International Stock Market Diversification among BRICS-P : A Cointegration Analysis

This study explores the benefits associated with the international portfolio diversification among BRICS-P economies. The dynamics of the globe are changing, and the economic transformations have made the emerging economies a prominent center for investments. The possibility of international diversification among the BRICS-P economies may help the investors in maximizing their utilities by earning a higher return with a given level of risk. To assess the benefits of diversification and to explore the long term and short tern dynamics of the selected stock markets, this study uses Auto Regressive Distributive Lag (ARDL) approach. The findings show that substantial portfolio diversification benefits exist when the funds of Brazil, Russia, South Africa and China are merged. The study also found that Pakistan and India’s funds are co-integrated, and that the prospect of diversification exists if the funds of these two economies are mixed. The results will help the investors in constructing their portfolios by merging the funds of the selected economies, because having a diversified portfolio leads to better risk return performance than having a portfolio with only native funds.


Introduction
Modern portfolio theories propose diversified portfolio for maximization of utility and minimization of risk.Investors can bring about an even more substantial reduction in the risk if they carry an internationally diversified portfolio.An internationally diversified portfolio can prove itself more efficient than the domestic ones on the global frontier (Bahlous & Yusof, 2014).By diversifying across different countries where economic cycles are not perfectly correlated, investors can typically minimize the variability of their returns.Grubel (1968); Haim and Sarnat (1970); Solnik and MacLeavey (1991) were the pioneers in documenting a relatively weak correlation among international securities than the domestic securities.Earlier studies have also suggested that weak correlation in international securities can lead to substantial gains from diversification (Cosset & Suret, 1995).
The theories also predict that when the markets are not perfectly correlated, benefits of international portfolio diversification can be achieved because the stock markets have volatility in their behavior.A market having consistent performance with other regions among all Asian stock markets and therefore, it has been rated as world's fifth best market.
Keeping in view the facts stated above, there is substantial need for exploring the benefits associated with portfolio diversification and investing in these evolving economies.Past studies have concluded that by diversifying the portfolio among different regions of the world, and among markets with differing maturity levels and differing company sizes would yield more substantial diversification benefits to the investors (Mensi et al., 2014;Sukumaran, Gupta, & Jithendranathan, 2015;Dhanaraj, Gopalaswamy, & Babu, 2013).This study is endeavoring to evaluate the diversification benefits among the BRICS-P economies.More specifically, the study strives to find out the answers to the following question: Can a nonnative investor of the BRICS-P economies have the opportunity to get any benefits of diversification among selected stock markets?Is there any long-run and the short-run relationship between selected stock markets?
The answer to these questions will be helpful for investors in understanding and undertaking actions for maximizing utility and minimizing risk.If the risk and performance analysis came up with some gains from diversification, this would help the investors in obtaining a higher level of utility.The investors can develop an optimal portfolio in this case by diversifying their investment portfolio among BRICS-P economies.
The study uses Time Series data set to analyze the extent of long term and short term investment dynamics among the selected economies.Auto Regressive Distributive Lag (ARDL) approach is used to gauge the effect of the temporal relationship and contemporaneous correlations in the funds of selected economies.If the chosen funds were found to be negatively or weakly correlated, it could be concluded that investors of these economies can hold a well-diversified portfolio.The study also stresses that even if the correlation turns out to be positive, investors can still yield the benefits of diversification if the correlation is not perfect.
The remaining part of the study is organized as follows.The next section of the study briefly reviews the past literature on international diversification along with the theoretical underpinnings.Section three discusses about the data and methodology employed for the study.Empirical findings are discussed in section four.And section five concludes the study with suitable policy implications and future recommendations.

Literature Review Theoretical Background
Our study is primarily based on the theoretical underpinnings of The Capital Asset Pricing Model (CAPM) introduced by Sharpe (1964) and Lintner (1965) and the Modern Portfolio Theory presented by Markowitz (1952).The Modern Portfolio theory postulates that selection of assets is not only based upon the unique characteristics of the securities.But instead, an investor needs to consider the co-movement of the securities.If investors take into account these co-movements, they will be able to develop a portfolio with the same expected return and lesser risk.The CAPM predicts that the expected return on an asset above the risk-free rate is proportional to the non-diversifiable risk.It is measured by the covariance of the asset return with a portfolio composed of all the available assets in the market.The modern portfolio theory considers how an optimizing investor should behave, whereas, CAPM is concerned with the economic equilibrium assuming that all investors are optimizing in a particular manner.These theories are of the view that rational investors who are seeking to maximize their utilities should hold a well-diversified portfolio to mitigate risk.They can do so by investing in diversified portfolios on an international level that would dominate domestic-only ones on the efficient frontier.An international portfolio of stocks from different regions or countries should earn a higher return for the same level of risk and carry less risk for the same level of return from a non-diversified portfolio (Bahlous & Yusof, 2014).

