The development of international investment

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Introduction

During the past recent decades, the global financial system has facilitated the speed of capital flaws and impressively increased its scale. This fact appears to be an inherent proof of worldwide globalization that becomes apparent in a sense of international investments drift. The possibility to construct a broad-based portfolio for investors has expanded beyond the domestic market and, thus, it allows for a higher degree of diversification. The domestic assets are subject to the shocks of the unique respective economy, and that is why they are more likely to correlate more. Comparing this to investing internationally, the latter reduces correlation between the stocks and, therefore, provides an attractive opportunity for the risk to be allocated over a larger scale of stocks in various economies.

In the process of international diversification, the investor comes up with the ordinary diversification principles. However, for a rational asset selection an investor should take into account several external factors, which are not considered in the context of domestic portfolio construction. The factors that quickly come to mind are, obviously, the exchange rate risk and the political risk. Still, both these risks are tightly coupled with a consideration of investing into a developing or developed country, a country with a sound macroeconomic fundamentals or a politically/economically instable country.

For such reasons, there exists a twofold standpoint when appraising the sources of global diversification benefits: whether the investors are better-off preserving the conventional diversification across the domestic assets, or whether investors are able to extract the gains that take origin from international investing, like the existence of various economic structures, each with its individual inner macroeconomic conditions (for instance, fiscal and monetary policies, growth prospects, balance of payments, public debt, etc.). This paper discusses the stated dilemma that the investors face when deciding on how to diversify the portfolio in terms of the risk-return trade-off.

It is expected that the international diversification brings the benefits to investors in terms of the increase in the Sharpe ratio; also, the benefits are expected to be as large for the emerging markets as for the developed ones, and thus, the developing economies should not be neglected when considering the optimum portfolio. For this issue, an econometric model is provided together with the appropriate tests on its practicality.

The paper is organized as follows. In the second section, a brief history of the evolvement of international investments is related. In the third section, the evidence of growing international investing is made, and some general risks that the investor may face are briefly discussed. Also, the past researches on international diversification issues are analyzed in essence. In the fourth section, the data used in the model estimation is described, it sources are revealed and the expected outcomes are sketched; moreover, the methodology of the analysis is outlined. In the fifth section, the model's application is shown with all the necessary tests on the coefficients and the viability of the model; the results are provided with their implications. Finally, a conclusion is driven together with the discussion of the potential weaknesses of the model.



1. The Dawn of International Investing

investing diversification financial

After the Second World War the world came up with a new system that allowed for higher degree of international cooperation - the Bretton Wood Agreement of 1944. Its main point lied in a sense of allowing getting involved deeper into the international trade and securing the inner economies by bringing into existence the international monetary system, which made possible for the countries to set their own interest rates, but obliging to fix the exchange rates across them. In such a way, the countries pegged their exchange rates against gold, but only United States could directly convert gold into $35 per ounce. Still, for the existence of the Bretton Wood system to be credential, the free movement of capital across the countries was restricted. Another innovation of the system was the introduction of International Monetary Fund, which was created to help countries finance the shortage of foreign currency and current account deficits. Whenever the question of decreased competitiveness of a country arose due to an increase in inflation of other members of the Bretton Wood Agreement, the IMF implemented the deflationary policy to restore the state.

Though the IMF financed the temporary deficits, the continuous printing of dollars in United States for the supplement of Vietnamese war and the current account deficit led to much higher inflation rate than was across other countries, and these shock appeared to be not the short-term one. This expansion finally resulted in the value of liabilities reserves in the dollar currency of foreign Central Banks being higher than the dollar value of gold sustained in United States. The consequence of the issue was an attempt of United States to ensure the rate of convertibility at $35 per ounce and not devaluing dollar due to the reason of another countries that held dollar-denominated assets experiencing then high capital losses and the whole reliance of the Bretton Wood system falling down because of the so-called importing of United States monetary policy to other members of the system. Eventually, the inflationary problem led to the Bretton Wood system collapsing in 1970-71 years. The countries were gradually freeing extensive capital controls since 1960s and were later switching to the floating exchange rate regime. At last, the capital was moving freely with the overthrow of the Bretton Wood system and, simultaneously, the countries were able to pursue the sovereign monetary policies for controlling inflation.

