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Statistics for Decision Making: Case Study-Mutual Funds to writer analysis report Essay Example

  • Category:
    Statistics
  • Document type:
    Assignment
  • Level:
    Undergraduate
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    2796

Report of Mutual Funds in Australia

A case Study: Mutual Funds, 2013

Location of Institution

Contents

3Executive summary

4Business Problem

4Statistical Problem

5Analysis

53.1 Descriptive statistics

53.1.1 Descriptive statistics for the Rate of return at based on funds characteristics of category

73.1.2 Descriptive statistics for the rate of return based on funds characteristics of risk

83.1.3 Descriptive statistics for the rate of return based on funds characteristics of objective

83.2 Hypothesis testing

103.2.1 Hypothesis testing that returns on funds with no fees are lower than return on funds with fees

123.2.2 Hypothesis testing that expense ratio of funds with no fees is lower than expense ratio of funds with fees

16Conclusion

16Implications

17References

Executive summary

The report provides an analysis of the returns and return rates of 121 mutual funds. The objective is to provide guidelines to help the clients to select a fund based on different characteristics. Descriptive statistics and hypothesis tests were used to calculate average returns and return rates for the different time periods and make inferences on whether or not certain conditions are true in the whole population. The analysis was important because it helped to compare the different mutual funds and determine which one is better than the others. In conclusion, returns for value objective are higher than returns of funds with growth objective and mutual funds in the small cap category have higher returns. I recommend that clients should purchase mutual funds with value objective because they have higher returns than funds with growth objective. I also recommend that clients should purchase mutual funds in the small cap category because they have higher returns.

Business Problem

There are many mutual funds available in the world today. There is a sample of 121 mutual funds from which one should choose one for their retirement account. Using business statistics help to analyze the different mutual funds and help determine the best fund that one should purchase for their retirement account. This help to minimize any loses that may arise when one purchases a poor fund. This decision is arrived at based on the returns; best and worst of the different funds.

Statistical Problem

The statistical methods for business data are descriptive and inferential statistics. Descriptive statistics generally describe the data using measures of central tendency and dispersion as well as the distribution of the data from which one can determine the distribution of the whole population[ CITATION Hol16 l 1033 ]. The distribution is determined by using graphs which will show whether the data is symmetrical or not. Hypothesis testing is used to test two hypotheses about the population[ CITATION Nag17 p 251-309 l 1033 ]. The t-test and ANOVA are of great importance in this case study. The null hypothesis is rejected if the p-value from the t-test is less than the level of significance[ CITATION Tae14 p 3 l 1033 ]. Hypothesis testing help to determine whether there is a difference between the different mutual funds.

Analysis

3.1 Descriptive statistics

3.1.1 Descriptive statistics for the Rate of return at based on funds characteristics of category

The descriptive statistics for large cap category show that there is a big difference in the average rates of return for the different time periods. The variance is a measure of variability which shows how close the values are to the mean. The variances for the three time periods are 84.2568, 15.9802 and 39.8883. There is higher variability in 2013. From the results of skewness, it is evident that the distributions of the data for the three different time periods are not symmetrical since the coefficient of skewness is greater than 0. The distributions are positively skewed.

Return 2013

3-Yr-Return

5Yr-Return

32.77380952

7.097619048

1.342857143

Standard Error

1.416290076

0.616832116

0.974537282

Standard Deviation

9.178608735

3.997528999

6.315723424

Sample Variance

84.2468583

15.9802381

39.88836237

Kurtosis

-0.332418832

-0.313400203

-0.632009343

Skewness

0.164818032

0.572323599

0.395427196

The descriptive statistics for mid cap category show that there is a big difference in the average rates of return for the different time periods. The variances for the three time periods are 170.6205, 20.9636 and 80.5888. There is higher variability in 2013. From the results of skewness, it is evident that the distributions of the data for the three different time periods are not symmetrical since the coefficients of skewness are not equal to zero. The distributions for 2013 and 5-year period are positively skewed while for 3-year period is negatively skewed.

