat and Shankar (2004) is modified to find the optimal portfolios in the EF.

3. Data and methodology 3.1. Data The data set of S&P/IFC daily price indices extending from July 2001 to the end of August 2008 is used in this study. However, for UAE, Qatar and Kuwait, ADX, DSM 20 and KIC indices are used, respectively, as they are not included in the S&P database. To control the impact of exchange rates, all prices are expressed in US dollars. All data were collected from the database managed by DataStream except for DSM 20, which was obtained directly from

the Doha stock market. The daily market rates of return are computed as logarithmic differences before estimating the correlation of the return series for countries within and between groups. During the past decade, many of the MENA countries tried to achieve high growth performance through improvements and reforms in their financial sectors. As a result of the success of these attempts, the economic growth in the emerging MENA countries recorded its highest levels in the last 4 years (World-Bank, 2007). Table 1 shows the market returns and risks for the first and second groups of MENA markets in panels A and B respectively. The return of the first group of MENA stock markets varied between 15.15% and 31.79% for Bahrain and Qatar respectively. Among the first group markets, Bahrain witnessed the minimum market risk (SD = 15.84% and LPM = 7.86%) and Saudi Arabia recorded the maximum risk (SD = 53.22% and LPM = 24.13%) during the 2001–2008 period. Among the second group of MENA markets, while Israel had the lowest average return with 10%, the highest average return was observed for the Egyptian stock market with 41%. The highest return volatility was also witnessed in Egypt (SD = 64.82% and LPM = 30.91%); meanwhile, the lowest return volatility occurred in Tunisia (SD = 16.10% and LPM = 6.39%). Overall, the average market return in the MENA region was high (first group = 23.46% and second group = 19.50%). This can be explained by two main factors: first, the MENA stock markets were generally insulated from the most influential aspects of the recent global financial crisis; and second, the years from 2002 to 2007 can be considered as “golden years” for the MENA region, especially for the oil producing countries. During this period, because of the surge in oil prices, MENA oil producing countries (known as the GCC countries) experienced a high rate of return in their stock markets. Table 2 shows the correlation coefficients of daily returns within and between stock markets of the first and the second group of MENA countries. While the return of the Egyptian stock market had a relatively high correlation with the returns of all the first group stock markets, the returns of other countries in the second group were very low and they sometimes had negative correlations with the first group of stock markets. Looking to the inter-group correlation coefficients, the highest correlation coefficient of daily stock market returns was between Egypt and Saudi with 0.125, whereas the lowest correlation coefficient was observed between Tunisia and Bahrain with −0.007. The results shown on the correlation coefficients matrix indicate that homogeneity across the first group is higher than across the second group of stock markets because the average correlation coefficients of daily returns between the markets of the first group are higher (0.103) than those of the second group (0.083). However, once the two sub-groups are combined, the average correlation coefficient is reduced to 0.062. This indi-

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Table 2 Correlation coefficients of daily returns between MENA and the Middle East. Bahrain

Kuwait

Oman

Bahrain 1 Kuwait 0.127 1 Oman 0.128 0.070 1 Qatar 0.034 0.092 0.133 Saudi 0.076 0.102 0.164 UAE 0.050 0.157 0.123 Egypt 0.106 0.094 0.123 Israel 0.018 0.046 −0.002 Tunisia −0.007 −0.003 −0.019 Turkey 0.006 0.080 −0.017 Average correlation within the first group Average correlation of daily returns within the second group Average correlation of daily returns between MENA countries

Qatar

Saudi

UAE

Egypt

Israel

Tunisia

1 0.053 0.210 0.071 0.027 −0.040 0.022

1 0.069 0.125 0.019 −0.013 0.018

1 0.060 0.018 −0.001 0.007

1 0.062 0.019 0.086

1 0.007 0.300

1 0.020

T 

Turkey

1 0.103 0.082 0.065

cates that inter-group international portfolio diversification in the MENA region may result in higher risk reduction benefits compared to intra-group portfolio investments.

LPM(n,i) = 1/(T − 1)

3.2. Method

n = the degree of LPM, fixed at 2 N = the number of countries T = the target rate or return, fixed at 0 T = the number of return observations for index in country i.

