International Diversification from a European Perspective –
The Influence of Investment Constraints for the EMU-Investor
Oliver Milke S1940104
Supervisor: Prof. Dr. L.J.R. Scholtens
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Abstract
My thesis analyses the benefits of international diversification for the Investor from the EMU zone. I use a GDP weighted Sharpe-Ratio maximizing approach with short sale constraints and GDP overweighting constraints, additionally I add the minimum-variance portfolio. Using this approach, I reject the hypothesis of a significant decrease of the standard deviation of returns. I conclude that the Sharpe-Ratio presents a good tool for the construction of diversified portfolios, using various constraints and the GDP weighting it provides feasible portfolio weights, which are relatively stable over time. For the EMU-investor, diversifying internationally allows for a significant increase of the Sharpe-Ratio and the mean-return, thus presenting obtainable benefits of international diversification. The results are surprising, since research so far assumed the standard deviation to be the significant factor; however, the findings are robust in- and out-of-sample.
JEL Classification: F36; G11; G15
Keywords: Euro, Investor, International Diversification, Asset Allocation, Constraints
I. Introduction
The benefits of diversification have been discussed very often, starting with Levy and Sarnat (1970) over Solnik (1974), Harvey (1995), Bekaert and Urias (1996) and Chiou (2008), just to name a few. All of them agree that international diversification in general is beneficial for the domestic investor. Nevertheless, I will make this case again, because I think that the environment for this case is changing frequently and deserves another update. Over the past 11 years, there have been quite severe changes to the world’s wealth allocation, which affects investment strategies and consequently the diversification benefits that result from these strategies. Therefore, I will consider this in my analysis. Moreover, many of the older studies took the Anglo-Saxon point-of-view, thus using USD or GBP as trading currency. While this is convenient for most of the world’s investors, for the investor in the European Monetary Union (EMU) 1 it might not, especially since nowadays investments often deal in Euro as well. We saw the introduction of the Euro on the financial markets on January 1, 1999 and the consolidation of the capital markets in Europe, the (re-)rise of the BRIC2 countries and other emerging markets. Many of these countries lowered the access limitations to their capital markets (again)3, which subsequently led to an investment increase to these same capital markets. Still, many investment barriers are not completely lifted, thus still giving foreign investors limitations on their investments, e.g. short sale constraints and investment limitations are still common4. On the other hand, new tools, like ETFs5, become more common, thus allowing institutional and private investors to diversify internationally more easily. Furthermore, the recent financial crisis did again prove the importance of a widespread asset allocation. While it primarily hit the developed markets, many of whom still struggle, emerging markets like China and Brazil, but also smaller markets like Peru, Morocco or Indonesia, already demonstrate climbing stock exchanges. A
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Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, and Spain. Of the founding members, only Luxembourg is left out of the EMU index. Late accessions to the EU are not considered, due to consistency (Cyprus, Malta, Slovakia, Slovenia, Estonia)
2 Brazil, Russia, India and China 3
Many emerging markets put up high investment barriers after the manifold crises in the 90s (Mexican crisis 1994-1995, Asian crisis 1997-1998 and the Russian crisis in 1998) to prevent themselves from hot-money (short-term capital in and outflows) or had restrictions on the maximum shares foreigners could possess in one asset
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Chiou (2009) discusses this further 5
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problem of many of those small markets, that has been around since Markowitz (1952) introduced his mean-variance approach, is the liquidity of their capital markets. In perfect capital markets, liquidity to trade assets is infinitely available at any time, while this is not achievable in reality; most developed financial markets do come close to this ideal. Many emerging markets on the other hand, do not possess a liquidity that would allow for an investment focus in these markets, this limitation is especially important for asset managers. While the mean-variance approach could produce corner solutions in the portfolio that force a strong investment in these markets, emerging markets often just do not offer possibilities to do so.Over the past decade, the integration of the European capital markets has been progressing further6; the introduction of the Euro increased the integration of the participating capital markets, averaging in a correlation of their MSCI indices towards each other of above 0.9. This presents another reason for international diversification for the EMU-investor: within the EMU-region, it is difficult to spread the asset allocation to achieve a beneficial diversification effect, since a significant gain in the risk-return ratio is difficult to achieve at this level of correlation.
Another point in most of the older studies is the use of market capitalization when it comes to investment constraints and portfolio weights. While this might seem intuitive at first, it does have one severe flaw: it does ignore the underlying wealth of a country or region as represented by assets not listed on the stock exchange7, thus some countries regions obtain capital flows with no assets to incorporate this same capital. Bubbles can be a consequence of too much liquidity on the stock markets, as could be seen in Japan in the 80s or in the Asian crisis in the 90s or recently during the US subprime crisis. Often, but not always, cheap money is a reason, sometimes it is just the growth opportunities small countries present. Before the Asian crisis, countries like Thailand attracted great investment money inflows, much of it so called “hot-money” or speculative money, which has the intention to participate in the stock market growth of these emerging markets. Since these countries often have an underdeveloped capital market and their stock indices do not represent the full range of that country’s assets, stock prices increase steady and fast because they cannot incorporate the rate of money growth. This is a possible cause of a bubble economy, with the consequence that the bubble collapses once the money is pulled out of the market. The market capitalization approach supports this kind of capital flows, by allocating more money to markets that are increasing in market capitalization. An investor who uses the market capitalization approach would have had high investments in Japan before the bubble collapsed and in Asian markets before the Asian crisis. Hamza et al. (2007) discuss this topic in depth in their study.
My analysis will address all these points in order to deal with my research question of obtainable benefits of international diversification for the EMU-investor: First, I consider the EMU region as one market, thereby accounting for the high integration of the EMU markets and their correlation among each other. Second, my thesis will account for currency fluctuations by converting all returns to Euro, thus eliminating any currency risk that occurred over the past decade. Many ETFs offered in Europe are denoted in Euro, thus applying a similar principle. Third, incorporating that many financial markets bear limitations for foreign capital, I will add upper boundaries and short sale constraints to my constructed portfolios, to obtain feasible
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E.g. see research by Laopodis (2009) 7
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investments and to avoid corner solutions and illiquidity of the portfolios. Fourth, to address the problems of the market capitalization approach I will use a GDP weighted approach. In doing so, the portfolios I construct are based on fundamental economic values and thus I obtain more stable weights, since the GDP usually does not change as drastically as financial markets do, e.g. compare financial markets decline and GDP declined during the financial crisis.In my thesis, I utilize the Sharpe-Ratio and the minimum-variance portfolio to construct the portfolios and obtain the weights for my strategies. Since the introduction of the reward-to-variability ratio by Sharpe (1966), it has become one of the most widely used tools to rank portfolios against each other and to show the outperformance to a benchmark. Since it allows incorporating of several constraints and is easily replicable, it presents a good tool for my analysis.
