In the early stage of the research about the international diversification, Markowitz develops the basic portfolio model which shows that the variance of the rate of return measured the portfolio risk. The mean-variance analysis build an efficient frontier for each portfolio, which illustrates the maximum return for a given level of risk (variance) and vice versa based on several assumptions. Markowitz portfolio theory emphasizes to maximize the portfolio expected return for a certain risk. It encourages to collect different level of assets to diversify the risk which is based on the fact that they have negative correlations. By using Markowitz method to construct optimal portfolio, it is important to distinguish mean and variance among securities. It makes possible to calculate the optimal weights of each risky assets in the portfolio by using the historical returns and variance-covariance matrix of the stocks. Asness (1996) believes that "a diversified portfolio provides more expected return per unit of risk." This confirms the significance of Markowitz model in constructing well diversified portfolio which leads to lower risk.
2.2 Benefits of International Portfolio Diversification
The benefit of international diversification has been widely documented, but most of research are from the American's perspective. Grubel (1968) uses modern portfolio theory to explain the potential benefits of holding international assets. He finds that if US investors invest in foreign security markets , they are likely to get a significant reduction in portfolio risk and develop a better portfolio return opportunity.Portfolio diversification helps to reduce the risks which are supported by Levy and Sarnat (1970), who cites that international diversifications offers additional chances to diminish portfolio risk. Mean rates of return and standard deviation are calculated based on the data from 28 countries, both developed and emerging, for the period of 1951 and 1967 in order to test the benefits of international diversification. It has showed that the observed stocks returns from any countries are highly correlated which indicates a reduction of risk through diversification.They also suggest the American investor should invest in developing countries. The gain from the portfolio diversification depends on the correlation between the US capital market and the aim market,therefore, they should invest in the countries like Denmark, Japan and Mexico which have low correlation with the US. Moreover, Bekaert and Urias (1996), De Roon, Nijman, and Werker (2001), Harvey (1995), and Li, Sarkar, and Wang (2003) suggest that U.S. investors benefit from combining emerging markets into a portfolio .
Solnik(1974) points that the variability of expected return of a well diversified international portfolio would be only one-tenth as risky as a ordinary security and one-second risky as a domestic diversified portfolio by analysis of seven European stock market. He uses stock returns from eight different countries over six years then it proves that selection across countries is superior compared to domestic diversification. The random diversification that Solnik’s chose indicates that an optimal portfolio does not need more than 30 stocks to achieve considerable gains, like well diversified portfolio could evade 90% of portfolio volatility, from either international or domestic.
Lessard(1976) uses the monthly percentage changes in market value weighted price indexes from 16 countries and 30 industries from the 1959 to 1973. He tries to explain the covariance structure of returns and suggests that international diversification could be better off, the return associated with 1 unit of risk of well-diversified portfolio is larger than the non-well diversified portfolio; even if it has same risk, the well diversified portfolio could have higher return.
Previous studies have shown that international diversification guarantee to reduce total risk without sacrificing expected returns (Cosset and Suret, 1995). The empirical results show that developing countries particularly in Latin America, East Asia, and Southern Europe,are likely to gain more from international diversification because they are not completely combined into the world market (Harvey 1995).
Boucrelle and Le Fur (1996) test the benefits of international diversification with correlations and return volatilities of different markets. It can provide the vehicle to construct the efficient frontier of the portfolio. Combining different stocks into one portfolio substantially reduces the systematic risk.
However, in a study of six equity markets for the period 1988-1997 (France, Germany, Italy, Japan, Canada, and the UK) , Hanna et al. (1999) find that there is no evidence to support the diversification gains to the US investors, which could be explained by the higher correlation between the US market and others.
2.3 The Role of Correlation
International diversification is considered as an investment approach that to combine securities from different stock markets with returns that are low-correlated asset in order to signiï¬cantly reduce the total risk of the portfolio. Therefore, the crucial factor that determines the portfolio risk for a given level of return is the correlation between the returns of the stocks that consist of that portfolio.
Grubel (1968) and Lessard(1973) find out that correlations of stock returns across international equity markets are quite low and statistically insignificant, even lower for emerging market. Longin and Solink(1995) showed that the stocks from seven major over the period 1960 to 1990 markets countries are less likely to move together, therefore, risks can be dramatically reduced.They also show that international correlation tends to rise as the volatility of the markets increase.
Ragunathan and Mitchell(1997) use the realised correlation coefficients to consist of equally weighted international portfolios. They show that equally weighted portfolio bring in diversification benefits. Moreover they presents evidence based on the data of 33 daily international stock market Indices by using the method of cointegration and multivariate GARCH .They show that identified the portfolios with negative and low positive correlation would reduce risks. However, Goetzmann et al. (2002) presents that the correlation between equity markets have increased towards the end of 20 century.By undertaking a maximum Sharpe ratio strategy, an investor pay more attention to improve the mean and variance of the investment .Dimson et al.(2002) analyze 16 countries for over 101 year beginning in 1900, believed that even though the correlation of stock markets has increased, international diversification still could lead to a reduction of portfolio risk. Jung et al (2003) analyze that the stock returns are positively correlated in emerging markets. On the other hand, Hentschel and Long(2004)find that in emerging markets , the diversification benefits would disappear when they are faced with short sales constraints or transaction costs. Statman(2004) estimates the US stock market and finds out that there is a clear tendency for correlations among individual stocks to decline over time in US market from 0.28 in 1960s to 0.08 in 1997. However, the internationally equity markets are becoming increasingly correlated.
