Graphical representation


Part A

For this part, monthly returns of national share indices of India (Bombay Stock Exchange) and Croatia (Crobex) through a period of five years starting 30 Nov 2004 till 30 Nov 2009 were used. Please refer Appendix 1.

Part B

It is clear from the graphical representation of the two datasets of returns (Appendix 2) wherein Indian index is the independent variable and Croatian index dependent; there is a positive correlation between the two datasets, although the exact degree can be understood from the calculated value of Pearson correlation coefficient. Correlation is found to be 0.672 under a two-tailed test and is significant at the 0.01 level. This means that the odds are less than 1 out of 100 that this is a chance occurrence and there is a ‘moderate' correlation between the two returns. There are moderate chances that if one share index rises (or falls), the other is likely to rise (or fall) as well.

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The ‘mean' values 0.163636 (BSE), 0.0042602 (CROBEX) show that average returns from the Indian market have been significantly higher than Croatian market. The ‘median' values 0.0322171 (BSE), 0.154183 (CROBEX) give us better indication of the central tendency of the data. The negative ‘mode' values -0.3066 (BSE), -0.31086 (CROBEX) are the most frequent returns, however, there are multiple modes i.e. there are two or more values appearing with the same frequency. Therefore the histogram of distribution has more than one bump (Appendix 2). The negative values above are the smallest among all the modes.

The ‘standard deviation' values 0.09367382 (BSE), 0.10374739 (CROBEX) suggest Croatian market has been more volatile compared to India or had a higher tendency of fluctuation in relation to the average return in a short period of time.

Skewness and Kurtosis are indicators of how normal are the distributions. ‘Skewness' values -0.765 (BSE) and -0.632 (CROBEX) suggest that the distribution of the data for both the countries has longer tails on the left of the mean peak. It is useful in estimating whether the future data point (return) will be more or less than the mean. There are more months with negative returns than the months with positive returns in both the countries. However, the positive values of means of returns in both the markets indicate that overall gain through positive returns have been more than overall loss through negative returns. Kurtosis figures 2.069 (BSE), 2.316 (CROBEX), both platykurtic distributions, show that Indian market was stable compared to the Croatian market and therefore had smaller price moves compared to the Croatian market.

R Square i.e. coefficient of determination 0.451 shows that 45.1% of the movements in the Croatian market can be explained by the movements in the Indian market and 54.9% are caused by other factors.

B value indicates the slope of the curve best representing the samples. Therefore, for every 1 unit change of return on Indian market corresponds to 0.744 unit change on the Croatian market. And the equation of the regression line can be given as Y = -0.008 + 0.744X

Beta tells that for every standard deviation, change in Indian market corresponds to 0.672 standard deviation change in Croatian market.

p-value under ‘Sig', 0.000 is significant as it is lower than 0.05. This is the evidence that the two returns are correlated based on the sample data taken out of the overall data and indicates that the return on Indian market predicts the return on Croatian market.

Durbin Watson, 1.727 is not significant since it is closer to 2 suggesting no serial autocorrelation.

Residual statistics show the difference between the values predicted by the regression equation and the observed values for mean and standard deviation is not significant.

Thus, Bivariate statistics are useful in understanding the relationship between two variables and the extent to which they vary in relation to one another (UIC 2009). Therefore, one can analyse trends in the two markets and predict market behaviour at a given time. The larger the sample size better is the reliability of findings. Under assumed normal circumstances; such an analysis can help gauge the scope of returns on investment in a particular market compared to the other at a given time. However, regression method assumes a linear relationship between the two returns and does not take account of the underlying cause of relationship (Statsoft 2009) between the two markets while other factors such as natural calamity or war may affect the markets exclusively.

Part C

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Multivariate statistics are useful in analysing more than two variables simultaneously wherein techniques such as factor analysis, multidimensional scaling and cluster analysis help summarise data and reduce number of variables necessary to describe it (Social Research Methods 2009).

Valadkhani et al (2008) used Factor Analysis to investigate the relationship between monthly stock market returns of 13 countries over a period of twenty years (1987-2007), pointing to the benefits of international diversification, using the Principal Component (PC) and Maximum Likelihood (ML) methods to show that returns of certain groups of countries were highly correlated depending on the geographic proximity and the level of economic development.

Their study searched for systematic co variation patterns among stock markets across Australia, Germany, UK, US and nine eastern countries. A factor analysis of the correlation matrix was conducted based on the co-movement of returns and the number of common factors was determined. The first factor related to geographic proximity in case of developing countries. The second factor related to the co-movements of returns in developed countries (Valadkhani et al 2008).

Therefore, it was concluded that the cross country co-movements of returns depend on the geographic location and level of economic development and that the risk reduction and significant increment of returns is possible through a range of stocks in countries from different continents including both developed and developing countries (Valadkhani et al 2008).