3.2.1. Optimization algorithm This study applies both M-V and M-LPM frameworks to overcome the international portfolio optimization problem and the issue of the behavior of EFs. The reasons for choosing the M-LPM approach beside the M-V framework are as follows: 1. Unlike the M-V approach, M-LPM does not assume that the returns are normally distributed (Stevenson, 2001). The normality hypothesis was rejected by the Jarque-Bera test for all variables of the Middle East and developed markets. 2. M-LPM can reflect investor preferences better than the traditional measure, which is variance (Brogan & Stidham, 2005). 3. The use of M-LPM produced superior results compared to variance in constructing an international portfolio (Stevenson, 2001). 4. Estrada (2002, 2006) and Hwang and Pedersen (2004) tested various risk measures and suggested that downside risk measures matter for analyzing emerging market equity indices. In the M-LPM framework, the portfolio optimization problem essentially involves selecting an optimal mix of equities in such a way that the probability of the portfolio return (Rp ) falling below the target return () is minimized; therefore, portfolio optimization can be defined as: Minimize

G(x) =

N N  

xi xj LPM(n, i)LPM(n, j) rij = LPM(n, p)

i=1 j=1 N

Maximize H(x) =



xi Ri = Rp

i=1

Subject to

N 

xi = 1 xi ≥ 0, i = 1, 2, 3, . . . , N

i=1

where: xi = the proportion of portfolio allocated to country i Ri = the expected return on index of country i Rit = the expected return for index i during period t Rp = the expected portfolio return LPM(n,p) = the portfolio risk

[Max(0, (Rit − )]n

t=1

However, in the M-V framework, other factors being equal, the portfolio risk would be obtained from the following equation: p2 =

N N  

xi .xj .ij

i=1 j=1



where xi is the share of asset i in the portfolio, hence i∈p xi = 1.  ij denotes the covariance between the returns of i and j, with ii = i2 and ij = ji = i · j · ij where ij ∈ [−1, 1] is the correlation coefficient. To solve the proposed models and to find the EFs, the Multiple Fitness Function Genetic Algorithm (MFFGA) developed by Solimanpur et al. (2004) and Solimanpur and Ranjdoostfard (2009) is modified and applied. The reasons for using this method are: (a) MFFGA considers a systematic uniform design-based approach to set the weights of objectives; (b) MFFGA applies multi-directional search to find more points distributed along the EF; (c) Unlike most other algorithms in which user-defined or randomly generated vectors are used to search the solution space, the MFFGA approach uses a uniform design method to construct uniformly directed search vectors; and (d) the mathematical background of the MFFGA is relatively comprehensive; therefore, it can be used in many fields as well as in finance, and particularly in portfolio optimization problems. In this approach, each portfolio is represented by one chromosome with num bits genes for each country (Fig. 2). Therefore, for a portfolio with N countries, the length of any chromosome would be N × num bits. A binary encoding system is used to represent the genes. If the decoded decimal value of country i be vi , the following equation is defined to obtain the portion of capital allocated to country i: xi =

vi

N

v i=1 i

where xi is the weight of capital allocated to country i and N is the number of equity markets. Therefore, for each of the chromosomes in the proposed coding system it would be obvious that xi ≥ 0 for i = 1, 2, 3. . . N and

N  i=1

xi = 1, refer to the automatic satisfaction

of the constraints of the optimization problem. This will greatly increase the calculation efficiency of the algorithms.

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Fig. 2. Representation of international portfolio in the proposed method with num bits genes.

To search the objective space, K fitness functions must be defined. If the objective functions, LPM(n, p) or  p and Rp , are represented by f1 and f2 respectively, the fitness function of direction k would be formed as follows: fitk (S) = wk1 f1 (S) + wk2 f2 (S) where the fitness of portfolio S with respect to the kth search direction is represented by fitk (S), the value of the first and the second objective functions for portfolio S, is indicated by fl (S) and f2 (S) respectively and the weights of objective functions are shown by wk1 and wk2 respectively. Since the values of risk and return vary in different ranges, it would be possible that an objective with a greater value dominates the contribution of other objectives. Therefore, the objective functions have been normalized as follows: fitk (S) = wk1 h1 (S) + wk2 h2 (S) where: h1 (S) =