Empirical Findings
Many empirical studies have focused on international diversification benefits.Some of them are summarized below.
The past literature is filled with studies that have tried to assess the diversification benefits and dependence of emerging markets on the global financial markets.A study of a similar kind was carried out by Mensi et al. (2014).They used Quantile Regression approach and investigated the impact of different global factors on the stock market of BRICS countries.The study suggested that the dependence structure is asymmetric and got influenced by the financial crunch that hit the US financial market.However, the uncertainty of the US economic policy failed to affect the BRICS stock market.Their findings were also supported by Patev, Kanaryan, and Lyroudi (2006) who reported that the evidence of no long-run co-integration among the US and Central Eastern Europe stock markets.The results of the study confirmed a reduction in diversification benefits during the crisis period and an increment in the same during the post-crisis period.Contradictory evidence was found by Guidi and Ugur (2014), who analyzed the co-integration of the South-Eastern European market with their developed counter parts.The study reported a higher degree of co-integration between the SEE markets and their developed counterparts.They also found the evidence of time-varying co-integration particularly for the periods of shocks such as financial crisis.The authors argued that despite the co-integration, diversification benefits still prevails in these markets.Similar kind of results was presented by Batareddy et al. (2012) who showed that because of the integration among markets, the selected Asian economies are not protected by the shocks created in the US and Japanese Stock markets.According to Johnson and Soenen (2009), the developed and emerging markets both are partially integrated with the world equity market.
Several studies have been undertaken in the past that showed the benefits of regional diversification.Significant research in this regard is of Dhanaraj et al. (2013).Their empirical findings showed that the US stock market dominates over the Asian stock markets.The authors postulated several reasons for this inter dependence.For instance, US is one of the largest economies in the world, a significant trading partner and supplier of capital to the Asian economies.The study also argued that Asian economies are susceptible to shocks originating in the US stock markets.However, the effects of these shocks vary considerably across markets.Similarly, Dunis, Sermpinis, and Karampelia (2013) examined the extent and promptness of integration among the five newest members of European Monetary Union (EMU) and the euro area.Results indicated that the selected states exhibited a variable but accelerated degree of integration after their accession to the EU.Whereas, EMU does not seem to have the same positive impact on the process.In the same way, Bahlous and Yusof (2014) tried to assess the benefits of international diversification for the investors who opt only for Islamic funds.In the authors' view, the Islamic fund's investors can maximize their utilities by investing in Islamic funds across the selected regions.Rua and Nunes (2009) also examined the co-movement among stock markets of Germany, Japan, the UK and the USA.The analysis showed that Germany exhibited a higher degree of co-integration with UK and USA over the whole sample period whereas, Japan presented a relatively low degree of co-integration with all the other states considered in the sample.Majid, Meera, and Aziz (2009) investigated the linkages among Association of Southeast Asian Nations (ASEAN) and found that for the non-native investors, the region of ASEAN is not beneficial for portfolio diversification.
Substantial portfolio diversification benefits exist for the emerging market economies.This hypothesis gets its support from a wealth of studies.For instance, (Zonouzi, Mansourfar, & Azar, 2014) postulated that several potential benefits like increasing rate of return or decreasing risks are associated with international portfolio diversification.The authors were also of the view that the investors who wish to diversify their portfolio among the emerging group of economies may get a higher rate of return with a given level of risk.On the same line of thought, (Li et al., 2003) presented the view that although the integration in the world equity market has reduced the diversification benefits, they are not vanished off completely.Results showed that advantages of international diversification remain considerable if short sell constraints are imposed by the emerging markets on the US investors or the non-native investors in US equity market.With the same token, Sharma and Bodla (2011) tried to investigate the portfolio diversification benefits among India, Pakistan, and Srilanka and showed that all of the selected Asian markets hold substantial diversification benefits in particular, whereas, diversification benefits exist for all South Asian markets in general.Hoque (2007) empirically examined that Japanese stock market has no impact on Bangladesh stock market, whereas, USA market shocks create an impact on Bangladesh stock market.The author argued that due to similar stock market trend in the selected economies, non-native investors cannot enjoy diversification benefits.Similarly, Boubaker and Jouini (2014) investigated the causal links between the equity markets of South-Eastern and Central Europe and developed countries, i.e., Western Europe and the US.They showed that because of the co-integration in the selected markets, the sensitivity to fluctuations in these markets increases both in short and the long run.Valadkhani, Chancharat, and Harvie (2008) in their study, provided the evidence that geographical vicinity and the level of economic development have a significant influence on the stock markets co-movements.If the investors want to reap comprehensive benefits of portfolio diversification, they should take these factors into account.According to Sukumaran et al. (2015), frontier markets can be an exciting place for portfolio diversification.The difference in the economic structure of developed markets with least developed ones makes the frontier markets considerable for portfolio diversification.

