A new selection strategy for portfolio diversification in the European Union.

Choudhury, Askar H. ; Naidu, G.N.

INTRODUCTION

The benefits of global portfolio diversification have been largely accepted and recognized by the investors in recent years. An extensive literature discussion in this research area appears in Solnik (1988). Benefits of portfolio diversification emerge from the motivation of minimizing risk and maximizing the return. One measure of portfolio risk is the portfolio variance. Portfolio variance depends on the variance of each asset and also the correlations among themselves. Thus, correlation plays a vital role in the creation of diversified portfolio. Researchers (Grubel, 1968; Bailey & Stulz, 1990; Divecha et al, 1992; Michaud et al. 1996) have shown that benefits of portfolio diversification are stemming from the relatively low correlations between equity markets in the global arena. Yet, the spurious nature of correlation between country indexes due to global market dominance may impact the likely benefits of global investment. A natural prevention of global market dominance in diversified portfolio creation is to use partial correlation with respect to the world market.

This paper explores the opportunities for investment diversification in the EU stock markets by employing partial correlation in portfolio creation. Research studies conducted recently showed that the central European stock markets are not yet integrated with the stock markets of the EMU members such as Germany. Gilmore and McManus (2002) conducted co-integration tests on stock markets of Germany, Poland, the Czech Republic and Hungary. They found no long-term relationship between the German market and the three central European markets. Naidu and Choudhury (2004) conducted co-integration tests on stock markets of France and the ten new members of the Union and found that the stock markets are not yet integrated. The lack of integration among the 25 EU stock markets offers an opportunity for investors in and outside of EU to diversify and reduce risk. Gilmore and McManus (2003) examined this very specific issue. They found that the U.S. investors and German investors can reduce risk by diversifying their equity portfolios into the central European equity markets such as Poland, Czechoslovakia, and Hungary. Naidu and Choudhury (2006) proposed that country's beta estimate offers a better insight to judge the extent of risk reduction achievable through international diversification.

Here, we propose partial correlation criterion to select assets in the portfolio and optimization of coefficient of variation to determine the proportion of asset allocation in EU countries for French and German investors. We evaluate their performance using Sharpe's Index and compare them with portfolios created by simple correlation criterion. In general, results based on performance measure indicate that partial correlation approach (i.e., partialing out the influence of world market) is superior to Markowitz approach (correlation based). Moreover, proportion of asset allocation based on optimizing the coefficient of variation produced portfolios that have positive risk-adjusted return.

RESEARCH METHODOLOGY

The idea of risk reduction using the correlation structure of returns determines the extent of benefits derived through diversification. This idea of smaller the degree of correlation the greater the benefit of diversification was popularized by Harry Markowitz (1959). However, in the context of global market the degree of correlation between two markets is also influenced by aggregated world market. Therefore, the apparent magnitude of a correlation between two specific markets may be due to the influence of world market on those markets. As for example, the level of correlations between France & Hungary and Germany & Hungary has decreased dramatically from 0.296271 and 0.315271 to 0.097316 and 0.093948 (see Table 1) respectively when calculated as a partial correlation with respect to the world market. Thus, partialing out the influence of world market to create portfolios for diversification may lead to a better performance.

Theoretical Background

As the global market in the international arena becomes more integrated, the developed markets have displayed greater synchronization compared to emerging markets. Therefore, recent liberalization of emerging markets and their increasing involvement into the world market creates an opportunity for portfolio diversification. Collectively all national equity markets together creates global capital market. Therefore, if we aggregate all the national equity markets we will have a great world equity market. Each national equity market has its own degree of volatility. However, the volatility relative to each other will be different. In the same way an equity market's volatility relative to an index of world equity market will be different. Just as one can estimate the risk of an asset relative to a market index, one can also estimate the risk of a national equity market relative to world equity market index. Thus, a country's correlation is the measure of its market's sensitivity to world market variability. Bekaert and Harvey (1997) concluded that market volatility is a function of the openness of its economy. Therefore, a country's correlation is indicative of integrator. The smaller the correlation, the more segmented is the country's market and hence better will be the gains from diversification. Consequently, international diversification pushes out the efficient frontier further by allowing investors simultaneously to reduce their risk and increase their expected return. Similarly, we can also study the sensitivity of a given equity market to the movements of another equity market of our interest. For example, if we want to know how sensitive the Hungarian equity market is relative to the movements in German equity market, we can examine this relationship by estimating country correlation for Hungary with respect to the German equity market. Markowitz (1959) theorized that the smaller the degree of correlation the greater is the benefits of diversification. However, this theory looks too simple when it comes to global diversification. In a global market, it is possible for a pair of countries to have a high degree of correlation between themselves and yet have low degree of partial correlation after purging the world market influence.

