Statistics for Decision-Making - Mutual Funds - Coursework Example

Statistics for Decision Making Case Study: Mutual Funds Name Tutor Course Institution Date Table of Contents 1.0 Introduction 3 1.1 Objectives 4 2.0 Business problem 4 4.0 Data analysis and interpretation 6 1.1Shares categories Analysis 6 1.2Performance of Assets based on growth risk 9 1.3Growth and value analysis 12 1.4Quarter and year-interval performance 13 1.5Expense ratio for shares 15 1.6Assets recorded by the shares categories 16 1.7Mutual funds and fees payment 18 1.84.9 Performance during the worst quarter 18 1.9Inferential Statistics 19 1.1T-Tests for 2013 Returns 19 6.0 General Conclusion 24 7.0 Implications 24 7.0 Bibliography 25 This report presents a case study where the investment analyst conducts an analysis to guide clients regarding investment decision on available mutual funds. SPSS (Statistical Package for Social Scientists) software was used for data entry and statistical analysis. The analyzed variables included: category of shares (small cap, mid cap, large cap); objective – objective of shares comprising the mutual fund–growth or value; assets, fees; expenses ratio; return; risk; best quarter and worst quarter. The performance variables (Expense ratio, 3 year return, 5 year Return and return 2013) were analyzed basing on funds characteristics (Category, Objectives, Risk and Fees). According to the statistical results’ analysis, small cap shares are the best option to consider in share investment plans of the company and individuals, followed by the large cap shares, basing on different characteristics; this information will be availed to the client for them to select among large cap, mid cap and small cap stocks. However, during recession the easier option to venture into is mid cap. In conclusion, the report recommends that the most reasonable investment choice for clients is small cap shares as per the statistical analysis. Statistics for Decision-Making: Analysis report of case study-mutual funds 1.0 Introduction Mutual fund is defined as the type of trust by a sponsor where trustees raise money using the sale of units to the public, using various schemes, in order to invest in securities according to the regulations (Gadhi & Perumal, 2016. This report presents a case study where the investment analyst for clients is required to make an analysis for clients. After the analysis, the investment analyst is required to provide guidelines for the clients to make reasonable decisions among the available mutual funds for their retirement account. 1.1 Objectives To provide general guidelines for clients to select a fund based on different characteristics To guide client to make a reasonable choice among the many funds available 2.0 Business problem In the current business world, there are numerous investment choices and mutual fund is booming sector that provides an opportunity for investors to generate income and returns (Joshi, 2013). The business problem in the case study involves making a decision to buy mutual funds for investors’ retirement account. Accordingly, the investment analyst is required to make analysis and reach the most suitable decision for clients purchasing mutual funds for their retirement account. 3.0 Methodology SPSS (Statistical Package for Social Scientists) software was used for data entry and statistical analysis. Descriptive statistics were used to provide an overview of the data. Pearson’s correlation test was used to measure the strength of the association and relationship between the variables. Regression analysis was used to determine overall fit and relative contribution of variables and all predictors. 4.0 Data analysis and interpretation 1.1 Shares categories Analysis Data was collected to understand share categories and their respective performance. Analyses are conducted based on frequencies and other descriptive statistics. Small Caps Performance Return 2013   5Yr-Return   3-Yr-Return   Mean 48.38333 Mean 12.71667 Mean 15.69167 Standard Error 1.461605 Standard Error 1.19124 Standard Error 0.713055 Median 46.75 Median 14.25 Median 15.55 Mode 62.4 Mode 25.9 Mode 15.2 Standard Deviation 11.32154 Standard Deviation 9.227302 Standard Deviation 5.523303 Sample Variance 128.1773 Sample Variance 85.14311 Sample Variance 30.50688 Kurtosis -0.89565 Kurtosis -0.58244 Kurtosis 1.002631 Skewness 0.32285 Skewness -0.26428 Skewness -0.39395 Range 43.9 Range 39.9 Range 27.2 Minimum 27.3 Minimum -11.1 Minimum 2.1 Maximum 71.2 Maximum 28.8 Maximum 29.3 Sum 2903 Sum 763 Sum 941.5 Count 60 Count 60 Count 60 From the category analysis of descriptive statistics, small cap category, 