I
University of Amsterdam
International Diversification After the Crisis:
Evidence from Mean-Variance Spanning Test
Master Thesis
Master in International Finance, Amsterdam Business School
Qimin Zhang
Student Number: 11389850
Supervisor: Philippe Versijp
II
ABSTRACT
The objective of this paper is twofold. First, it examines the benefits of international diversification to emerging markets for investors from developed countries. Monthly return data for three broad developed equity market indices and twenty-two emerging equity market indices (five in Latin American, eight in EMEA and nine in Asia) are analyzed using mean-variance spanning test. The emerging equity indices are also organized according to their geographical regions to test the cross-section of the diversification benefits. Moreover, the step-down test proposed by Ken and Zhou (2008) is applied to identify the source of rejection of the spanning hypothesis. Second, this paper investigates the effect of the 2008 financial crisis on international diversification benefits. To accomplish this, the analysis covers two sample periods before and after the crisis. The empirical results show that for both periods investors can gain diversification benefits by adding emerging market indices to their portfolios, while the benefits vary by regions and mainly come from the improvement in the global minimum-variance portfolio rather than the tangency portfolio. The differences between the pre- and post-crisis results show that global equity markets become more integrated after the crisis, driving down the benefits of international diversification.
III
Table of Contents
CHAPTER 1. Introduction ... 1
1.1 Research Background and Motivation ... 1
1.2. Research Question ... 2
1.3. Structure ... 3
CHAPTER 2. Literature Review ... 3
2.1. Portfolio Optimization Theory ... 3
2.2. International Diversification ... 4
2.3. Emerging Market Diversification ... 5
2.4. Mean-Variance Spanning Test ... 6
CHAPTER 3. Methodology ... 7
3.1. Mean-Variance Spanning ... 8
3.2. Step-Down Test ... 9
3.3. Measurement of Diversification Benefits ... 10
CHAPTER 4. Description of the Data ... 11
CHAPTER 5. Standard Correlation Coefficient Analysis ... 15
5.1. Change in The Efficient
Frontiersof Benchmark Assets Pre- and Post-Crisis ... 15
5.2. Diversification Benefits Between Developed Markets and Latin American Emerging
Markets ... 17
5.3. Diversification Benefits Between Developed Markets and EMEA Emerging Markets ... 21
5.4. Diversification Benefits Between Developed Markets and Asian Emerging Markets ... 25
5.5. Diversification Benefits Between Developed Markets and Emerging Markets ... 29
IV
5.5.2. Cross-Section of Diversification Benefits Between Developed and Emerging Markets
... 30
CHAPTER 6. Empirical Results from The Test for Spanning ... 33
6.1. Spanning Test for Developed Markets and Latin American Emerging Markets ... 33
6.2. Spanning Test for Developed Markets and EMEA Emerging Markets ... 36
6.3. Spanning Test for Developed Markets and Asian Emerging Markets ... 39
6.4. Spanning Test for Developed Markets and All Emerging Markets ... 42
6.5. Economic Gains for International Diversification ... 44
CHAPTER 7. Conclusion ... 45
REFERENCE ... 48
APPENDIX A. Power of Step-Down Test of Spanning ... 52
1
CHAPTER 1. Introduction
1.1 Research Background and Motivation
International diversification benefits, especially from exposure to emerging equity markets, have attracted enormous attention from individual and institutional investors from the developed countries. Jorion and Miller (1997) describe two main characteristics of emerging markets that attract investors. First, the high growth of these economies yields higher average equity returns. Second, their low correlations with developed markets lead to a reduction in portfolio risk. Empirical studies done by DeSantis (1994), Divecha et al. (1992), Harvey (1995), and other authors reveal substantial evidence of diversification benefits from investing in emerging equity market indices. There are other findings in the literature showing that the cross-country correlations rise during crises when diversification benefits are most needed (Le, 1991; Forbes & Rigobon, 1999; Hyde, Bredin & Nguyen, 2007). However, the surged correlations do not last long. They decrease when economies recover from the crises and therefore the possibility of diversification rises again. Harvey and Viskanta (1994) find that correlations between countries are highest when countries are in recession and lowest when in expansion. Hyde, Bredin & Nguyen (2007) observe that from 1991 to 2006, though correlations have generally increased over time due to increasing financial integration, they were higher between crisis-hit Asian-Pacific markets during the Asian financial crisis and peaked between these markets and the EU/US markets during the 2000-2003 bear market. Some literature even shows that economic gains from international equity diversification are substantial even during the crisis time despite the growing market correlations (Bouslama & Ouda, 2014; Vermeulen, 2011). Forbes & Rigobon (1999) argue that the standard correlation analysis leads to upward biased results during a period of crisis since the correlation coefficients are upward biased. They find that tests based on the adjusted correlation coefficients show no contagion across markets. This paper contributes to the above academic discussions by applying a mean-variance spanning method to analyze international diversification benefits during pre- and post-crisis periods.
More importantly, there are some unprecedented phenomena caused by the subprime crisis in 2007. The most outstanding example is the unconventional monetary policy, named Quantitative Easing, adopted by the major developed economies (e.g., U.S., U.K., EU and Japan) with the aim to boost
2 investment and stimulate growth after the crisis. It led massive capital flows into the emerging markets from the developed world, which is unprecedented. A research performed by De Nederlandsche Bank (Vermeulen, 2011) on international equity investors' foreign portfolios before and during the financial crisis for 22 sources and 42 destination countries proves statistically that during the crisis investors have larger positions in foreign stock markets which are relatively less correlated with the domestic market, and this relationship is not present before the crisis. However, it leaves an interesting question that whether the increasing weights of emerging markets in the portfolio of international investors reduce the diversification benefits in the post-crisis period given the higher integration between emerging and developed markets. So far very little finance literature can be found on this topic. The aim of this paper is, therefore, trying to shed some light on this topic by investigating the international diversification benefits before and after the subprime crisis through a mean-variance spanning approach.
1.2. Research Question
As discussed above, this thesis uses mean-variance spanning test to find whether there are benefits to diversification between emerging and developed stock markets and applies different measures to assess the extent of diversification gains in periods before and after the financial crisis. In addition to testing the overall diversification benefits between the two groups of markets, the cross-section of diversification benefits is also tested in this paper by testing mean-variance spanning between the benchmark assets and the test assets in each region (Americas, EMEA and Asia) in both pre- and post-crisis periods. Then the differences between the two periods are used as a proxy for effect of the post-crisis on international diversification possibilities. By doing each step of the research, we are going to answer the following questions:
1. Did the emerging stock markets provide diversification benefits to the developed stock markets
before the financial crisis? If so what was the main driver of such diversification?
2. Do the emerging stock markets provide diversification benefits to the developed stock markets
after the financial crisis? If so, what is the main driver of such diversification?
3
1.3. Structure
The remaining part of this thesis is structured as follows. Chapter 2 provides a brief Literature Review on International Diversification and mean-variance spanning tests. Chapter 3 describes the sources used to obtain the data and provides a summary of the descriptive statistics on monthly index returns. Chapter 4 explains the methodology of the thesis. Chapter 5 shows the results of the traditional mean-variance optimization analysis. Chapter 6 gives the empirical results on the gains of diversification into the emerging markets for investors holding a portfolio of developed equity market indices and they are compared with the results from the traditional mean-variance optimization analysis. Lastly, Chapter 7 concludes the main findings of the thesis and gives answers to the research questions.
CHAPTER 2. Literature Review
2.1. Portfolio Optimization Theory
The objective of portfolio diversification is to improve the risk-return trade-off for investors. Markowitz (1952) firstly introduces the Modern Portfolio Theory (MPT), which provides a mathematical framework to resolve the portfolio optimization problem based on a risk-return relationship. It reveals that an asset's risk and return should not be assessed by how it contributes to a portfolio's overall risk and return, not by itself.