Return 2013

3-Yr-Return

5Yr-Return

46.19474

15.01578947

6.210526316

Standard Error

2.996669

1.050404076

2.059493703

Standard Deviation

13.06218

4.578605217

8.977124926

Sample Variance

170.6205

20.96362573

80.58877193

Kurtosis

0.409484

0.194173255

-0.729359969

Skewness

0.724428

-0.313910951

0.178490855

The descriptive statistics for small cap category show that the averages for the 3 and 5-year period do not have a huge difference but the average for 2013 is bigger than for the two time periods. The variances for the three time periods are 128.1773, 30.5069 and 85.1431. There is higher variability in 2013. From the results of skewness, it is evident that the distributions of the data for the three different time periods are not symmetrical since the coefficients of skewness are not equal to zero. The distribution for 2013 is positively skewed while for 3 and 5-year period are negatively skewed.

Return 2013

3-Yr-Return

5Yr-Return

48.38333333

15.69166667

12.71666667

Standard Error

1.461604966

0.71305538

1.191239602

Standard Deviation

11.32154339

5.523303226

9.227302279

Sample Variance

128.1773446

30.50687853

85.14310734

Kurtosis

-0.89564758

1.002631349

-0.582436593

Skewness

0.322850439

-0.393947311

-0.264281608

3.1.2 Descriptive statistics for the rate of return based on funds characteristics of risk

The descriptive statistics for average risk show that there is a big difference in the average rates of return for the different time periods. The variances for the three time periods are 41.8782, 192.4330 and 65.5101. From the results of skewness, it is evident that the distributions of the data for the three different time periods are not symmetrical since the coefficients of skewness are not equal to zero. Since the coefficients are positive, the distributions are positively skewed.

3-Yr-Return

Return 2013

5Yr-Return

42.96304348

4.247826087

Standard Error

0.95414681

2.045318346

1.19337033

Standard Deviation

6.471338519

13.87202394

8.093831372

Sample Variance

41.87822222

192.4330483

65.51010628

Kurtosis

-0.383804036

-0.334783597

-0.889110579

Skewness

0.301086481

0.586115957

0.633148778

The descriptive statistics for high risk show that there is a big difference in the average rates of return for the different time periods. The variances for the three time periods are 58.0190, 165.2606 and 104.0426. From the results of skewness, it is evident that the distributions of the data for the three different time periods are not symmetrical since the coefficients of skewness are not equal to zero. Distributions for 2013 and 3-year period are negatively skewed while distribution for the 5-year period is positively skewed.

3-Yr-Return

Return 2013

5Yr-Return

12.61764706

45.99411765

1.458823529

Standard Error

1.84739951

3.117885673

2.473893972

Standard Deviation

7.617023311

12.85537196

10.20012615

Sample Variance

58.01904412

165.2605882

104.0425735

Kurtosis

-0.571708967

0.711316025

0.397848037

Skewness

-0.055033838

-0.552536602

0.781679105

The descriptive statistics for low risk show that there is a big difference in the average rates of return for the different time periods. The variances for the three time periods are 58.0190, 165.2606 and 104.0426. From the results of skewness, it is evident that the distributions of the data for the three different time periods are not symmetrical since the coefficients of skewness are not equal to zero. The distribution for the 3-year period is negatively skewed while distributions for the 5-year period and 2013 are positively skewed.

3-Yr-Return

Return 2013

5Yr-Return

13.15517241

41.36206897

12.36551724

Standard Error

0.765084927

1.631595606

1.136943695

Standard Deviation

5.826713208

12.42586193

8.658705217

Sample Variance

33.95058681

154.4020448

74.97317604

Kurtosis

-0.688652279

-0.092747083

-0.996457714

Skewness

-0.152800329

0.358426997

0.12986944

3.1.3 Descriptive statistics for the rate of return based on funds characteristics of objective

The descriptive statistics for growth objective show that there is a big difference in the average rates of return for the different time periods. The variances for the three time periods are 84.2108, 50.7337 and 160.0888. There is higher variability in data for 2013. From the results of skewness, it is evident that the distributions of the data for the three different time periods are not symmetrical since the coefficients of skewness are greater than zero. The distributions are positively skewed.

5Yr-Return

3-Yr-Return

Return 2013

2.520408163

11.09591837

40.85306122

Standard Error

1.310949374

1.017537373

1.807517141

Standard Deviation

9.17664562

7.122761613

12.65261999

Sample Variance

84.21082483

50.73373299

160.0887925

Kurtosis

0.565568342

-0.591673886

-0.414731767

Skewness

1.00009196

0.385748005

0.321378135

The descriptive statistics for value objective show that there is a small difference in the average rates of return for the 3 and 5-year period. The average for 2013 is higher than for the 3 and 5-year period. The variances for the three time periods are 71.3663, 30.5113 and 175.4016. There is higher variability in data for 2013. From the results of skewness, it is evident that the distributions of the data for the three different time periods are not symmetrical since the coefficients of skewness are greater than zero. The distributions 2013 and 5-year period are positively skewed. The distribution for 3-year period is negatively skewed.