Second, considering each of the groups as a separate sample, the behavior of EFs in different holding periods is analyzed. In the second step, the Mann–Whitney U test is used to test for the predictability of the short-term EFs’ behavior through the behavior of the long-term EFs. In particular, in the event of similarity between EFs in different holding periods, the behavior of optimal portfolios in short-term holding periods would be predictable through the behavior of optimal portfolios in long holding periods. 4. Results 4.1. Portfolio optimization Using the M-V and the M-LPM frameworks, Figs. 3 and 4 demonstrate the EFs of optimal portfolios constructed by the samples of the first, the second and the combined MENA stock markets. Both the M-V and the M-LPM models show that the most superior EF belongs to the first group of MENA stock markets. This is followed

f1 (S)



max{f1 (S  ) ∀S  ∈ ˝}

The normalized value of the objective function 1 for portfolio S is denoted by the function h1 (S), and ˝ stands for the set of all portfolios under evaluation. To form search directions, MFFGA applies uniform design technique. To calculate search directions, the numbers of directions are considered as levels and objective functions are treated as factors of matrix. Hence, search directions are calculated as: W = [wkl ]k×2 ;

wkl =

ukl

2

u l=1 kl

where W(K,2) = [wkl ]k×2 is the uniform design matrix. Each row of the matrix W is a search vector and wkl is the weight of the objective function l in fitness function k. The genetic algorithm is programmed in Matlab.1 Fig. 3. Efficient Frontiers of international portfolios using the M-V framework.

3.2.2. The behavior of EFs The consistency of equity markets in portfolio diversification is a desired trait for international investments. Consistency here refers to the ability to provide efficient and stable investment opportunities for international investors in long and short holding periods. This feature is evaluated through the long- and short-term behavior of EFs. Using monthly returns of market indices from the 2001 to 20072 period, the long-term behavior of EFs is investigated. In the case of the short holding period, 2 years in-sample data from the 2006 to 2007 period are utilized. The analysis is carried out at two levels: first, the behavior of long- and short-term EFs of the first group, the second group and the combined MENA stock markets are graphically compared.

1 The program consists of eleven function files: one main function and 10 subfunctions. 2 The data for 2008 is excluded for this part of study due to the effects of the recent global crisis which started in 2007 and is still an ongoing issue.

Fig. 4. Efficient Frontiers of international portfolios using the M-LPM framework.

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G. Mansourfar et al. / The Quarterly Review of Economics and Finance 50 (2010) 415–423 Table 4 Optimal capital allocated to the second group of MENA stock markets.

Fig. 5. Efficient Frontiers of the Middle East.

by the superiority of EF of the combined MENA stock markets and then by the EF of the second group stock markets. This implies that at intra-group diversification level, the first group of stock markets can provide more benefits of portfolio diversification compared to the second group. It can also be concluded that at inter-group diversification level it may be worthwhile for investors from the second group of MENA countries to diversify their international portfolios by including equities from the first group. Although the stock markets of the first group provide dominant international portfolios for investors from the remaining MENA countries, they restrict the opportunity of taking higher risk and return investments compared to the portfolios which are diversified by only the second group of MENA stock markets. For example, based on the M-V method, the yearly return of optimal portfolios of the second group of stock markets varies between 12.9% and 40%, whereas it varies between 20.9% and 29.7% when the stock markets of the first group are added to them (EF of MENA). Since M-V and M-LPM methods define the portfolio risk in different ways, it should be noted that the M-V EF is not directly comparable with its M-LPM counterpart. However, some of their effects on the portfolio optimization can be highlighted. For example, Fig. 5 shows the EFs of the first group under both M-V and M-LPM frameworks. From a graphical comparison it is evident that under the M-LPM model, investor’s aversion to negative returns has the effect of pushing the EFs outward to the left of Markowitz’s classical M-V model to produce efficient portfolios that are stochastically dominant. This phenomenon has been reported by Grootveld and Hallerbach (1999) as: “the M-LPM model with a target level of 0% produces portfolios deviating the most from M-V portfolios”. To gain further insights and to explore the optimal capital allocation among capital markets, three important portfolios from the EFs of the first group, the second group and all MENA stock markets are selected: the minimum risk-return portfolio, the median risk-return portfolio and the maximum risk-return portfolio.