According to the MPT, it is possible to construct an ‘efficient frontier’ of optimal portfolios which maximize the expected return for a desired level of risk, defined as variance (standard deviation). Based on the Expected Return-Variance (E-V) rule proposed by Markowitz, only the portfolios located on the efficient frontier should be chosen by investors since those portfolios represent the optimal combinations of all the risky assets. The idea behind the optimal portfolio can be described in two ways: the portfolio with the highest expected return for a given level of risk, or the portfolio with the lowest risk for a given level of expected return. While the two statements are equivalent as they both lead to a
4 higher mean-variance efficiency. Thus, the efficient frontier is compromised out of a series of points of which each represents a distinct capital allocation among the assets. Each allocation produces a particular return for a particular level of risk (Abidin et al., 2004).
The three components going into constructing an optimal portfolio are the mean return of assets, the standard deviation of returns and the correlation coefficient of the pair of assets. Thus it is very important in estimating the correlations in order to obtain optimal portfolio weights to achieve the highest risk-return trade-off. One of the main constraints of many MPT based portfolio optimization models is that they assume constant correlations, e.g., Bollerslev (1990) tries to simplify the conditional correlation matrix by assuming the correlations constant. However, following studies show correlations in equity returns change over business cycles (Erb, Harvey & Viskanta, 1994; Longin & Solnik, 1995). Moreover, the cross-country correlations usually rise during a period of crisis (Le, 1991; Forbes & Rigobon, 1999; Hyde, Bredin & Nguyen, 2007). The more recent study by Solnik and Mcleavey (2009) shows that while the integration of financial markets provides more opportunities for foreign investors, it increases the correlation among those markets. If the correlations were changing over time, the assumption of the models is miss-specified.
2.2. International Diversification
International diversification is a more enhanced approach towards portfolio optimization, which entails foreign investments. The benefits of international diversification have been well documented in the academic literature. Grubel (1968) finds that U.S. investors could achieve higher risk-return trade-off by investing part of their portfolios in foreign stock markets. He identifies the countries with low correlation with U.S. and shows that the mean-variance efficient portfolios created with those courtiers could offer higher return with the same risk, or the same return with lower risk compared with the U.S. only portfolio. Levy and Sarnat (1970) make an analysis on international correlations across 28 countries for the 1951-1967 period, and conclude that diversification benefits exist between the developed and developing equity markets. Solnik (1974) shows that inclusion of international assets to a domestic portfolio can achieve a great reduction of the total portfolio risk. Moreover, Solnik and Odier (1993) demonstrate that constructing such a portfolio implies that the efficient frontier will be more to the left
5 compared to a portfolio without international diversification. In this thesis, we use the same approach to illustrate the gains from international diversification.
However, the works mentioned above use unconditional variances and correlations. The more recent literature on international diversification starts taking the changing correlation into consideration. De Santis and Gerard (1997) find that international diversification provides persistent long-term gains, even though it is not able to protect U.S. investors from short-term market declines due to the contagious effect of U.S. market. Gupta and Donleavy (2009) use Asymmetric Dynamic Conditional Correlations Model to analyze the benefits of international diversification from an Australian investor’s perspective and conclude that the risk-return trade-off increases significantly after investing part of the Australia only portfolio in the foreign equity market, showing that there are still gains to be obtained by international diversification. In general, despite that correlation between markets changes over time, it remains low in the sense of still leaving sufficient room for diversification (Solnik &Odier, 1993; Abidin et al., 2004; Solnik & Mcleavey, 2009).
Furthermore, there are also studies which examine the effect of the crisis on international diversification benefits. By comparing domestic and international portfolios for several periods of pre-, during- and post-crisis over a 17-year sample, Abidin et al. (2004) find that in general the international portfolios performed better than the domestic ones from a Malaysian investor’s perspective, but this is not always the case. In some sub-periods, especially during the crisis, the domestic portfolios showed better performances. Studies conducted by Bouslama and Ouda (2014) and Vermeulen (2011) show that despite the rising correlations across markets during the crisis time, investors can still benefit from international diversification. A more recent study of Syamala and Wadhwa (2016) investigates the co-movement of various world market stock indices before and after the 2008 financial crisis in order to analyze the potential gains from international diversification for India investors. The results suggest that the dynamics of the world market indices have been changed by the crisis as they are no longer moving together in the way before the crisis. Consequentially, the optimal country allocations also change after the crisis.
6 The argument supporting emerging market diversification is developed by Divecha, Drach and Stefek 1992; Wilcox, 1992; Speidell and Sappenfield, 1992). The emerging markets differ from the more developed markets in terms of a number of financial, economic and structural characteristics. Gupta (2006) summarizes the key characteristics identified in the literature of relevance to international diversification: Institutional Infrastructure, Market Regulation, Liquidity, Market activity, Market size and Market Pricing. The differences between emerging and developed markets are expected to lead to gains to investors with emerging market exposures. However, those gains are also dependent on the degree of market integration. Many studies focusing on the attractiveness of emerging markets in international diversification are motivated by the fact that emerging markets have lower correlations with developed markets than the developed markets themselves (Speidell & Sappenfield, 1992; Kohers et al., 1998; Harvey, 1995; Lagoarde-Segot and Lucey, 2007; Gupta and Donleavy, 2009). However, the growing financial integration of emerging markets has put their attractiveness in check. On the one hand, Li et al. (2003) show that even as the world equity markets become more integrated, it does not eliminate the diversification benefits of investment in emerging markets. Fadhlaoui et al. (2009) find that the degree of financial integration increases in the long run for seven developed equity markets countries (United States, Canada, United Kingdom, France, Germany, Italy, and Japan) and three Central European emerging markets (Czech Republic, Hungary and Poland), but it does not seem to affect the benefits of international diversification in these emerging markets. But on the other hand, some studies highlight a decrease of diversification benefits of emerging markets. Bordo (2003) show that the positive effect of financial markets liberalization in emerging countries seems to disappear due to the series of crises that occurred in Asia and Latin America. Garza-Gómez and Metghalchi (2006) find that the benefits of investing in emerging markets to U.S. investors during the period from 1988 to 2003 are small. Moreover, the study by Christoffersen et al. (2012) documents that though adding emerging markets to a portfolio still has larger diversification benefits than adding additional developed markets, those benefits are getting smaller in an absolute sense. Thus, there is an ongoing debate on the pertinence of emerging markets in international diversification.
2.4. Mean-Variance Spanning Test
The mean-variance spanning test is first introduced by Huberman and Kandel (1987) as a statistical tool to analyze whether adding a ‘new’ set of risky assets allows investors to improve the efficient frontier derived from a given set of risky assets. It is a regression-based test of the hypothesis that adding the
7 ‘new’ risky assets does not enlarge the efficient frontier, referred as ‘spanning’. The study of Huberman and Kandel (1987) has received considerable attention in the literature thus many applications and various extensions have been generated. Harvey (1995) investigates 20 emerging equity markets and shows that the emerging market returns are not spanned by the developed market returns. For five out of the nine emerging markets that they study, the spanning tests conducted by Errunza et al. (1999) find evidence suggests that direct investment in the emerging markets provide significant diversification benefits beyond the mimicking portfolios created from U.S. traded securities which are highly correlated with the IFC indices of those markets. Gerard et al. (2002) use the mean-variance spanning test to investigate the effects of industrial structure and country factors on the efficiency of international diversification strategies. They find that country-specific factors rather than industrial structure are the main drivers of international diversification benefits. De Roon et al. (2001) extends the spanning test to consider transaction costs and short-selling constraints. Their study shows that adding emerging markets to a U.S. investor’s portfolio results in significant diversification benefits when the transaction costs are small or there is no constraint on short sales, but they disappear after short-selling constraints are imposed or transaction costs rise. Driessen and Laeven (2007) argue that low benefits for a U.S. investor are not a surprise since the U.S. has one of the most developed financial markets and the most diversified economies. They apply the same empirical framework with De Roon et al. (2001) in fifty-two countries and find that the spanning tests reject the hypotheses for all the countries with an absence of constraints. When the short selling constraint is imposed, eighteen out of fifty-two countries do not show strong evidence of diversification benefits for mostly the developed markets and the rest countries exhibit a decline in the significance of their diversification benefits. Kan & Zhou (2008) develop a new step-down spanning test that helps to identify the origin of the rejection of the spanning hypothesis. We will discuss more about this in the methodology section.