The major impact caused by the collapse of the system was the increased banking activity; it allowed for a higher competition and, moreover, the banks were the able to diversify their activity across different regions in order to avoid the credit risk concentration. This, definitely, led to a higher level of financial stability. With the development of the offshore banking and the introduction of Eurocurrency, the international capital markets substantially expanded the scale of operations across the world; this fact gave a promotion to the financial markets integration.



2. The Intuition Behind Diversifying Across Nations

The processes of globalization and integration of financial markets allowed for higher international exchange of assets, which is driven by international diversification benefits. Since the investor cannot predict the returns of assets, and all the countries experience different behaviour of assets, the investors are able to extract the benefits for their portfolios by reducing the risk when including assets of other countries. For showing the existence of potential benefits, we may turn to the correlation matrix below, from which is seen clearly the existence of imperfect correlation between the returns, the fact that stands for the opportunity to achieve diversification advantages.

2.1 Why do investors diversify across different countries

At first, we shall address to the global markets for equities. In the appendix, one may find the table of market capitalizations and its growth of developed (table 5) and emerging (table 6) countries over 2003-2014 years period and observe the pattern of variability of market capitalization as a percentage of GDP. This fact would propose the differentiation in economic structure across the markets and the reasoning of why do investors may prefer to diversify across emerging markets.

The sample is divided into the developed and developing countries according to the World Bank definition of such. That is, European, Pacific and North American countries are related to as developed ones, while Latin America, Asia, Eastern Europe, Middle East and Africa regions are treated as emerging markets. In the appendix, table 4 lists the countries in the region layout. The model estimated further in the paper also considers this very sample.

If the investor holds a passive portfolio, he would then choose a portfolio of equities of countries with the largest markets capitalizations of listed domestic companies, like Singapore, Hong Kong and Canada, to achieve the diversification benefits. Nevertheless, the investors who want to hold an active portfolio should consider the equities of emerging markets. For instance, they may be interested in adding the fastest growing Chinese or Philippines equities into the portfolios. Comparing the tables 2 and 3 it is clearly seen that the market capitalization growth is extremely large in emerging countries (counting more than 1000% growth); that is why those who seek for diversification should not ignore the developing markets' stocks since the risk-reward trade off would be sturdy.

2.2 Potential problems

As has already been mentioned, the investor comes up with the diversification principles as in the original framework. However, in the international consideration, he should take into account the potential exchange rate and country risks.

The exchange rate risk arises whenever the investor chooses foreign assets to be included into the portfolio. It is the exchange rate risk that constitutes a significant part of the volatility of returns on foreign assets. For instance, whenever the investor changes his local currency for the foreign, buys foreign assets and later sells them, converting the proceeds back into the local currency, the total return that the investor gets may be separated into the return on foreign assets and the return on foreign currency in relation to the local one. The risk can really be crucial for the investor; while, for instance, the annualized standard deviation for Canadian dollar in 2014 was 1.9%, the standard deviation of US index was 2.4%. So, the exchange rate risk would constitute alone about 79% of the risk on index. Still, since the correlation is almost always less than perfect. Following Markowitz predictions, this suggests that the exchange rate risk is partly diversifiable, for instance, by the use of forward or futures contracts or by borrowing and lending in foreign money markets.

The next issue over which the investors' concerns rise is the country risk. This risk implies the possibility of country's borrowers not to meet their obligations. To consider the constituents of country risk, we may refer to some political and social components, like stability of the government, corruption, open economy conflicts, rule of law, ethnical and demographic issues etc., and to economic factors, for instance to GDP statistics, current account balance, inflation rate, foreign debt etc. The main problem that arises in estimating the country risk is that it is measured in part subjectively due to the political and social variables contribution. Generally, the country risk is addressed to by the Country Risk Guide maintained by the Political Risk Services group. PRS measures the country risk by summing the political, financial and economic components and dividing them by 2. The political risk is rated out of 100; the economic and financial risks are rated out of 50 each. The composite risk is estimated in scale out of 100, with the higher value implying the lower country risk.

Another important risk, which agents face during investing internationally, is related to the available liquidity of stocks. Financial markets in emerging economies are less developed and thus, the trading volumes are usually lower as compared to the developed markets. This prevents international investors from buying stocks, because a single, big enough buying order may significantly push up the stock prices. Moreover, the liquidity risk is even more important in the times of rising concerns over the emerging economy. It implies that shareholders are not able to sell their holdings even if they would like to.