5Yr-Return

3-Yr-Return

Return 2013

11.30416667

13.62777778

Standard Error

0.995589722

0.650975019

1.560811842

Standard Deviation

8.447858925

5.523706202

13.24392765

Sample Variance

71.36632042

30.5113302

175.4016197

Kurtosis

-0.847264222

-0.435925684

-0.205049728

Skewness

0.111954288

-0.103686289

0.358645998

3.2 Hypothesis testing

The steps of hypothesis testing are: setting the hypotheses, deciding on decision rule, calculating the value and then making conclusions[ CITATION Mur14 l 1033 ][ CITATION Met16 l 1033 ].

3.2.1 Hypothesis testing that returns on funds with no fees are lower than return on funds with fees

H0: µ1≥µ2

H112

Where µ1 represents the average returns on funds with no fees in 2013 and µ2 represents the average returns on funds with fees in 2013

Reject H0 if the p-value is less than 0.05

T-Test: Two-Sample Assuming Unequal Variances

With fees

42.60515

Variance

183.5565

120.597663

Observations

-0.03131

P(T<=t) one-tail

t Critical one-tail

At 0.05 level of significance, since the p-value is 0.4876 > 0.05, fail to reject the null hypothesis and conclude that there is no sufficient evidence to conclude that the returns on funds with no fees are lower than returns on funds with fees is 2013.

H0: µ1≥µ2

H112

Where µ1 represents the average returns on funds with no fees for 3-year period and µ2 represents the average returns on funds with fees for 3-year period.

T-Test: Two-Sample Assuming Unequal Variances

With fees

12.41340206

13.36666667

Variance

42.28971435

30.91884058

Observations

-0.725958688

P(T<=t) one-tail

t Critical one-tail

At 0.05 level of significance, since the p-value is 0.2360 > 0.05, fail to reject the null hypothesis and conclude that there is no sufficient evidence to conclude that the returns on funds with no fees are lower than returns on funds with fees for a 3-year period.

H0: µ1≥µ2

H112

Where µ1 represents the average returns on funds with no fees for 5-year period and µ2 represents the average returns on funds with fees for 5-year period.

T-Test: Two-Sample Assuming Unequal Variances

With fees

7.59690722

8.354166667

Variance

91.0428028

113.3730254

Observations

-0.3182307

P(T<=t) one-tail

t Critical one-tail

At 0.05 level of significance, since the p-value is 0.3762 > 0.05, fail to reject the null hypothesis and conclude that there is no sufficient evidence to conclude that the returns on funds with no fees are lower than returns on funds with fees for a 5-year period.

3.2.2 Hypothesis testing that expense ratio of funds with no fees is lower than expense ratio of funds with fees

H0: µ1≥µ2

H112

Where µ1 represents the average expense ratio of funds with no fees and µ2 represents the average expense ratio of funds with fees.

Reject H0 if the p-value is less than 0.05

T-Test: Two-Sample Assuming Unequal Variances

With fees

1.340825

1.370417

Variance

0.221133

0.112578

Observations

-0.35444

P(T<=t) one-tail

t Critical one-tail

At 0.05 level of significance, since the p-value is 0.3623 > 0.05, fail to reject the null hypothesis and conclude that there is no sufficient evidence to conclude that the average expense ratios of funds with no fees are lower than expense ratios of funds with fees.

3.2.3 Hypothesis testing of whether there is a significant difference between the different categories of the mutual funds

H0: µ12= µ3

H11≠µ2≠µ3

Where µ1, µ2 and µ3 represent the average returns in 2013 for large, mid and small cap respectively.

Reject H0 if the p-value is less than 0.05

Anova: Single Factor

Variance

32.77381

84.24686

46.19474

170.6205

48.38333

128.1773

Source of Variation

Between Groups

3153.775

26.41624

3.306609E-10

Within Groups

14087.75

119.3877

At 0.05 level of significance, reject the null hypothesis of no difference since the p-value is less than 0.05 and conclude that there is a significant difference between the average returns across the mutual fund categories in 2013. The mutual fund category which performed better was small cap with an average of 48.3833.