CHAPTER 3. Methodology
This section introduces the mean-variance spanning test, which was firstly introduced by Huberman and Kandel (1987), and how it is applied to examine the diversification possibility between developed and emerging markets before and after the financial crisis in 2008. The measurements of diversification benefits used in this thesis are also presented.
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3.1. Mean-Variance Spanning
The concept of mean-variance spanning is straightforward. If the mean-variance frontier of a set of K (K ≥ 2)1 risky assets does not shift after adding another N risky assets, we say the portfolio of the K assets
spans the larger portfolio of N+K assets. In another word, there are no diversification benefits. Usually, we call the first set of K risky assets as the benchmark assets and the second set of N risky assets as the test assets.
De Roon & Nijman (2001) and Kan & Zhou (2008) have provided detailed discussions on various approaches used for testing for mean-variance spanning. In this paper, we use the regression-based approach introduced by Huberman and Kandel (1987) to test our hypotheses. let
𝑅𝑅
1𝑡𝑡 and 𝑅𝑅2𝑡𝑡 denotethe vectors of returns of K benchmark assets and N test assets, respectively. Then 𝑅𝑅𝑡𝑡= [𝑅𝑅1𝑡𝑡′ 𝑅𝑅2𝑡𝑡′ ] is
the raw returns on N+K risky assets at time t.
Define the expected returns on N+K risky assets as
𝜇𝜇 = 𝐸𝐸[
𝑅𝑅
𝑡𝑡]≡
�𝜇𝜇𝜇𝜇12�, and the covariance matrix of the N+K assets as 𝑉𝑉
= 𝑉𝑉𝑉𝑉𝑉𝑉[𝑅𝑅
𝑡𝑡] ≡ �𝑉𝑉
𝑉𝑉
11𝑉𝑉
12 21𝑉𝑉
22�.
We estimate the regression of the returns of the N test assets on the returns of the K benchmark assets:
𝑅𝑅
2𝑡𝑡= 𝛼𝛼 + 𝛽𝛽𝑅𝑅
1𝑡𝑡+ 𝜖𝜖
𝑡𝑡With 𝐸𝐸[𝜖𝜖𝑡𝑡] = 0𝑁𝑁 and 𝐸𝐸[𝜖𝜖𝑡𝑡𝑅𝑅𝑡𝑡] = 0𝑁𝑁×𝐾𝐾 to obtain consistent estimates of 𝛼𝛼, an N dimensional vector of
intercepts, and 𝛽𝛽, a N × K dimensional matrix of slope coefficients. Define δ = 1𝑁𝑁− 𝛽𝛽1𝐾𝐾 where 1𝑁𝑁 is
an N dimensional vector only containing ones. Then to prove the null hypothesis of spanning is true (there is no diversification benefit), α and δ must satisfy the following restrictions:
𝐻𝐻0: 𝛼𝛼 = 0𝑁𝑁, 𝛿𝛿 = 0𝑁𝑁
𝛼𝛼 = 0𝑁𝑁 tests whether the weights of the N test assets in the tangency portfolio based on the N+K assets
are zero, and 𝛿𝛿 = 0𝑁𝑁 tests whether the weights of the N test assets are zero in the global minimum
variance portfolio (GMV). Therefore, when both 𝛼𝛼 and 𝛿𝛿 equal to zero, we can observe that the return of each test asset can be written as the return of a portfolio of benchmark assets plus the return of an
1 Huberman and Kandel (1987) do not specify the constraints on K, but K ≥ 2 is an implicit condition for mean-variance spanning test. in the paper of Gungor and Luger (2013) this condition is explicitly stated.
9 orthogonal error term with zero expectation. In another word, adding the test assets can only increase the variance of the efficient portfolios of the benchmark assets with a given expected return.
Kan & Zhou (2008) have compared three multivariate tests of mean-variance spanning, which are the Likelihood Ratio test (LR test), the Wald test and the Lagrange Multiplier test (LM test). in finite samples, the three tests must have the following relation:
Wald ≥ LR ≥ LM
Thus, if LM test rejects the null hypothesis, the other two tests also must reject. If Wald test cannot reject the null, the other two tests also must not reject. In another word, LM favors acceptance while Wald favors rejection. In this paper, we test the hypothesis using all the three tests.
3.2. Step-Down Test
The three tests of spanning discussed in the previous section are joint tests of
𝛼𝛼 = 0
𝑁𝑁and 𝛿𝛿 = 0
𝑁𝑁,
thus they
cannot distinguish whether the significance of the test is mostly contributed by the change of the global minimum variance portfolio (GMV) or by the change of the tangency portfolio on the mean-variance frontier. In fact, the distance between the global minimum-mean-variance portfolios of the K benchmark assets and the N+K assets has the determinant influence on the results of the three spanning tests comparing to the distance between the two tangency portfolios (Kan & Zhou, 2008). This is because the spanning tests inevitably place heavy weights on the estimates 𝛼𝛼� and little weight on the estimates 𝛿𝛿̂. Consequentially, a small difference between the two GMVs, which is not necessarily economically important, could easily become statistically significant, while a significant difference between the two tangency portfolios, which is of great economic importance, is difficult to detect statistically.To mitigate the problem, Kan & Zhou (2008) propose a step-down test to examine the two components of the spanning hypothesis (𝛼𝛼 = 0𝑁𝑁 an 𝛿𝛿 = 0𝑁𝑁d) individually instead of jointly. According to their
procedure, we first test 𝛼𝛼 = 0𝑁𝑁
,
and then test 𝛿𝛿 = 0𝑁𝑁 but conditional on the constraint 𝛼𝛼 = 0𝑁𝑁. Bothtests are similar to the GRS F-test. The spanning hypothesis can only be accepted when both tests are accepted.
10 There are two main advantages of the step-down test. One is that it allows us to identify whether the rejection is caused by the improvement in GMV portfolios, in tangency portfolios or both. To be more precise,
𝛼𝛼 = 0
𝑁𝑁test the significance of the reduction in the variance of the GMV portfolio and 𝛿𝛿 =0𝑁𝑁test the significance of the increase in the Sharpe ratio of the tangency portfolio. The second is that it
allows us to adjust the significance levels to the two tests respectively based on their relative economic importance.
However, though the step-down test can reveal more information on the source of rejection and thus take into account the economic significance of the departure from the spanning hypothesis, it still faces the challenge of different power in rejecting the hypothesis of two components. As examined by Kan & Zhou (2008), when assigning the same level of significance to the first and the second test, the spanning test can only reject spanning for a test asset that doubles the slope of the asymptote to the efficient frontier of the benchmark assets with probability less than 20%. In contrast, the probability to reject spanning for a test asset that reduces the standard deviation of the GMV portfolio of the benchmark assets by 0.003 per month is more than 80%. A table presenting the probabilities of rejection of step-down test for those two cases is provided in the Appendix A.