My results confirm that it is beneficial for the EMU-investor to diversify internationally. By doing so, the EMU-investor is able to significantly increase his mean return and his Sharpe-Ratio, which is established by the in- and out-of-sample results. The standard deviation of returns can be lowered significantly by following the minimum-variance portfolio approach, while the Sharpe-maximized approaches do not yield a significant reduction of the volatility. My thesis further proves that the more tight the constraints, i.e. adding overweight constraints, get for the investor, benefits of diversification decline, but still exist, while the portfolios are more feasible and less biased towards a few emerging markets.
I organize the remainder of my thesis as follows. Section II presents past research done in this field of work and explain the theories used in my approach. Section III contains my hypothesis and the methodology applied to construct the portfolios used in my research. Section IV describes the data used in my analysis and shows the reason why the EMU-investor should diversify internationally. In Section V, I present the results of my research and checks for the robustness of the results in out-of-sample tests. Section VI concludes my thesis and summarizes the findings.
II. Literature Review
I present an overview over the work that has been done on international diversification and the potential outcomes that can result by diversifying internationally, which I consider most important for my thesis. The articles I discuss explain the assumptions I integrate in my work and build the framework for the analysis that follows in the next sections. First, I am going to present the theoretical approaches and improvements over the year followed by a review the beginnings of the idea of international diversification and in the end discuss the latest research results, to which I will relate in my thesis.
Diversification has been a widely discussed topic in the academic research for about half a century now, from the time when Markowitz (1952) published his article on the possible risk reduction through the combination of assets with low correlations in one portfolio, whereas risk is defined by the volatility of the portfolio returns8. His mean-variance efficient frontier changed the way portfolios are constructed, by quantifying the motives for diversification. Following Markowitz (1952) portfolio selection approach and the capital asset pricing model, e.g. Lintner (1965), Sharpe created a measurement to rank mutual funds according to their risk-return performance. In his first article, Sharpe (1966) names the reward-to-variability ratio. Over time,
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this ratio has been widely discussed, amid those discussions about its usefulness, e.g. Israelsen (2003, 2005) and Scholz (2007), or variations of his ratio to increase its accuracy, e.g. Christie (2005). Sharpe (1994, 1998) himself reviewed his ratio, arguing about its weaknesses and strength, concluding that it is the most convenient ranking tool, despite its flaws. Eling and Schuhmacher (2007) state, that it is indeed the best known and understood performance measurement from a practitioner’s point-of-view, thus supporting Sharpe’s (1966, 1994) case. Eling and Schuhmachers (2007) further show, that the Sharpe-Ratio is even consistent under non-normal distribution.9 Based on this theoretical consideration I ground my analysis on the Sharpe-Ratio and use it to construct the portfolios.Concerning the Sharpe-Ratio, Opdyke (2008) came up with an intuitive way to solve for the problem of statistical significance testing even under non-normally distributed returns in order to rank the performance of different mutual funds. He further develops the research of Jobson and Korkie (1981), who first presented an approach to generate one- and two-sides confidence intervals for Sharpe-Ratio. His work is based on the problem that Sharpe-Ratios are frequently used to display the return per unit of volatility, but often lack the statistical evidence that these ratios are indeed statistical significant from zero and not just a result of random volatility of their underlying assets, especially under non-normal distribution. He furthermore incorporates the research of Christie (2005), who provided a way to of asymptotic distribution of the Sharpe-Ratio under only the restriction of stationarity and ergodicity, thus obtaining results under more realistic circumstances. Consequently, Opdyke (2008) presents a simple way to test for the significance of a constructed Sharpe-Ratio and testing for its statistical deviation from the benchmark, which usually is the common index the compared funds try to outperform. I consider this approach to be very useful and implement it to test for the significance of the Sharpe-Ratios I obtain from the constructed portfolios in my analysis.
With the increasing integration of the worldwide financial markets, the opportunity of international diversification has been discussed in the literature. Levy and Sarnat (1970) were among the first to write about the possible gains of diversifying internationally. In their research, they construct an efficient frontier, taking historical data of 28 countries into consideration, of which then only seven countries are included in their optimal portfolio, most of them developing countries with low correlations to the US capital market. Most of the common, developed markets were excluded, which is due to the high correlation amongst each other and to the US market in general, which implies a relatively low degree in achievable risk reduction. Levy and Sarnat (1970) conclude that the investor can gain a significant reduction in risk by preferring countries with low correlations to each other. This is especially the case for developing countries and less present on the more common markets.
This analysis was taken further by Solnik (1974), who focused on the possible risk-reduction obtainable through international diversification in comparison to the same risk-reduction in risk achievable by national and industry-wide diversification. Solnik (1974) argues that, according to the capital asset pricing model (CAPM), the unsystematic risk can be diversified so that only the systematic risk remains. His study was conducted on the US and seven major Europe countries at that time, to identify the level of diversifiable risk and how many assets
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Eling and Schumacher (2007) explicitly refer to elliptically distributed data, but mention with reference to Fung and Hsieh (1999) that even without the assumption of elliptically distributed data, the mean-variance analysis
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would be necessary to achieve that target. He concluded that the US at that time already had a low level of risk (27%) compared to major countries like Germany (43.8%). Furthermore, while domestic portfolios obtained their peek risk-reduction at an asset level of around 20, international portfolios could still benefit at holding 50 assets and above. He compared his results to the obtainable diversification level achievable by domestic and sector diversification, both underperformed international diversification. His results lead him to the conclusion that it is necessary to diversify internationally:“In Summary, the benefits from international diversification are so large that they should rapidly resuscitate the development in the U.S. of successful international mutual funds […]” Solnik (1974)
Based on Levy and Sarnat (1970), Solnik (1974) and the recent economic events I explained in the introduction, I consider international diversification as a necessary tool in modern portfolio construction. Thus, I test for benefits of international diversification in my analysis.
Jorion (1985) argued that mean-variance approach, e.g. used for the CAPM, has serious defects, the most important one being the poor out-of-sample performance of the constructed portfolios. Furthermore, due to the maximization of the Sharpe-Ratio to construct the optimal portfolio, the weights in such a portfolio are extremely unstable. Just adding a few observations can change the whole portfolio-structure. Moreover, the maximization of the Sharpe-Ratio often leads to corner solutions, which many assets having a zero-weight or relatively large portions going to countries with small indices – the portfolio of Levy and Sarnat (1970) is a good example for this. In Jorion’s (1985) opinion, the main reason for these problems is the reliance on past returns to build the optimal allocation of assets; he on the other side put the risk in the center of attention. In his analysis, he compared the out-of-sample performance of the classical mean-variance portfolio, the minimum-mean-variance portfolio and an approach called “Bayes-Stein estimator”, which was developed by Jorion (1986) and is a way to equalize the returns of the individual assets. He concluded that the minimum-variance portfolio performed best out-of-sample, therefore indicating that the minimum-variance portfolio when used as a forecast tool, it accurately predicts the volatility of the stock, while it vastly overestimates the returns. Jorion (1985) concludes that most of the diversification benefits are likely to result from the reduction in risk. I use Jorion’s findings as hypotheses for my thesis, testing if the volatility of stock returns is still the stable factor in portfolio construction. Especially the recent financial crisis with its volatile stock markets could have influenced Jorion’s (1985) findings.
