Global Markets

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Figure 5.13: residual vs predicted Y-values plot for Fama-French regression, equity focused funds, Nordic markets

The plot above and the additional plots in the appendix shows no to little signs of heteroscedasticity.

The only plot which shows some tendencies of heteroscedasticity are the residual plot with the fee variable on the x-axis. The tendency is not strong and hence the assumption about homoscedasticity in the error terms are assumed to hold in this regression.

Interestingly, and maybe a bit surprising, the error plot above looks almost exactly the same as the one in the previous regression, in the sense that the two additional factors have failed to explain the variance in the outliers. This means that even though the R-squared has increased by two

percentage points, the residuals looks almost exactly the same.

87 thereafter the focus will turn to equity focused funds and in the end the Fama-French Three-Factor Framework will be applied to extend the model and hence hopefully increase the reliability of the coefficient estimates obtained.

As said, the first regression below will not be limited in terms of asset classes the funds invest in and therefore it includes all funds investing in the global markets, which in the dataset used are 1,272 funds or more than 37% of the total amount of funds included. This shows that even though it is funds directed towards Nordic investors, there are more funds focusing on global markets than on the Nordic markets. The regression gives the following output shown below in table 5.20.

Table 5.20: CAPM regression, all asset classes, global markets

The results shown are for the intercept and the market return somewhat on line with what has been reported earlier. The intercept is small but still significant even at 99% confidence level. The market return is an indication of the correlation of the fund returns with the market return, and are highly significant, also at a 99% confidence level. It indicates that the funds are positively correlated with the market, which is not at all surprising. The fee variable is in this case almost equal to zero. It is far from significantly different from zero as the p-value is almost one and therefore, there seems to be no significant relationship between the fee the funds charge and their return.

The regression returns a R-squared value of 0.2207 which is in the low end compared to the similar regression for Emerging and Nordic markets, which returned R-squared values of 0.2825 and 0.3106 respectively. This means the regression methodology fits the funds with a geographical focus area of the global markets a little bit worse than the same methodology fitted emerging and Nordic markets.

As has been done for the other markets, there is obviously also a risk of heteroscedasticity in this regression which can possibly disable the use of the conclusions just drawn. The test for this will be

88 performed using the residual plots, which are all shown in appendix 14. The residual plot with the fee variable on the x-axis are also printed in figure 5.14 below.

Figure 5.14: residual vs fees plot for CAPM regression, all asset classes, global markets

The graph above shows a fairly stable variance in the residuals. There are a few outliers around a fee of 0.02, but apart from those, the estimated model seems to fit the return data quite well. The additional plots shown in the appendix has no indication of heteroscedasticity, and therefore there is no reason to doubt the assumption of homoscedasticity in this regression. This effectively means the conclusions drawn above can be trusted.

5.2.4.1 Equity-Focused Funds

Capital Asset Pricing Model Regression

The regression above has been dealing with all asset classes, whereas this section will focus on the equity focused funds. Of the 1,272 funds with a geographical focus area of the global markets, above 41% are focusing on equities only. In total that amounts to 527 funds, which will be analysed in the following using the methodology explained earlier. This regression gives the results presented in table 5.21 below.

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Table 5.21: CAPM regression, equity focused funds, global markets

Compared with the regression above the intercept and market return coefficient estimates have both increased and are still both highly significant at a 99% confidence level. The fact that the estimates increase should not come as a surprise, as the data now only includes equity focused funds, which in general delivers higher returns. At the same time the CAPM framework is created for explaining equity returns, so the fact that the correlation with the market return is higher is also not surprising.

The coefficient estimate of the fee variable has changed a lot compared to the previous regression. It is now negative and significantly different from zero, even at 99% confidence level. This means the regression finds a significant negative relationship between fees and returns.

The regression reports a R-squared value of 0.2663, which has then increased around 4.5 percentage points compared to the regression including all asset classes. This means the

methodology used is better at explaining the return of equity focused funds than the average of bond focused, money market focused and mixed asset focused funds. As mentioned earlier, this is no surprise as the CAPM framework has its roots in explaining equity returns. Although the R-squared value has increased it is still lower than the comparable regressions for emerging and Nordic

markets, which reported R-squared values of respectively 0.2947 and 0.3108.

The residual plots used for testing for heteroscedasticity in the error terms can be seen in appendix 15. The looks of them are very similar to the regression above, although there are of course fewer observations. The outliers which is seen in the residual plots of the previous regression are also present here, meaning it was the equity focused funds which caused the outliers in the first place as well. This means that the plots look very similar, and hence the same conclusion about no existence of heteroscedasticity is also reached here, implying the conclusions drawn are valid.

90 Fama-French Three-Factor Model Regression

As has been done with the other geographical focus areas as well, the reliability of the estimates reported will be sought to be enhanced by extending the theoretical framework used from CAPM to Fama French Three-Factor model. This effectively means that two extra variables will be added, Small-Minus-Big and High-Minus-Low to the already used variables in the regression above. This will allow the results to be cleaned in the sense that variance related to the "Small-firm effect" and the "Value premium" are explained by the additional factors. This further enhances the reliability of the coefficient estimate, since it is now for sure explaining these two factors.

The Fama French Three-Factor regression for the global markets using only equity focused funds reports the following results seen in table 5.22.

Table 5.22: Fama French 3-factor regression, equity focused funds, global markets

The results seen in the table above have not changed a lot compared to the regression using the CAPM framework. All of the three coefficient estimates are very similar to the ones reported earlier and are still statistically significant at a 99% confidence level. The additional factors added, SMB and HML, are both highly significant at a 99% confidence level as well. The interpretation of these results is that it enhances the reliability of the estimate of the fee variable. One worry before this regression could be that the fee estimate included some of the variance which could be explained by the "Small-firm effect" and the "Value premium". The fact that the estimate is almost the same, leads to the conclusion that the coefficient estimate for the fee variable did not include any variance which can be explained by SMB and HML.

The R-squared value of the regression has increased by a little over two percentage points to 0.2888 but is still lower than the comparable regressions for the emerging and Nordic markets, which reported R-squared value of 0.3019 and 0.3310 respectively.

91 The residual plots used for the graphical test for heteroscedasticity are found in appendix 16. They are again very similar to the previous two regressions and are showing the same outliers. This means that the two additional factors have not been able to explain the variance in the outliers. That said, there is no reason seen in the plots to doubt the assumption of homoscedasticity and hence the conclusions drawn are more reliable.