The correlation between domestic and foreign stocks is relatively lower compared to rely domestic securities which is mainly due to the reason that most of countries have different fiscal ,monetary policy and different industry structure ( Lagoarde-Segot and Lucey, 2007:2).This highlights the importance of correlation for developing countries to reduce the risk of a portfolio.
Rezayat (2002) and Yavas et al.(2004) analyze the U.S , European and Japanese markets and they show that the there are potential benefits for international portfolio diversification. The main results are American investors can realize diversification benefits in Japan. In addition, for American and European investors would gain less benefits if they invest exclusively in Europe or just in the US. International investment portfolio are more attractive to investors because of the more chance to reduce risk than can be done by a domestic strategy.( e.g.,Dimson et al., 2002) . Jonathan and Andrew(2005) examine the benefits of international portfolio diversification for UK investors, and find out that there is a significant increase in the Sharpe and certainty equivalent return(CER) when invest internationally ,even in the presence of short selling restrictions. Arnold, G (2005) illustrate that lower correlation between returns from different stock markets enables investors to grasp better opportunities to reach lower risk by international portfolio diversification.
The benefits of international diversification are evident, by adding low correlation assets into the portfolio can significantly reduce the risk of the portfolio, especially when the market has a high volatility. However, correlation is not steady and has the tendency to increase in periods of high volatility. Therefore, investment decision can not be made only based on the correlation of assets, there are more factors should be considered.
2.4 Market integration and co-movement
The degree of international market integration is one of the most important factors that effect the effectiveness of international diversification. By taking an investigation of monthly international equity returns of 1960-1990, Longin and Solnik find that whenever the market volatility is high, the correlation would rise as well. In terms of stock market integration and interdependencies, Madura( 2003) indicates that correlations significatively increased over time. Bekaert and Harvey (1995),Bekaert et al. (2005), De Jong and De Roon (2005), point out that the degree of global market integration varies throughout time.The degree of the integration of international financial markets has gradually increased, but the less developed markets are still less integrated than are developed countries.
On the other hand, many researchers have examined the co movement of world exchange indices (e.g., Grubel and Fadner, 1971; Ripley,1973; Joy et al., 1976; Hilliard, 1979; and Philippatos et al., 1983).Meric and Meric(1997) find that the co-movement of 12 Eupoean equity markets after the 1987 crash and conclude that the co-movement has increased significantly after the crash which indicates that the benefit of international diversification has dropped after the crash. In this paper, we would like to briefly discuss the effect of 2008 financial crisis on Chinese stock market from international diversification perspective .
In comparison with the increasingly tendency of international portfolio, the advantage of investment in domestic market could not be ignored. By analysis the paper from Donald R. Lessard, it can conclude into three aspects, first is the covariance of securities in domestic market are less than the ones in different market which means the fluctuations are not that much. Secondly, the various types of barriers like the transaction costs, currency costs, tax regulations etc , which stop some investors diversifying their equities internationally. Last one is the rate of exchange rate makes it possible to fluctuate substantially.
2.5 Optimal number of stocks in one portfolio
The rate of risk-reduction benefits along with the increasing number of securities in a portfolio has been measured by a number of researchers. Evans and Archer(1968) they take portfolio's standard deviation as the measure of risk. They express the idea that for a randomly selected and equally weighted portfolio, the benefit of expanding from a portfolio has been little when there are more than 8-10 securities in a portfolio. Bloomfield , Leftwich and Long(1977) cite that the large portion of the benefits of portfolio diversification is obtained with a portfolio of 20 stocks. Later, Bird and Tippett(1986) demonstrate the method used by Evans and Archer (1968) was mis-specified by deriving an more precise parametric relationship between risk and portfolio size. They conclude that the benefit of risk-reduction can be obtained by increasing the number of securities suggested by Evans and Archer. From the paper of Meir Statman( 1987) ,he compares the costs and benefits of diversification by using the data from mid-1980s and reaches the conclusion that at least 30 stocks should be requited for an optimally diversified portfolio. Dimson et al (2000) indicates that the number of stocks to achieve a given level of diversification has increased in recent period. Holding more stocks in a portfolio can scatter the risk level. However, there are different options of the optimal number of stocks in one portfolio. Most of the studies demonstrated that the benefit of diversification can be achieved from 10-15 securities in one portfolio (Moa, 1970; Jacob 1974; Klemkosky and Martin 1975; Elton and Gruber, 1977)
The above examples from the literature clearly point out that international equity markets are becoming increasingly correlated. The aim of this study is to expand upon the literature from Chinese equity perspective using monthly data to focus on the relative short-run period among five different equity markets.( China, Hong Kong, U.S. , UK and Japan )
2.6 Efficiency Frontier
Efficiency frontier is combined with portfolios which have two characteristics. On one hand, that portfolio has the highest rate of return in comparison with others which have the same level of risk. One the other hand, it could have the lowest risk level compared with the portfolios with same level of return.
To construct efficiency frontier is not easy. Kumar and Gulati (2010) use linear programming to construct efficiency frontier for 27 public banks in India and indicate that it does not confirm that higher efficiency will bring out high effectiveness and performance. Huang (2009) uses new fuzzy theory and Variable precision rough set model to construct a better portfolio through stock selection and forecasting. Wang and Moore (2009)analyses the change in volatility under crisis period which can be in index to indicate the impact of financial crisis.