The last but not least remark is that the data for cross border holdings is not transparent enough due to the existence of offshore jurisdictions. It is a quite common practice to invest not directly, but rather using an offshore; the main reason for this is tax evasion and sometimes safety. This issue may lead to a so-called home bias, because this results in an underestimation of international holdings and the risk exposure to foreign stocks.



2.3 Literature Review

There are a great number of papers that elaborated the benefits of investing internationally. For example, Harvey (1995) argued that this potential gain stems from the evidence of low correlation between developing and developed countries' equity markets, the fact that reduces the overall portfolio risk. The Asian, Mideast, African and Latin American markets experience high volatility and expected returns. Therefore, the research showed that whenever the investor adds the assets of emerging markets, he hugely improves his portfolio opportunities. Secondly, Harvey studied why the developing countries have high expected returns. Should we address the asset pricing model, we would come up with the logic of high exposure to risk factors, which drives the expected returns upwards. However, Harvey found out that such model cannot explain the cross-section of the returns, possibly because of the assumption of perfect integration of capital markets. Thirdly, Harvey estimated the time series data for emerging markets. His main conclusion was that developing countries differ from the developed ones, because they are more vulnerable to some local shocks rather than global ones, due to being segmented from developed market, and emerging countries are much more predictable in their returns. Harvey provided the following intuition for such conclusion: when studying the time variation, one may observe that the risk loadings in developed countries are approximately constant, because the economy's structure is rather stable. This would not be the same with the emerging market - due to the development of industrial structures, the risk exposure changes. One may observe it by the variations in national index, which is the weighted average of the exposures of listed domestic companies. Also, as have been mentioned, domestic companies are more likely to be influenced by local news, rather then by global. For the conduction of analysis, Harvey used the conditional asset pricing model, which allows for time variations. He collected data on more than 800 equities on emerging markets from International Finance Corporation; expected returns and conditional risk were based on both domestic and global information, while the world risk was based only on global information.

Another survey of interest is that of Cosset and Suret (1995), which studies the factor of political risk inherent in business in the context of international diversification. Such risk is defined as the one that appears in case of business discontinuities that are hard to predict and that arise from the political decisions. Cosset and Suret analyzed how the risk-return trade-off improves if the assets of politically risky countries are included. The political risk applies to all countries, and that is why the estimation of two groups (namely, emerging and developed markets) would be incorrect. The similar logic may be traced here - the existence of low correlation between high and low political risk nations results in a decrease in volatility. It was also shown that the average return on the portfolio consisting of countries of high, middle and low political risk appeared to be higher than the portfolio that included the low political risk countries only. In the analysis, Cosset and Suret use a conventional mean-variance optimization.

Though one may draw a parallel between emerging markets and high political risk countries, such relationship is not always that close. Political risk is inherent in both developed and developing countries and, being a sub-category of country risk, it has a direct influence on the business environment within a sovereign state. In other words, in case a country is incapable to secure foreign currency to service the debt, the agents of that country are exposed to the risk of not being able to meet their foreign currency debt obligations, i.e. to the country risk.

Driessen and Laeven (2007) in their study found the confirmation to the above conclusions - since the emerging markets are less integrated with the developed countries, there is a scope for benefits of investing internationally, and the risk-return trade-off is lowered when not including foreign assets into portfolio. The gains from diversification have contracted with the betterment of country risk; however, there are still a lot of opportunities from which to extract the privileges. The main concern for developing countries' investors should be the existence of restrictions to global investments, and this issue gives rise to the introduction of mutual funds that would be oriented internationally. The authors run the GDP per capita, market capitalization of listed domestic companies, trade to GDP, private credit to GDP and the country risk estimated by PRS on the change in Sharpe ratio for 52 countries (emerging and developed ones), where the expected returns were calculated by MSCI and S&P/IFC indices for time period of 1985-2002. The deeper insight into the model sense is provided in the further section.