Methodology Data
The study aims to explore the short run and long run investment dynamics among the BRICS-P economies.Therefore, in line with the given objective, the study employed seven stock indexes to measure the extent of integration among them.Yahoo Finance is used to obtain data.The selected countries are Brazil, Russia, India, China, South Africa and Pakistan which is a good representation of emerging economies of the world.Monthly data was taken for the period from November 2003 to October 2016.Following Bahlous and Yusof (2014), we did not include information on the dividend in our analysis as the purpose of this study is to evaluate the benefits of international portfolio diversification and for evaluating it, we do not need to have information on dividends of different funds.

Statistical Technique
The study adopted the Auto Regressive Distributed Lag (ARDL) approach Pesaran, Shin, and Smith (1996) to check the long run association among the selected emerging economies.It is a regression model of one variable on its past and past and present values of other considered variables.This approach has got numerous practical advantages.First and foremost, this approach can be used to check the existence of a relationship between variables regardless of the fact that the considered variables are stationary or not.The regressors need not be integrated on I (0) or I (1).The ARDL model does not require a unique level of integration for variables (Narayan & Narayan, 2006).Secondly, the ARDL model takes into consideration sufficient numbers of lags so that a general-to-specific modelling framework can be captured (Laurenceson & Chai, 2003).Moreover, Narayan and Narayan (2006) also endorsed that the ARDL co-integration model is efficient and unbiased, and in addition to it, it can explain the short run and long run components of the model simultaneously.
The ARDL model specifications used in the present study are as follows, It is worth to mention here that in the present study, index prices are I (0) series and their first difference that is index returns are I (1) series.The chosen indexes are IBOVESPA for Brazil, MICEX for Russia, BSE SENSEX for India, SSE for China, EZA for South Africa, and KSE-100 for Pakistan.Finally, S&P500 has been taken as a measure for the global market.
To evaluate short run portfolio diversification dynamics, Error Correction Model (ECM) is used.Using simple linear transformation, a dynamic error correction model can be derived from ARDL (Banerjee, Dolado, Galbraith, & Hendry, 1993).The purpose of using ECM is that it integrates the short run dynamics with the long run equilibrium, without causing any change in the long run information.The ECM specifications can be given as, In the given ECM specifications, the summation sign terms in the given specification are signifying the error correction dynamics whereas, the n s terms are representing the long run relationships.In the long run, the null hypothesis of no co-integration can be given as, H o : n 1 = n 2 = n 3 = n 4 = n 5 = 0.This null hypothesis is tested against the alternate hypothesis of at least one non-zero result i.e., H 1 : n 1 = 0 or n 2 = 0 or n 3 = 0 or n 4 = 0 or n 5 = 0 using F-test, where the critical values if F-test vary depending upon the notion that whether the variables are I(0) or I(1) stationary.Following the given notion, three types of outcomes can arise depending upon if the data are I(0), contains both I(0) and I(1) values or it is I(1) only.If the calculated F-statistics exceeds the upper bound level, the null hypothesis is rejected and we say that co-integration exist among variables.However, if the calculated F-statistics is lesser than the lower bound level, we cannot reject the null hypothesis that further validates the non-existence of co-integration.If the value of the f-statistics lies between the upper and lower bound, the results remain in conclusive (Pesaran et al., 1996).
To determine the suitable lag length that can be used and to select the ARDL model that can be estimated, the study used Akaike Information Criteria.

