The Kruskal Wallis Test and the Mean Betas Finance Essay

The descriptive statistics results of different markets are shown in Table 1, Table 2 and Table 3. The daily yield averages of BRIC countries, Nordic countries and North American countries are 0.077572581, 0.019607 and -0.02738 respectively. The yield average of BRIC region is quite higher than other regions. This explains why international idle money constantly has flowed into emerging economies in recent years. The yield average of North American region is negative because of the failure of US top banks. Similarly, we can clearly see that large fluctuation existed in every market and the result showed high skewness. The kurtosis value of almost every stock exceeded 3 in every markets, which specified the yield distribution of three markets were non-normal and comparing with each other, Nordic countries and BRIC countries had more understandable and larger skewness and higher kurtosis so the likelihood that the yield of Nordic market and BRIC market kept away from the average was higher and higher risk existed in Nordic countries and BRIC countries and the markets were not stable. Although the yield average of BRIC region was obviously higher than other market, it was not mature like them, and large fluctuation existed in it. Table 4, Table 5 and Table 6 describe the descriptive statistics of beta and R-Square.R-square tells us that whether the movements of a portfolio are explained by movements in the market index or not. In other words, it measures how dependable the stock's beta is in evaluating its market sensitivity. Most of the R2 values as found in our observations are significant and specifies that the beta measurement is relevant to its actual performance. Figure 1, Figure 2 and Figure 3 describe the normality plot of beta for different market. It appears that betas of all markets are not normally distributed.However; Nordic region shows slight normality in the betas distribution particularly in the crisis period. Table 4 reports about the one sample statistics of Beta for all regions and all periods. Simply speaking, beta (?) is a measure of risk or volatility related with a portfolio of investment as compared to the total market as a whole. A beta equals 1 means that an investment's volatility or price movements are similar to the market's price movements. It can be supposed that an investment is less volatile than the market if ? < 1 but is more volatile than the market if ? >1.It is evident from the table that the value of beta for North America is slightly higher than 1 but significantly greater than other regions for the 10 year period. There is minor difference between the beta of BRIC and Nordic for the overall duration. All the markets have higher beta in the crisis period. North American banking sector showed more volatility than the market in the crisis period while other two became less volatile than the market. During the pre-crisis period all the markets have beta less than 1 but North American market has the highest beta among the three yet again. As a whole, it is cleared that North American market statistically doesn't seem significantly risky but it is riskier than other markets. Chart 1 represents the mean beta comparison and illustrates that the North American market is riskier than other two markets.Particluarly in the crisis period, the North American banking sector proved to be very risky. Table 5 reports the results of our analysis concerning mean systematic-risk differences significance test. The negative mean differences in Panel A evidently suggest us to reject the null hypothesis but the significance values are not in favour of alternative hypothesis at 5% level of significance. The risk of BRIC banking stock is greater than Nordic ones. However, during the crisis period Nordic banking stock turned out to be more risky than the BRIC ones. Panel C says that the North American banking stocks are more risky than the Nordic banking stocks in all the periods. Interestingly, the mean differences between Nordic and North America are greater in pre-crisis period than in during crisis period. The results are not significant statistically at 5% level except for the pre crisis period. Panel B rejects the null hypothesis based on the positive mean differences value indicating that North American banking stocks are riskier than BRIC ones. Yet, looking at the F-value and 5% significance level, we cannot reject our null hypothesis for all the panels A, B and C. This indicates that the risk between two regions is not significantly different. Overall, the mean systematic-risk differences significance t test supports us to conclude that the North American banking stocks are the riskiest among the three. The cause behind the increased risk in the North American banking stocks may be the unstable economic conditions in the last 10 years. Similarly, the BRIC banking stocks being less risky than Nordic in crisis period implies that the existing financial crisis has less impact in BRIC regions. Table 6 represents the Mann Whitney Non Parametric test. The table clearly shows that Nordic and BRIC's banking stocks are significantly less risky than that of North America for the whole period, pre-crisis period and crisis period. Panel A statistics says that the Nordic banking sector is less risky than that of BRIC banking sector for the whole period of observations and sub-period of pre-crisis. But the result is opposite for the crisis period and supports previous t-test. Nordic banking stocks are riskier than BRIC stocks in this period. However, these all facts are not significant in statistical terms. Panel B says that the North American banking sector is more risky than BRIC's.This result is for all the periods and supported by z-statistics value of -2.19,-2.06 and -1.92.These findings are statistically significant at 5% level of significance. Once again North American banking stocks are proved to be riskier. Panel C which also supports the result from t-test indicates that they are riskier than Nordic for all the period. But the risk level was higher in pre crisis period and statistically significant at 5% level of significance. These findings illustrate the fact that mean betas are not equal to each other and are independent sample. Table 7 gives the result of our Friedman test. It gives the x2 statistic value of 4.8 (p=0.0907), 9.10 (p=0.0106) and 3.70 (p=0.1572) for overall period, pre-crisis period and crisis period respectively. The overall period and crisis period are not statistically significant at 5% significance level leaving no evidence to reject the null hypothesis. But the pre-crisis period is statistically significant at 5% significance level and there is evidence to support the alternative hypothesis. Table 8 is also a non parametric inferential statistic sign test. According to this table, we cannot reject the null hypothesis except in the pre-crisis period for Nordic and North America because the mean betas were not significantly different from each other in most cases. I further performed the Kruskal Wallis test in order to test whether the three mean betas of independent sample are not equal. For this, Table 9 summarizes the result. The results suggest that there is not a statistically significant difference at 5% significance level between Nordic, BRIC and North America except for the pre-crisis period. These results are similar to the Friedman test's results. The North American banking stocks were found significantly higher than that of BRIC and Nordic. Also the chi square statistics undoubtedly indicate that there is no mean difference between the three samples.

Cite this page