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Financial Crisis and the Effectiveness of International Diversification Investment in the Emerging markets
Bachelor Thesis Finance Ickju Ahn
10690689
Supervisor: Dr. Doettling Robin
Bachelor Economics & Business, specialization Economic & Finance Faculty of Economics and Business
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Statement of Originality
This document is written by Ickju Ahn who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents
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Abstract
This paper investigates whether diversifying the investment through emerging stock market is yet powerful even after the financial crisis and finds that diversification benefits change over time. In particular, we study the linkage between three different benchmark markets indices and international stock markets. We measure global correlation and suggest that after 2011, the diversifying the portfolio through emerging stock market does not provide better results than the diversifying through developed market. We also compute the market indices risks using the variance-covariance method and historical simulation VaR method. The risk of emerging markets certainly decreased after the financial crisis, but still appear with the higher value than the developed market. Thus, the paper concludes that risk sharing through emerging stock market does not find helpful after the financial crisis. Combining the result of correlation and risk measurement, the conclusion was made that after the financial crisis, the international diversification investment would provide more benefit when the portfolio is structured with developed markets rather than emerging market.
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Table of content
1. Introduction 5
2. Literature Review 6
3. Methodology 8
3.1 Markowitz modern portfolio theory
3.2 The concept of VaR and measurement method 3.2.1 Variance Covariance method
3.2.2 Historical simulation method 3.2.3 Monte Carlo method
4. Empirical analysis 13
4.1 Data analysis 4.2 Correlation analysis
4.3 Markowitz risk diversification effect 4.4 Historical Simulation VaR Analysis
5. Conclusion 26
6. Reference 27
7. Appendix 39
7.1 Hedging Currency Risk 7.2 VaR Method
7.2.1 Variance-Covariance model 7.2.2 Monte-Carlo approach
7.3 Mean, Minimum, Maximum, 0.5% 1% Percentile of each country 7.4 Portfolio risk with different number of indices
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1. Introduction
It is currently accepted as conventional theory, as demonstrated in Markowitz’s writing, that the risk involved with diversified investments are reduced in comparison to investments made in concentrated concert. For example, in a stock market, one stock may plunge more than 50 percent in a few months, whilst it is improbable that ten stocks will fall, on average, as much to the same extent. The international diversification portfolio also evolved this intuitive theory, in which financial specialists invest more assets in various markets, rather than more within a single market, adjusting the risk and raising returns. Utilizing this theory, traditional investors have invested in diversified investments in low-risk, low-return markets such as the US and other developed markets, blending these safe options with high-risk and high-return emerging markets to lower risk and improve return. However, Forbes and Rigobon, 2002; Gilmore et al., 2010, Eiling and Gerad 2015 and other many researchers claim that reciprocal movements of global stock returns due to the greater integration of financial globalization, with higher degree of capital fluidity, causes a higher level of association between the profitability of one stock market with the health of another. This creates the situation where diversification based upon market preference may not provide the safety that many investors seek for, especially in the long-term. Furthermore, without a doubt, the risk of investing in emerging markets became larger as the stock market volatility of emerging markets increased after the financial crisis. Taking such a standpoint, this paper will consider whether the traditional international diversification investment method is yet powerful even after the financial crisis.
For investigating whether the traditional international diversification investment is efficient, it should be primarily considered to measure the correlations between the countries and see what kind of portfolio could bring the most profitable outcome. Second, utilizing the variance-covariance model and the VaR method to demonstrate the risk of each country’s equity indices and attempt to find out the smallest risk value when creating a portfolio. Finally, these two values will be combined to predict which portfolio will yield the greatest gain and the lowest risk value.
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2. Literature Review
The study of Levy and Sarnat (1970) and Solnik (1974) demonstrates that investors can have better risk-return opportunities when they make international diversification rather than domestic diversification. In particular, Levy and Sarnat (1970) adopted a portfolio selection model developed by Markowitz and Tobin, and show that even in the case of a correlation between countries, it is possible to reduce risk through diversified investments if they are not perfectly correlated. Furthermore, Roll (1992), Griffin and Karolyi (1998) contend that international diversification can be beneficial because the correlation coefficients among the countries are relatively small in the international stock market. The more the international capital markets are integrated, the more corresponding the stocks in different markets move. Recently, research has been actively conducted to find that correlation coefficients between countries are increasing. Login and Solnik (1995) found that the average correlation of stock returns in the seven major markets increased significantly between 1960-1990, and those international correlation coefficients had a tendency to increase considerably more when markets were unstable. Solnik and Roulet (2000) used cross-sectional data from stock markets of 15 developed countries to demonstrate that correlation coefficients between equity markets increased over time. There is a slight difference in the value of the correlation coefficient depending on the periods and the samples, but in most papers, the correlation coefficient has generally been increasing over the period.
Since the benefits of international diversification are derived from the relatively small correlation between countries, it is expected that the growth in correlation coefficient will reduce the benefits of international diversification. Goetzmann, Li, and Rouwenhorst (2005) show that the risk of diversified international investment decreases compared to the past, as the correlation of internationally diversified portfolios increases. While existing evidence is mainly focused on developed markets, Eiling and Gerad (2015) demonstrate that the linkages between emerging stock markets are growing as well. The study’s compilation thirty-two developing market samples over a twenty-year period concluded that there is a positive impact on correlations across regions, correlations between emerging regions, and correlations between emerging markets and the rest of the world. Another paper from Aloui et al. (2010) shows that empirical investigation of the extreme financial interdependencies of BRIC and the US market during the 2004-2009, similarly according to Dimitriou et al. (2013), they investigate the
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contagion effect of the financial crisis in a multivariate fractionally integrated asymmetric power dynamic conditional correlation framework during the period 1997-2012. These two papers conclude that correlations among the BRICS and USA have increased from the crisis, and their dependence is larger in bullish than in bearish markets.
As stock market returns could exhibit common extreme variations, it is not sufficient to make international investment decisions with only knowing the degree of a time-varying correlation coefficient. When investors measure the extreme variations of stock market returns, the VaR (value at risk) model is typically applied. According to the Holton (2002), the beginning of VaR can be followed back to the New York Stock Exchange in 1922, and earliest work about VaR measure was published by Leavens (1945). Moreover, these works independently developed by Markowitz (1952) and Roy (1952). Presently, the Basel has been imposed on financial institutions to meet the capital requirement based on VaR. Thus, the effectiveness of methodologies has turned out to be more concerned. The earliest critics come from Beder (1995). Beder implements Monte Carlo and historical VaR measures to calculate sixteen different VaR measurements for each of three portfolios. However, there is inconsistency on the measurements for each portfolio, and Beder concluded that VaR as “Seductive but dangerous.” Another criticism is from Gençay et al. (2003) that VaR provides highly volatile quantile forecast compare to the GPD model. Although there are critics of the VaR method, other researchers such as Hopper (1996) showed VaR method is still valid. He analyses VaR calculation approaches and vulnerabilities after studying the possibilities and size measurement methods for potential losses of various companies including financial institutions. As a result, it is difficult to get an answer on how often the maximum risk is generated through VaR, but it still has a significant meaning as a risk management method.