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Jagannathan (1991). They find that, in practice, it is hard to achieve the performance of the IFC indices, due to their omission of transaction costs; further, the US mutual funds do not yield any significant gain benefits from international diversification in the unconditional test, whereas the UK mutual funds on the other hand do yield significant gains. In the conditional tests both, UK, and US produce significant gains, but mention a lack of power for this test. Therefore, they reject that equity indices of developed countries span the mean-variance efficient frontier of all the international equity markets.Similar to Bekaert and Urias (1996), other research was done on investment barriers, especially in emerging markets. De Roon, Nijman and Werker (2001) and Li, Sarkar and Wang (2003) identify short sale constraints as a major constraint, limiting the diversification possibilities on emerging financial markets but come to different conclusions. De Roon, Nijman and Werker (2001) investigated the possibility to extend the efficiency set of the US investor by investing in emerging markets. Therefore, they use a mean-variance spanning test to conduct this research using a similar methodology as provided by Hansen and Jagannathan (1991) but extend it to account for short sales. They conclude that, in the absence of market friction there is indeed a possible gain in return and risk-reduction by diversifying international for the US investor. In the presence of short sales or transaction costs, these potential benefits vanish and thus no further outperformance is achieved. Consequently, they reject the hypothesis of extending the spanning of the mean-variance frontier by including emerging markets, but do have significant evidence for including some Latin American or Asian countries, thus indicating that there is a problem in their approach when increasing the number of markets. Li, Sarkar and Wang (2003) come to a different result in their study for the US investor. Using a Bayesian approach to deal with the problem of short sale constraints in the mean-variance spanning, they imply that these constraints indeed lower the possible benefits of international diversification, but do not eliminate them. In their methodology, they use two different measures: the reduction in the standard deviation and the increase in expected returns. A drawback of their analysis is the lack of an out-of-sample test and they do not test for transaction costs, which limits the potential for practical use. I present the spanning test to show alternatives for the Sharpe-Ratio testing. Since I use Opdyke’s (2008) methodology for differences in Sharpe-Ratios, I use the Sharpe-Ratio to construct my portfolios. The Sharpe-Ratio offers sufficient detail and allows me to incorporate all constraints necessary for my portfolio construction. On the other hand, the papers presented in this paragraph offer a good motivation for the use of short sale constraints in the case of international diversification; hence, I will incorporate them in my methodology.
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on country specific return characteristics. Industries on the other hand have very little to do with the cross-sectional difference in return volatility and account for less than 10% of a countries variance, depending on the indices weight. The cause therefore is that industries are much more diversified across countries than vice versa. Hargis and Mei (2006) confirm their results using a different model. They decompose equity returns into cash flow, interest rate and discount rate components to test for diversification effects. Their result is similar to that of Heston and Rouwenhorst (1994), implying that indeed country diversification is of greater benefit compared to industry-wide, mainly due to emerging markets and their lack of integration in the world financial markets. Ehling and Ramos (2006) likewise research this topic, but include short sale constraints, using a mean-variance-efficiency test. This test, they argue, solves the problem for short sale constraints that De Roon, Nijman and Werker (2001) encountered by creating a benchmark out of the combination of industry as well as country factors. Ehling and Ramos (2006) conclude that both are statistically equivalent strategies, thus both compute similar outcomes, but the country indices efficient frontier spans wider than the comparing industry frontier when using no constraints, additionally both gain large short positions. When the short sale constraints are used, country diversification outperforms industry diversification, but Ehling and Ramos (2006) indicate that the evidence is statistically weak. Based on these articles I analyze country diversification as diversification factor in my research.An essential aspect of the portfolio construction is the benchmark used for the performance measurement of the portfolio and the resulting weighting of the individual countries in the constructed portfolio. Hamza et al. (2007) consider this in their paper comparing three alternatives, namely market capitalization, GDP and equally weighted approaches. According to Hamza et al. (2007), the advantages of the market cap approach are the uniformity with the market consistency criterion10, the better reflection of the investable opportunities, its suitability for passive investment strategies due to low turnover and high liquidity and that it is generally in line with the CAPM, as Roll and Ross (1994) establish. On the other hand the disadvantages do raise concerns: CAPM has been rejected, see e.g. Fama and French (1992), and Hamza et al. (2007) mention that the market cap approach can lead to large long positions in case one market continuously outperforms its competitor or has a higher market capitalization than its GDP would indicate. This was the case for Japan in the 80s and it has been the case for US for the past decades. To solve for this problem they suggest using either a GDP or an equally weighted approach. The GDP weighted approach better represents the actual wealth of a country and is more stable over time, which would help avoiding investing in bubbles, but is only adjusted once a year and even that does lag behind due to time needed to compute these numbers. The equally weighted approach on the other side is very simple to construct and distributes the allocation independently of any fundamental values or key figures. However, its advantage of assigning an equal weight to even the smallest market is also a disadvantage, since liquidity issues can slow down or even stop the allocation to one country; furthermore the lack of a benchmark is criticized. Testing these three strategies on the MSCI EAFE index and countries Hamza et al. (2007) conclude that equally weighted and GDP both outperform the market cap approach significantly by more than 1%. As a reason for this, they name the low rebalancing and low concentrations, especially in the case of the equally weighted portfolio. A recent study by MSCI Barra (2010)
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comparing GDP and market cap indices comes to the same result but fails to explain the fundamentals underlying it. Grounded on the research presented in this paragraph I decide for a GDP weighted approach in my analysis, due to the benefits of stability of the portfolio weights and the low distribution to emerging markets.Ever since the Euro became reality on January 1, 1999, much research has been conducted on the market integration of the Euro-stock-markets. The question evolved, whether the financial markets become more integrated, as predictions forecasted or if something different would occur. Kempa and Nelles (2001) compare the performance and analyses the correlations between European stock markets with and without currency volatility in the 90s. They do identify potential gains, but mention that these gains get smaller when corrected for exchange rate volatility. Fooladi and Rumsey (2002) support this; they argue that the stock market integration worldwide is proceeding, while currency correlations seem to be declining. Syllignakis (2006) finds evidence for higher integration after the Euro was introduced in 1999 throughout all the members of the monetary union, but as Laopodis (2005) shows, there are still potential benefits through diversification in the Euro-zone. Recently Laopodis (2009) identified a decoupling from fundamental values throughout the monetary union, implying that the domestic real economic activity, inflation and short-term interest rates might still be important, but are continuously less important in determining the national stock markets. Due to the financial crisis of 2007, it is to be expected that the integration process even accelerated, see e.g. Campbell, Koedijk and Kofman (2002) on increasing correlations during bearish markets. Thus, my research will take the approach of combining the European Monetary Union (EMU) to one unified portfolio, which is treated as domestic portfolio.