[ILLUSTRATION OMITTED]

[ILLUSTRATION OMITTED]

Partial correlation between country i and country j with respect to the World Market can be expressed as (Neter, Wasserman, and Kutner, 1990):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [r.sub.i,j] Correlation coefficient between [i.sup.th] market returns and [j.sup.th] market returns.

For example,

[[rho].sub.Hungary, France] = 0.30 [[rho].sub.Hungary, Germany] = 0.32

[Partial Correlation.sub.Hungary, France] = 0.09 [Partial Correlation.sub.Hungary, Germany] = 0.09

In this example, the difference in correlations and partial correlations may produce different portfolios. Therefore, even though Hungary and France or Hungary and Germany had higher degree of correlation (0.30 & 0.32), their partial correlations imply that they offer better gains from diversification compared to other markets that do not have such an overpowering world market influence. In fact, Hungary moved up to the second portfolio level from the third portfolio level when portfolios are created by partial correlations instead of correlations (see Exhibit 1 and Exhibit 2). This example demonstrates that better gains from diversification may be achieved by using partial correlations rather than the simple correlations. In addition, the relational stability between two countries for the diversification purposes may be more desirable when their correlations and partial correlations remain same (or similar) in the long run. On the basis of this theory we develop two sets of portfolios using: a) correlations and b) partial correlations as a criterion.

Diversification Strategy

Portfolios are constructed for the purpose of diversification in the EU stock markets for French and German investors respectively. We identify the opportunity for portfolio diversification using both correlation and partial correlation criterion for selecting the country into a portfolio. For example, a French investor may look at the remaining 24 countries and select the country with the smallest correlation or partial correlation to invest. The country with the next highest correlation or partial correlation could be the second investment to add to the portfolio. Following this procedure the investor will allocate funds to the markets in an ascending order of the country's correlation or partial correlation value --- the smallest correlation or partial correlation country will be chosen first and the highest correlation or partial correlation country will be chosen last. In this process of portfolio selection three strategies are adopted. First, majority fund allocation (80%) was applied to the home country and rest of the 20% was equally divided among the four other countries (5% each). This is called Home country strategy (HOME). So a French investor will have 80% of the funds invested in French stock market and 20% outside of France. Second, funds are equally (20% each) allocated to all five countries in the portfolio. This is called Naive strategy (NAIVE). Third, proportion of funds that are allocated to five different countries is determined by optimizing the coefficient of variation (calculation is done via a nonlinear optimization program in SAS) and the strategy is called Optimum strategy (OPTM). Following these procedures, the French investor will have five portfolios (five-assets each). Similarly, five portfolios are constructed for the German investor. In total, we have 10 portfolios constructed and calculated for each strategy to measure the performance. The risk-return characteristics of these portfolios are estimated for the eight year period, 1995-2002. We hope to demonstrate that partial correlation based approach to portfolio diversification offers a new way to build globally diversified portfolios. We have evaluated each portfolio performance using Sharpe's Index.

The Optimum strategy (OPTM) involves identifying the optimum proportion of funds allocated among five different countries in each portfolio. To attain that, coefficient of variation (CV) is optimized (minimized in this case) with respect to proportions (weights or percentages) of fund allocations. Therefore, the objective function f (W) is optimized (by calling SAS nonlinear optimization sub-routine NLPTR into the SAS program) as below.

Minimize:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where W and: [mu] are defined below.