3.3. Measurement of Diversification Benefits
In this paper, we are not only going to test for the existence of diversification benefits between the developed and the emerging stock markets, but also need to compare the diversification benefits in periods before and after the crisis to see whether those has increased or not. Therefore we must assess the extent of diversification gains.
Petrella (2005) describes three measures for diversification benefits. The first measure is the gain in expected returns obtained by “moving from an efficient portfolio made of only K benchmark assets to an efficient portfolio derived from N+K assets, with both efficient portfolios having the same variance” (Petrella, 2005). It means that in this paper the diversification benefits of incorporating emerging stock markets can be expressed in terms of return increments over portfolios with the same level of risk that only include developed stock markets.
11 The second measure is the reduction in portfolio risk. Assuming that some investors are only interested in the efficient portfolio with minimum risk and do not care about the expected return, the diversification benefits then can be measured by the difference between the standard deviations of the GMV portfolio computed for the benchmark assets and the GMV portfolio computed for the benchmark and the test assets.
The third way to measure the diversification benefits is to compute the Sharpe ratio. According to the modern portfolio theory (Markowitz, 1952), where there exists a risk-free asset without any constraint on lending and borrowing at the risk-free rate, investors who care only about the mean and variance of their portfolios will always choose to invest in the tangency portfolio of the risky assets. Therefore, in this case, the magnitude of diversification benefit is assessed by computing the change in Sharpe ratios of the tangency portfolios of the K benchmark assets and the N+K assets.
Given the economic meaning of the step-down test and the interests of rational investors which is either in the GMV portfolio or the tangency portfolio, in this paper, we apply the second and third ways to measure the diversification benefits. After quantifying the gains obtained by adding the same test assets to the same set of benchmark assets but in two different periods (pre- and post-crisis), we can compare those gains to see whether the crisis has significantly increased international diversification possibility or not.
CHAPTER 4. Description of the Data
In order to investigate the benefits of international diversification to emerging markets for investors in developed countries and how those benefits have been changed by the 2008 financial crisis, we take two eight-year samples of monthly data. The first one is from May 1999, when the Asian crisis has ended, to May 2007, when the subprime crisis has not erupted (95 observations). The second is from March 2009 to March 2017, which represent the post-crisis period up to the most recent available observations (95 observations). The period in between of those two, from June 2007 to February 2009, is defined as the crisis time (Eptas & Leger, 2010). Data during the crisis period is not included in our dataset due to the relations between the developed and emerging markets during that time were distorted and not persistent.
12 22 out of total 24 emerging market indices included in the Morgan Stanley Capital International (MSCI) Emerging Market Index (Figure 1) are used as the test assets, which consist of five Latin American countries, six European, two African and nine Asian countries. Indices of Qatar and the United Arab Emirates, which are also included in the MSCI Emerging Market Index, are excluded from our dataset since available monthly observations on those two countries are incompatible with our sample periods (data only available after May 2005). The index captures large and mid-cap representation and covers approximately 85% of the free float-adjusted market capitalization in each country and with 839 constituents it covers approximately 85% of the free float-adjusted market capitalization in each country. The Indices for the Americas, Europe, and Pacific region in the MSCI Developed Market Index serve as the benchmark assets (Figure 1), which captures large and mid-cap representation across 23 Developed Markets (DM) countries. With 1,652 constituents, the index covers approximately 85% of the free float-adjusted market capitalization in each country. The dataset is similar to the ones used by Harvey (1995) and De Room et al. (2001), except that we use MSCI Americas, which includes U.S. and Canada, instead of U.S. alone, replace Japan with the MSCI Pacific index, modify and expand slightly the sample of emerging markets. For all these indices we use unhedged monthly holding returns in U.S. dollars. The indices for both the emerging markets and the developed markets are calculated with dividends reinvested. In addition, to test the cross-section of diversification benefits, the emerging markets are also organized according to their geographical regions: Americas, EMEA and Asia. All data are obtained from the MSCI database.
13 Noticeably, to estimate the tangency portfolio and the Sharpe ratio we need the risk-free rate data. In this paper the monthly risk-free rate is assumed to be zero. This is because, as argued by Jorion (1985) and Petrella (2005), the zero risk-free rate assumption with monthly returns reduces the effects of the estimation risk in the mean-variance optimization2.
Some basic summary statistics for monthly returns are given in table 1. Table 1 provides mean returns and standard deviations for the three benchmark indices as well as for the emerging markets. Table 2 shows mean returns and standard deviations of each sample group on an equally weighted base.
Table 1: Descriptive Statistics for Benchmark Indices and Emerging Markets
Panel A: Benchmark Assets
Pre-crisis
May 1999 to May 2007 March 2009 to March 2017 Post-crisis Mean (%) ST. Dev. (%) Mean (%) ST. Dev. (%)
NORTH AMERICA 0.15 4.16 1.10 3.75
2 Petrella (2005) argues that" In the optimisation process, the monthly risk-free rate is assumed to be zero. It is well known that mean-variance optimisation suffers from two main problems: poor out-of-sample performance of the optimal portfolio, and instability of the optimal portfolio's weights. Both issues pertain to the general question of the estimation risk in the practical application of mean-variance optimisation. With a positive risk-free rate, the optimal portfolio would have an even higher return per unit of risk than when assuming a zero rate of interest, and any undesirable characteristic of the tangency portfolio would be accentuated. Thus, as Jorion (1985) points out, the zero risk-free rate assumption with monthly returns reduces the effects of the estimation risk."
14
EUROPE 0.52 4.56 0.51 5.35
PACIFIC 0.44 4.63 0.58 4.27
Panel B: Emerging Markets
Pre-crisisMay 1999 to May 2007 March 2009 to March 2017 Post-crisis Mean (%) ST. Dev. (%) Mean (%) ST. Dev. (%) Latin America Brazil 1.46 10.81 0.05 9.23 Chile 1.07 5.79 0.20 6.12 Colombia 1.85 9.61 0.36 7.66 Mexico 1.47 6.87 0.57 5.80 Peru 1.79 7.15 0.59 7.34 EMEA Czech Republic 2.16 7.43 -0.45 6.91 Egypt 1.76 9.29 0.19 9.64 Greece 0.28 7.76 -2.74 13.74 Hungary 1.43 8.47 0.69 10.05 Poland 1.17 9.19 0.32 8.38 Russia 2.35 11.57 0.31 9.15 South Africa 1.33 7.35 0.52 6.51 Turkey 1.03 16.99 0.39 9.15 Asia China 0.49 8.64 0.47 6.25 India 1.46 7.92 0.80 7.49 Indonesia 1.05 11.42 1.02 7.19 Korea 1.22 9.38 0.84 6.41 Malaysia 0.95 6.07 0.42 4.86 Pakistan 1.45 10.18 0.91 5.90 Philippines -0.10 7.72 1.13 5.85 Taiwan 0.00 8.46 0.76 5.54 Thailand 0.51 10.03 1.17 6.40
Table 2: Descriptive Statistics for Country Groupings
Pre-crisis
May 1999 to May 2007 March 2009 to March 2017 Post-crisis Mean (%) ST. Dev. (%) Mean (%) ST. Dev. (%)
Developed 0.37 4.45 0.73 4.46
Emerging 1.19 9.00 0.39 7.53
15
EMEA 1.44 9.76 -0.10 9.19
Asia 0.78 8.87 0.84 6.21
CHAPTER 5. Standard Correlation Coefficient Analysis
In this chapter, we adopt a standard Markowitz inspired mean-variance optimization approach to analyze the diversification benefits between developed and emerging markets as well as their differences in the pre- and post-crisis periods. In total five portfolios are constructed to estimate the diversification benefits between those markets. The first portfolio only contains the three developed market indices thus serves as the benchmark portfolio. The second portfolio includes all the developed and emerging market indices. The overall diversification benefits between developed and emerging markets are obtained by comparing the optimal mean-variance performance of the two portfolios. The other three portfolios consist of the benchmark indices and indices of the emerging markets in one of the Latin America, EMEA and Asia group. Analyzing those three portfolios provides us some insights into the diversification benefits depend cross-sectionally on characteristics of the underlying markets. Differences in the optimized performance of each portfolio during the pre- and post-crisis periods reflect the effect of the crisis on global diversification possibilities.