Egypt

Israel

Tunisia

Turkey

Return

Risk

Panel A (M-V) Min risk-return Med risk-return Max risk-return

4.47% 68.83% 95.67%

11.82% 1.62% 0.43%

78.59% 27.13% 3.46%

5.11% 2.43% 0.43%

13.21% 32.00% 39.75%

2.26% 21.05% 38.72%

Panel B (M-LPM) Min risk-return Med risk-return Max risk-return

4.07% 72.61% 97.64%

27.91% 1.98% 0.47%

63.08% 25.08% 1.42%

4.94% 0.33% 0.47%

12.77% 33.03% 40.32%

0.46% 5.15% 9.17%

Using the M-V and M-LPM methods, Tables 3–5 summarize the results of capital allocation to each of the sampled equity markets. For example, for the sample of the second group and using M-V model, in the interest of selecting the minimum risk-return portfolio, 4.47% of the whole capital should be allocated to the Egyptian stock market and 11.82%, 78.59% and 5.11% of the whole investable fund should be allocated to Israeli, Tunisian and Turkish equity markets, respectively. As another example, looking to the M-V model results of stock markets from the first group, while with the minimum risk-return portfolio the largest percentage (44.87%) and the smallest percentage (0.43%) of capital are respectively allocated to the Bahraini and Qatari stock markets, with the maximum risk-return portfolio, Bahrain receives the smallest portion of the whole capital (2.29%) and the largest fraction of fund (68%) is allocated to the Qatari stock market. This means that for the intra-group portfolio investment, if investors are interested in having lower risk-return portfolios, the largest portion of their capital should be allocated to the Bahraini stock market. In addition, with both M-V and M-LPM methods, the proportion of optimal capital allocated to each of the first group countries changes significantly by moving on the EFs from minimum risk-return portfolio toward maximum risk-return portfolios. Nevertheless, moving on the EF curve does not significantly change the magnitude of the capital allocated to the Saudi stock market in that it remains the smallest recipient of capital in constructing intra-group optimal portfolios. This implies that the stock market of Saudi Arabia plays the least influential role among the markets in the same group. Comparing the results of M-V and M-LPM models shows that the changes of the allocated capital to each of stock markets reflect investor’s aversion to negative returns as a crucial behavior. When the sample of the first group is combined with the second group of MENA countries, the results of portfolio optimization using both M-V and M-LPM approaches show that to achieve efficiently diversified international portfolios, the first group of MENA equity markets potentially attract more investable capital compared to the second group of MENA stock markets. For example, using the M-V model, if investors are interested in maximum riskreturn portfolio, the optimal allocation of capital for the first and

Table 3 Optimal capital allocated to the first group of MENA stock markets. Bahrain

Kuwait

Oman

Qatar

Saudi

Panel A (M-V) Min risk-return Med risk-return Max risk-return

44.87% 13.59% 2.29%

18.45% 14.71% 11.14%

26.28% 43.10% 5.14%

0.43% 17.44% 68.00%

5.13% 3.25% 4.57%

Panel B (M-LPM) Min risk-return Med risk-return Max risk-return

37.06% 8.20% 4.16%

32.89% 17.97% 4.71%

24.71% 39.06% 14.68%

5.18% 18.95% 56.23%

0.00% 0.20% 2.22%

UAE

Return

Risk

4.84% 7.91% 8.86%

20.47% 25.14% 29.17%

4.30% 5.72% 11.64%

0.17% 15.63% 18.01%

21.57% 25.56% 28.40%

0.93% 1.19% 1.73%

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Table 5 Optimal capital allocated to combined MENA stock markets. Bahrain