One of the predictions of portfolio theory is that the investments in risky assets have weights that are proportional to the weights in the tangency portfolio (i.e. the market portfolio). This rationale can be translated into the sense of the investment weights of assets of different countries being proportional to the size of the respective economy. Nevertheless, there is an empirical evidence of so-called “home bias” - the anomaly according to which the agents tend to invest more of their wealth into the assets of domestic economy. When investigating the home bias, French and Poterba (1991) took six largest stock markets (Unites States, Japan, United Kingdom, France, Germany and Canada) for 1975-1989-time period and calculated the returns on MSCI indices for each country with hedging against the exchange rate risk under three-month forward contract, then investigated the correlation (.502), which suggested the evidence of risk reduction possibility. Next, the authors assumed constant relative risk-aversion utility of investors. Following the maximization rule, the expected returns of holdings of assets of each country were calculated. It appeared that home (US) expected returns were higher than the returns on other countries' equities. French and Poterba stated that institutional constraints couldn't fully explain such choices. For instance, the disparity between the tax burden of foreign equity income and the domestic one is not as great, and also the great capital flaws across the globe highlight that the transaction costs cannot explain the tendency towards domestic investments. Besides, the ambiguity concerning the statistical estimation of expected returns does not allow for the prediction of domestic returns being higher than foreign. Additionally, investors cannot make predictions concerning the volatility of returns on the basis of historical data, and therefore, they are also exposed to the risk concerning the unfamiliarity with foreign markets and institutions.

Moreover, Lewis (1999) proposed that the government restrictions and information costs still might give reasons for the home bias puzzle solution: the latter states that an investor should have an accurate understanding of corporate governance and accounting standards to draw correct information about unlisted companies, while the former recalls the capital restrictions in emerging economies and the existence of taxes and other legal constraints. Lewis used a standard mean-variance analysis to draw the conclusions on the equity home bias puzzle. First, he summarized the annualized monthly returns of market indices by Morgan Stanley for the 1970-1996 for Unites States, Canada, France, Germany, Italy, Japan and United Kingdom. The indices were translated into dollars for the data to be comparable across countries. Next, Lewis calculated the standard deviations of the returns, explaining the volatility coming from two sources: the country risk that affects the local stock market returns, and the exchange rate risk. Next, the author calculated the correlation matrix and suggested that the existence of low correlation between the returns indeed provides the investors with benefits of diversifying internationally. Finally, Lewis calculates the optimal weights for each country's assets to be included into the portfolio, which resulted in the most weight being attributed to the home country (US in the paper). Together with this finding, Lewis's main contribution to the topic was the attempt to explain the equity home bias in the linkage with the consumption home bias. Consumption home bias stands for the possibly greater correlation between local consumption and local output, rather than in the case when investors sell the proportion of claims on output to foreign investors. The rationale is that those investors, who choose to diversify across the domestic assets, rather than internationally, will not allocate their risks towards domestic output optimally. So, the deviation of home consumption from the world one will be highly correlated with the deviation of home output from the world level. Still, this intuition is quite subjective and does not necessarily hold empirically.

All in all, numerous studies were elaborated on the topic of international investments, and the continuous process of integration of financial markets will never stop provoking the new unlit aspects to be discussed.



3. Description of the Model

3.1 Data analyzed

As the core of my analysis, I tried to estimate the factors that impact the Sharpe ratio across different economies, both developed and emerging. The Sharpe ratio is a standard measure of the risk-return trade-off, with an increase standing for the portfolio being more attractive to investors, and vice versa.

As have been mentioned above, I took some insights from the model estimated by Driessen and Laeven (2007). In their research, the authors considered the change in the Sharpe ratio from the perspective of local investors, when the portfolio consisted of developed market stocks (USA, Europe, Japan) was added to the portfolio of stocks of domestic economy. They showed that the inclusion of developed market stocks provides diversification benefits for local investors, which is evident from the increase in the Sharpe ratio for investors in emerging markets.

Despite the idea of diversification is simple as it allows investors to have exposures to different risks, which are not perfectly correlated with each other, and at the same time, to achieve higher expected return, the underlying factors which might provide such diversification benefits are not obvious. Therefore, my research aims to investigate factors that impact Sharpe ratios in different markets that might allow constructing portfolio with cross-border holdings and provide significant diversification benefits.

To learn the benefits, which the diversification across different countries may constitute, the paper considers 48 countries in the sample: 26 developing countries (i.e. the Latin America, Asia, Eastern Europe, and Middle East & Africa regions) and 22 developed countries (i.e. Europe, Pacific and North America regions). These countries were divided according to the World Bank separation of countries into emerging and developed. In the appendix, the table 1 shows the list of the countries analysed.