Showing international diversification from a German perspective, Gerke, Mager and Röhrs (2005) are using a time rolling investment strategy. They rebalance the portfolio periodically, to test for the out-of-sample efficiency of the minimum-variance portfolio and the maximized Sharpe-Ratio approach with short sales constraints, further they add a home bias weighting for the German market. In their test, they prove the benefits of risk-reduction through international diversification. Moreover, the minimum-variance portfolio performs best out-of-sample, therefore proving the evidence of Levy and Sarnat (1970), that risk-reduction is more stable over time than returns. Using a more practical approach Chiou (2008) shows how to construct diversified international portfolios for the US investor. He applies short sale and overweight constraints on the market capitalization in order to deal with the liquidity problem, which Markowitz (1952) does not take into account and which, according to Bekaert and Harvey (2003), is especially found on small emerging markets, due to the sometimes-unachievable corner solutions of the unconstrained efficient frontier. Thus, he can tackle the problem of limited money in- and outflows and limited ownership in some emerging countries11 and thereby he is able to construct realistic portfolios. His aim is to identify if the diversification effect is still significantly different from zero when the constraints are taken into account. By making use of a similar methodology and data as Gerke, Mager and Röhrs (2005) and employing calendar rebalancing. Chiou (2008) concludes that the short sale and overweight constraints do indeed limit the risk-reduction but do on the other hand expand the range of possible assets and limit the portfolio time-variation, therefore reducing transaction costs. These papers motivate the use of constraints in my analysis and reasons for the assumption of limited liquidity available on financial markets.
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Table 1 - Literature overview on papers for international diversification and mean-variance allocation most important for my researchAUTHOR METHODOLOGY DATA RESULTS
Solnik (1974) Construction of international portfolios and computing of average risk, comparing country vs. sector, CAPM
Simple weekly returns of 300 European Stocks from seven European countries from 1966- 1971
Substantial gain in risk reduction, 1/10 of the risk of a typical security and 1/2 the risk of a well-diversified US portfolio, international portfolio diversification beats sector diversification
Jorion (1985) Mean-variance test with new and old return-estimators, comparing classical Sharpe maximization, MVP and his “Bayes-Stein” estimator; in- and out-of-sample test
Logarithmic value-weighted monthly returns of seven major equity markets worldwide from 1971-1983
Bayes-Stein estimators beats the classical approach, but the best performing is the MVP-approach, indicating that volatility is more stable over time and that this is the true benefit of international diversification
Sharpe (1966) Mean-variance approach, CAPM, introduction of the Sharpe-Ratio
34 open-end mutual funds 1954-1963 Measurement reward-to-variability ratio (Sharpe-Ratio) presented. Tests prove it as a good ranking tool, to show differences in the performance of mutual funds. Acknowledges that some differences cannot be explained by the ratio.
Eling, Schumacher (2007)
Empirical study on Sharpe-Ratio compared to 12 other performance measurements, compare ranking of hedge funds with the different performance measurement tools
2763 hedge funds from 1985-2004, data from ehedge, 2106 surviving funds,657 dissolved funds, 229.47 billion USD under management (~1/4 of worldwide hedge fund volume)
Choice of performance measure does not affect the ranking of hedge-funds, even without normal-distribution, mean and variance sufficient to explain return distribution, Sharpe-Ratio might be best tool for performance measurement, since it is best understood and best known Li, Sarkar, Wang
(2003)
Mean-variance spanning test improved by using Bayesian approach to deal with constraints, separate risk and return measure
Monthly return in USD for indices returns provided by MSCI and IFC for developed and emerging markets
Lower diversification benefits with constraints, but yet existent and significant, but no transaction costs nor out-of-sample test
Heston, Rouwenhorst (1994)
Regression to identify industry specific effects for country indices variance
Monthly returns of 829 firms comprising the MSCI indices of 12 European countries 1978-1992
Generally higher volatility and lower correlation between country indices than industry indices, industry volatility does not explain country volatility, country diversification is to be preferred over industry diversification
Hamza, Kortas, L'Her and Roberge (2007)
Comparing performance of market cap, GDP and equally weighted indices, performing robustness checks and rebalancing simulations
Monthly returns of the indices used to compute the MSCI EAFE index, exclude trading costs
Equally weighted outperforms GDP weighted and this outperforms market cap weighted, they indicate market cap could probably be the worst portfolio constructed
Chiou (2008) Sharpe-Ratio to construct max SR-Portfolio and MVP with short sale and overweight constraints
Monthly returns for indices computing the MSCI World-Index
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III. Theory & Methodology
I ground my analysis on the points I discuss in the introduction and the literature presented in the previous section, especially the articles summarized in Table 1. In line with Solnik (1974), Heston and Rouwenhorst (1994) and others, I analyze if international diversification is beneficial for the domestic investor. I further include short sale constraints, as suggested by Li, Sarkar and Wang (2003) and overweight constraints, as suggested by Chiou (2008) and Bekaert and Harvey (2003), to deal with limited liquidity often present on smaller financial markets. I line with Chiou (2008, 2009) I utilize the Sharpe-Ratio, as presented by Sharpe (1966) and refined by Christie (2005) and Opdyke (2008), to analyze the effects of international diversification for the EMU-investor. I will first examine the performance of a Sharpe-Ratio maximized portfolio with short sale constraints in comparison to a domestic benchmark portfolio to check if there are obtainable benefits from international diversification, in either risk reduction, excess return or both. Based on this framework my hypotheses are:
H1a: By diversifying internationally with short sale and constrain overweight constraints, the EMU investor can significantly increase his mean return, when compared to the EMU index.
H1b: By diversifying internationally with short sale and overweight constraints, the EMU investor can significantly decrease his volatility, when compared to the EMU index.
H1c: By diversifying internationally with short sale and overweight constraints, the EMU investor can significantly increase his Sharpe-Ratio, when compared to the EMU index.
Subsequently, I perform out-of-sample tests as robustness check for the results of the in-sample portfolios. According to Jorion (1985), the optimized portfolios, when used as a forecast tool, predict the volatility of the stockprecisely, while the method does not predict returns accurately. Based on his results I derive the following hypotheses:
H2a: In an out-of-sample test, the in-sample optimized portfolios predict the standard deviation of the portfolios.
H2b: In an out-of-sample test, the in-sample optimized portfolios cannot predict the mean return of the portfolios.
I analyze the effect of international diversification for the EMU-investor by increasing the investment horizon of a diversified domestic portfolio, represented by the GDP12 weighted EMU-index, to a diversified international portfolio. The resulting Sharpe-Ratios of this expanded investment horizon indicate if a benefit of international diversification exists for the EMU-investor. In case of significantly increased Sharpe-Ratios compared to the domestic portfolio, a benefit of international diversification exists. In addition, my analysis uses GDP weights as suggested by Hamza et al. (2007) and MSCI Barra (2010) to separate it from similar studies like Chiou (2008) or Gerke, Mager and Röhrs (2005).