5.1. Change in The Efficient Frontiers of Benchmark Assets Pre- and Post-Crisis
The unconditional correlations among the benchmark indices in pre- and post-crisis period are shown in table 3 and table 4, respectively. We can see that before the crisis the North America and Europe has a high correlation with 0.825. The correlation even becomes higher in the post-crisis period, reaching at 0.879. The Pacific exhibits relatively low pre-crisis correlations with the North America and the Europe, with correlation 0.581 and 0.558, respectively. While in the post-crisis period, the correlations of the Pacific with the other two markets rise sharply to 0.796 and 0.832, indicating that the whole developed markets become more integrated due to the effect of the crisis.
16 North America Europe Pacific
North America 1.000
Europe 0.825 1.000
Pacific 0.581 0.558 1.000
Table 4: Post-crisis correlation between three benchmark indices
North America Europe Pacific North America 1.000
Europe 0.879 1.000
Pacific 0.796 0.832 1.000
In order to see how the changes in the mean returns, standard deviations and correlations of the indices move the efficient frontier of the benchmark portfolio, we calculate the mean return and standard deviation of the global minimum variance (GMV) portfolio and the tangency portfolio (TP) in both pre- and post-crisis periods. The risk-free rate used to compute the TP is set to be zero. As discussed in Chapter 3, investors are interested either in the efficient portfolio with minimum risk and do not care about the expected return, or in the portfolio that maximizes the risk-adjusted excess return to a given risk-free rate. Therefore, changes in the efficient frontier are measured by the difference between the standard deviations of the GMVs and the Sharpe ratios (SR) of the TPs in both periods.
Table 5: Changes in GMV and TP on the efficient frontier of the benchmark assets
Pre-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
0.29 3.87 1.42 8.54 0.1658
Post-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
1.17 3.56 1.81 4.42 0.4086
Changes
∆R-GMV (%) ∆σ-GMV (%) ∆R-TP (%) ∆σ-TP (%) ∆SR-TP
0.88 -0.31 0.39 -4.12 0.2428
From table 5 we can see that in the post-crisis period the standard deviation of the GMV is 3.56%, decreased by 8% compared to its pre-crisis standard deviation at 3.87%. While the Sharpe ratio is more than doubled after the crisis, rising from 0.1658 to 0.4086. The increase is mostly contributed by the substantial reduction in the standard deviation of the TP, where the mean return only increases by 0.39%
17 compared to its pre-crisis level. The results show that the benchmark portfolio has an overall better mean-variance performance in the post-crisis period.
5.2. Diversification Benefits Between Developed Markets and Latin American Emerging
Markets
In this section, we analyze the diversification benefits between the developed markets and the emerging markets in Latin America. First, we look at the unconditional correlations among the markets. During the pre-crisis period, Brazil and Mexico exhibit the highest correlations with the developed markets, with average correlation 0.647 and 0.646, respectively. The lowest correlations of the developed markets are with Colombia, where the average correlation is 0.216. On the other hand, Europe shows the highest average correlation with all the Latin American markets at 0.528, followed by North America with average correlation at 0.51 and Pacific at 0.403.
Table 6: Pre-crisis correlation between benchmark indices and emerging markets in Latin America
North America Europe Pacific Brazil Chile Colombia Mexico Peru North America 1.000 Europe 0.825 1.000 Pacific 0.581 0.558 1.000 Brazil 0.688 0.755 0.499 1.000 Chile 0.635 0.654 0.472 0.646 1.000 Colombia 0.245 0.254 0.150 0.266 0.319 1.000 Mexico 0.727 0.676 0.537 0.693 0.595 0.361 1.000 Peru 0.254 0.301 0.355 0.526 0.372 0.218 0.444 1.000
During the post-crisis period, we observe that most correlations increase except those of Brazil and Chile with North America and Europe. The most significant change happens in Colombia, whose average correlation with the developed markets surges to 0.478, more than doubled to its pre-crisis level. Moreover, the post-crisis correlations are less divergent than the pre-crisis ones. During the post-crisis period, the average correlations range from 0.735 for Mexico to 0.454 for Peru, while the average pre-crisis correlations range from 0.647 for Brazil to 0.218 for Colombia. The results indicate that the Latin American countries become more integrated with the developed markets after the crisis. In addition, the average correlations of the North America, Europe and Pacific with Latin America all increase as well
18 during the post-crisis period. Noticeably the Pacific shows average correlation at 0.59, which becomes the highest compared to the North America at 0.581 and the Europe at 0.579.
Table 7: Post-crisis correlation between benchmark indices and emerging markets in Latin America
North America Europe Pacific Brazil Chile Colombia Mexico Peru North America 1.000 Europe 0.879 1.000 Pacific 0.796 0.832 1.000 Brazil 0.657 0.653 0.692 1.000 Chile 0.556 0.583 0.610 0.718 1.000 Colombia 0.436 0.504 0.493 0.740 0.646 1.000 Mexico 0.758 0.720 0.727 0.765 0.684 0.609 1.000 Peru 0.498 0.437 0.427 0.681 0.570 0.605 0.581 1.000
To measure how the increased integration affects the diversification benefits, we calculate the mean returns and standard deviations of the GMV and tangency portfolios of the expanded portfolio in both periods. The results in the Panel A of Table 8 show that before the crisis, by adding the Latin American indices into the benchmark portfolio, it reduces the standard deviation of the GMV portfolio by 23% to 2.98%, and improves the Sharpe ratio of the TP from 0.166 to 0.34.
During the post-crisis period, the GMV portfolio of the expanded portfolio has a standard deviation at 3.12%, which is higher than 2.98% before the crisis. While the expected return of the GMV portfolio also rises from 0.27% to 1.17%, resulting in an increase in mean-variance efficiency of the portfolio. However, in this paper, the increase in mean-variance efficiency of the GMV portfolio is less relevant than the volatility since investors who are interested in the GMV portfolio usually do not care about the return. The post-crisis Sharpe ratio of the TP also increases to 0.461. The gain in Sharpe ratio is due to the increase in the expected return as well as the decrease in the volatility. The changes suggest that the same group of assets have a much better performance for their tangency portfolio after the crisis, but their GMV portfolio shows a higher volatility as well, despite the decrease in the volatility of the GMV portfolio of the benchmark assets.
Moreover, the diversification benefits of adding the Latin American indices, as shown in the Panel B, decrease significantly during the post-crisis period. The standard deviation of the GMV portfolio only reduces by 12% and the Sharpe ratio of the TP only increases by 0.052 comparing to the benchmark. The
19 results are consistent with the observation of increased cross-country correlations. Therefore it confirms that the developed markets and the Latin America become more integrated after the crisis so that the diversification benefits between those two groups of markets decrease.
