Equity-Focused Funds

Capital Asset Pricing Model Regression

Like for the regressions which had no filter on geographical focus areas, a regression will also be conducted focusing only on equity focused funds, which are focusing on emerging markets. Of the 483 funds in total which has emerging markets as their geographical focus area, a total of 364 of these are equity focused and are therefore included in this regression. The regression yields the results presented in table 5.15 below.

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Table 5.15: CAPM regression, equity focused funds, emerging markets

From the table it can be seen that the intercept is significant at 99% confidence level. Even though this cannot be seen from the p-value itself, it can instead be seen by the absolute value of the t-statistic exceeding 2.326. The market return is still highly significant even at 99% confidence level, while the latter variable, the fee, is statistically insignificantly different from zero with a p-value as high as 0.70. This is an interesting result as the previous regression with all asset classes showed the fee variable being significant even at 99% confidence level. The interpretation of an insignificant coefficient estimate is that it isn't possible to conclude anything about a relationship between the fee and return.

The regression has a R-squared value of 0.2947, which is on line with what was found for the similar regression with no filter on the geographical focus area on the equity focused funds.

As has previously been done for the regressions, the test for heteroscedasticity will also be performed here using residual plots. The residual plots are shown in appendix 9. Also, the residual plot with the fee variable on the x-axis are shown below in figure 5.8.

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Figure 5.8: residual vs fees plot for CAPM regression, equity focused funds, emerging markets

The graph above does not show significant indication of heteroscedasticity, but it shows that there could be a small difference in variance of residuals across fees. This can both be due to how large the most extreme residuals are for a given level of x, but it could also be due to there being a higher intensity in small residuals for some level of x. The latter part could be the case above as it seems the for some levels of fee, there is a very high intensity of residuals around 0, which is obviously great, but that could also lower the variance. A similar pattern is seen in the two other residual plots shown in appendix 9. However, the conclusion is that there is no clear indication of

heteroscedasticity and hence the assumption of homoscedasticity is not breached in this regression.

Fama-French Three-Factor Model Regression

Since the overall regression surprisingly showed an insignificant coefficient estimate for the fee variable, the analysis will be extended in terms of theoretical framework used, in the sense that the additional factors in Fama-French's Three-Factor model will be included. The reason is that this improves the reliability of the estimates and the added variables can potentially explain some variance not previously explained, which might change the coefficient estimates or the standard errors. The regression performed present the results shown in table 5.16 below.

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Table 5.16: FF3-factor regression, equity focused funds, emerging markets

The first thing to note is, that only the HML variable is significantly different from zero, while the SMB factor is insignificant, implying that there seems to be no "small firm effect" in the returns of equity focused funds. The table also shows that including the additional variables does not change a lot for the other variables. The intercept is still significant, and the coefficient estimate is almost the same. The same goes for the market return and also for the fee variable, which both have not changed much when including the additional variables in the regression. The R-squared value has increased to 0.3019, probably mostly due to the HML factor which has some significant explanatory power.

The residual plots used for testing for heteroscedasticity are shown in appendix 10 and the two residual plots with the extra Fama-French factors on the x-axis, SMB and HML respectively, are shown below in figures 5.9 & 5.10.

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Left figure 5.9: residual vs SMB plot for Fama French 3-factor regression, equity focused funds, emerging markets Right figure 5.10: residual vs HML plot for Fama French 3-factor regression, equity focused funds, emerging markets

The graphs above show the residual distribution over different values for the two Fama-French factors, Small-Minus-Big and High-Minus-Low. In general, there seems to be no pattern leading to suspect heteroscedasticity, except for a few outliers in the HML plot to the right. The residual plot with predicted y-values on the x-axis, shown in appendix 10, has a weak pattern indicating a smaller variance for higher predicted y-values. The pattern does however not seem to be significant enough to reject the assumption of homoscedasticity. The two last plots do not have any clear pattern and hence the assumption of homoscedasticity are assumed to hold in this regression and the conclusions drawn above can be trusted.