As there are various models of VaR, studies have been done on which models are most effective and which factors have a large impact on the VaR measurement. Hendricks (1996) used historical data to compare (1) the equally weighted variance-covariance approach, (2) the exponentially weighted variance-covariance method, and (3) historical simulation approach. As a result, he found that certain methods did not show superior results, and above all, confidence level had a significant effect on the performance of the VaR approach. Also, Jordan (1995) empirically analyzed VaR using the daily stock price of American Airlines, Ford, IBM, Nam-Warner, Seagram during 1992.1.2 ~ 1993.12.31. The results show that the method of
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calculating VaR depends on the correlation and volatility of market risk factors and is strongly influenced by the estimation of the market value response to changes in risk factors.
Furthermore, Dimitris et al. (2010) provide an outline in demonstrating the effect of the financial crisis on the calculation of VaR, particularly the implications of the most recent global financial crisis about VaR estimates for emerging and developed markets. Generally, the crisis period seems to affect the forecasting performance of the VaR model mainly in the emerging markets and developed markets appear to be less affected.
3. Theoretical Background on the effect of international diversification investment
3.1 Markowitz Modern Portfolio Theory
There are various models for measuring the correlation of countries’ equity market, but in this paper, I will examine the most common model which is called modern portfolio theory to find the correlation.
One of the fundamental principles of modern portfolio theory is the risk reduction effect of diversified investment. Diversified investment refers to investing in different kind of assets to avoid a portfolio being overexposed to one risk; which is achieved by increasing the number of shares in a portfolio,
Portfolio risk is further partitioned into systemic risk and idiosyncratic risk. As more securities are included in the portfolio, the individual risk is offset, and the volatility of the portfolio returns is consequently lowered. However, increasing the quantity of shares cannot eliminate all risks. This is because all securities included in the portfolio are subject to common macroeconomic factors, which is called systemic risk.
σ𝑝2 = ∑ ∑ 𝑤 𝑖𝑤𝑗𝐶𝑜𝑣(𝑟𝑖, 𝑟𝑗) 𝑛 𝑗=1 𝑛 𝑖=1 (1)
From the e144quation (1), wi and wj denote the shares of stock i and stock j, and ri and rj denote the returns of stock i and stock j. In the case of a simple investment strategy that invests in the same weighted portfolio, the ratio of investing in individual stocks is 1/n. In this case, equation (1) can be replaced with equation (2)
9 σ𝑝2 = ∑1 𝑛𝜎𝑖 2 + ∑ ∑ 1 𝑛2𝐶𝑜𝑣(𝑟𝑖, 𝑟𝑗) 𝑛 𝑗=1 𝑗≠1 𝑛 𝑖=1 𝑛 𝑖=1 (2)
The mean of variance and the mean of covariance are defined as
σ2 ̅̅̅ =1 n∑ 1 𝑛𝜎𝑖 2 𝑛 𝑖=1 (3.a) 𝐶𝑜𝑣 ̅̅̅̅̅(𝑟𝑖, 𝑟𝑗) = 1 𝑛(𝑛 − 1)∑ ∑ 𝐶𝑜𝑣(𝑟𝑖, 𝑟𝑗) 𝑛 𝑗=1 𝑗≠1 𝑛 𝑖=1 (3.b)
Therefore, the portfolio variance can be expressed as
𝜎𝑝2 = 1 𝑛𝜎̅̅̅ +2
𝑛 − 1
𝑛 𝐶𝑜𝑣̅̅̅̅̅(𝑟𝑖, 𝑟𝑗) (4)
The right side of the first term will become zero when the n become larger. This term is a unique risk or non-systemic risk that can be eliminated through a diversified investment. The second term is a systemic risk that cannot be diminished even n increases unless the mean covariance between stock returns become zero. Thus, the irrevocable risk of a diversified portfolio is determined by the covariance of constituent stocks, and the covariance relies on upon the systemic variables which influence the economy in general.
If the portfolio is composed of diversified international investment, the size of systematic risk become smaller that of diversified domestic investment. This is because the correlation between countries is lower than the correlation between local firms and the systematic factors that have a common effect on the whole world are relatively small. Therefore, when diversified international investment is more dominant than diversified domestic investment, the size of the covariance is lower, and thus, lowering the portfolio risk.
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𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡(𝜌𝑖𝑗) =𝐶𝑜𝑣(𝑖, 𝑗)
𝜎𝑖𝜎𝑗 (5)
3.2 The concept of VaR and measurement method
Although there are various conventional risk measurements, include beta, duration, convexity, delta, and gamma. The explanation behind utilizing VaR disregarding these different measures is that these risk measures cannot be summed up. For instance, what is the risk of a portfolio comprising of stocks and bonds if the Beta measures the risk of the stock and the duration measures the risk of the bond? It might likewise be difficult to add the same delta. For example, the delta of the interest rate cap with the interest rate as the underlying asset and the delta of the stock options cannot be added together. It also has the additional disadvantage that it is difficult to apply the position limit effectively. Compared to traditional risk measurement methods, VaR has the following advantages.
First, VaR allows us to measure the complex portfolio of securities consisting of different market factors and financial instruments and makes it possible to measure the risk to the market for the entire portfolio. Second, VaR can measure risk in a unified way, providing managers with a simple way to compare the magnitude of risk exposed in other business sectors, assess efficiency adjusted based on risk, and allocate capital. Third, VaR is straightforward and easy to understand. Given the level of significance, not only does it present the maximum loss of a portfolio of securities within a given period, but also presents a risk situation suitable for shareholder and external communication. Fourth, VaR fully considered the correlation between the changes in other asset prices, which shows that the dispersion of investment portfolio contributed to the reduction of risk. Fifth, VaR is appropriate for regulatory authorities to manage risk.
VaR is the expected amount of maximum loss of a holding asset that can occur over a target period within a given confidence level. This can be expressed using the following probability equation.
P(∆A > V) = 1 − α
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1 − α: Confidence level α: Significance level Here, the absolute value of V is VaR at the confidence level of the holding assets. ∆A is not an absolute value, and a negative value of ∆A indicates a loss, and a positive value of ∆A indicates a profit. When the probability of ∆A is greater than V in the confidence level, which means that V is the smallest value among the ∆A values that can occur at a given confidence level, that is the maximum amount of loss. Generally, V appears with a negative value, therefore when the absolute value of V is obtained, this value means VaR. Also, the level of confidence implies the probability that the losses incurred in the asset will not exceed the VaR. Moreover, if an investor assumes the higher the level of trust, the value of VaR become larger.