Table 8: Diversification benefits of adding Latin American countries into the benchmark assets
Panel A: Pre-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
Developed 0.29 3.87 1.42 8.54 0.166
Developed &
Latin America 0.27 2.98 3.85 11.32 0.340
∆ -0.02 -0.89 2.43 2.78 0.174
Panel B: Post-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
Developed 1.17 3.56 1.81 4.42 0.409
Developed &
Latin America 1.17 3.12 1.76 3.82 0.461
∆ 0.00 -0.44 -0.05 -0.60 0.052
The changes in the efficient frontiers are visualized in Figure 1 and Figure 2 for the pre- and post-crisis period respectively. The orange frontier is for the developed markets and the blue one is for the developed and Latin American markets. The diversification benefits can be represented by the gap between the two frontiers. The solid and dash lines are the empirical capital market lines depicting the efficient frontiers, with a slope equal to the Sharpe ratio of portfolio P and P’ (the tangency portfolios). The figures also plot the monthly mean return and standard deviation of each index. We can see that before the crisis, all the Latin American markets except Brazil lie outside the frontier formed by the benchmark indices. In the post-crisis period, however, all markets fall into the inner area of the frontier formed by the benchmark indices. Moreover, from the figures we can see that after the crisis the distribution of the indices become less scattered comparing to the case in the pre-crisis period.
20
Figure 2: Post-crisis Portfolio Frontiers by developed and Latin American emerging equity markets using month returns
P P' North America Europe Pacific Brazil Chile Colombia Mexico Peru -4,0% -3,0% -2,0% -1,0% 0,0% 1,0% 2,0% 3,0% 4,0% 5,0% 0,0% 2,0% 4,0% 6,0% 8,0% 10,0% 12,0% PO RT FO LIO R ET UR N STANDARD DEVIATION
Efficient Frontier (1999-2007)
21
5.3. Diversification Benefits Between Developed Markets and EMEA Emerging Markets
In this section, we analyze the diversification benefits between the developed markets and the EMEA markets. Again we first look at the unconditional correlations among the markets. During the pre-crisis period, the average correlations of the EMEA markets with the developed markets range from 0.599 for South Africa to 0.305 for Egypt. Among the developed markets, Europe exhibits the highest average correlation with the EMEA markets at 0.518. The North America and Pacific are correlated with the EMEA markets at a similar level, with average correlations at 0.442 and 0.433, respectively.
Table 9: Pre-crisis correlation between benchmark indices and emerging markets in EMEA
Pre-crisis
North America Europe Pacific Czech Republic 0.302 0.452 0.291 North America Europe Pacific Brazil Chile P P' Colombia Mexico Peru -0,5% 0,0% 0,5% 1,0% 1,5% 2,0% 2,5% 3,0% 0,0% 1,0% 2,0% 3,0% 4,0% 5,0% 6,0% 7,0% 8,0% 9,0% 10,0% PO RT FO LIO R ET UR N STANDARD DEVIATION
Efficient Frontier (2009-2017)
22 Egypt 0.225 0.286 0.405 Greece 0.354 0.606 0.371 Hungary 0.429 0.557 0.345 Poland 0.518 0.616 0.445 Russia 0.586 0.452 0.498 South Africa 0.532 0.596 0.669 Turkey 0.593 0.577 0.440
After the crisis, we see that the correlations between the Pacific and all the EMEA markets increase substantially. For North America and Europe, except their correlations with Turkey slightly decreasing, those with all the other EMEA markets increase as well. Europe still has the highest average correlation with the EMEA at 0.678, while the Pacific becomes the second with average correlation at 0.614. North America has an average correlation at 0.597.
On a country level, the post-crisis average correlations with the developed markets range from 0.729 for Poland to 0.381 for Egypt. The Czech Republic shows the highest increase in its average correlation, rising from 0.348 to 0.629. The rising correlations indicate that the EMEA markets in general become more integrated with the developed markets after the crisis. Noticeably, though most of the correlations with the developed markets increase, the variance of the average correlations becomes larger. This is different with the average correlations between the Latin America and developed markets, where we see a reduction in the divergence.
Table 10: Post-crisis correlation between benchmark indices and emerging markets in EMEA
Post-crisis
North America Europe Pacific Czech Republic 0.605 0.727 0.556 Egypt 0.321 0.395 0.427 Greece 0.649 0.726 0.647 Hungary 0.680 0.792 0.683 Poland 0.717 0.811 0.660 Russia 0.661 0.724 0.672 South Africa 0.667 0.684 0.706 Turkey 0.475 0.567 0.564
The mean returns and standard deviations of the GMV and tangency portfolios formed by the benchmark and EMEA indices in both periods are presented in Table 11. The results in the Panel A show
23 that before the crisis, by adding the EMEA indices into the benchmark portfolio, it reduces the standard deviation of the GMV portfolio by 21% to 3.05% while increasing the expected return of the GMV portfolio to 0.33% from 0.29%. The Sharpe ratio of the TP also rises from 0.166 to 0.386, which is mostly due to the gain in the expected return of the TP.
During the post-crisis period, the GMV portfolio, as shown in the Panel B, has a standard deviation at 3.04%, which is slightly below the pre-crisis level. However, the amount of reduction in the standard deviation compared to the benchmark decrease, which is less than 15%.
The post-crisis Sharpe ratio of the TP increases from 0.409 to 0.544, which represents a much smaller improvement comparing to the improvement of Sharpe ratio during the pre-crisis period. In addition, the standard deviation of the TP also increases comparing to the benchmark, indicating the gain in Sharpe ratio is due to the increase in the expected return. The results suggest that though the expanded portfolio shows a much better overall performance during the post-crisis period (lower volatility of GMV and higher SR of TP), the diversification benefits of adding the EMEA indices diminish substantially in the same period. This is in line with the observation of increased cross-country correlations and confirms the rising integration across the developed and EMEA markets in the post-crisis period.
Table 11: Diversification benefits of adding EMEA countries into the benchmark assets
Panel A: Pre-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
Developed 0.29 3.87 1.42 8.54 0.166
Developed & EMEA 0.33 3.05 4.15 10.75 0.386
∆ 0.04 -0.82 2.73 2.21 0.220
Panel B: Post-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
Developed 1.17 3.56 1.81 4.42 0.409
Developed & EMEA 1.08 3.04 2.53 4.65 0.544
∆ -0.09 -0.52 0.72 0.23 0.135
Figure 3 and Figure 4 plot the efficient frontiers of the benchmark portfolio and the expanded portfolio in the pre- and post-crisis period respectively. The orange frontier is for the developed markets and the blue one is for the developed and EMEA markets. The solid and dash lines are the empirical capital market lines with a slope equal to the Sharpe ratio of portfolio P and P’ (the tangency portfolios). The figures also plot the monthly mean return and standard deviation of each index in the portfolio.
24 Noticeably that during the pre-crisis period, Russia, the Czech Republic, Egypt and South Africa lie above the frontier formed by the benchmark indices. However, during the post-crisis period, all those countries fall below the upper bound of the frontier, with the Czech Republic and Greece even falling outside the lower bound of the frontier due to their substantial negative returns. In addition, here we also observe the same pattern as the case in the previous section that the distribution of the indices become more concentrated during the post-crisis period.
Figure 3: Pre-crisis Portfolio Frontiers by developed and EMEA emerging equity markets using month returns
Figure 4: Post-crisis Portfolio Frontiers by developed and EMEA emerging equity markets using month returns
North America Europe Pacific P P' Czech Republic Egypt Greece Hungary Poland Russia
South Africa Turkey
-3,0% -2,0% -1,0% 0,0% 1,0% 2,0% 3,0% 4,0% 5,0% 0,0% 2,0% 4,0% 6,0% 8,0% 10,0% 12,0% 14,0% 16,0% 18,0% PO RT FO LIO R ET UR N STANDARD DEVIATION
Efficient frontier (2009-2017)
25
5.4. Diversification Benefits Between Developed Markets and Asian Emerging Markets
In this section, we analyze the diversification benefits between the developed markets and the Asian markets. Table 12 and Table 13 present the unconditional correlations among the markets in both periods respectively. Before the crisis, the average correlations of individual Asian markets with the developed markets range from 0.579 for South Korea to 0.167 for Pakistan. Among the developed markets, North America instead of the Pacific shows the highest average correlation with the Asian markets at 0.411. Pacific has the second highest average correlation at 0.383, closely followed by Europe with correlation at 0.366.