2013 returnspresented the highest number of shares (mean of 48.38333) followed closely by 3-year return of 15.69167 shares by mean and finally the 5-year return whose mean was 12.71 shares. This shows that smaller cap mutual funds are preferred on short term than on long term basis. Figure 1: small cap mean share returns The data below shows the mid cap category returns. Return 2013   5Yr-Return   3-Yr-Return   Mean 46.19474 Mean 6.210526 Mean 15.01579 Standard Error 2.996669 Standard Error 2.059494 Standard Error 1.050404 Median 46.1 Median 5.7 Median 15 Mode #N/A Mode #N/A Mode #N/A Standard Deviation 13.06218 Standard Deviation 8.977125 Standard Deviation 4.578605 Sample Variance 170.6205 Sample Variance 80.58877 Sample Variance 20.96363 Kurtosis 0.409484 Kurtosis -0.72936 Kurtosis 0.194173 Skewness 0.724428 Skewness 0.178491 Skewness -0.31391 Range 48.4 Range 32.3 Range 18.1 Minimum 29.6 Minimum -9.1 Minimum 5.5 Maximum 78 Maximum 23.2 Maximum 23.6 Sum 877.7 Sum 118 Sum 285.3 Count 19 Count 19 Count 19 From the descriptive statistics in the mid cap category, 2013 returns presented the highest number of shares (mean of 46.19474 slightly lower than in the small cap) followed by 3-year return, which was almost equal to that of small cap of 15.01579shares by mean and finally the 5-year return whose mean was 6.210526 shares, equal to half of the small cap shares in the same period. This shows that more mid cap mutual funds are equally preferred on short term than on long term basis. Large cap Return 2013   5Yr-Return   3-Yr-Return   Mean 32.77381 Mean 1.342857 Mean 7.097619 Standard Error 1.41629 Standard Error 0.974537 Standard Error 0.616832 Median 32.4 Median 0.35 Median 6.95 Mode 27.2 Mode -3.2 Mode 2.6 Standard Deviation 9.178609 Standard Deviation 6.315723 Standard Deviation 3.997529 Sample Variance 84.24686 Sample Variance 39.88836 Sample Variance 15.98024 Kurtosis -0.33242 Kurtosis -0.63201 Kurtosis -0.3134 Skewness 0.164818 Skewness 0.395427 Skewness 0.572324 Range 38.6 Range 25.9 Range 15.5 Minimum 14.9 Minimum -11.1 Minimum 1.4 Maximum 53.5 Maximum 14.8 Maximum 16.9 Sum 1376.5 Sum 56.4 Sum 298.1 Count 42 Count 42 Count 42 From the statistics table in the large cap category, 2013 returns also presented the highest number of shares with a mean of 32.77381 followed by 3-year return, which was less than half of mid cap of 7.0976 shares by mean and finally the 5-year return whose mean was lowest at 1.342857 shares. The data implies a decrease in returns as the return period increases which means that mutual funds are preferred on short term than on long term basis. 1.2 Performance of Assets based on growth risk The table below illustrates data about Performance of mutual fundsbased on various periods of risk. Table 1: Mean Performance of mutual funds based on risk Return 2013   5Yr-Return   3-Yr-Return   Mean 41.36207 Mean 12.36552 Mean 13.15517 Standard Error 1.631596 Standard Error 1.136944 Standard Error 0.765085 Median 40.25 Median 12.2 Median 14.2 Mode 35.8 Mode 16.8 Mode 15.3 Standard Deviation 12.42586 Standard Deviation 8.658705 Standard Deviation 5.826713 Sample Variance 154.402 Sample Variance 74.97318 Sample Variance 33.95059 Kurtosis -0.09275 Kurtosis -0.99646 Kurtosis -0.68865 Skewness 0.358427 Skewness 0.129869 Skewness -0.1528 Range 55.4 Range 30.8 Range 23.4 Minimum 15.8 Minimum -2 Minimum 2.1 Maximum 71.2 Maximum 28.8 Maximum 25.5 Sum 2399 Sum 717.2 Sum 763 Count 58 Count 58 Count 58 As shown in the table above, the total sum of assets of mutual funds at low risk category was higher in 2013 returns at 2399 than in 3-year return period whose total was 763 and 5-year return whose sum was smallest at 717.2 or a mean of 12.36. The table below is a summary of sum and variation of mutual funds at different levels of risk for comparison Risk level 2013 return 5-Yr-Return 3-Yr-Return Sum Sample variation Sum Sample variation Sum Sample variation Low 2399 154.402 717.2 74.97318 763 33.95059 Average 1976.3 192.433 195.4 65.51011 547.4 41.87822 High risk 781.9 165.2606 24.8 104.0426 214.5 58.01904 For 2013 returns, the sum of fixed assets of mutual funds dropped as risk increased. Returns were lower during high risk, and highest at low risk. The same trend was replicated for 3-year and 5-year return periods implying risk level influences the rate of return of mutual funds. This is shown in the figure below. Figure 2: Total assets of shares categories against risk level It is evident from the bar chart that the shares categories at low risk recorded the highest total sum of asset while the shares categories at high risk recorded the lowest return on investment. 