Next, the target period or the holding period of an asset is a period for measuring the amount of change in the holding assets. If an investor takes the longer target period, there is more possibility of price change on an asset, and thus it increases the value of VaR. Therefore, the target period should be determined differently depending on nature of the property held. In the case of a financial institution, such as a securities company, VaR should be measured on a daily basis since their turnover rates are significant. If the position is changed slowly like a pension fund, VaR should be measured on a longer-term basis. In general, the target period will be determined about the liquidity of the assets held since it corresponds to the maximum time limit required to dispose of assets. For example, the Basel Committee’s internal model requires banks to calculate VaR with a confidence level of 99% and a holding period of 10 trading days. The following section I will describe and compare the VaR methods.
The approach of VaR can be divided into parametric and nonparametric methods. In the parametric method, the VaR can be computed analytically by using the standard deviation of the return distribution with established confidence level. In the non-parametric method, the VaR can be computed directly from the return distribution of a given position.
When VaR is estimated by the parametric method, it is critical to obtain the standard deviation. The simplest way to estimate the standard deviation is using the assumed constant standard deviation of historical data. Hence, in reality, the standard deviation is non-constant variable. Therefore, the moving average model, the exponential model, and the GARCH model
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are considered to be more appropriate methods to apply these models can catch the time-varying standard deviation.
In other VaR calculations, VaR measurement methods can be divided into local valuation method and full valuation method regarding a distribution of future cash flows which is different from the parametric and non-parametric approach. In the local valuation method, the VaR can be obtained by making assumptions about return distributions for market risks, and by using the variances in and covariance across these risks. The full valuation method is a method of measuring risk by fully revaluating the value of a portfolio using a scenario. Historical simulation methods, bootstrapping, and Monte Carlo simulation methods are included in this method.
The most favored model among the various VaR models is the variance-covariance method, the historical simulation method, and the Monte Carlo simulation model. In this paper, these three methods are briefly described below and appendix, but the applied model in this article is limited to the historical simulation model.
3.2.1 Historical simulation Model
The historical simulation method is a method that easily realizes the full valuation method. This method can be divided into the empirical distribution method and the bootstrapping method. In this paper, VaR is measured by the empirical distribution method. The empirical distribution is a probability distribution obtained by sorting the basic market price observations used in the sample in order of magnitude and then giving the same probability value to each observation. Consequently, the VaR estimation method using the empirical distribution is a method of calculating the value of the portfolio at each point in time from the past market price data and then estimating the VaR corresponding to the given confidence level from the probability distribution of the portfolio values.
For example, suppose you use the market return data R1, R2 ..., R99 over the past 100 days to obtain a VaR that corresponds to a 5% significance level (95% confidence level). Then the 5percent sample data is some amount between the 4th worst case of return and the 5th worst case of return. Then the difference between this portfolio value and the average value of the portfolio distribution is the VaR value.
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As this method use actual price, this method can accommodate linearity and non-normal distribution. Also, it can reflect both gamma-risk, Vega-risk, and correlation, and it is not based on a particular assumption of the valuation model or the assumption of specific price changes of an underlying asset. Furthermore, this method can also take into account the thick tail and is not exposed to model risk as it is not based on a particular valuation model. Therefore, historical simulation is robust and intuitive. On the other hand, the disadvantage of the historical simulation method is that this approach requires a relatively large amount of data, and the frequency of the historical data and the period for estimating the VaR should be matched. For example, if you want to calculate monthly VaR, you should construct the monthly return data for the past five years. Also, it is difficult to predict VaR at a probability of 1% or less. At the same time, a general historical simulation method gives the same weight to all observations. This can change the measure of risk significantly if the historical data of the measurement date are excluded from the analysis.
4. Empirical analysis
This section contains the analysis of empirical correlation and the VaR results. I will first introduce the different datasets that I use and investigate the interaction between various stock market indices; divide into three periods 2002-2006 pre-period of the financial crisis, 2007-2011 during the crisis, and 2012-2016 pro-period of the financial crisis. Subsequently, I will measure the VaR with historical simulation approach with these periods and explain the results.
4.1 Data and process
Daily closing U.S. dollar returns for eight developed markets, including Australia, Germany, Hong Kong, Japan, The Netherlands, Singapore, the UK and the US, are from DataStream over the period January 1, 2002, to December 30, 2016.
Daily closing U.S. dollar returns for eight emerging markets, including Brazil, China, Indonesia, South Korea, Philippines, Thailand, Turkey, are from DataStream over the period January 1, 2002, to December 30, 2016.
Used daily return instead of weekly return, since each target period is short Given the previous data, the methodology used for this study is described below:
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Calculate the correlations of 15 countries with the three different benchmark market indices, which are the Netherlands, Japan, and the US. Moreover, analyzing the correlation data of prior to, during, after the crisis to find out whether it is stable or structurally changed, measure the risk with the variance-covariance and VaR method and investigate the change of these values.
Table 1 contains descriptive statistics using emerging and developed market index data for the period January, 1, 2002 to December 30, 2016. While the cross-country variations are significant, Table 1 shows that the average annualized return in the developed markets 6.554%, versus 13.214% in the emerging markets. However, the annualized standard deviation of emerging market is 27.31% corresponding to only 21.65% in the developed market. This means that investing in developed countries generates more stable outcomes than the emerging market. Both developed market and emerging market tends to be negatively skewed with average -0.09002 and -0.09884 respectively. This means investors can meet a greater chance of extremely negative outcomes in both markets, but especially in emerging market. Furthermore, excess kurtosis appears in both developed markets and emerging markets but slightly higher in emerging markets indicating more tail risk.