In the light of earlier research suggesting lower market risk and lower total risk of portfolios of multinational firms than for portfolios of domestic firms, in 1995, Goldberg and Heflin undertook a study to investigate association of degree of international involvement (DOI) and both nondiversifiable systematic risk and total risk of firms with multinational presence and, changes in DOI and changes in systematic and total risk.

In their study, daily return data available from Center for Research in Security Prices starting 1977 to 1987 was used to measure systematic risk by market model beta and total risk by variance of return (Goldberg and Heflin 1995).

Results of their study suggested that even after controlling for other factors associated with it, the systematic risk is negatively related to the DOI and intertemporal changes in systematic risk are negatively related to intertemporal changes in the degree of international involvement. Therefore increasing DOI decreases systematic risks. However, DOI was found not to be negatively related to total risk and intertemporal changes in total firm risk were found to be marginally positively related to intertemporal changes in DOI. This could increase total risk as DOI is not negatively related to total risk arising out of currency, political and other risks of international operations (Goldberg and Heflin 1995).

In 2006, a study carried out by Campa and Fernandes focused on determinants of country and industry specific factors in international portfolio returns using a sample of forty eight countries (19 emerging markets and 27 developed countries) and thirty nine industries over last thirty years. They segregated investment returns into determinants such as world portfolio, industry specific factors and country specific factors and reported an increased importance of global industry factors in explaining investment returns in the last ten years (Campa and Fernandes 2006).

Their findings point to financial market globalisation as the main driving force behind the significant rise in the global industry shocks. Thus, more globalised firms are prone to higher industry shocks. The number of countries practicing financial liberalisation was found to have increased. Therefore, in emerging markets, country factors were found to have been declining in importance and country level shocks becoming less relevant (Campa and Fernandes 2006).

Subject to correlated shocks across countries, industry specific returns get affected differently compared to world market portfolio. Higher international financial integration within an industry gives rise to increase in the importance of industry specific factors (Campa and Fernandes 2006).

Their study also identified financial market activity as an important determinant of the magnitude of country and industry effects. Therefore, higher trading activity in a country or industry can be a reason of higher country or industry shocks, respectively. Further, it was found that if economic activity in a country is isolated from the world economic activity, country specific returns will be large compared to world market portfolio and shocks to country's economic situation will have a significant impact on the returns. Also, country factors are significant for countries with more specialized production activity (Campa and Fernandes 2006).

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You and Daigler (2009) argued that most of the research that began in 1970s, when international diversification and globalisation became important; it relied on constant correlations and the diversification benefits to US investors while ignoring the characteristics of international stock portfolios and benefits to non-US investors, and that except correlation, standard deviation and return, other factors affecting international portfolio diversification such as skewness and kurtosis have not received due attention.

In order to understand the effects of extreme market conditions on diversification and correlation measures, they examined factors other than correlation for major bull and bear markets of late 1990s and early 2000s using a weekly data split into two periods - start of January 1997 to end of March 2000, a strong bull market and start of March 2000 to end of December 2002, a major bear market. The study brought forth key insight that benefits of diversification are time-varying, are affected by non-normality and depend on the country employed (You and Daigler 2009).

The results show that diversification based entirely on constant correlation can project a false picture since correlations vary over time rendering the approach imperfect. Therefore, it is important to take account of conditional or time varying correlation. Along with return and standard deviation, if skewness and kurtosis are included as important factors to gauge the diversification benefits, the benchmark (country) becomes the determinant of advantage of diversification. The study of possible association between these factors reveals a positive relation between standard deviation and skewness and between standard deviation and excess kurtosis, and a negative relation between correlation and risk (You and Daigler 2009).

Their findings challenge the validity of the established belief in superiority of internationally diversified portfolios and points to the possible cost saving benefit of avoiding a wide-ranging diversification policy. However, the authors point to the need of additional research to verify their conclusions (You and Daigler 2009).

In conclusion, statistical methods provide an empirical approach. Results of expert studies undertaken since 1970s (e.g. Grubel in 1968, Levy and Sarnat in 1970, Solnik in 1974) have pointed to benefits of international diversification mainly in terms of reduction of risks.

Over time, however, there has been a constant spread and connectedness of production, communication, technologies and also of economic and cultural activity around the world. Therefore globalisation has created integration of markets across the world rendering diversification benefits a time bound phenomenon. It has also put an apparent limit on both risk reduction and increased returns.

There are various schools of thought bringing variety of insights for investors. Driessen and Laeven (2007) concluded that local investors in both developed and developing countries can benefit substantially from international diversification even if investors in developing countries are assumed not to be able to short sell stocks, and thus provide with a hopeful picture. However, Stoichev (2004) incorporated transaction costs and taxes to arguably demonstrate that the benefits of international diversification are exaggerated in academia and in practice.

The changing degree of globalisation warrants constant review of various factors that can affect countries and industries individually and as integral parts of market networks and expert statisticians have been employing various research methodologies to verify the validity of guidelines provided by earlier research and to suggest newer ways to build effective international diversification strategies.