Measures of Performance

To evaluate the performance of a portfolio, both return and risk should be incorporated into the performance measure. A portfolio is said to be mean-variance efficient if it possess the highest level of expected return at a given level of risk. Equivalently, it is efficient if it has the lowest level of risk for a given level of expected return. Thus, the desire for global (external) diversification is to optimize the risk-reward ratio, which also reinforces the importance of country selection strategy for an optimum portfolio. Portfolios that are diversified globally have more potential to lower the risk for the same level of expected return, or to increase the return for the same risk level. Consequently, the risk-reward ratio of a globally diversified portfolio is potentially far better-off.

Coefficient of variation (CV) measures the relative variability and can be used to measure the standardized risk with respect to the mean. Therefore, coefficient of variation can be considered a risk-reward ratio. Coefficient of variation of a portfolio return is expressed as,

CV [sub.p] = [[sigma].sub.p]/[[mu].sub.p] x 100

The smaller the CV the better is the performance of the portfolio. Thus, a portfolio is considered to be more diversified if the CV is smaller in magnitude.

William Sharpe (1966) developed a composite (risk-adjusted) measure of portfolio performance called the reward-to-variability ratio. This measure also known as Sharpe's Performance Index (PI), which can be expressed as,

[PI.sub.p] = [[mu].sub.p] - r/[[sigma].sub.p]

Where, [[sigma].sub.p] = standard deviation of [p.sup.th] portfolio return [[mu].sub.p] average return of [p.sup.th] portfolio, r = risk-free rate = for this period. Therefore, the higher the values of the index better the performance of that portfolio on risk-adjusted basis.

Performance of a portfolio diversification will be evaluated by using the expected return and standard deviation of return for a portfolio consisting of a proportion of assets invested in the home country and the remaining portion of assets invested in four other countries (or markets). We will attempt to develop and evaluate three different strategies to determine the proportion (weights) of asset allocation in constructing a portfolio.

The expected return and variance of a portfolio is expressed as,

[[mu].sub.p] = W' [mu] and [V.sub.p] = W' [summation] W

where, W is the vector of portfolio weights (or proportion) for different markets,: is the mean vector of returns of markets in the portfolio, and [summation] is the variance-covariance matrix. For example, the mean and variance of a portfolio with only two markets (assets) can be written as,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Where [[mu].sub.1] average return of market-1, [[mu].sub.2] average return of market-2, [[sigma].sub.1] standard deviation of return of market-1, [[sigma].sub.2] standard deviation of return of market-2, [[sigma].sub.1][[sigma].sub.2] covariance of returns between market-1 and market-2.

EMPIRICAL RESULTS

The data for this study covers the period, 1995-2002. The daily data for all the stock market indices of the EU region were obtained from Global Financial Data, Inc. and SourceOECD. The daily returns were computed and annualized. Since, the correlation structure of returns has been one of the bases for judging the diversification (risk reduction) potential. We have estimated the correlation structure of annualized daily stock returns among the EU equity markets and presented in Table 1, along with mean and standard deviation. As pointed out earlier in the paper, for certain markets the correlation structure does not give us adequate picture of diversification potential when global diversification is sought. However, partial correlation criteria may have a greater potential for global diversification. Therefore, we estimated partial correlation for all the EU stock markets with respect to the world market. This helps to observe the relationship between two markets independent (without the influence) of world market. We have used Morgan Stanley Capital International Index to represent World Equity Market. These partial correlations are also reported in Table 1.

As discussed in the methodology section above, a set of 10 portfolios were created using Markowitz approach (correlation). We have also created another set of 10 portfolios using partial correlation as the basis for market (country) selection. The set of portfolios appear in Exhibit 1 and Exhibit 2. As can be seen from these exhibits, the least correlated country (asset) portfolio and the lowest partial correlation portfolio are exactly identical in composition of countries. Furthermore, the first portfolio constructed at the lowest risk level is the same regardless of the investors' home market. The portfolio composition changes, however, as the correlation and the partial correlation levels ascend. For example, the portfolio-2 for French investor has a slightly different composition using partial correlation than correlation criterion. A similar change in composition occurs to German investors in portfolio-3. Therefore, it appears that at or above second level of screening, using correlation as selection basis produces portfolio that is different in composition than that produced by the partial correlation as the selection criterion.