Table 1: Descriptive Statistics for daily return on 8 DM and 8 EM January, 1, 2002 to December 30, 2016 (Dollar basis)
Mean Std. Deviation Variance Skewness Kurtosis
AUS 8.72% 24.25% 0.058807 -0.6430 8.463 GBR 4.18% 22.47% 0.050484 -0.0910 9.613 GER 6.96% 22.88% 0.052363 0.3180 10.398 HKG 7.36% 21.06% 0.044368 0.0460 7.751 JAP 5.87% 21.64% 0.046843 -0.1070 4.569 NLD 4.72% 23.73% 0.056297 -0.0840 7.053 USA 6.70% 19.29% 0.037198 -0.0560 9.456 SGP 7.92% 17.87% 0.031947 -0.1020 6.377 BRA 12.49% 32.60% 0.106246 -0.0160 6.166 CHL 8.38% 18.49% 0.034197 -0.2110 9.838 CHN 14.35% 29.44% 0.086696 0.4290 9.220 IDN 18.20% 27.05% 0.073172 -0.3960 7.850 KOR 11.61% 29.01% 0.084185 0.3340 20.575 PHL 13.68% 20.13% 0.040511 -0.4980 5.242 THL 14.78% 24.08% 0.058002 -0.3900 8.098 TUR 12.23% 37.67% 0.141924 -0.0430 5.409 DM 6.55% 21.65% 0.047288 -0.0900 7.960 EM 13.21% 27.31% 0.078117 -0.0988 9.050
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4.2 Correlation analysis
Table 2 represents the correlation coefficient between US stock returns and the other 15 countries stock returns included in the sample. In the case of Australia, Japan, and Indonesia, correlation coefficient has been continuously increasing during the sample periods, other countries showed an increasing trend during the financial crisis but then dropped after the crisis period. In the case of the Netherlands and Germany, the correlation coefficients are at least 0.6 since 2002 indicating that the stock market of these two countries and the stock market of the US have maintained high correlation since 2002.
In the first sample period, the correlation coefficient between the UK stock market and the US stock market showed the relatively small correlation of 0.422, but after the financial crisis, the correlation between the UK stock market and the US stock market rapidly increased to 0.65 and more; which is also similar to the figures of the Netherlands and Germany. Overall, after the financial crisis, European stock market indices have been integrated with the US stock market. Asian stock markets are also seeing gradually integrating with the US stock market, with Korea, Indonesia, and the Philippines showing a correlation of 0.5 and more. On the other hand, in the case of Singapore and Thailand, the correlation was surprisingly low, and the correlation difference between pre-crisis period and the post-crisis period was also tiny. The equity indices in South America and the stock market in the US also showed a very low correlation, with Chile showing the lowest correlation across all sample countries. One interesting point is that since the financial crisis, the stock market of the developed countries excluding Asian countries has a very high correlation with the US stock market, and show increasing market integration. However, the US stock market and the Asian developed stock market have relatively small correlation than other developed markets. Therefore, it can be considered that Asia region has a relatively low correlation with the US market, but again, these are not the case for the correlation between emerging markets and the US stock market. As a result, it can be seen that the correlation between Asian developed markets and the US market is similar to that of Asian emerging equity markets and the US stock market, or larger in the emerging stock markets. This implies that diversifying the portfolio with Asian emerging markets are no longer valid, but rather that diversified investment in developed market can bring more profits.
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Table 2. Correlation Coefficient between the US stock returns and the other 15 countries stock returns
2002-2006 2007-2011 2012-2016 AUS 0.492 0.855 0.604 GBR 0.422 0.658 0.774 GER 0.632 0.763 0.842 HKG 0.432 0.553 0.540 JAP 0.470 0.464 0.641 NLD 0.573 0.700 0.742 USA 1.000 1.000 1.000 SGP 0.326 0.411 0.365 BRA 0.217 0.352 0.273 CHL 0.184 0.254 0.223 CHN 0.379 0.667 0.572 IDN 0.407 0.538 0.599 KOR 0.663 0.684 0.624 PHL 0.293 0.580 0.570 THL 0.358 0.319 0.396 TUR 0.409 0.507 0,337
Time-Lags: GBR, GER, NLD, TUR
<Graph 1> is a graphical representation of the average correlation coefficient between the US stock returns and the stock returns of developed and emerging markets. In the developed market's indices, it can be confirmed that there is a high correlation with the US market index since 2002, and this has been steadily rising, showing a close correlation of 0.7 in the last sample period. In the emerging market's indices, the situation was similar to that of the developed market, but it was surprisingly found that the correlation had decreased after the
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 2002-2006 2007-2011 2012-2016 <Graph 1>
Average correlation coefficient trend between the
USA and other markets
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second sample period. This means that the effects of international diversification are still significant when mixed with emerging markets rather than only make a diversification in developed markets.
Table 3 represents the correlation coefficient between Dutch stock market and the other 15 countries. As expected, the correlation with other European countries grew over time. Especially after the financial crisis, the correlation with the neighboring country Germany was 0.931, and the average correlation with European countries was over 0.85.
Table 3. Correlation Coefficient between the Dutch stock returns and the other 15 countries stock returns
2002-2006 2007-2011 2012-2016 AUS 0.289 0.717 0.476 GBR 0.723 0.882 0.858 GER 0.794 0.819 0.931 HKG 0.251 0.405 0.338 JAP 0.232 0.330 0.294 NLD 1.000 1.000 1.000 USA 0.391 0.498 0.408 SGP 0.267 0.452 0.343 BRA 0.474 0.906 0.795 CHL 0.318 0.525 0.447 CHN 0.218 0.547 0.421 IDN 0.253 0.448 0.320 KOR 0.334 0.525 0.382 PHL 0.081 0.261 0.236 THL 0.244 0.394 0.375 TUR 0.517 0.883 0.757 Time-Lags: JAP
Unusually, the correlation between South American countries and the Netherlands market was high, especially in the case of Brazil, it showed the highest correlation of 0.906 among all countries during the financial crisis period. Unlike the US stock market, the correlation with other developed markets except for European markets was not high. In the case of Australia, the correlation was 0.717 at the time of the financial crisis, but there was a relatively low correlation of 0.476 thereafter. The average correlation between Singapore, Japan, Hong Kong and Dutch stock market was also small with 0.250, 0.396, and 0.325, respectively. Correlations between Asian emerging markets and the Dutch equity market created a situation similar to that of the US, except for the first sample period, which showed a slightly higher correlation with the advanced Asian market. As a result, when Dutch stocks are included in the investment portfolio, it can be expected that investing in other developed countries excluding European
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markets are bringing better results than diversifying into emerging markets.
<Graph 2> represents the average correlation coefficient changes between the Netherlands and other markets over the sample period. Unlike <graph 1>, it can be seen that the correlation between emerging and developed markets has decreased after the crisis. Also, the correlation between emerging and developed markets was not significantly different, because the correlations with developed countries except for European developed market are generally lower than those of emerging markets. Overall, it is expected that there will be stronger international diversification effects compare with the USA market case.
Table 4 shows the correlation between Japan and the stock market in 15 countries. In Japan, the volatility of the correlation in the financial crisis period was much greater than in other benchmark countries. In particular, emerging economies showed a rapid increase in correlation, with Brazil, China, Korea and Turkey showing an average correlation of 0.7 in the country. After the second sample period, excluding the Hong Kong stock market, the correlation between Japanese stock market and the rest of the markets have dropped sharply. In more detail, the correlation in the remainder of the countries except for Hong Kong, Australia and Korea stock market was less than 0.4. The country with the most rapid correlation decline
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 2002-2006 2007-2011 2012-2016 <Graph 2>
Average correlation coefficient trend between the
Netherlands and other markets
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was Korea, with a correlation of 0.892 during the financial crisis period, but since then it showed up with 0.424 which is lower correlation than the first sample period. In conclusion, when Japan was placed in the benchmark market, international l diversification was effective in the rest of the countries except for a few countries, and the effects are higher than when the Netherlands or the US were benchmarked.