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The outcomes of my investment decisions are assessed through determining the changes compared to the benchmark portfolio, using the three different characteristics: Sharpe-Ratio, return and standard deviation. As mentioned above, many countries, especially emerging countries, do not allow short selling on their financial markets. I deal with this by including a short sale constraint to the portfolio construction process. Furthermore, especially small markets are often not as liquid as developed markets as mentioned by Bekaert and Harvey (2003), thus, to avoid corner solutions; I will use several overweight constraints to the country’s GDP while constructing the weights of the portfolio. The constraints are based on Chiou (2008), who proposed the constraints to deal with limited liquidity on emerging financial markets. Furthermore, I combine the constraints with the GDP weighted approach, as suggested by Hamza et al. (2007). The portfolios I create are each based on the previous 60 month of historical data, the usual timespan used in historical analysis. Furthermore the portfolios contain several boundaries: all portfolios are Sharpe-Ratio maximized, they are short sale constraint and have increasing restrictions on the upper boundary of their GDP overweighting, I report the case for three, five and ten times overweighting as proposed by Chiou (2008). Additionally I report the minimum-variance portfolio with short sale constraints. In the out-of-sample testing, the portfolios are rebalanced monthly, quarterly and yearly, as suggested by Arnott and Lovell (1993). The returns of the out-of-sample test are then tested for equality compared to their ex-ante predictions, to test for significant changes. Thus, I create a time-rolling portfolio optimization case for the European investor.Benninga (2008) describes the process of portfolio construction as follows: In a universe with
N
risky assets, a portfolioP
is described as a set of assets with different weightsi
w
with the sum of the individual weights equal to one.(1)
(
...
)
1
1 2 1
N i i Nw
w
w
w
P
Additionally I include the minimum-variance portfolio
P
MVP, which is the portfolio that has the lowest variance among all feasible portfolios. It is defined by12
The return of a portfolioR
Pand its connected risk
Pare calculated as(3)
N i i i Pw
r
R
P
R
P 1*
and
N j ij j i N i Pw
w
1 1
where
w
iis the weight of the individual assetsr
iis the return of the corresponding asset and ij
is the covariance between two assets. For the MVP,
Pis minimized and constraints are incorporated. (4)
N j ij j i N i Pw
w
1 1min
N i w U w i N i i 1, 0, 1,..., 1
Urepresents the restriction to the portfolio weight and is calculated based on GDP weighting in the world portfolio, e.g. U(5)indicates an overweighting of five times the GDP weight in the constructed portfolio.
In order to create the risk-return maximized portfolios I utilize the Sharpe-Ratio
SR
. Sharpe (1966, 1994) has developed the Sharpe-Ratio as a measurement for the excess return per unit of risk. The Sharpe-Ratio is part of the modern portfolio theory, thus sharing its assumptions, e.g. normal distribution of returns. In practice, this restriction barely holds, yet it provides a good framework for my analysis, which has been widely used despite its shortcomings, as Ehling and Schuhmacher (2007) state. Opdyke’s (2008) refined approach incorporates improvements to use the Sharpe-Ratio under these conditions. The Sharpe-Ratio is calculated using the excess return of the constructed portfolioR
P
R
M , withR
M as market return13, divided by the risk of the portfolio
P. (5) P M PR
R
SR
13
13
Equation (5) needs to be maximized, additionally I include the short sale and overweight constraints,w
i
0
andU
w
i respectively.(6) P M P
R
R
SR
max
N i w U w i N i i 1, 0, 1,..., 1
Although unlimited liquidity is assumed within the modern portfolio theory, Chiou (2008) argues that in practice it is not the case, as explained in the literature review. He applies upper boundaries to the portfolios constructed to deal with this problem, an approach I incorporate as well to deal with the limited liquidity on small financial markets.
As mentioned in the literature review, Opdyke (2008) came up with an approach to test for the p-values of the Sharpe-Ratio.14 Therefore, I will make use of his method to validate if the deviations from the benchmark are significant and if their returns are significantly different from zero, when looked at individually. His methodology supports the comparison of Sharpe-Ratios, which allows me evaluate them in relation to a benchmark, which is the EMU index.
IV. Data Description
In my thesis, I utilize the countries used to construct the Morgan Stanley Capital International All Country World Index GDP (MSCI ACWI GDP Weighted Index) to test for diversification effects for the EMU investor. I collected the data using DataStream, Eurostat and the database of the IMF.
The weights of a GDP weighted indices are based on a country’s gross domestic product rather than on its market capitalization. Therefore, these indices are constructed to avoid overweighting countries with high market capitalization15, like the US, and underweighting countries with less advanced, and thus less capitalized, capital markets. This especially applies to emerging markets like Brazil and China, but also bank-oriented countries like Germany. Furthermore, GDP weights tend to be more stable over the time, which leaves them less vulnerable to market peaks. MSCI Barra (2010) argues that GDP weighting could therefore lead to the avoidance of market bubbles and an overall risk reduction.
The MSCI ACWI GDP Weighted Index world index consists of 45 countries, 24 developed16 and 21 emerging17 markets. The countries in this index represent the relative share of a region in terms of GDP compared to the worlds GDP. I substitute the countries of the European Monetary Union with their index (EMU GDP Index). I use the Euribor 3M rate as a proxy for the
14 For an extensive description of his approach, see Opdyke (2008) 15
For further information see literature review, e.g. Hamza et al. (2007) 16
Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Israel, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, the United Kingdom and the United States
17
14
risk-free interest rate obtainable on the EMU capital market. Collecting monthly data for the period from May 1999 to April 2010, this accumulates to 4884 observations once constructed to continuously compounded returns, and GDP measured in current prices from 1998 to 2008. Since my thesis focuses on the EMU-Investor, all the returns and the GDP used to construct the portfolios are denominated in Euro, to account for exchange rate fluctuations.The investment cycle is starting in May, it is picked due to the circumstances the MSCI GDP indices are constructed. Evaluating the GDP of a country does take some time until dependable numbers are released, since the indices are based on these numbers, they are rebalanced annually in May. Consequently, in order to construct a reliable comparison to the benchmark, I adjusted the starting period to be in line with that of the MSCI indices. Therefore, when I refer to e.g. year 2002, I refer to the period of May 2002 to April 2003.
Figure 1 – Average annual MSCI stock market return correlation of the eleven EMU countries that build the GDP weighted EMU index to the EMU Index from 1999 to 2009
Correlation of the eleven countries that build the EMU GDP Weighted MSCI Index to the index itself over the period from 1999 to 2009. Annual correlations are displayed above the corresponding year. The trend line indicates the raising trend over time. Source: self-created figure with data from Eurostat
I decided to combine the EMU18 region to a single market due to several reasons. First, due to common currency within this region, there is no exchange rate risk. Second, the high integration of the EU financial markets allows to easily accessing capital markets within other countries of the EU. Third, as Figure 1 displays, the average correlation of the eleven EMU countries, which form the index, has been above 0.9 most of the time during the last decade. Two drops below this level occurred in this period, once at the beginning of the recent financial crisis in 2007, and once in late 2009, when the Greek crisis was about to emerge. The two events explain the substantial drop in correlation in Figure 1. As Laopodis (2009) recently identified, the national markets in the EU, and thus EMU, do trade more and more on a regional basis, that is EU/EMU, and less on national variables.
18 Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, and Spain.