Results of ARDL Estimates (Long and Short Run)
The data employed for the study is the log price returns of stocks.Since it is a return series, it is assumed to be stationary at level, and hence, the problem of unit root does not exist in the data.However, the data was explored for the problem of unit root, and as assumed, it was found to be stationary at level (results not reported for the sake of brevity).The next step involves estimating Equations (7-12) using the appropriate lag-length.Table 4.2 present the ARDL model estimates, long-run coefficients and short run estimates for all the models tested (Models 7-12).The results for each model are presented in panel A for long-run estimates or coefficients and panel B for short-run estimates and panel C for the bound test.
In addition, panel A also provides information about which lagged values and which variable matters for the prediction of the future values of the endogenous index in the model.For example in Equation 7, the endogenous index investigated is Pakistan stock market.Panel A shows that Pakistan stock market's value at time 't' is negatively linked to India.These results could be exploited for forecasting purposes and could be very useful for fund managers of both economies who are actively managing their funds over short time horizons.(4,0,4,0,1,1,2) (3,0,3,2,2,4,2) (4,2,2,1,4,0,4) (2,0,0,0,3,0,0) (4,2,0,0,0,0,1) (4,4,0,0,0,0,0 Panel A provides information about which lagged values and which variable matters for the prediction of the future value of the endogenous index in the model.For example in Equation 7, the endogenous index investigated is Pakistan stock market.Panel A shows that Pakistan stock market's value at time t is insignificantly linked to India.These results could be exploited for forecasting purposes and could be very useful for fund managers of both economies who are actively managing their fund over short time horizons. For Model 7 (Table 4.2, panel A), we found a significant positive relationship of Pakistan's stock market with South Africa as the p-value of the long run estimate is less than 0.05.It means that both markets move together yielding no diversification benefits.However, Pakistan's stock market has an insignificant correlation with that of the markets of China, India, Russia and USA.Hence we can conclude that investors in Pakistan can yield diversification benefits by combining their portfolios with Chinese, Russian, and Indian funds.
For Model 8 (Table 4.2, Panel A), we found a significant negative correlation between Brazil and India, and an insignificant correlation of Brazil with Pakistan, China, and US SP500.It means that Brazilian investors can reap diversification benefits with any of the given funds.However, South African and Russian Market are found positively associated with Brazilian Market showing that no diversification benefits exist among these markets for Brazilian investors.
For Model 9, (Table 4.2, panel A), an insignificant relationship of Russian stock market with Pakistan, Brazil and India showing that diversification benefits exist for Russian investors in these markets.For Model 10, (Table 4.2, panel A) insignificant negative correlation of India with Brazil, Pakistan, South Africa and US S&P500 is found.It reflects that Indian investors can enjoy the benefit of diversification in the longer run by investing in Brazil, Pakistan, South African and US market stock market.For Model 11, (Table 4.2, panel A), it is found that the correlation of Chinese stock market with Pakistan, Brazil, S&P500 and Russia is insignificant which represents the fact that Chinese investors can invest in these markets to get diversification benefits in long run.For Model 12, (Table 4.2 panel (A), for South African investors there is an opportunity to get diversification benefits by investing in countries like Pakistan, Brazil, Russia, India and US as there is an insignificant relationship among these markets.
In addition to it, as observed in panel B for all the models (7-12), it seems that the ECM have the correct significant value to specify the significance of the co-integrating relationships for all the models tested.The short run dynamics of relationships among the BRICS-P economies is captured by the Error Correction Representation and can be interpreted as following.
In model 7, (table 4.2, panel B), the ECM based ARDL approach shows that changes in none of the observed markets have a significant short run impact over Pakistan's stock market.
In ECM of model 8, it is established that changes in Russian and US stock markets have short run effect on Brazilian market whereas, Brazilian Market remain unaffected by any changes in the rest of markets in short run.
In model 9, the ECM specification showed that changes in the Brazilian and Indian funds can impact Russian funds in the shorter run.Whereas, Russian fund remains unaffected by the changes in the rest of the observed markets in the shorter run.
For model 10, the ECM specification showed that Indian market is highly susceptible to changes occurring in Russian and Chinese stock markets.However, the rest of the observed markets in short run do not impact Indian funds in the short run.
For model 11, the ECM specification shows that changes in Indian and South African markets impact Chinese funds in the short run.However, it remains unaffected by any changes in the rest of the studied stock markets.
For model 12, the ECM specification represented that South African Funds are only affected by changes occurring in Chinese funds in the short run.None of the other observed markets affect the South Asian funds in the short run.
To identify the co-integration among the data series, ARDL Bound test is applied (Pesaran et al., 1996;Pesaran, Shin, & Smith, 2001).To evaluate whether the series are co-integrating or not, F-statistics is used.When the upper bound critical value is lesser than the calculated F-statistics, the null hypothesis of no co-integration is rejected.As the table 4.2, panel C shows, the upper bound critical value is lesser than the calculated F-statistics for all models, hence, we reject the null hypothesis and conclude that all series are co-integrating in the long run.
For the ease of interpretation, the results of ARDL test have been summarized in Table 4.3.by considering that substantial diversification benefits exist if the coefficient in panel A and B are either negative and significant (negative correlation) or not significant (no correlation); while if the coefficient is positive and significant (positive correlation), diversification benefits are not found.