The basic factors were taken from the analysis of Driessen and Laeven. These are the gross domestic product per capita, trade to GDP, credit to GDP, market capitalization of listed local companies and the country risk. Still, I added some innovations to the explanatory variables in the regression:

1) Instead of the direct level of GDP per capita I estimated the impact of its growth.

2) In addition to the above-listed variables, I took the volatility of exchange rate measured as the annualized volatility of monthly returns, and the global risk sentiment measured as the Sharpe ratio for United States market.

3) Instead of the country risk measure provided by PRS I took the index of economic freedom as an instrumental variable for country risk.

4) Besides the linear relationship of domestic credit to GDP, I also estimated the potential negative impact of high debt levels of credit on Sharpe ratio as a quadratic term. The intuition behind is that too much debt results in a greater financial instability and concerns the whole economy.

To conduct an empirical analysis, I have used data from various sources. At first, the monthly data on stock market index returns was collected from Thomas Reuters Data Stream. This index was elaborated by MSCI - Morgan Stanley Capital International, and is used to evaluate the stock market performance of each of the country. Since the dependent variable, which measures the international diversification benefits, is the change in Sharpe ratio, I firstly calculated the monthly returns on indices; secondly, I calculated the annualized returns as:

Also, I calculated the annualized volatility of monthly returns, and finally, the Sharpe ratio was computed as:



As for the risk-free rate, I used the United States monthly effective federal funds rate, the data on which was collected from the Federal Reserve Bank of St. Louis Economic Research resource.

Next, I collected the data from World Development Indicators of the World Bank on the following:

§ GDP per capita (in current US dollars)

§ Stock market capitalization of listed companies (in current US dollars)

§ Trade to GDP (in %)

§ Domestic credit to GDP by financial sector (in %)

As defined by the World Bank, stock market capitalization, or market value, is the number of shares multiplied by the share price for domestic companies listed. The values are given by end-of-the-year, and they are converted into US dollars using the year-end rates of exchange. Market capitalization is estimated in billions. GDP per capita is the gross domestic product divided by the total country's population given at the middle of the year. It is also calculated in current US dollars. Trade to GDP measures the sum of export and imports as a percentage of gross domestic product. Finally, the domestic credit to GDP measures the debt outstanding to different sectors as a percentage of gross domestic product, given by the monetary authorities and depositary institutions.

The next important issue in the analysis is the consideration of country risk. Most often the literature weights out the data collected from International Country Risk Guide developed by PRS group (Political Risk Services group), described earlier in the paper. However, because of the fact that the data from this resource was unavailable, I took as a proxy the index of Economic freedom. The index of economic freedom stands for the aggregated statistics for the government limits, efficiency of regulatory organs, rule of law and the openness of markets, each of which considers different variables to calculate the weighted index. The countries are then assigned the scores from 0 to 100, where 0 is the least economically free country and 100 is the freest one.

Finally, the exchange rate volatility was also considered. Since the parameters are estimated in the US dollars, I took the exchange rate history of each of the country as indirect exchange rate quotations to dollar from Thomas Reuters Data Stream. The volatility was calculated from the monthly returns, which is then aggregated to the yearly basis.

It is expected that the risk-return trade-off for an investor improves when diversifying across countries with different economic patterns. Thus, the international diversification provides benefits in terms of an increase in the Sharpe ratio. For that reason, we would expect the following outcomes of explanatory variables:

§ Positive relationship between the Sharpe ratio and the growth of GDP per capita; the higher is the growth value, the larger the markets grows, the higher should be the Sharpe ratio;

§ Positive relationship between the Sharpe ratio and the market capitalization of listed domestic companies; the higher the value of market capitalizations, the more developed is the financial market;

§ Unclear relationship between the Sharpe ratio and trade to GDP; since some countries produce relatively more non-tradable goods, this relationship may be biased;

§ Positive relationship between the Sharpe ratio and the linear term of domestic credit, since increasing debt may be a good signal for countries, meaning that they are on the road of boosting growth and are able to repay the debt; after some point, the debt overhang problem may appear, so that the relationship between the Sharpe ratio and the quadratic term of domestic credit (long-run effect) is negative;

§ Negative relationship between the change in Sharpe ratio and the foreign exchange rate volatility; increasing volatility raises the exchange rate risk;

§ Positive between global risk factor and Sharpe ratio (Sharpe ratio of United States is used a global factor to derive the privilege of the international diversification. In other words, whenever the Sharpe ratio of United States increases, this is recognized as the period of the low risk, driving the investors to become more optimistic and to undertake investments of higher risk. Therefore, US Sharpe ratio is only considered as an explanatory variable);

§ Positive relationship between the change in Sharpe ratio and the index of economic freedom; the higher the index value is, the more safe and sound are the governmental bodies.

