Analysis

Among the many investment choices available today, mutual funds, a market basket of a portfolio of securities, is a common choice for those thinking about their retirement. They need to have some information to make a reasonable choice among the many funds that are available today. The research here is done to provide a general guideline to the clients to select a fund based on different characteristics.

The data file here contains information regarding 11 variables from a sample of 121 mutual funds. The names of the mutual funds are omitted from the database. The variables are category, objective, assets, fees, expense ratio, return, five-year return, three-year return, risk, best and worst quarter. Analysis has been done on the above stated variables and an inference have been drawn on the basis of the results.

The data set here contains 11 variables. The variable objective denotes the type of shares comprising the mutual fund – small cap, mid cap and large cap. The variable objective denotes the objective of shares comprising the mutual fund–growth or value. The third variable assets denote the assets of a person in million dollars. The fourth variable fees denotes the sales charges – yes or no. The fifth variable expense ratio denotes the ratio of expenses to net assets in percentage of the year 2013. The variables return, five-year return and three-year return are respectively the twelve-month  return in 2013, annualized return 2009 – 2013, annualized return 2011 – 2013. Risk denotes the risk-of-loss factor of the mutual fund classified as low, average or high and quarter denotes the best and the worst quarter.

At first, descriptive analysis of the 11 variables have been conducted. The whole analysis has been done using the statistical software SPSS. Initially, the rate of return based on the funds characteristics of category for the year 2013 has been analyzed. From the results it is clear that, the rate of return for small caps has a standard deviation of 11.322 which is high. Thus it can be said that the rates vary quite much for small caps. The rates of return for mid cap also varies a lot from the mean of the values. Large caps has the least standard deviation among the three categories. Thus, the rates of return for large caps varies less than the other two. Investing in large caps will give a more constant result and thus, it is better to invest in large-caps than small-caps and mid-caps (Jagric et al. 2015). The comparison is shown by a boxplot. All the three categories are positively skewed. The skewness for large caps is close to zero. Thus, it is weakly skewed and close to being symmetric (Blanca et al. 2013). Thus, large caps will be a much better and reliable category to invest than the other two categories (Bodie 2013).

Rate of Returns based on Fund Categories

Secondly, Rate of Returns based on Risk categories has been analyzed. The risk has been categorized into three levels-low, average and high. From the results it is clear that, the standard deviation of the three categories are very close. Thus, nothing can be inferred about their variability. The category with high risk has a negative value of skewness. Thus it can be said that, risk is more as rate of return increases. Average risk has a moderately positive skewness. Thus, the risk is average with low returns. The skewness for low is weakly positive. Thus it is almost symmetric. Thus, risk is low with average rate of return. Thus, mutual funds with average rate of return should be chosen in order to experience lower risk (Petajisto 2013). The comparison is also expressed diagrammatically in the form of a boxplot.

Thirdly, the rate of return has been analyzed on the basis of the objectives – Growth and Value. The results from the table clearly states that, the standard deviation of the two categories of objectives are very close. Nothing can be inferred about which variable has more values closer to the mean from here. The skewness measures are weakly positive and very close. Thus, growth and value, both the objectives are balanced among themselves. The rate of return does not depend much on the basis of objectives. This has also been stated by Ferreira (2013). The comparison has also been represented diagrammatically using a boxplot.

Many investors believe that returns on funds with no fees are lower than return on funds with fees (Fund 2017). This claim has been tested at 5 per cent significance level, in terms of 2013 return, 3-year return and 5-year return. The null hypothesis for the first case that is rate of return 2013 has been taken as

H₀₁: Returns on funds with no fees are equal to return on funds with fees.

The table clearly states that the P (T<=t) one-tail is 0.489, which is less than the significance level 0.025 (one-tail). Thus, the null hypothesis is accepted. Thus, returns on funds with no fees is not lower than the returns of funds with fees.

For the second case, 5-year returns on funds is tested. The null hypothesis is same as H_01. The results of the analysis states that, the p-value one tail is 0.367, which is greater than the one-tailed level of significance 0.025. Thus, the null hypothesis is accepted. It can thus be said that there is no significant difference between the 5-year return on funds with fees and without fees. 

Rate of Returns based on Risk Categories

The results of t-test for 3-year return on funds shows that the p-value is 0.255, which is greater than the one tail level of significance. Thus, the null hypothesis is accepted. It can thus be said that, the 3-year return on funds does not differ significantly with fees or without fees.

Many investors believe that expense ratio of funds with no fees are lower than expense ratio of funds with fees (Malkiel 2013). This claim is tested at 5 per cent significance level. The null hypothesis is given as;

H₀₂: Expense ratio of funds with fees is equal to expense ratio of funds without fees.

Independent sample t-test is performed to test the above stated hypothesis. From the results of the t-test it is clear that the p-value is 0.386 which is less than the one-sided level of significance (0.025). Thus, the null hypothesis is accepted.  Expense ratio of funds with fees is not higher than expense ratio of funds without fees.

The performance of different types of mutual funds categorized by their types (small cap, mid cap, large cap) during 2013, the three-year period from 2011-2013 and the five-year period from 2009-2013 is tested separately using independent sample t-test (Sullivan III 2015). At first, difference of performance between small caps and mid-caps is tested for return 2013. The null hypothesis is stated as;

H₀₃: The performance on return 2013 does not differ significantly for small cap and mid cap.