Table 4. Correlation Coefficient between the Japanese stock returns and the other 15 countries stock returns
2002-2006 2007-2011 2012-2016 AUS 0.350 0.782 0.42 GBR 0.150 0.489 0.25 GER 0.221 0.478 0.279 HKG 0.470 0.464 0.641 JAP 1.000 1.000 1,000 NLD 0.192 0.494 0.254 USA 0.262 0.519 0.309 SGP 0.349 0.457 0.234 BRA 0.294 0.684 0.299 CHL 0.142 0.390 0.168 CHN 0.347 0.794 0.384 IDN 0.416 0.546 0.278 KOR 0.626 0.892 0.424 PHL 0.201 0.460 0.313 THL 0.357 0.386 0.205 TUR 0.144 0.566 0.185
Time-Lags: GBR, GER, NLD, USA, BRA, CHL, TUR
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 2002-2006 2007-2011 2012-2016 <Graph 3>
Average correlation coefficient trend between the
Japanese and other markets
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From the <Graph 3>, it can be seen that the average correlation between Japanese stock market with developed and emerging markets are quite different from the correlations we have observed so far. First, the correlation between the Japanese stock market and the emerging stock market was higher since 2002, and the trend continued until the financial crisis period. This indicates that during the first and the second term, the diversification investment was more efficient when invested in the developed markets. Even after the financial crisis, the average correlation between developed and emerging market was not significantly different. Given the risks of the stock market, it is expected that investing in developed countries will have lower risks and generating greater profits.
4.3 Markowitz risk diversification effect
Before explaining the effect of portfolio risk diversification, it is necessary to see the risk for each market in line with the sample period. Table 5 represents the individual market risk over the period, and clearly, in all sample times, the developed markets have lower individual market risk than the emerging markets. In the first term, Japanese stock market has relatively high risk than other developed markets, while Singapore had the lowest. In the emerging markets, Turkey had an overwhelmingly high market volatility with 42.76 percent while the market risk of Chile was only 14.43 percent. During the financial crisis period, most of the markets faced the higher market risk than the previous period. In particular, Turkey, China, and Brazil suffered the largest market volatility with average 40 percent.
Table 5. Annualized historical volatility January, 1, 2002 to December 30, 2016
2002-2006 2007-2011 2012-2016 AUS 15.43% 34.53% 18.27% GBR 16.33% 30.61% 17.65% GER 18.05% 30.28% 18.12% HKG 15.42% 29.07% 15.77% JAP 20.73% 24.98% 18.74% NLD 19.30% 31.78% 17.52% USA 15.76% 26.48% 12.92% SGP 14.96% 24.26% 12.09% BRA 28.26% 39.34% 28.99% CHL 14.43% 24.45% 14.80% CHN 22.14% 40.33% 21.99% IDN 26.57% 32.72% 20.43% KOR 26.22% 38.87% 18.10% PHL 17.29% 24.57% 16.78%
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THL 23.95% 28.78% 18.41%
TUR 42.76% 40.36% 28.30%
DM 17.00% 29.00% 16.39%
EM 25.20% 33.68% 20.98%
After the second sample period, the market volatility has returned to the 2002-2006 level or even dropped further.
For explaining the diversification effect of reduction risk, 6 equally weighted portfolios were created which are;
(USA, DM), (USA, EM), (NLD, DM), (NLD, EM), (JAP, DM), (JAP, EM). DM: AUS, GBR, GER, HKG, JAP, NLD, USA, SGP
EM: BRA, CHL, CHN, IDN, KOR, PHL, THL, TUR
Since the created portfolios are diversified into eight main market indices, the overall portfolio variance can be calculated as 1
8𝜎 2+7
8𝐶𝑜𝑣(𝑟𝑖,𝑡, 𝑟𝑗,𝑡) which can be indicated from the formula (4). Then the portfolio risk or volatility rate should be √1
8𝜎 2+7
8𝐶𝑜𝑣(𝑟𝑖,𝑡, 𝑟𝑗,𝑡) Table 6 shows the 6 different portfolio and its covariance change over the period. The portfolios consist of three benchmark markets with developed markets and emerging markets. And the table 7 demonstrate the created portfolio risk and it can be seen that the created portfolio has lower risk than individual volatility.
Table 6. Covariance of portfolios
Covariance USA (DM, EM) Covariance NLD (DM, EM) Covairance JAP (DM, EM)
2002-2006 2007-2011 2012-2016 2002-2006 2007-2011 2012-2016 2002-2006 2007-2011 2012-2016 DM 1.29% 2.91% 1.71% DM 1.35% 3.23% 1.63% DM 0.97% 3.23% 1.13% EM 1.44% 2.59% 1.54% EM 1.46% 3.57% 1.83% EM 1.65% 4.12% 1.23%
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Table 7. Portfolios risk (n=8)
Portfolio risk USA (DM, EM) Portfolio risk NLD (DM, EM) Portfolio risk JAP (DM, EM)
2002-2006 2007-2011 2012-2016 2002-2006 2007-2011 2012-2016 2002-2006 2007-2011 2012-2016 DM 12.80% 23.57% 12.87% DM 13.48% 24.82% 13.62% DM 12.22% 20.37% 11.97% EM 12.40% 17.46% 12.03% EM 13.35% 25.21% 13.51% EM 14.08% 22.63% 11.87%
First, in the case of the US stock market, diversified investment lead to the decrease of its market risk with approximately 2percent, 4percent, and 3percent for each sample period. Moreover, it is shown that diversifying with the emerging stock market is more efficient to reduce the risk. Therefore, if we consider the market correlation and market risk of the USA market, it is deemed to bring more profit and mitigate the risk when the diversification implied to the USA market with emerging market indices. Second, with the Dutch market, there is not much difference between the developed market and emerging market of risk reduction effect. Rather, the market risk was slightly higher when diversified investments were made in emerging markets. Unlike the US case, consider the correlation and market risk, it can be concluded that there would be slightly beneficial from diversifying the portfolio with developed market, but the benefit would be small. Hence, if we exclude the European stock markets from the both developed and emerging markets, diversifying in the developed market will give more profit and reduce the risk. The last case of Japanese stock market, it is shown entirely different figures from the case of US. Risk reduction did not give the favorable figure when the portfolio diversification is made with emerging market. As it is mentioned in the correlation part, Japanese stock market has the shallow relationship between the Asian developed stock market while it has the higher correlation with Asian emerging market indices. Therefore, similar to the Dutch market case, it would be better to make a diversified portfolio with developed markets, mainly Asian developed markets.