3.2 Methodology

I estimate the regression using first the pooled OLS approach, and secondly, I use the panel data approach via Stata program to estimate the time variations across the countries. The standard specification for panel data estimation is:

where are the explanatory variables, is an unobserved heterogeneity and is a trend of the dependence on time.

Putting the parameters in the model above, we obtain:

The variables of econometric models are:

§ sr_i - the Sharpe ratio;

§ lgdp_i - the growth of GDP per capita;

§ cap_i - market capitalization of listed domestic companies;

§ trade_i - trade to GDP;

§ cred_i - domestic credit to GDP;

§ fx_i - foreign exchange rate volatility;

§ ecfr_i - the index of economic freedom;

§ sent_i - the global risk factor;

§ е_i - the error term.

Also, the appropriate tests on the presence of heteroscedasticity, serial correlation, multicollinearity and non-stationarity are provided. The summary of the sample is:



4. Application of the Model and General Results

To start analysing the idea of the paper, we should first choose the correct model for further estimation. At first, we may use the pooled OLS regression to fit the model, treating all the observations for all time periods as a single sample. The model is as follows:

It is clearly observable that the coefficients, except for the exchange rate volatility, the index of economic freedom and the global sentiment, are insignificant, which may have resulted due to multicollinearity. However, having checked the correlation matrix, we admit that no severe multicollinearity is present. Then, we may be interested in examining heteroscedasticity of error terms:

H₀: у²_ui = у²_u = 0

P > ч² = 0.0000 (since it is < 0.05, reject the null hypothesis)

The result states that the variance of the error term is not constant; thus, the standard errors are inefficient and, as a consequence, the tests are invalid.

Third, the estimated standard errors mistakenly assume that errors are independent of countries over the given time period. Whenever we wish to control to heteroscedasticity and serial correlation, we should use cluster-robust standard errors. Below is the output, which implies that even after the application of such standard errors, the only coefficients, which are statistically significant, are the exchange rate volatility, the index of economic freedom and the global sentiment. Checking later whether the use of pooled OLS is appropriate will give us an unfavourable result.

Now we proceed to the panel data analysis. Our panel is describes as strongly balanced, because there is an observation for every unit of observation of every time period.

So, let us start with the fixed effects model. The fixed effect estimation considers the interrelation between the explanatory and the outcome variables within a particular basis (that may be a country, a company, etc.). Each basis of estimation possesses its own personal characteristics that may have an impact on the explanatory variables or not. When estimating the model by fixed effects, we make an assumption that something within our basis may have an effect or bias the explanatory or dependent variables and, therefore, we should control for this. This fact provides an intuition to the assumption of the correlation between the error term of the basis and the explanatory variables. The time-invariant features disappear in the fixed effect model, so that one is able to learn the net effects of the explanatory variables on the dependent one.

At first, we would test the evidence of unobserved heterogeneity: the F-test implies that the fixed effects models should be chosen over the pooled OLS model, since P > F = 0.000 (test for all u_i = 0) - it is inappropriate to use pooling.

So, it appears that all coefficients, except for the long-run effect of domestic credit to GDP, the exchange rate volatility and the index of economic freedom, are significant, meaning that the coefficients may be used in explaining the relationship. Still, we should check whether the tests provide the valid results on significance. Applying the test on heteroscedasticity, which examines whether the variance of the error term is constant or not across the observations, we may see if the tests are valid:

H₀: у²_ui = у²_u = 0

P > ч² = 0.000 (since it is < 0.05, reject the null hypothesis)

The result implies that there is a presence of heteroscedasticity in model. Though the coefficient estimates are unbiased and consistent, the standard errors are inefficient and the tests appear to be invalid, the fact that may lead to the incorrect conclusions about the significance.