H0: µ12= µ3

H11≠µ2≠µ3

Where µ1, µ2 and µ3 represent the average returns from 2011-2013 for large, mid and small cap respectively.

Reject H0 if the p-value is less than 0.05

Anova: Single Factor

Variance

7.097619

15.98024

15.01579

20.96363

15.69167

30.50688

Source of Variation

Between Groups

1955.988

977.9942

40.74342

3.5164E-14

Within Groups

2832.441

24.00374

4788.429

At 0.05 level of significance, reject the null hypothesis of no difference since the p-value is less than 0.05 and conclude that there is a significant difference between the average returns across the mutual fund categories in for the period between 2011-2013. The mutual fund category which performed better was small cap with an average of 15.6917.

H0: µ12= µ3

H11≠µ2≠µ3

Where µ1, µ2 and µ3 represent the average returns from 2009-2013 for large, mid and small cap respectively.

Reject H0 if the p-value is less than 0.05

Anova: Single Factor

Variance

1.342857

39.88836

6.210526

80.58877

12.71667

85.14311

Source of Variation

Between Groups

3249.257

1624.629

23.63981

2.32327E-09

Within Groups

8109.464

68.72427

11358.72

At 0.05 level of significance, reject the null hypothesis of no difference since the p-value is less than 0.05 and conclude that there is a significant difference between the average returns across the mutual fund categories in for the period between 2009-2013. The mutual fund category which performed better was small cap with an average of 12.7167.

3.2.4 Hypothesis testing that returns on funds with value objective are lower than return on funds with growth objective

H0: µ1≥µ2

H112

Where µ1 represents the average returns on funds with value objective in 2013 and µ2 represents the average returns on funds growth objective in 2013

Reject H0 if the p-value is less than 0.05

T-Test: Two-Sample Assuming Unequal Variances

40.85306122

Variance

160.0887925

175.4016197

Observations

-1.244453245

P(T<=t) one-tail

0.108038692

t Critical one-tail

-1.659356034

At 0.05 level of significance, fail to reject the null hypothesis since the p-value is greater than 0.05 and conclude that there is no sufficient evidence to conclude that the returns for growth objective are lower than returns for value objective in 2013.

H0: µ1≥µ2

H112

Where µ1 represents the average returns on funds with value objective and µ2 represents the average returns on funds growth objective for the period between 2011 and 2013.

Reject H0 if the p-value is less than 0.05

T-Test: Two-Sample Assuming Unequal Variances

13.62777778

11.09591837

Variance

30.5113302

50.73373299

Observations

2.09599142

P(T<=t) one-tail

0.019510916

t Critical one-tail

-1.66276545

At 0.05 level of significance, reject the null hypothesis since the p-value is 0.0195 which is less than 0.05 and conclude that there is sufficient evidence to conclude that the returns for growth objective are lower than returns for value objective in 2013.

Conclusion

The analysis based on descriptive statistics and hypothesis tests represent the average rates of return and returns for 2013, 2011-2013 and 2009-2013 for the different mutual funds. The average returns for the mutual funds are important to an analyst in determining the best mutual fund that the clients should purchase for their retirement accounts. The mutual fund with the highest returns in a year is the top priority of the any analyst. It is evident that returns for value objective are higher than returns of funds with growth objective and mutual funds in the small cap category have higher returns.

Implications

An analyst should consider the different aspects of a fund before advising the client to reduce losses which may occur from purchasing a mutual fund which performs poorly over the years. Clients should purchase mutual funds with value objective because they have higher returns than funds with growth objective. Clients should purchase mutual funds in the small cap category because they have higher returns.

References

Holcomb, Z.C., 2016. Fundamentals of descriptive statistics. Routledge.

Metler, C.A., & Reinhart, R.V., 2016. Advanced and multivariate statistical methods: Practical application and interpretation. Routledge.

Murphy, K.R., Myors, B., & Wolach, A., 2014. Statistical power analysis: A simple and general model for traditional and modern hypothesis tests. Routledge.

Naghettini, M., 2017. Statistical Hypothesis Testing. In Fundamentals of Statistical Hydrology (pp. 251-309). Springer International Publishing.

Taeger, D., & Kuhnt, S., 2014. ‘Statistical hypothesis testing’. Statistical hypothesis testing with SAS and R, pp. 3-16.