15
Table 2 presents the country statistics for the dataset, total GDP growth in current prices converted to Euro from 1998 to 2008, GDP weights in 1998 and 200819, the change in GDP weight, the mean returns of every country index and its standard deviation. I further group the indices into eight regions: EMU, Oceania, North America, South America, Europe, East Asia, Middle East, and Africa and constructed regional indices according to their weight in that region. Additionally Table 2 shows the average and median Sharpe-Ratio in that time and its peak and low. The highest GDP growth in this period can be seen in Russia, Indonesia and China, with 375.33%, 310.34% and 225.48% respectively. On the other hand, some countries did shrink during the same period, namely Japan, by 3.92%, and Hong Kong by 1.06%. The major economies concerning GDP weight are the EMU region, the US and Japan both in 1998 and 2008, which combined present 69.01% in 1998 and 58.70% in 2008. This shows a decline by more than 10%, which is almost completely attributed to the US and Japan. The reason, why the EMU zone performs quite stable in this overview, can partly be attributed to the fact that all the data is converted to Euro. The strength of the currency over the past few years, the Euro increased continuously to other currencies, increases the GDP of EMU countries compared to the rest of the world, e.g. in Euro-terms the US GDP has been decreasing since 2007. Nevertheless, the table displays that the developed markets are decreasing in overall weight, while emerging markets like China, Russia and India are gaining in importance in terms of GDP weight, with China soon to be the third biggest economy in this world, overtaking Japan.Table 2 further gives the mean return and standard deviation of returns of the selected countries. The average return amongst all countries during the selected period is 0.50% per month. Noticeable is the difference from this equally weighted average of all countries to the GDP weighted world and EMU indices, which represent the developed countries only. Most of the emerging markets perform better than the average of all countries used in the comparison, especially the South American markets, where two out of the top three performers are located, namely Colombia and Peru, with Czech being the second. The only developed countries performing better than the average are Canada and Denmark. On the other hand, the worst performing countries in mean return are primarily developed countries, e.g. the UK, the US and the EMU region. The standard deviation amongst these two groups differs substantially, with developed countries usually having a standard deviation of 4-7%, e.g. UK or Switzerland, whilst the emerging markets range from 8-16%, e.g. Turkey or Brazil. If the standard deviation and the return are incorporated in the comparison by using the Sharpe-Ratio, the picture changes partly. In the risk-return adjusted overview, developed countries perform better. With Denmark and Australia, two developed countries lead the chart, but with the UK, it also has one of the worst performances. The emerging markets do not underperform on average compared to the developed countries, but have the lowest Sharpe-Ratio performing country, namely Taiwan. This contradicts previous research, e.g. Bekaert and Harvey (2003), which said that developed countries perform better in risk-return-adjusted comparisons. In the last columns, I present the individual countries maximum and minimum Sharpe-Ratio, to show the median peak and low over the time analyzed for each region.
19 Even though the returns are used until April 2010, it is still considered as the 2009 portfolio, due to the
16
Table 2 - Country statistics of all countries constructing the MSCI ACWI GDP weighted index with EMU countries combined to represent one marketCountry/ Market GDP Growth 1998-2008 GDP Weight 1998 GDP Weight 2008 Change Weight Mean Return StDev of Return Region
Sharpe-Ratio(Excess Return/Standard Deviation of Return) Median Max Time Min Time
Australia 98.79% 1.40% 1.85% 0.45% 0.43% 5.79% Oceania 0.22 2.54 Mar-09 -3.13 Nov-08 Brazil 43.15% 3.01% 2.87% -0.14% 1.11% 10.32% S.America 0.12 2.11 Sep-05 -2.91 Oct-08 Canada 86.67% 2.20% 2.73% 0.54% 0.60% 6.55% N.America 0.17 2.14 May-09 -3.23 Oct-08 Chile 63.72% 0.28% 0.31% 0.03% 0.70% 6.50% S.America 0.02 2.65 Jan-09 -3.18 Sep-01 China 225.48% 3.63% 7.88% 4.25% 0.31% 9.09% E.Asia 0.09 3.87 Jun-99 -3.68 Aug-01 Colombia 89.75% 0.35% 0.44% 0.09% 1.49% 9.65% S.America 0.19 2.62 May-01 -2.55 Oct-08 Czech 167.01% 0.22% 0.39% 0.17% 1.43% 7.70% Europe 0.18 2.74 May-99 -3.54 Oct-08 Denmark 50.18% 0.62% 0.62% 0.00% 0.59% 5.59% Europe 0.23 2.53 Apr-09 -3.36 Oct-08 Egypt 46.70% 0.30% 0.30% -0.01% 1.12% 9.62% M.East 0.10 3.27 Jan-05 -2.42 Nov-08 EMU 49.35% 24.19% 24.08% -0.11% -0.12% 5.88% EMU 0.14 2.17 Apr-09 -3.05 Oct-08 Hong Kong -1.06% 0.59% 0.39% -0.20% 0.03% 6.44% E.Asia -0.06 2.71 Nov-99 -2.80 Sep-01 Hungary 142.93% 0.17% 0.28% 0.11% 0.68% 9.56% Europe 0.22 2.20 Feb-05 -4.87 Oct-08 India 113.55% 1.48% 2.11% 0.63% 1.12% 9.68% E.Asia 0.12 2.76 May-09 -2.68 Jun-08 Indonesia 310.34% 0.34% 0.93% 0.59% 1.00% 10.95% E.Asia 0.14 2.91 Jun-99 -3.16 Oct-08 Israel 41.04% 0.39% 0.37% -0.02% 0.48% 7.82% M.East 0.14 2.98 Feb-00 -2.73 Sep-01 Japan -3.92% 13.69% 8.77% -4.92% -0.24% 5.35% E.Asia -0.05 2.69 Aug-03 -2.82 Dec-00 Malaysia 135.63% 0.26% 0.40% 0.15% 0.64% 6.47% E.Asia 0.10 2.96 Aug-99 -2.71 Jun-00 Mexico 98.10% 1.50% 1.98% 0.48% 0.80% 8.06% N.America 0.07 2.16 Mar-09 -3.49 Oct-08 Morocco 70.31% 0.14% 0.16% 0.02% 0.36% 5.35% M.East -0.05 4.06 Jan-06 -2.73 May-06 New Zealand 83.11% 0.19% 0.24% 0.04% -0.20% 6.34% Oceania 0.04 1.90 Mar-09 -3.54 Jun-08 Norway 129.58% 0.53% 0.82% 0.28% 0.47% 7.86% Europe 0.19 1.54 Feb-04 -4.25 Sep-08 Peru 74.46% 0.20% 0.24% 0.03% 1.30% 8.57% S.America 0.17 3.33 Mar-09 -3.44 Oct-08 Philippines 96.40% 0.23% 0.30% 0.07% -0.28% 7.96% E.Asia -0.07 2.60 Jan-02 -2.80 Jun-08 Poland 136.21% 0.61% 0.96% 0.35% 0.36% 10.05% Europe 0.09 2.43 Oct-01 -3.36 Oct-08 Russia 375.33% 0.97% 3.06% 2.09% 1.29% 12.08% Europe 0.14 3.75 Dec-99 -3.21 Nov-00 Singapore 69.33% 0.29% 0.33% 0.04% 0.28% 7.31% E.Asia 0.07 2.54 Jun-99 -3.22 Sep-01 South Africa 57.86% 0.48% 0.50% 0.02% 0.67% 7.55% Africa 0.14 2.38 Mar-09 -2.63 Oct-08 South Korea 106.26% 1.23% 1.69% 0.46% 0.69% 9.88% E.Asia 0.04 2.98 Jun-99 -2.28 Feb-09 Sweden 47.16% 0.90% 0.88% -0.02% 0.23% 8.16% Europe 0.01 2.40 Feb-00 -2.45 Mar-01 Switzerland 40.68% 0.97% 0.91% -0.06% 0.04% 4.40% Europe 0.17 2.14 Mar-09 -3.39 Nov-08 Taiwan 12.25% 0.98% 0.73% -0.25% -0.23% 8.83% E.Asia -0.18 2.75 Jan-01 -2.78 Sep-01 Thailand 86.76% 0.40% 0.50% 0.10% 0.31% 9.34% E.Asia -0.02 2.72 Jan-01 -2.69 Feb-00 Turkey 108.62% 0.95% 1.32% 0.37% 0.54% 16.30% M.East 0.16 3.08 Dec-99 -3.52 Nov-00 UK 39.69% 5.16% 4.80% -0.36% -0.33% 4.63% Europe -0.07 2.23 Apr-09 -3.17 Nov-08 US 24.55% 31.13% 25.85% -5.29% -0.28% 5.15% N.America 0.01 1.97 Mar-00 -3.13 Nov-08