More than that, I investigated the stationarity of series. The series that resulted to be unstationary were the index of economic freedom, the exchange rate volatility and the domestic credit to GDP. To deal with this issue, a first difference was taken (d_ecfr, d_fx, d_cred, d_credq, respectively).

We also may be interested in the test of serial correlation. For this case, I shall apply the Lagrange-Multiplier test:

H₀: no first-order correlation

P > F = 0.2314 (the result is > 0.05; thus, we do not reject the null hypothesis)

The result means that the observations are not subject to serial autocorrelation. In the presence of heteroscedasticity problem, standard errors are incorrectly measured, and for the remedy against this issue we shall consider the robust standard errors.

Having applied robust standard errors, we obtained the model with efficient standard errors and hence, with valid tests. The coefficients of linear and quadratic terms of domestic credit to GDP appeared to be inefficient, but still, the signs for them are as expected.

Next, let us turn to the random effects model estimation. The difference between the fixed and the random effects models lies in a sense that the latter assumes the variation across the different basis to be random and uncorrelated with the explanatory variables considered in the model.

Estimating the model under the random effects, the explanatory variables of the capitalization of domestic firms, trade to GDP and domestic credit to GDP appear to be insignificant in explaining the Sharpe ratio.

To learn out, whether we should use the fixed or random effects as the correct model, we should provide the Hausman test, which examines whether the random effects model coefficients are statistically different from the fixed effects ones.

H₀: difference in coefficients is not systematic (choose random effects model)

P > ч² = 0.000 (since it is < 0.05, reject the null hypothesis)

So, it thus may be concluded that the explanatory variables are endogenous, and hence, we should use the fixed effects model in estimation.

Having provided the analysis, we come to the point that the mode should be estimated under the fixed effects as the true specification.

I have also extended the analysis to changing the units of measure the GDP variable. While initially the GDP is measured per capita in constant US dollars, I turned to measuring GDP at market prices in constant local currency (lngdp). The idea behind the extension is that in case the correct specification will also be the fixed effects, then the results will be robust, making my estimations applicable.

When comparing the pooled OLD and the fixed effects model, we get that P > F = 0.000 (test for all u_i = 0), meaning that the fixed effects models should be chosen over the pooled OLS model. Proceeding to the comparison of the fixed and random effects models under Hausman test, we get:

H₀: difference in coefficients is not systematic (choose random effects model)

P > ч² = 0.0000 (since it is < 0.05, reject the null hypothesis)

Again, we conclude that the fixed effects model should be chosen for the estimation as the correct specification. Thus, the results are robust.

Having chosen the correct specification, now we may proceed to the final part of the analysis, where the benefits of including the assets of the countries investigated into the portfolio are estimated. For this purpose, I use the least square dummy variable model to understand the fixed effects. The explanatory variables' effects are interceded across the countries. Each dummy, therefore, shows the additional effect on the improvement in Sharpe ratio for each particular country.

As I estimate the model by taking China as the reference country, the effects of China are measured by the constant term, while the effects of other countries are measured by the constant term plus the respective coefficient. Below is the summary of the output, which shows the significance of the coefficients of each dummy. The insignificant coefficients are written in italics, while the coefficients of the highest values are written in bold (the inclusion of assets of these countries might give the highest risk-return improvement). India and Pakistan have negative coefficients, implying the decrease in the risk-return trade-off when including their respective assets into the portfolio.

The model outcome is therefore the following:

Taking everything into consideration, we come to the point that indeed, the investor should consider carefully the diversification of risk of his portfolio to be spread across assets of various governments. Both developed and emerging markets may provide substantial gains for the investor in terms of the improvement in the Sharpe ratio when adding international assets.

Having identified the correct specification, we may see that our expected results hold except for the growth of GDP: the higher is the market capitalization of listed domestic companies for a country, the higher the Sharpe ratio is expected to be; the index of economic freedom also positively relates to the Sharpe ratio, meaning that the investor should be rather interested in more “safe” governments; besides, the exchange rate volatility decreases the Sharpe ratio, since the resulted risk may be high due to the increased volatility of exchange rate when converting the returns into local currency. A contribution to the determination of the Sharpe ratio is made by the global sentiment, because it assures the risk-on/risk-off behaviour of investors. More than that, as expected appeared to be the signs of domestic credit to GDP, providing together the illustration to a so-called debt-overhang problem. Finally, the regression sets out the expected sign for trade to GDP; with the increase its value, the Sharpe ratio is expected to be lower.