Table 12: Pre-crisis correlation between benchmark indices and emerging markets in Asia
Pre-crisis
North America Europe Pacific North America Europe Pacific P P' Czech Republic Egypt Hungary Poland Russia South Africa Turkey
Greece -3,0% -2,0% -1,0% 0,0% 1,0% 2,0% 3,0% 4,0% 0,0% 2,0% 4,0% 6,0% 8,0% 10,0% 12,0% 14,0% PO RT FO LIO R ET UR N STANDARD DEVIATION
Efficient Frontier (2009-2017)
26 China 0.538 0.421 0.457 India 0.368 0.471 0.540 Indonesia 0.353 0.328 0.376 Korea 0.625 0.505 0.607 Malaysia 0.312 0.323 0.158 Pakistan 0.139 0.200 0.162 Philippines 0.345 0.240 0.270 Taiwan 0.516 0.427 0.379 Thailand 0.503 0.379 0.502
In the post-crisis period, we see an increase in all the correlations, indicating all the Asian emerging markets become more integrated with each of the three developed markets. It is also interesting to see that after the crisis the rank of the average correlations of the developed markets with the Asia completely changes, where the Europe and Pacific show nearly the same highest correlations at 0.618 and 0.616 while the North America has a correlation only at 0.597.
On individual Asian country level, Korea still has the highest average correlation with developed markets at 0.72 and Pakistan with the lowest one at 0.416. Malaysia exhibits the highest increase in its average correlation, rising from 0.264 to 0.628. Even the lowest increase, shown by Thailand, is at 0.138. Moreover, despite the overall increase in the correlations, we see that the divergence among the correlations reduces, showing the same pattern as the average correlations between the developed markets and the Latin America.
Table 13: Post-crisis correlation between benchmark indices and emerging markets in Asia
Post-crisis
North America Europe Pacific
China 0.655 0.672 0.706 India 0.609 0.645 0.661 Indonesia 0.521 0.521 0.568 Korea 0.720 0.739 0.701 Malaysia 0.616 0.639 0.628 Pakistan 0.407 0.463 0.379 Philippines 0.547 0.588 0.574 Taiwan 0.725 0.701 0.696 Thailand 0.577 0.593 0.628
27 Table 14 shows the mean returns and standard deviations of the GMV and tangency portfolios formed by the benchmark and Asian indices in both periods. Before the crisis, by adding the Asian indices into the benchmark portfolio, it reduces the standard deviation of the GMV portfolio by 23% to 2.98%. The Sharpe ratio of the TP rises from 0.166 to 0.327, which is mostly due to the gain in the expected return of the TP.
During the post-crisis period, the GMV portfolio of the expanded portfolio has a standard deviation at 3.05%, which is higher than 2.98% before the crisis. The amount of reduction in the standard deviation only represents a 14% decrease compared to the benchmark, which is also lower than the percentage before the crisis.
Unlike the big jump in the pre-crisis Sharpe ratio, the post-crisis Sharpe ratio of the TP is only slightly improved from 0.409 to 0.459. While the gain is from both increase in the expected return and decrease in the volatility. Overall, in the post-crisis period, the benchmark and Asian assets show a better mean-variance performance for their tangency portfolio while a higher volatility for GMV portfolio, though the volatility in the benchmark decreases. Moreover, the diversification benefits of adding the Asian indices in the post-crisis period decrease substantially. The results are consistent with the observation of increased cross-country correlations and thus the rising integration across the developed and Asian markets in the post-crisis period.
Table 14: Diversification benefits of adding Asia countries into the benchmark assets
Pre-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
Developed 0.29 3.87 1.42 8.54 0.166
Developed & Asia 0.24 2.98 3.97 12.15 0.327
∆ -0.05 -0.89 2.55 3.61 0.161
Post-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
Developed 1.17 3.56 1.81 4.42 0.409
Developed & Asia 1.01 3.05 1.94 4.23 0.459
∆ -0.16 -0.51 0.13 -0.19 0.050
The efficient frontiers of the benchmark portfolio and the expanded portfolio in both periods are plotted in Figure 5 and Figure 6, respectively. The orange frontier is for the developed markets and the blue one is for the developed and Asian markets. The solid and dash lines are the empirical capital market lines
28 with a slope equal to the Sharpe ratio of portfolio P and P’ (the tangency portfolios). The figures also plot the monthly mean return and standard deviation of each index in the portfolio. The previously observed pattern, which the distribution of the indices becomes less scattered in the post-crisis period, is also shown in the figures in this case. However, unlike the previous two cases, here we see that most of the Asian markets lie inside the frontier formed by the benchmark indices in both periods.
Figure 5: Pre-crisis Portfolio Frontiers by developed and Asian emerging equity markets using month returns
Figure 6: Post-crisis Portfolio Frontiers by developed and Asian emerging equity markets using month returns
North America Europe Pacific P P' China India Indonesia Korea Malaysia Pakistan Philippines Taiwan Thailand -2,0% -1,0% 0,0% 1,0% 2,0% 3,0% 4,0% 5,0% 0,0% 2,0% 4,0% 6,0% 8,0% 10,0% 12,0% 14,0% PO RT FO LIO R ET UR N STANDARD DEVIATION
Efficient frontier (1999-2007)
29
5.5. Diversification Benefits Between Developed Markets and Emerging Markets
5.5.1. Overall Diversification Benefits Between Developed and Emerging Markets
In this section, we analyze the diversification benefits when combining all the emerging market indices with the benchmark assets. The mean returns and standard deviations of the GMV and tangency portfolios formed by the benchmark and all emerging market indices in both periods are presented in Table 15.
During the pre-crisis period, by adding the emerging market indices into the benchmark portfolio, the standard deviation of the GMV portfolio decreases from 3.87% to 2.16%, representing a 44% reduction. The Sharpe ratio increases to 0.508 only due to the increase in the expected return.
During the post-crisis period, the GMV portfolio has a standard deviation at 2.38%, which is only 33% lower than the benchmark. This number is above the pre-crisis level, even though the standard
North America Europe Pacific P P' China India Indonesia Korea Malaysia Pakistan Philippines Taiwan Thailand -0,5% 0,0% 0,5% 1,0% 1,5% 2,0% 2,5% 3,0% 0,0% 1,0% 2,0% 3,0% 4,0% 5,0% 6,0% 7,0% 8,0% PO RT FO LIO R ET UR N STANDARD DEVIATION
Efficient Frontier (2009-2017)
30 deviation of the GMV portfolio of the benchmark assets decreases after the crisis. The Sharpe ratio of the TP increases from 0.409 to 0.61, which represents a much smaller improvement comparing to the pre-crisis level. While the post-crisis improvement is mostly gained from the decrease in volatility and the pre-crisis improvement is mostly gained from the increase in expected return.
Overall, the results indicate that the post-crisis diversification benefits decrease even when considering all the emerging markets. The results confirm the observation of decreasing diversification benefits between developed markets and emerging markets in each region, as discussed in the previous sections.