If we put more market indices in each portfolio, the risk of portfolio could be dropped since the idiosyncratic risk can be diversified further. The table 8 from the appendix showed the discrepancy of portfolio risks with different number of indices
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4.4 Historical Simulation VaR Analysis
In this section, another risk measure method will apply to see whether it gives similar conclusion with previous risk measurement. Table 6 and 7 show the value at risk of developed markets and emerging markets with the different confidence level. The developed markets VaR (confidence level 0.5% and 1%) during 2002-2006 was certainly smaller than the emerging markets. In particular, Hong Kong showed up with the lowest VaR at both confidence level with 2.89% and 2.45% respectively, while Japan becomes the riskiest market among the developed market. The reason behind may because Japan faced the IT bubble at that period. In the emerging markets, China’s VaR was only 2.95% and 2.61%, which is significantly smaller than other emerging markets. This may be because free trading of stocks was more recently reintroduced in 1990 and that Chinese government often actively interfere with the running of the stock market through direct manipulation of stock prices by shifting regulations to the government’s desire. Therefore, it can be expected that it has a relatively small VaR than other emerging markets. Whilst, the Turkey, had the largest VaR among all countries, which may have been caused by the low level of political stability and weak macro-economic factors at this period.
As expected, the value of VaR during the financial crisis period have surged in both developed and emerging markets. The average of VaR in the developed markets is 6.745(α=0.5%) and 5.167%(α=1%), versus 7.81%(α=0.5%) and 6.013%(α=1%). This figure, when compared with previous sample period shows a VaR increase of at least 1.5% in each market. While the VaR of the Australian stock market was the highest in the developed market at approximately 9%, Singapore and Hong Kong remained below 6% with the only small change from the previous sample period. From this, it can be predicted that the Singapore and Hong Kong stock markets have relatively strong macroeconomic factors in comparison to other countries since even during high degrees of stock market fluctuation, its market indices do not demonstrate high levels of volatilities. Among the emerging stock markets, VaR of Brazilian, Chinese and Korean stock markets have increased by more than 4% over the previous sample period.
However, after the financial crisis, VaR values have decreased markedly, and these values become similar or even smaller than the 2002-2006 values. It still Japanese stock market tends
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to be riskier than other developed markets, Singapore and Hong Kong appear with significantly low VaR. In addition, since the financial crisis, the risk of the Korean stock market has fallen sharply compared to the previous sample period, which is the largest drop among all sample markets. In more detail, the decline was about 10 percent to 3.37 percent at the 0.5 percent of the significant level, and 7.14percent to 3.04 percent at the significance level of 1 percent.
Table 6. VaR (α=0.5%) 2002-2006 2007-2011 2012-2016 AUS 3.18% 8.99% 3.17% GBR 3.65% 7.19% 3.30% GER 3.52% 6.26% 3.95% HKG 2.89% 5.94% 3.31% JAP 3.98% 5.97% 4.31% NLD 3.89% 7.10% 3.61% USA 3.11% 6.64% 2.64% SGP 2.91% 5.86% 2.22% BRA 5.56% 9.27% 5.65% CHL 2.58% 6.89% 2.58% CHN 4.76% 7.51% 4.31% IDN 6.85% 7.94% 4.52% KOR 5.02% 9.99% 3.37% PHL 3.59% 5.65% 4.25% THL 4.42% 6.95% 3.70% TUR 8.82% 8.28% 5.34% Table 7. VaR (α=1%). 2002-2006 2007-2011 2012-2016 AUS 2.67% 6.06% 2.81% GBR 2.98% 5.71% 2.76% GER 3.17% 5.50% 3.16% HKG 2.45% 4.85% 2.64% JAP 3.34% 4.53% 3.32% NLD 3.70% 5.77% 3.14% USA 2.76% 5.07% 2.35% SGP 2.59% 3.85% 1.85% BRA 4.98% 7.60% 4.60% CHL 2.43% 4.82% 2.28% CHN 4.01% 6.67% 3.49% IDN 4.39% 5.79% 3.78% KOR 4.47% 7.14% 3.04% PHL 2.93% 4.56% 3.04% THL 3.70% 4.75% 3.35% TUR 7.23% 6.79% 4.62%
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Graphs 4 and 5 show the trend of VaR changes. As it is mentioned earlier, it can be seen that the value of VaR drops to a tremendous value after the financial crisis. The result of these is different from the expectation of this paper. Since it is predicted that the VaR of the developed market between 2012-2016 was expected to be the same or slightly lower than before the financial crisis period and the emerging market was expected to grow larger, hence it tended to be smaller in both markets, which breaks the expectations. Therefore, it can be anticipated that the value of VaR has decreased as the stock market of each country has become more mature
0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 2002-2006 2007-2011 2012-2016 <Graph 5>
VaR change over the period
(α=1%)
Developed market Emerging market
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 2002-2006 2007-2011 2012-2016 <Graph4>
VaR change over the period
(α=0.5%)
26 since the financial crisis.
If we re-evaluate the previous six portfolios with VaR method and correlation measure, it can be expected that the USA market will give slightly better result when the portfolio is diversifying with emerging market, but the result is worse than when the variance-covariance method is applied. It is because VaR in emerging markets values are larger than those of developed countries while the previous variance-covariance method showed up with reversed value. For the Dutch and Japanese portfolio cases, it is certain that diversifying the portfolio with developed market would provide more profit with less risk as these markets have low correlation with developed market as well as slightly low risk.
5. Conclusion
This study investigates whether traditional international diversification investment method is yet powerful even after the financial crisis. The study was conducted utilizing Markowitz portfolio theory and historical simulation VaR method with using the daily returns of the market index of eight emerging and eight developed countries. The findings of this study are as follows. First, regardless of emerging and developed market indices, the correlation between the countries had the largest correlation value during the financial crisis, and only slightly different results appear when the US index was benchmarked, but there were no major changes. Secondly, the variance-covariance model and the VaR model give the different value of market indices risk, but these two different risk measurements show the similar trend of risk change in the entire sample period. Moreover, the last, after the financial crisis, the traditional international diversification investment would be only valid when the portfolio is constructed with the US stock markets. If the portfolio is built with other benchmark markets such as Dutch and Japanese market indices, international diversification investment should be made with developed markets.