Table 2 presents the mean, standard deviation, coefficient of variation, and Sharpe's Index for all 10 portfolios constructed using the correlation-based (Markowitz) screening criterion. Each portfolio is evaluated for three strategies of proportion of asset allocation. Sharpe's Index values are mostly negative implying that eight out of ten portfolios constructed using Markowitz approach underperformed the risk-free assets (short-term government debt) in their respective home markets. The degree of underperformance varied greatly among the 10 portfolios. Yet, optimum diversified portfolio produced expected return (4.07 and 4.09 for French and German respectively), two and a half times more than the expected return received in the home country alone, at the same risk level.

Table 3 displays the mean, standard deviation, coefficient of variation, and Sharpe's Index for 10 portfolios constructed using the partial correlation as the basis for screening. Each portfolio is evaluated for all three strategies of proportion of asset allocation. While a majority of portfolios constructed using partial correlation approach produced negative values of Sharpe's Index, the second set of portfolios for French showed uniquely positive values of Sharpe's Index and lower values for coefficient of variation. Thus, partial correlation based method of constructing portfolios produced superior performance of risk-adjusted returns compared to Markowitz method. Using optimum strategy for determining proportion of asset allocation, the stock markets of Cyprus, Turkey, Hungary, and Greece offered an opportunity for investors in France to diversify and construct portfolios with superior risk-adjusted performance in the EU. The evidence supports the argument that portfolio risk can be substantially reduced or expected return can be enhanced by employing optimum strategy (OPTM) for portfolio diversification in the European Union.

CONCLUSION

The simplest way to measure the benefit of a portfolio diversification in the European Union is to estimate how much portfolio diversification can reduce the variance and or increase the expected return of a diversified portfolio compared to the home country's variance and expected return. International portfolio diversification is advocated to earn higher returns with lower risk in a world of less integrated capital markets. Markowitz approach to domestic diversification was simply extended to global diversification by Levy and Sarnat (1970) and Solnik (1974). Little attention has been directed toward the investigation of reducing global market influence for potential diversification gain in international arena. This paper proposes a method of portfolio selection on the basis of partial correlation criterion by seeking market relationship that is independent of world market. Portfolios are constructed using both partial correlation approach and Markowitz (correlation) approach for two different home markets France and Germany. Then, the performances of these portfolios have been measured for three different strategies in determining the proportion of asset allocation in the portfolio. An interesting finding is that, the two different approaches produce portfolios with different composition of markets, but the composition of markets stay same for the first portfolio in both home markets. Further analysis reveals that partial correlation approach produces superior portfolios as opposed to Markowitz approach. Moreover, the optimum strategy that minimizes the coefficient of variation to determine the proportion of asset allocation has a better potential for diversification compared to two other strategies considered in this paper.

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Askar H. Choudhury, Illinois State University

G. N. Naidu, Illinois State University

TABLE 1: Correlations, Partial Correlations, Means, and Standard
Deviations of Annualized Daily Stock Market Returns (1995-2002)

Country France Germany World
 (Correlations) (Correlations) (Correlations)

Cyprus 0.059046 0.046494 0.038089
Czech 0.351897 0.324579 0.306574
Hungary 0.296271 0.315279 0.337839
Latvia 0.008884 -0.01817 0.023028
Lithuania 0.020614 -0.0047 0.018747
Poland 0.36543 0.378087 0.319775
Slovak 0.029986 0.022593 0.032422
Slovenia 0.020692 0.01494 -0.0049
Turkey 0.16319 0.158906 0.138863
Austria 0.426421 0.468396 0.346697
Belgium 0.683377 0.647613 0.584029
Finland 0.62046 0.599263 0.533238
France 1 0.76984 0.660969
Germany 0.76984 1 0.689527
Greece 0.234955 0.232911 0.235565
Ireland 0.447095 0.43481 0.362534
Italy 0.601259 0.603676 0.487409
Luxemburg 0.281296 0.261491 0.233913
Portugal 0.495286 0.462819 0.406607
Spain 0.789752 0.695305 0.60665
Netherlands 0.835584 0.779351 0.651458
Denmark 0.568403 0.561496 0.468453
Sweden 0.735656 0.680177 0.60467
England 0.789947 0.701462 0.655697
World 0.660969 0.689527 1