Kuwait

Oman

Qatar

Saudi

UAE

Egypt

Israel

Tunisia

Turkey

Return

Risk

Panel A (M-V) Min risk-return Med risk-return Max risk-return

17.02% 6.71% 0.33%

3.64% 18.62% 3.76%

19.42% 5.83% 8.84%

18.10% 14.03% 18.33%

4.13% 2.56% 19.64%

10.33% 19.95% 1.64%

0.41% 16.33% 36.50%

10.50% 2.03% 2.95%

13.72% 12.62% 3.60%

2.73% 1.32% 4.42%

20.97% 25.47% 30.38%

4.39% 7.99% 18.46%

Panel B (LPM) Min risk-return Med risk-return Max risk-return

16.57% 2.45% 4.86%

27.66% 6.81% 5.31%

7.25% 22.52% 5.77%

25.30% 21.16% 15.78%

7.10% 11.17% 27.62%

0.15% 14.35% 1.06%

5.03% 15.08% 34.29%

0.00% 2.91% 2.88%

9.91% 3.09% 0.91%

1.04% 0.45% 1.52%

24.18% 27.56% 29.85%

1.26% 2.12% 4.19%

the second group would be equal to 52.54% and 47.46% respectively. This means that the first group of MENA stock markets is a potential avenue for investors from the second group to gain from international portfolio diversification. However, determining whether the potential benefits enjoyed by using the first group equities in an inter-group portfolio diversification is a transitory feature or a long-term phenomenon is a crucial question that is empirically addressed in the following section. 4.2. The long and the short-run behavior of EFs 4.2.1. First level Fig. 6 illustrates the long-term EFs. In the long holding period, the EF of the first group of MENA stock market dominates other EFs. However, in the higher rate of risks and returns (monthly risks more than 0.45% and monthly returns more than 2.4%), it is dominated by the EF of the second group of MENA stock markets. Another observation is that the EF of the second group shifts upward to the left and becomes superior once all MENA stock markets are considered in one sample. This implies that in the long holding period, the intra-group diversified portfolios of the first group of MENA equities are more beneficial compared to international portfolios which are diversified by other stock markets from MENA. Moreover, for the long holding period, it would be more beneficial for investors from the second group of MENA countries to diversify their portfolios by investing in the equities of the first group rather than investing only the markets of their same group. It is also noted that the increasing rates of risks and returns among optimal portfolios made by the equities from the first group are not harmonized as compared to the second group and the MENA equity markets. This phenomenon is represented by the decreasing slope of the first group’s EFs over an increasing rate of the risk. Fig. 7 demonstrates the short-term EFs. Despite the performance of long-term EFs, in the short holding period the EF of the first group

markets is dominated by EFs of the second group of MENA stock markets. This implies that in the short holding period, the intragroup diversified portfolios of the second group of MENA equities are more beneficial compared to the other samples. Moreover, it can be seen that in the short holding period it may be worthy for investors from the first group of MENA markets to diversify their international portfolios through investing in the equities of the second group. This is because the EF of the combined MENA markets is superior to the EF of the first group. From the results it can also be inferred that with the lower rate of portfolio risk and return (monthly portfolio risk less than about 0.11%), MENA stock markets in combination provide more beneficial portfolios compared to the second group of stock markets. 4.2.2. Second level Figs. 8–10 show the EFs of the long and the short holding periods for each group of stock markets. As the period grows longer, the EFs of the first group and all MENA markets become more dominant; while, in the second group, as the period grows shorter, the EF becomes more superior.

Fig. 7. Efficient Frontiers in the short-term.

Fig. 6. Efficient Frontiers in the long-term.

Fig. 8. Long- and short-term Efficient Frontiers (first group).

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G. Mansourfar et al. / The Quarterly Review of Economics and Finance 50 (2010) 415–423 Table 7 Mann–Whitney U Test for equality of intra-regional Efficient Frontiers. H0:equality of returns

1st group 2nd group MENA

H0:equality of risk

Z statistics

P value

Z statistics

P value

−5.27 −8.85 −3.932

0.0001 0.0001 0.0001

−2.860 −8.85 −2.828

0.004 0.0001 0.005

the long- and short-term EFs are rejected at the 5% level of significance. This is because the P-values of the Mann–Whitney U tests for both dimensions of EFs are much less than ˛-value (0.05). This implies that neither the returns nor the risks of long and short-term EFs are statistically equal. Consequently, the long-term EFs in any of the first group, the second group or all MENA markets can be used to predict the behavior of the short-term optimal portfolios in terms of their risks and returns.

Fig. 9. Long- and short-term Efficient Frontiers (second group).

5. Conclusion

Fig. 10. Long and short-term Efficient Frontiers (MENA).

Regardless of the EFs’ superiority in terms of the investment opportunity sets, the long-term EFs of all samples provide opportunities for selecting the desired investments among a wider set of portfolio risks. However, the short-term EFs offered by the intra and inter-group diversified portfolios do not have this advantage because the risks of their optimal portfolios are restricted. More likely, the long-term EFs of the first group and of the combined MENA stock markets are the superior EFs. This means that in the long holding period, investing in the first group and in MENA stock markets not only would be more beneficial, but investors would also be able to choose their portfolios among a wider set of investment opportunities. The variations of monthly risks across different holding periods are set out in Table 6. While the absolute value of the changes between the ranges of the first and the second group markets is 45% and 41% respectively, it is 16% for all MENA stock markets. This implies that when investors shift from a long-term to a short-term portfolio investment, the inter-group diversification provided by the combined MENA stock markets can provide more stable investment opportunities compared to intra-group portfolio selections by the first and the second group of stock markets. Table 7 represents the results of the Mann–Whitney U tests. The hypotheses of equality of not only returns but also risks between Table 6 Monthly risk ranges across different holding periods (intra-regional optimization). Sample

Period

Min risk

Max risk

Range

1st group

Long Short

0.12% 0.18%

0.63% 0.24%

0.51% 0.06%

2nd group

Long Short

0.13% 0.11%

0.64% 0.21%

0.51% 0.10%

MENA

Long Short

0.09% 0.09%

0.36% 0.18%

0.27% 0.09%

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