There are several limitations of this study, the critical part was the autocorrelation of stock market data during the financial crisis period, and the stock market 's daily return data did not follow the normal distribution. In order to overcome these limitations, in the future study, it would be suggested to use GARCH model and Copula function rather than reflecting the dependency structure by the correlation coefficient.
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7. Appendix
7.1 Hedging Currency Risk
However, international diversification investments add additional risks. Errunza and Losq (1987) argue that the risks of international investment can be divided into three categories:
(1) the exchange rate volatility, the risk of purchasing power, (2) the political risk, rate of taxes
(3) Regulation, capital mobility, lack of information, and investment risk.
The exchange risk in diversified international investment can be defined as the possibility that the return of investment will fluctuate due to unexpected currency fluctuations. In this case, the exchange risk is mainly reflected in the exchange rate change in the process of converting the return rate of the investment target country to the return rate of the investor. However, the effect of the sudden exchange rate fluctuation on the investment yield can be seen not only in the conversion process but also on the other side. For example, a change in the exchange rate could affect the interest rate, modify the rate of return, or affect the financial activities of institutions, resulting in a change in the rate of return. The following paragraphs further illicit the difference between when a currency risk is hedged and when it is not.
When an investor in country i invests in another country j, the yield and risk can be calculated as follows.
𝑅𝑖,𝑡 = (1 + 𝑟𝑗,𝑡)(1 + 𝑒𝑗,𝑡) − 1
(6.a) If we denote the price of j stock at time t as 𝑝𝑗,𝑡 we can say that 𝑟𝑗,𝑡 = (𝑝𝑗,𝑡− 𝑝𝑗,𝑡−1)/𝑝𝑗,𝑡−1 when the dividend yield is ignored. If the spot exchange rate for the j-currency is s, then the foreign-currency investment yield 𝑒𝑗,𝑡 for the j-currency is (𝑆𝑗,𝑡− 𝑆𝑗,𝑡−1)/𝑆𝑗,𝑡−1. Thus, 𝑅𝑖,𝑡 is the return on investment at time t when the i-country investor gains from overseas investment in securities. And this formula can be derived further as follow;
𝑅𝑖,𝑡 = 𝑟𝑗,𝑡+ 𝑒𝑗,𝑡+ 𝑟𝑗,𝑡𝑒𝑗,𝑡
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As 𝑟𝑗,𝑡𝑒𝑗,𝑡 is commonly an insignificant constant, it could be disregarded altogether. Hence, the return on investment can be approximated as follows
𝑅𝑖,𝑡 ≈ 𝑟𝑗,𝑡+ 𝑒𝑗,𝑡
(7) Referring to the previous formula the portfolio variance can be formulated as
𝜎𝑝2(𝑅𝑖,𝑡) ≈ 𝜎𝑝2(𝑟𝑗,𝑡) + 𝜎𝑝2(𝑒𝑗,𝑡) + 2𝑐𝑜𝑣(𝑟𝑗,𝑡, 𝑒𝑗,𝑡) (8) Adapting formula (8) on (1) then the variance of internationally diversified portfolio without currency risk hedging is
σ𝑝2 = ∑ ∑ 𝑤 𝑖𝑤𝑗𝐶𝑜𝑣(𝑅𝑖,𝑡, 𝑅𝑗,𝑡) 𝑛 𝑗=1 𝑛 𝑖=1 (9)
And the Covariance of this portfolio is
𝐶𝑜𝑣(𝑅𝑖,𝑡𝑅𝑗,𝑡) = 𝐶𝑜𝑣(𝑟𝑖,𝑡, 𝑟𝑗,𝑡) + 𝐶𝑜𝑣(𝑒𝑖,𝑡, 𝑒𝑗,𝑡) + 𝐶𝑜𝑣(𝑟𝑖,𝑡, 𝑒𝑗,𝑡) + 𝐶𝑜𝑣(𝑟𝑗,𝑡, 𝑒𝑖,𝑡) (10)
When investors attempt to hedge the exchange risk, they use the forward exchange rate. The forward exchange rate could be denoted as 𝐹𝑖,𝑡−1, which is settled at time t-1 for the currency of i country in case of hedging the exchange rate risk. The futures exchange rate premium for the currency of the investment target is 𝑓𝑖,𝑡 = (𝐹𝑖,𝑡−1− 𝑆𝑖,𝑡−1)/𝑆𝑖,𝑡−1 . Furthermore, when foreign currency is exchanged at maturity, the uncertain return rate is 1 + E(𝑟𝑖,𝑡) + (1 + 𝑒𝑖,𝑡) − 1 and the certain return 1 + E(𝑟𝑖,𝑡) + (1 + 𝑓𝑖,𝑡) − 1). Therefore, if the foreign investor expects the foreign exchange receivables to be sold in forward exchange, the yield of the hedging portfolio will be as follows.
𝑅𝑖,𝑡ℎ = [𝑟𝑖,𝑡− E(𝑟𝑖,𝑡)](1 + 𝑒𝑖,𝑡) + [1 + E(𝑟𝑖,𝑡)](1 + 𝑓𝑖,𝑡) − 1 (11.a)
𝑅𝑖,𝑡ℎ = 𝑟𝑖,𝑡+ 𝑓𝑖,𝑡 + 𝑟𝑒𝑖,𝑡+ E(𝑟𝑖,𝑡)(𝑓𝑖,𝑡− 𝑒𝑖,𝑡) (11.b)
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𝑅𝑖,𝑡ℎ ≈ 𝑟𝑖,𝑡+ 𝑓𝑖,𝑡 (12)
And the variance and covariance of hedging portfolio can be expressed with approximate formulas
σ𝑝2(𝑅𝑖,𝑡ℎ) ≈ σ𝑝2(𝑟𝑖,𝑡) (13)
𝐶𝑜𝑣(𝑅𝑖,𝑡ℎ, 𝑅𝑗,𝑡ℎ ) ≈ 𝐶𝑜𝑣(𝑟𝑖,𝑡, 𝑟𝑗,𝑡) (14)
Hence, the difference of variance between currency risk hedged and non-hedged are 𝜎𝑝2(𝑒𝑗,𝑡) + 2𝑐𝑜𝑣(𝑟𝑗,𝑡, 𝑒𝑗,𝑡) and the difference of covariance between hedged and non-hedged are 𝐶𝑜𝑣(𝑒𝑖,𝑡, 𝑒𝑗,𝑡) + 𝐶𝑜𝑣(𝑟𝑖,𝑡, 𝑒𝑗,𝑡) + 𝐶𝑜𝑣(𝑟𝑗,𝑡, 𝑒𝑖,𝑡). Since the correlation values affect by these two values hedging the currency risk would provide more accurate correlation between the markets.