Country France Germany Mean Std Dev
 (Partial * (Partial *
 Correlations) Correlations)

Cyprus 0.057608 0.04837 2.548886 31.61424
Czech 0.247331 0.171775 0.840479 15.25584
Hungary 0.093318 0.094988 1.428562 17.77597
Latvia 0.002168 -0.04513 3.682336 32.09027
Lithuania 0.030142 -0.03859 2.885802 54.48763
Poland 0.193474 0.181609 2.975744 26.76885
Slovak -0.01259 -0.0077 0.951593 18.09857
Slovenia 0.038167 0.021164 1.634605 19.97969
Turkey 0.07028 0.077605 9.048344 46.25241
Austria 0.268252 0.225224 0.468229 9.771192
Belgium 0.537781 0.407067 1.024673 14.19741
Finland 0.364432 0.330889 3.905338 29.09374
France 1 0.596944 1.64994 18.26091
Germany 0.596944 1 1.794359 19.6342
Greece 0.097316 0.093948 2.399457 22.49086
Ireland 0.275083 0.234488 0.92267 12.63724
Italy 0.422716 0.352264 1.408155 15.88367
Luxemburg 0.165545 0.09329 0.854859 12.86015
Portugal 0.320371 0.191465 0.706565 11.05724
Spain 0.684668 0.489938 1.788768 18.33543
Netherlands 0.763377 0.590349 1.674792 18.23667
Denmark 0.414377 0.32492 0.853833 11.13353
Sweden 0.566881 0.448312 1.672451 18.13933
England 0.679595 0.476048 0.96971 14.10533
World 0.057608 0.04837 0.632045 10.78917

* Partial correlations are calculated with respect to World Index.

TABLE 2: Portfolio performance on three different strategies.
(Correlation is used for portfolio selection)

Portfolios of Strategy MEAN STD CV % Sharpe
investment Index

French-1 OPTM 2.00 11.34 567.80 -0.18
 HOME 1.78 15.22 856.33 -0.15
 NAIVE 2.16 15.45 715.21 -0.12
French-2 OPTM 4.07 18.10 444.38 0.00
 HOME 2.06 15.90 770.87 -0.13
 NAIVE 3.30 15.07 456.56 -0.05
French-3 OPTM 2.18 17.55 804.72 -0.11
 HOME 1.61 16.04 999.11 -0.15
 NAIVE 1.47 12.78 867.59 -0.20
French-4 OPTM 1.21 11.58 959.06 -0.25
 HOME 1.51 16.06 1060.21 -0.16
 NAIVE 1.11 10.70 965.80 -0.28
French-5 OPTM 3.28 24.33 741.15 -0.03
 HOME 1.74 17.58 1010.69 -0.13
 NAIVE 2.01 16.93 842.32 -0.12
German-1 OPTM 2.05 11.44 558.55 -0.18
 HOME 1.89 16.16 853.66 -0.13
 NAIVE 2.19 15.39 702.93 -0.12
German-2 OPTM 4.09 18.14 443.33 0.00
 HOME 2.18 16.94 777.67 -0.11
 NAIVE 3.33 15.16 455.31 -0.05
German-3 OPTM 1.96 15.47 791.07 -0.14
 HOME 1.74 17.22 987.41 -0.13
 NAIVE 1.59 13.26 832.42 -0.19
German-4 OPTM 3.12 23.16 741.72 -0.04
 HOME 1.73 17.50 1010.34 -0.13
 NAIVE 1.55 12.63 817.05 -0.20
German-5 OPTM 1.65 15.14 918.82 -0.16
 HOME 1.73 18.02 1041.56 -0.13
 NAIVE 1.54 14.44 938.87 -0.17

 Percent (%) allocation in portfolio

Portfolios of Strategy Home Four other countries *
investment

French-1 OPTM 30.05 22.08 2.85 26.13 18.90
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
French-2 OPTM 16.06 16.24 30.30 21.51 15.88
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
French-3 OPTM 42.71 14.75 0.00 42.53 0.00
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
French-4 OPTM 25.26 23.67 9.34 14.72 27.00
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
French-5 OPTM 0.00 76.12 15.34 0.00 8.54
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
German-1 OPTM 29.63 22.35 3.05 26.05 18.92
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
German-2 OPTM 16.30 16.34 30.24 21.25 15.87
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
German-3 OPTM 27.99 9.08 0.00 36.19 26.74
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
German-4 OPTM 10.66 7.03 0.00 10.90 71.41
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
German-5 OPTM 13.72 30.35 0.00 22.96 32.97
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00

* See assigned countries of a portfolio in Exhibit 1.