World 50.03% -0.15% 4.86% 0.11 1.96 Apr-09 -2.78 Feb-09
17
The worldwide best performance in my sample period was on average achieved in August 2003, after the central banks around the globe lowered the interest rates to low levels, e.g. Euribor 3M in August 2003 is 2.14%, down from 4.35% in August 2001. In October 2008 was the worst period over the past decade, during the peak of the financial crisis. On regional levels the picture differs, while the record downturns still reside in October 2008 for the majority of the countries, the peaks differ considerably. For the East Asian region, the best performance was achieved in 1999, after the Asian Crisis was put behind and the markets started to recover, while for others it were boom periods in 2005 or 2009. This shows that the obtainable benefits of diversification are volatile. Hence, portfolio strategies need to be flexible to incorporate the changes.Figure 2 – Correlation of Stock Returns of the GDP weighted World Regions to the GDP weighted EMU Index from 1999-2004 and 2005-2009
Correlation of the EMU GDP Weighted MSCI Index to the GDP weighted regions. Sample Period is 1999 to 2009 and split after 2004 to show changes over time.Source: self-created figure with data from IMF and DataStream
Figure 2 displays the correlations of the different GDP weighted regions to the EMU index over the period from 1999 to 2009. I split the sample in the middle to display changes that occur over time in correlations. As I already showed in Figure 120, the members of European Monetary Union itself had a very high correlation to the index and to each other. Over the time other European countries, which are not part of the EMU or even the EU yet, on average increased their correlation with the EMU index. A good example for this is Norway, which is neither but increased the correlation to the index from 0.56 to 0.94. Similar correlation developments with the EMU index go for Oceania and Africa, while North America was stable over the period. In contrast to this, the regions of South America, East Asia and the Middle East have their correlation decreased significantly, with South America now having the lowest correlation to the EMU index of all regions, including Colombia, which has the lowest overall correlation amongst all countries with the EMU index of 0.1. This change of the correlation can be explained with the
20
18
recent financial crisis, in which developed countries were involved stronger, while emerging markets and commodity supplying countries recovered fast.Considering the descriptive statistics, the high correlation amongst EMU countries, low risk-adjusted returns and changing correlations suggest that different regions grow together. Hence, while old investment locations present less growth potential, new arise and therefore new investment strategies and foci are need, part of which is accounted for in this thesis.
V. Results
In this section, I report the estimation results obtained by applying the models of the previous section to identify diversification effects of international diversification for the EMU-investor. The first part of this section will deal with the in-sample results, where I optimize the Sharpe-Ratio according to each limitation and compare the obtained weights of each strategy to the other, in terms of average and median return, volatility and the Sharpe-Ratio. I further emphasize the impact of each limitation in the investment strategy on the outcome for the investor. The second part contains the discussion of the different portfolio weights of each strategy and the last section presents the out-of-sample results, which uses the weights obtained in the in-sample optimization and applies them to the following periods.
V-I In-Sample Results
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Table 3 –Statistic results of the in-sample returns for each strategy 05.2004-04.2010SS OW(3) OW(5) OW(10) MVP EMU
Mean 0.0217*** (-21.9199) 0.0083*** (-6.9146) 0.0111*** (9.9187) 0.0139*** (-12.9237) 0.0037*** (-2.9908) 0.0013 Median 0.0233*** (10.3384) 0.0095*** (6.0592) 0.0128*** (7.8133) 0.0152*** (8.7642) 0.0040*** (3.2623) -0.0002 Maximum 0.0315 0.0204 0.0241 0.0248 0.0103 0.0134 Minimum 0.0119 -0.0022 -0.0005 0.0030 -0.0027 -0.0065 Std. Dev. 0.0056 (1.1891) 0.0065 (1.7714) 0.0063 (0.5837) 0.0061 (0.1857) 0.0037*** (7.6473) 0.0056 Skewness -0.1190 0.0679 -0.0843 -0.1325 -0.1524 0.6064 Kurtosis 1.4519 1.9708 2.1314 2.0722 1.7521 2.1507 Jarque-Bera 7.3595 3.2331 2.3486 2.7929 4.9502 6.5768 Probability 0.0252 0.1986 0.3090 0.2475 0.0842 0.0373
This table shows the outcome of the historical returns of the different investment strategies: the average, the median, maximum, minimum, the standard deviation (Std. Dev.) , skewness, kurtosis and the test for normality, the Jarque-Bera, of the according strategy to the benchmark over the 72 tested portfolios per investment strategy from 05.2004 – 04.2010. The strategies are: short sale constraint (SS), GDP three times overweight (OW(3)), GDP five times overweight (OW(5)), GDP ten times overweight (OW(10)), minimum-variance portfolio (MVP) and European Monetary Union GDP weighted index (EMU).
The significance levels reported are: * Significant at 10%; ** Significant at 5%; *** Significant at 1%; t-statistics in parentheses
The average and median returns in the optimized portfolios are positive and significantly reject the hypothesis of equality to the benchmark, the EMU index. 21 The short sale constraint portfolio shows the highest performance, with an average return of 0.0217 and a median return of 0.0233 per month, whereas the most restricted portfolio, the three times GDP overweight portfolio does have an average return of 0.0083 and a median return of 0.0095 per month. The minimum-variance portfolio does have the lowest average and median return of the computed portfolios, with 0.0037 and 0.0040 respectively. All portfolios outperform the EMU index and thus show that by optimization an increase in performance is achieved, which supports H1a. None of the Sharpe-Ratio optimized portfolios does differ significantly from the benchmark in its standard deviation, while the minimum-variance portfolio on the other hand does, having the lowest volatility with 0.0037 per month. Thus, I reject H1b for all Sharpe-Ratio maximized portfolios, and do not reject it for the minimum-variance portfolio. This points out that, by using the Sharpe-Ratio optimization, the mean return is the changing variable.