Discussion
The purpose of the given study was to identify portfolio diversification benefits that exist among the BRICS-P economies.To serve the purpose, monthly data of the stock returns of the given economies, i.e., Brazil, Russia, India, China, South Africa and Pakistan were used for the period November 2003 to October 2016.We used ARDL approach for testing the long run relationships among these economies.To test the short run co-integration dynamics, Error Correction specification is used.The rationale of using these techniques is that these methods can be used for predictive purposes and, are more useful methods instead of the traditional methodology that utilizes a static covariance matrix to find an efficient frontier at a given point of time.
The results of the long run analysis provided the evidence that there exist substantial portfolio diversification benefits among all BRICS-P states namely, Brazil, Russia, China, India, South Africa and Pakistan.All of these results are in line with a number of past studies, such as, (Sharma & Bodla, 2011), who found that portfolio diversification benefits exist among emerging markets.The findings of Zonouzi et al. (2014) that with the given level of risk, the economies of the emerging markets can assure a greater rate of return also lend support to our findings.Li et al. (2003) was also of the view that although the integration of the global equity markets has reduced the diversification benefits, however, they have not finished off completely.In the same vein, Sukumaran et al. (2015) also showed that the difference in the economic structures between developed and less developed markets makes these markets attractive place for portfolio diversification.
We also used US S&P500 to represent the major global stock returns and checked the dependence of BRICS stock returns on S&P 500.The results showed that the stock returns of BRICS-P countries are not dependent on the global stock return nor in the short run, neither in the long run.Russia was the only country which is found to be affected by the global stock returns both in short and long run.The reason of such kind of relationship between the BRICS-P and global funds could be the existence of asymmetric dependence structure in these markets as explained by (Mensi et al., 2014).Because of this asymmetric dependence structure, the funds of BRICS-P economies do not get affected due to any stress or turmoil occurring in the global financial market and hence, the investors of these economies can reap diversification by diversifying their portfolio using the global funds.
The existence of diversification benefits between Pakistan and India is another important implication of the study.The investors of both countries can reap potential benefits if they invest in either fund, both in the short and long run.It is an important conclusion and it should be taken into account by the investors as well as the economic policy makers and governments officials of both the countries.To realize the untapped advantage of portfolio diversification between these countries, there is a need for addressing several impediments.The financial policies should be designed in such a way that helps the investors of both of these countries in merging their portfolios.

Table 4 .
1 shows the descriptive statistics of the dataset used.From the given table, it can be seen that Russian Stock market, with a minimum value of -0.540 and a maximum of 0.654, shows the highest volatility as its standard deviation is the highest among all the markets with a value of 0.033 and the lowest volatile market is Pakistan with the standard deviation of 0.013 among BRICS-P countries, a minimum value of -0.060 and a maximum value of 0.083.In a similar way, Brazilian funds took a minimum value of -0.121 and the maximum value of 0.137 where as the standard deviation is 0.018.The minimum value of India is -0.118, and the maximum value is 0.160, and standard deviation is 0.015.The minimum value of China is -0.093, and the maximum value is 0.090, and standard deviation is 0.017.The minimum value of South Africa is -0.721 and the maximum value is 0.206, and the standard deviation is 0.026.

Table 4 .3
Summary of benefits of diversification based on ARDL models