7.2.1 Variance-Covariance Model
The variance-covariance method is a parametric approach and the market risk component follows a normal (or Gaussian) distribution. Thus, VaR can be computed on the assumption that the profit and loss of a portfolio with a normal distributed. It can be calculated with simple formula:
7.2.2 Monte-Carlo approach
Monte Carlo simulation method is divided into two stages. First, it specifies stochastic processes and a coefficient process of variables. Second, it simulates possible parameters of all variables. In the first step, factors such as risk and correlation are derived from historical data or option data. In the second phase, it simulates possible price changes for all variables and calculates the market value of the portfolio during the target period. This can be used to calculate the probability distribution and then calculate the VaR. This method has been evaluated as the most efficient way to calculate VaR and can take into account various types of risk, including non-linear price risk, volatility risk, and model risk. It can also consider thick tail and extreme situations. However, the most significant disadvantage is that computation takes prolonged periods of time.
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7.3 Mean, Minimum, Maximum, 0.5% 1% Percentile of each country
Statistics 2002-2006
AUS GBR GER HKG JAP NLD USA SGP BRA CHL CHN IDN KOR PHL THL TUR
Mean 0.076% 0.047% 0.056% 0.056% 0.053% 0.046% 0.025% 0.068% 0.111% 0.079% 0.127% 0.141% 0.096% 0.081% 0.090% 0.114% Minimum -3.655% -4.611% -5.184% -4.188% -7.219% -7.171% -3.987% -4.241% -7.614% -3.933% -7.570% -14.983% -7.080% -4.513% -16.306% -15.738% Maximum 3.791% 4.860% 5.508% 4.017% 5.663% 5.899% 5.513% 4.879% 13.883% 2.963% 8.367% 7.657% 8.756% 4.727% 11.432% 17.009% Percentiles .5 -3.107% -3.607% -3.462% -2.833% -3.923% -3.844% -3.083% -2.838% -5.445% -2.498% -4.634% -6.711% -4.922% -3.512% -4.331% -8.703% 1 -2.598% -2.934% -3.118% -2.394% -3.285% -3.650% -2.732% -2.521% -4.869% -2.348% -3.884% -4.249% -4.370% -2.844% -3.613% -7.111% Statistics 2007-2011
AUS GBR GER HKG JAP NLD USA SGP BRA CHL CHN IDN KOR PHL THL TUR
Mean 0.020% -0.010% -0.005% 0.010% -0.017% -0.021% 0.007% 0.019% 0.054% 0.038% 0.031% 0.074% 0.032% 0.057% 0.062% 0.027% Minimum -14.765% -9.868% -8.260% -10.939% -8.459% -10.852% -8.980% -7.973% -14.975% -10.020% -12.647% -13.599% -18.408% -11.336% -11.755% -13.998% Maximum 8.739% 12.543% 17.659% 11.170% 11.292% 10.726% 11.518% 9.755% 15.067% 12.766% 17.014% 14.393% 27.957% 8.503% 9.225% 16.708% Percentiles .5 -8.972% -7.203% -6.269% -5.934% -5.991% -7.116% -6.638% -5.837% -9.216% -6.855% -7.482% -7.864% -9.956% -5.593% -6.886% -8.256% 1 -6.039% -5.724% -5.504% -4.840% -4.542% -5.794% -5.062% -3.831% -7.541% -4.785% -6.641% -5.712% -7.103% -4.503% -4.687% -6.761% Statistics 2012-2016
AUS GBR GER HKG JAP NLD USA SGP BRA CHL CHN IDN KOR PHL THL TUR
Mean 0.006% 0.011% 0.030% 0.019% 0.031% 0.030% 0.048% 0.005% -0.019% -0.020% 0.010% 0.005% 0.010% 0.021% 0.023% 0.001%
Minimum -5.893% -11.695% -7.414% -5.577% -6.020% -7.529% -3.933% -4.540% -7.100% -4.461% -5.818% -6.750% -5.115% -7.323% -5.861% -10.627%
Maximum 3.816% 5.960% 5.847% 5.214% 6.237% 5.761% 3.699% 3.287% 11.013% 4.420% 5.975% 6.585% 4.497% 5.442% 6.146% 8.147%
Percentiles .5 -3.165% -3.293% -3.925% -3.287% -4.282% -3.585% -2.591% -2.210% -5.669% -2.602% -4.299% -4.518% -3.358% -4.234% -3.677% -5.344%
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7.4 Portfolio risk with different number of indices
N: Number of indices
Table 7. Portfolios risk
N Portfolio risk USA (DM, EM) Portfolio risk NLD (DM, EM) Portfolio risk JAP (DM, EM)
2002-2006 2007-2011 2012-2016 2002-2006 2007-2011 2012-2016 2002-2006 2007-2011 2012-2016 8 DM 12.797% 23.575% 12.868% DM 13.477% 24.817% 13.620% DM 12.221% 20.369% 11.966% EM 12.401% 17.457% 12.027% EM 13.353% 25.209% 13.513% EM 14.077% 22.632% 11.870% 10 DM 12.702% 23.486% 12.866% DM 13.274% 24.589% 13.492% DM 11.888% 20.222% 11.715% EM 12.292% 17.129% 12.000% EM 13.144% 24.996% 13.381% EM 13.839% 22.561% 11.614% 15 DM 12.575% 23.368% 12.864% DM 12.997% 24.282% 13.319% DM 11.430% 20.024% 11.372% EM 12.145% 16.683% 11.965% EM 12.860% 24.710% 13.202% EM 13.517% 22.467% 11.264% 20 DM 12.511% 23.309% 12.863% DM 12.857% 24.127% 13.232% DM 11.194% 19.924% 11.196% EM 12.070% 16.455% 11.947% EM 12.716% 24.565% 13.112% EM 12.716% 24.565% 13.112% 25 DM 12.472% 23.273% 12.862% DM 12.772% 24.034% 13.180% DM 11.050% 19.864% 11.090% EM 12.026% 16.317% 11.936% EM 12.628% 24.478% 13.058% EM 13.253% 22.391% 10.976% 30 DM 12.446% 23.249% 12.862% DM 12.715% 23.971% 13.144% DM 10.952% 19.824% 11.018% EM 11.996% 16.224% 11.929% EM 12.569% 24.419% 13.021% EM 13.186% 22.372% 10.903% 40 DM 12.414% 23.220% 12.861% DM 12.643% 23.893% 13.100% DM 10.830% 19.773% 10.928% EM 11.958% 16.107% 11.920% EM 12.496% 24.346% 12.976% EM 13.102% 22.348% 10.810% 50 DM 12.394% 23.202% 12.861% DM 12.600% 23.846% 13.074% DM 10.756% 19.743% 10.873% EM 11.935% 16.037% 11.915% EM 12.451% 24.302% 12.948% EM 13.052% 22.333% 10.755%