21
20
Table 4 –Statistic results average Sharpe-Ratio historical returns 05.2004-04.2010SR SS SR OW(3) SR OW(5) SR OW(10) SR MVP SR EMU
Mean 0.3715* 0.1160 0.1629 0.2094 0.0414 -0.0072
Median 0.3648** 0.1007 0.1452 0.1806 0.0454 -0.0480
Maximum 0.6624 0.4306 0.4757 0.5211 0.2739 0.2805
Minimum 0.1265 -0.0853 -0.0531 0.0050 -0.1738 -0.1665
Std. Dev. 0.1626 0.1421 0.1394 0.1427 0.1310 0.1220
This table shows the outcome of the Sharpe-Ratio of the different investment strategies: the average, the median, maximum, minimum, and the standard deviation (Std. Dev.) of the according strategy over the 72 tested portfolios per investment strategy from 05.2004 – 04.2010. The strategies are: short sale constraint (SS), GDP three times overweight (OW(3)), GDP five times overweight (OW(5)), GDP ten times overweight (OW(10)), minimum-variance portfolio (MVP) and European Monetary Union GDP weighted index (EMU).
The significance levels reported are: * Significant at 10%; ** Significant at 5%; *** Significant at 1%
Table 4 shows the results for the average Sharpe-Ratio computed over the 72 periods. The outcomes are similar to the previous table, with the short sale constraint portfolio outperforming the more restricted portfolios. The average and median Sharpe-Ratio is 0.3715 and 0.3648 per month respectively. The lowest Sharpe-Ratio optimized portfolio is the three times GDP overweight, with an average Sharpe-Ratio of 0.1160 and a mean Sharpe-Ratio 0.1007 per month. The benchmark does have a negative average and median Sharpe-Ratio during the 72 periods. However, the only significant result is the Sharpe-Ratio optimized short sale constraint portfolio, being significant in the average at the 0.10 confidence level and in the median at 0.05 confidence level, while the others cannot substantiate a considerable deviation from zero. Noticeable is the high volatility amongst all the ratios, indicating that the obtainable benefits of diversification do differ during the selected period. The decrease of the Sharpe-Ratio, while increasingly restricting the optimization process, is in line with the findings of Chiou (2008), who proved this for the US market.
Figure 3 displays graphically the over-time performance of the Sharpe-Ratio to illustrate the differences amongst the diverse strategies. The timeline of the Sharpe-Ratios shows the obtainable benefits of diversification. A higher Sharpe-Ratio indicates a higher return per unit of risk; all the strategies outperform the EMU-index in Figure 3 and thus show that international diversification is able to yield beneficial results. The Sharpe-Ratios were the highest during the boom period from 2005-2008 and peak during the market maximum shortly before the financial crisis. Thus, the results show that the risk-return ratio is higher during bull markets, and is decreasing during bear markets. 22
22
21
Figure 3 – Sharpe-Ratio of the historical returns 05.2004-04.2010
This figure shows the progress of the Sharpe-Ratio of the different investment strategies over the 72 tested portfolios per investment strategy from 05.2004 – 04.2010. The strategies are: short sale constraint (SS), GDP three times overweight (OW(3)), GDP five times overweight (OW(5)), GDP ten times overweight (OW(10)), minimum-variance portfolio (MVP) and European Monetary Union GDP weighted index (EMU)..
I present the average Sharpe-Ratio difference, calculated using Opdyke’s (2008) methodology, to the benchmark in Table 5. The ranking amongst the optimized portfolios, in respect to their risk-return ratio, stays the same, yet the average and median increases slightly. In this case, I test the significance for the deviation from the benchmark; however, the results for this test are mixed. Three out of the five portfolios show significant outperformance: the short sale and ten times GDP overweight constraint portfolio at the 5% level and the five times GDP overweight constraint portfolio at the 10% level.
Table 5 –Statistic results average Sharpe-Ratio difference to benchmark (EMU-index) historical returns 05.2004-04.2010
SR SS SR OW(3) SR OW(5) SR OW(10) SR MVP
Mean 0.3787** 0.1283 0.1701* 0.2165** 0.0485
Median 0.3866** 0.1059 0.1828* 0.2253** 0.0584
Maximum 0.5175 0.3641 0.2247 0.2969 0.1767
Minimum 0.2204 0.0136 0.0825 0.1278 -0.0798
Std. Dev. 0.0766 0.0918 0.0373 0.0392 0.0577
This table shows the outcome of the Sharpe-Ratio difference of the different investment strategies: the average, the median, maximum, minimum, and the standard deviation (Std. Dev.) of the according strategy to the benchmark over the 72 tested portfolios per investment strategy from 05.2004 – 04.2010. The strategies are: short sale constraint (SS), GDP three times overweight (OW(3)), GDP five times overweight (OW(5)), GDP ten times overweight (OW(10)), minimum-variance portfolio (MVP).
The significance levels reported are: * Significant at 10%; ** Significant at 5%; *** Significant at 1%
22
methodology of Opdyke (2008) that the results from the less constraint portfolios do support H1c, and therefore present an improvement in the risk-return behavior towards the EMU-index, while the strict constraints for the three times GDP overweight and MVP portfolio fail to achieve this. This result contradicts the findings of De Roon, Nijman and Werker (2001), who said that short sale constraints alone already render international diversification useless. My findings indicate that this is not the case, but it is possible if the constraints applied are very strict, as in the case of the minimum-variance and the three times GDP overweight portfolio. Adding tight upper weighting boundaries, e.g. three times overweight, to the short sale constraint can lead to the elimination of obtainable diversification benefits. This confirms the results of Chiou (2008), Li, Sarkar and Wang (2003), Bekaert and Urias (1996) and Gerke, Mager and Röhrs (2005). Interestingly, the standard deviation of the constructed portfolios is considerably smaller the lower the constraints are, although the benchmark did not perform significantly different from zero. Especially the standard deviation of the five and ten times GDP overweight constraint portfolio do have a low volatility towards the benchmark, indicating a stable outperformance close to the reported mean.Figure 4 shows the Sharpe-Ratio over time when adjusted for the difference to the EMU index. In general, the trend of the ratio proceeds flatter compared to the original, as implied by the lowered standard deviations presented in the previous table. Thus, the maximum and minimum of each portfolio is closer to the median. Notable is the drop of the Sharpe-Ratio in the MVP at the end of the boom period in 2007 and the negative period in the beginning, indicating an underperformance of this portfolio to the benchmark twice. The composition of the MVP, which is presented in the next section, explains this partially.
Figure 4 – Sharpe-Ratio Difference to Benchmark of the historical returns 05.2004-04.2010