Table 15: Diversification benefits of adding all emerging countries into the benchmark assets
Pre-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
Developed 0.29 3.87 1.42 8.54 0.167
Developed & EM 0.27 2.16 4.42 8.71 0.508
∆ -0.02 -1.71 3.00 0.17 0.341
Post-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
Developed 1.17 3.56 1.81 4.42 0.409
Developed & EM 0.88 2.38 2.38 3.90 0.610
∆ -0.29 -1.18 0.57 -0.52 0.201
5.5.2. Cross-Section of Diversification Benefits Between Developed and Emerging Markets
In the previous sections, we have discussed the changes in the diversification benefits of adding different groups of emerging market indices from a time perspective, e.g., pre-crisis vs. post-crisis. In this section, we analyze the cross-section of the diversification benefits between the developed and emerging markets. Table 16 summarize the diversification benefits of adding Latin America, EMEA, Asia and all emerging markets in both pre- and post-crisis periods.
We can see from the Panel A that before the crisis, Latin America and Asia both reduce the volatility of the GMV portfolio to 2.98%, lower than 3.05% by EMEA, though the difference is trivial. While the expected return of the GMV portfolio of DM and Latin America is higher than that of DM and Asia. Thus from the GMV perspective, Latin America brings the highest diversification benefits, followed by Asia and then EMEA. On the other hand, when we look at the Sharpe ratio, we see that the tangency
31 portfolio formed by DM and EMEA has the highest Sharpe ratio and the one formed by DM and Asia has the lowest ratio. In other words, EMEA makes the highest contribution to the improvement in the mean-variance efficiency of the tangency portfolio.
During the post-crisis period, we see that, as shown in the Panel B, DM and EMEA shows the lowest volatility of their GMV portfolio and the highest Sharpe ratio of their tangency portfolio. Therefore it is easy to conclude that EMEA has an overall superior diversification benefits to Latin America and Asia. For the latter two, Latin America shows better capabilities in improving the Sharpe ratio while Asia has higher potential in reducing the volatility of the GMV portfolio.
To conclude, regarding the capability to reduce the standard deviation of the GMV portfolio, the rank before the crisis is Latin America > Asia > EMEA, which is reversed after the crisis EMEA > Asia > Latin America. But in terms of the capability to improve the Sharpe ratio of the tangency portfolio, in both pre- and post-crisis periods the rank remains the same: EMEA > Latin America > Asia.
Table 16: Summary of Diversification benefits of adding each group of risky assets into the benchmark assets
Panel A: Pre-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
DM & LATIN AMERICA 0.27 2.98 3.85 11.32 0.340
DM & EMEA 0.33 3.05 4.15 10.75 0.386
DM & ASIA 0.24 2.98 3.97 12.15 0.327
DM & EM 0.27 2.16 4.42 8.71 0.508
Panel B: Post-crisis
GMV-Mean (%) GMV-ST. Dev. (%) TP-Mean (%) TP-ST. Dev. (%) TP-SR
DM & LATIN AMERICA 1.17 3.12 1.76 3.82 0.461
DM & EMEA 1.08 3.04 2.53 4.65 0.544
DM & ASIA 1.01 3.05 1.94 4.23 0.459
DM & EM 0.88 2.38 2.38 3.90 0.610
Figure 7 and Figure 8 plot the efficient frontier of each portfolio discussed above in the pre- and post-crisis period respectively. “DM” represents developed markets and “EM” represents all emerging markets. In order to make the two graphs comparable, we set the scale of the X-axis and Y-axis on the same level. We see that the gap between the efficient frontier formed by DM and the efficient frontier formed by DM and EM in Figure 7 is much bigger than that in Figure 8, indicating a decrease in the diversification benefits. When we look at the efficient frontiers formed by DM and one of the sub-groups of EM, we see that the differences among the three efficient frontiers in Figure 7 are much
32 smaller than those in Figure 8, suggesting that the discrepancy among the diversification benefits of the Latin America, EMEA and Asia becomes larger during the post-crisis period. Moreover, in Figure 8 the efficient frontier formed by DM and EMEA spans the efficient frontiers formed by DM and the other two sub-groups of EM, which is not observed in Figure 7. Those observations confirm the previous analysis.
Figure 7: Pre-crisis Portfolio Frontiers for each sample group using month returns
Figure 8: Post-crisis Portfolio Frontiers for each sample group using month returns
-2,0% -1,0% 0,0% 1,0% 2,0% 3,0% 4,0% 2,0% 3,0% 4,0% 5,0% 6,0% 7,0%
Efficient Frontier (1999-2007)
Efficient Frontier_DM&LATIN AMERICA Efficient Frontier_DM&EMEA Efficient Frontier_DM&ASIA Efficient Frontier_DM&EM Efficient Frontier_DM
33
CHAPTER 6. Empirical Results from The Test for Spanning
Previously we have analyzed the diversification benefits of adding different groups of emerging markets into the benchmark indices and their trend of changes across different time periods by using the mean-variance optimization approach. In this chapter, we apply various spanning tests to the same combinations of assets to investigate whether those observations are supported by strong statistical evidence.
6.1. Spanning Test for Developed Markets and Latin American Emerging Markets
Table 17 shows Wald, Likelihood Ratio (LR), Lagrange Multiplier (LM) test statistics and the associated ρ value for the hypothesis that the returns on the indices for the North America, Europe and Pacific span
-2,0% -1,0% 0,0% 1,0% 2,0% 3,0% 4,0% 2,0% 3,0% 4,0% 5,0% 6,0% 7,0% Efficient Frontier_DM&LATIN AMERICAS Efficient Frontier_DM&EMEA
Efficient Frontier_DM&ASIA Efficient Frontier_DM&EM Efficient Frontier_DM
34 the returns for each emerging market in Latin America. The tests are performed using monthly data over the two 10-year sample periods. For each country, the three tests offer the same results in accepting or rejecting the hypothesis. The joint tests for spanning for all the Latin American emerging markets show that spanning is always rejected at any confidence level for both periods, which confirms that adding all five Latin American markets into the benchmark results in a significant improvement in mean-variance efficiency.
Interestingly, the results from the pre-crisis period show that all three tests reject spanning at the 5% confidence level for Brazil, Mexico and Peru, while the results from the post-crisis period show that spanning is only rejected for Brazil. Moreover, for all individual countries, the ρ values associated with each type of test are smaller for the pre-crisis period while larger for the post-crisis period, indicating that the evidence against the rejection of spanning is weakened for the latter period. The same pattern can be observed for the joint tests for spanning for all the countries. Overall, the pre-crisis period offers more rejections of the spanning hypothesis than the post-crisis period. As argued by Kan & Zhou (2008), this could be interpreted as evidence that the developed and emerging Latin American equity markets are becoming more integrated in the post-crisis period, hence reducing the benefits of international diversification. The results are consistent with our previous analysis.
Table 17: Mean-Variance Spanning Tests on Five Latin American Equity Indices
Pre-crisis
Country Wald p-value LR p-value LM p-value
Brazil 30.108 0.000*** 26.154 0.000*** 22.862 0.000 Chile 2.588 0.294 2.554 0.294 2.52 0.2943 Colombia 5.242 0.087* 5.103 0.087* 4.968 0.087* Mexico 12.886 0.003*** 12.084 0.003*** 11.347 0.003 Peru 8.348 0.022** 8.001 0.022** 7.674 0.022** All 75.564 0.000*** 59.128 0.000*** 47.485 0.000*** Post-crisis Brazil 11.669 0.005*** 11.006 0.005*** 10.392 0.005*** Chile 1.385 0.517 1.375 0.517 1.366 0.517 Colombia 1.119 0.587 1.113 0.587 1.106 0.587 Mexico 3.695 0.176 3.625 0.176 3.556 0.176 Peru 0.495 0.790 0.493 0.790 0.492 0.790 All 35.494 0.001*** 30.486 0.001*** 26.405 0.002***
3 Kan and Zhou (2008) prove that If there is only one test asset, all the three tests are increasing transformations of the F-test, thus yield the same P value. But for N > 1, the three tests give different ρ values.