The most important insight, which may be drawn from the current research, is the inverse relationship between the Sharpe ratio and the GDP growth per capita. Though the results contradict the initial expectations, this issue has been raised recently, and the considerations indeed prove such negative correlation. As stated, there is no proved relationship between the growth of gross domestic product per person and the returns. For instance, the professor from the University of Florida, Jay Ritter, states that “the most important factor explaining the apparent negative correlation between GDP growth and stock returns is that the latter is determined by earnings growth per share, not economy-wide corporate earnings growth”. The empirical evidence may be seen from China example: this country is considered to be one of the highest growing ones with a growth equaling to 9.4% for last 20 years to 2011, though the annualized stock market returns were -5.5%.

Finally, the investor should consider the inclusion of different countries' assets, both emerging and developed ones. For instance, the regressions predicts that the inclusion of assets of European sovereigns, like Austria, Belgium, Denmark, Ireland, Netherlands, Sweden, Switzerland, and of Pacific region, like Hong Kong and Singapore most greatly improves the risk-return trade-off. Since the coefficients of most developing economies are also statistically significant (like South Korea, Malaysia, Thailand, Czech Republic, Argentina, Mexico etc.), they also should be taken into account when seeking the ways for diversification. Still, the highest improvement to the Sharpe ratio is brought by the inclusion of assets of developed countries as seen from the estimation.



Conclusion

Having provided the theoretical concepts of the international diversification, reviewed the past researches on this issue and provided the analysis on the benefits of cross-border investments in terms of improvement in the Sharpe ratio, the definite conclusions may be drawn. Indeed, the continuous integration of financial markets and globalization has facilitated the movement of investments across the borders. The advantages from this, as a consequence, may be extracted by investors: the key principles of diversification hold in the international framework, allowing the investors to reduce the risk when including the assets of various countries in the portfolios.

The aim of my work was to analyse the criteria that the investor may consider when diversifying across different countries, both developed and emerging ones. To see the gains from his diversifying strategies, the Sharpe ratio was taken as an orient. The factors, which constitute to its improvement, are not obvious; therefore, the regression model was constructed to learn out the potential influence of each explanatory variable.

The resulted model showed that the investor is better off when including the assets of both developed and developing countries assets. He should review, still, the soundness of the government in terms of the country risk, which is positively related to the Sharpe ratio. The trade to GDP might influence negatively the value of the Sharpe ratio; however, one should ascertain the trade pattern of each country. The exchange rate volatility constitutes much to the dependent variable, with higher volatility implying the lower risk-return trade-off. An important factor to be considered is the global risk measure, which constitutes to the investor optimism regarding the financial markets. The last, but not the least factor that appeared to be significant is the market capitalization of domestic companies, the factor that has a direct relationship with the Sharpe ratio. An interesting relationship is the negative correlation between the growth of GDP per capita and the Sharpe ratio. These issue raises a lot of debates is at this juncture, but does not have a clear established sign.

The potential weaknesses of the model should be considered. The first is the use of the index of economic freedom as a proxy for the country risk, since generally the models use the country risk as defined by the Political Risk Service group, which appears to be much more enclosing. The broader range of political, social and economic variables is desirable, since it may play a crucial role in the decision of whether or not to invest in a particular country's assets.

The next weakness may be due to incomplete consideration of the exchange rate risk. It would be better to estimate the volatility of exchange rate implied from option prices, because such method gives a better measurement for the downside risk of the exchange rate depreciation, rather than simple historical calculation of volatility. Still, the availability for such data is limited.

So, the further research is needed. First, it may be interesting to look at the Sharpe ratio influencers before and after the financial crisis of 2008, since the macroeconomic and regulatory policies have changed; crisis definitely constituted to the each explanatory component used in the analysis. Second, the regression may be checked separately for emerging and developed markets to see the extent of variation in coefficients for each group. More than that, other explanatory variables may be included into the analysis, concerning structural reforms, demographic issues, etc. Finally, the above-stated weaknesses should be considered and overcame.

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