Note: Five portfolios have been created using correlations in
ascending order for each home country (France & Germany).

OPTM--Percentage allocation obtained by using optimization of CV.

HOME--Percentage allocation is dominated by 80% in the home country.

NAIVE--Percentage allocation is equally weighted (20%) for all five
countries in the portfolio.

TABLE 3: Portfolio performance on three different strategies.
(Partial correlation is used for portfolio selection)

Portfolios of Strategy MEAN STD CV % Sharpe
investment Index

French-1 OPTM 2.00 11.34 567.80 -0.18
 HOME 1.78 15.22 856.33 -0.15
 NAIVE 2.16 15.45 715.21 -0.12
French-2 OPTM 4.57 20.42 446.99 0.02
 HOME 2.09 16.02 766.28 -0.12
 NAIVE 3.42 15.95 467.09 -0.04
French-3 OPTM 1.91 15.07 787.80 -0.14
 HOME 1.58 15.90 1008.56 -0.16
 NAIVE 1.36 11.38 838.11 -0.24
French-4 OPTM 2.81 20.74 738.04 -0.06
 HOME 1.64 16.52 1007.82 -0.15
 NAIVE 1.61 12.86 799.71 -0.19
French-5 OPTM 1.60 15.16 948.53 -0.16
 HOME 1.61 17.11 1059.39 -0.14
 NAIVE 1.51 14.63 969.22 -0.17
German-1 OPTM 2.05 11.44 558.55 -0.18
 HOME 1.89 16.16 853.66 -0.13
 NAIVE 2.19 15.39 702.93 -0.12
German-2 OPTM 4.09 18.14 443.33 0.00
 HOME 2.18 16.94 777.67 -0.11
 NAIVE 3.33 15.16 455.31 -0.05
German-3 OPTM 2.23 18.01 806.21 -0.10
 HOME 1.73 17.20 992.59 -0.14
 NAIVE 1.55 13.23 853.93 -0.19
German-4 OPTM 2.92 21.52 737.27 -0.05
 HOME 1.74 17.52 1005.42 -0.13
 NAIVE 1.59 12.81 805.98 -0.19
German-5 OPTM 1.59 15.10 951.23 -0.16
 HOME 1.69 17.87 1057.88 -0.13
 NAIVE 1.37 13.74 999.88 -0.20

 Percent (%) allocation in portfolio

Portfolios of Strategy Home Four other countries *
investment

French-1 OPTM 30.05 22.08 2.85 26.13 18.90
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
French-2 OPTM 21.45 18.70 34.63 0.08 25.14
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
French-3 OPTM 32.46 29.14 37.75 0.65 0.00
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
French-4 OPTM 0.12 22.64 6.14 63.87 7.24
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
French-5 OPTM 11.54 36.70 0.00 30.63 21.12
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
German-1 OPTM 29.63 22.35 3.05 26.05 18.92
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
German-2 OPTM 16.30 16.34 30.24 15.87 21.25
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
German-3 OPTM 40.30 14.02 0.00 43.53 2.15
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
German-4 OPTM 8.06 0.00 22.47 4.80 64.68
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00
German-5 OPTM 25.24 37.90 2.37 34.50 0.00
 HOME 80.00 5.00 5.00 5.00 5.00
 NAIVE 20.00 20.00 20.00 20.00 20.00

* See assigned countries of a portfolio in Exhibit 2.

Note: Five portfolios have been created using partial correlations in
ascending order for each home country (France & Germany).

OPTM--Percentage allocation obtained by using optimization of CV.

HOME--Percentage allocation is dominated by 80% in the home country.

NAIVE--Percentage allocation is equally weighted (20%) for all five
countries in the portfolio.