From the test results, it is clear that the p-value (one-tailed) is 0.241, which is higher than the one-tailed level of significance (0.025). Thus, the null hypothesis is accepted (Triola 2013). There is no difference in performance of small and medium caps for return 2013.

Secondly, difference of performance between small caps and large-caps is tested for return 2013. The null hypothesis is stated as;

H₀₄: The performance on return 2013 does not differ for small cap and large cap.

From the test results, it is clear that the p-value (both-tailed) is 0.000, which is less than the both-tailed level of significance (0.05). Thus, the null hypothesis is rejected (Wasserstein and Lazar 2016). There is a difference in performance of small and large caps for return 2013.

Thirdly, difference of performance between mid-caps and large-caps is tested for return 2013. The null hypothesis is stated as;

H₀₅: The performance on return 2013 does not differ for mid cap and large cap.

Rate of Return based on Objectives

From the test results, it is clear that the p-value (both-tailed) is 0.000, which is less than the both-tailed level of significance (0.05). Thus, the null hypothesis is rejected. There is a difference in performance of mid and large caps for return 2013.

Fourthly, difference of performance between small-caps and mid-caps is tested for 5-year return. The null hypothesis is stated as;

H₀₆: The performance on 5-year return does not differ significantly for small cap and mid cap.

From the test results, it is clear that the p-value (both-tailed) is 0.009, which is less than the both-tailed level of significance (0.05). Thus, the null hypothesis H₀₆ is rejected (Welsh and Knight 2015). There is a significant difference in performance of small and mid-caps for 5-year return.

Fifthly, difference of performance between small-caps and large-caps is tested for 5-year return. The null hypothesis is stated as;

H₀₇: The performance on 5-year return does not differ significantly for small cap and large cap.

From the test results, it is clear that the p-value (both-tailed) is 0.000, which is less than the both-tailed level of significance (0.05). Thus, the null hypothesis H₀₇ is rejected. There is a significant difference in performance of small and mid-caps for 5-year return.

Sixthly, difference of performance between mid-caps and large-caps is tested for 5-year return. The null hypothesis is stated as;

H₀₈: The performance on 5-year return does not differ significantly for mid cap and large cap.

From the test results, it is clear that the p-value (both-tailed) is 0.018, which is less than the both-tailed level of significance (0.05). Thus, the null hypothesis H₀₈ is rejected. There is a significant difference in performance of mid and large-caps for 5-year return.

Next, difference of performance between small-caps and mid-caps is tested for 3-year return. The null hypothesis is stated as;

H₀₉: The performance on 3-year return does not differ significantly for small cap and mid cap.

From the test results, it is clear that the p-value (both-tailed) is 0.631, which is more than the both-tailed level of significance (0.05). Thus, the null hypothesis H₀₉ is accepted. There is no significant difference in performance of small and mid-caps for 3-year return. 

Again, difference of performance between small-caps and large-caps is tested for 3-year return. The null hypothesis is stated as;

H₁₀: The performance on 3-year return does not differ significantly for small cap and large cap.

From the test results, it is clear that the p-value (both-tailed) is 0.000, which is less than the both-tailed level of significance (0.05). Thus, the null hypothesis H₁₀ is rejected. There is a significant difference in performance of small and large-caps for 3-year return.

Comparison of Returns on Funds with Fees vs No Fees

Finally, difference of performance between mid-caps and large-caps is tested for 3-year return. The null hypothesis is stated as;

H₁₁: The performance on 3-year return does not differ significantly for mid cap and large cap.

From the test results, it is clear that the p-value (both-tailed) is 0.000, which is less than the both-tailed level of significance (0.05). Thus, the null hypothesis H₁₁ is accepted. There is a significant difference in performance of large and mid-caps for 3-year return.

Many investors believe that returns on funds with value objective are lower than return on funds with growth objective.  To test this claim at 5 per cent significance level, in terms of 2013 return and 3-year return, independent sample t-test is performed separately. The null hypothesis is stated as,

H₁₂: Return 2013 on funds with value objective and growth objective are equal.

The t-test results show that the p-value (0.220) is more than the level of significance (0.05) for return 2013 and the p value (0.030) is less than the level of significance (0.05) for 3-year return. Thus, return on funds for 2013 do not vary significantly with value objective and growth objective. The rate of return on funds for the time period of 2011-2013 is more for value objective than growth objective. 

General Conclusion

The analysis above states that, yearly rate of return is more constant for large caps, making it a more reliable category to invest. The risk is low when rate of return is average. Rate of return does not vary with growth objective or value objective. The t-test results state that, Return on funds with fees does not differ significantly with return on funds without fees, that is, the sales charges. Expense ratio of funds with fees does not differ significantly with expense ratio of funds without fees. The performance on return 2013 is more for small and mid-caps than large caps.  Again, for 5-year return, the return for small caps and mid-caps is more than large caps and the return on small caps is more than mid-caps. For 3-year return also, return on small cap and mid cap is more than large cap. The return on funds for 2013 do not vary significantly with value objective and growth objective. The rate of return on funds for the time-period of 2011-2013 is more for value objective than growth objective.

The rate of return for large cap is constant. Thus, it is more secure to invest large capital. This will result in the economic growth of the province. The expense ratio is more for small and medium caps. Thus, from the view point of expense ratio also, investing in large caps is much better.

References

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