1.3 Growth and value analysis The growth patterns for the mutual funds were assessed as per the descriptive statistics shown below. Return 2013   5-Yr-Return   3-Yr-Return   Mean 40.85306 Mean 2.520408 Mean 11.09592 Standard Error 1.807517 Standard Error 1.310949 Standard Error 1.017537 Median 40.4 Median 0.3 Median 13 Mode 37.5 Mode -3.2 Mode 2.6 Standard Deviation 12.65262 Standard Deviation 9.176646 Standard Deviation 7.122762 Sample Variance 160.0888 Sample Variance 84.21082 Sample Variance 50.73373 Kurtosis -0.41473 Kurtosis 0.565568 Kurtosis -0.59167 Skewness 0.321378 Skewness 1.000092 Skewness 0.385748 Range 52.1 Range 38.4 Range 27.9 Minimum 15.8 Minimum -11.1 Minimum 1.4 Maximum 67.9 Maximum 27.3 Maximum 29.3 Sum 2001.8 Sum 123.5 Sum 543.7 Count 49 Count 49 Count 49 By mean, the growth pattern was generally low other than in the 2013 return period. The long term 5-year return period specifically performed very poorly recording the lowest mean of 2.520408 shares. By sum, 2013 had the highest sum of shares (2001.8), followed by 3-year return period with about a quarter the value of 2013 period and the lowest sum being for the 5-year return period with 123.5 shares.Value was estimated as shown by the descriptive statistics below. Return 2013   5Yr-Return   3-Yr-Return   Mean 43.825 Mean 11.30417 Mean 13.62778 Standard Error 1.560812 Standard Error 0.99559 Standard Error 0.650975 Median 42.1 Median 11.25 Median 14.55 Mode 35.8 Mode 16.8 Mode 15.3 Standard Deviation 13.24393 Standard Deviation 8.447859 Standard Deviation 5.523706 Sample Variance 175.4016 Sample Variance 71.36632 Sample Variance 30.51133 Kurtosis -0.20505 Kurtosis -0.84726 Kurtosis -0.43593 Skewness 0.358646 Skewness 0.111954 Skewness -0.10369 Range 63.1 Range 33.2 Range 24.9 Minimum 14.9 Minimum -4.4 Minimum 2.1 Maximum 78 Maximum 28.8 Maximum 27 Sum 3155.4 Sum 813.9 Sum 981.2 Count 72 Count 72 Count 72 Using mean as a standard measure of value, 2013 return period had the best value of 43.825 followed by 3-year return period with 13.62 than 5-year return period with 11.30. 1.4 Quarter and year-interval performance The survey aimed at determining the best quarter performance as well as year interval performance. Results were as displayed in the table below. Category Data Total large cap Sum of Best Quarter 1001.9   Sum of 3-Year-Return 298.1   Sum of 5-Year-Return 56.4 mid cap Sum of Best Quarter 580.6   Sum of 3-Year-Return 285.3   Sum of 5-Year-Return 118 small cap Sum of Best Quarter 1915.5   Sum of 3-Year-Return 941.5   Sum of 5-Year-Return 763 Total Sum of Best Quarter 3498 Total Sum of 3-Year-Return 1524.9 Total Sum of 5-Year-Return 937.4 The small cap shares category recorded the highest sum of best quarter return whose value was 1915.5 followed closely by large cap shares category (1001.9). Mid cap shares category recorded the least return during its best quarter (580.6) compared to the large cap shares category and the small cap shares category. All the three categories recorded lowest returns after 5 years with small cap shares category recording 763, mid cap shares category 118 while large cap recording slightly lower than mid cap (56.4). Moreover, the small cap shares category recorded more returns in their 3rd year (941.5) than the one they recorded during the 5th year (763). The same results were displayed by the large cap shares category that recorded 298.1 in their 3rd year and 56.4 in their 5th year. Similarly, mid cap share category displayed the same trend of results recording 285.3 in their 3rd year and 118 in their 5th year. The results in this section imply that returns on shares invested reduced as time increased whose implication was a reduction the capital investments. 1.5 Expense ratio for shares The sum of expense ratio for shares categories at low risk was higher (79.92) followed by the sum of expense ratios for average risk shares categories (58.9) while those at high risk recorded the least sum of expense ratio (24.3). This indicates that mutual fund types associated with high risks incur expenditure less than mutual funds with low risks. Analysis of Expense ratio at various types of mutual funds Table 2: Expense ratio at various types of mutual funds Category Total Expense ratio Large Cap 51.73 Mid Cap 25.69 Small Cap 85.53 Grand Total 162.95 The total of expense ratio also varies with the type of mutual funds type. Figure 3: Expense ratio at various types of mutual funds As indicated in the figure above, the small cap mutual funds category recorded the highest sum of expense ratio (85.53).The large cap mutual funds category followed closely with 51.73. The mid cap mutual funds category recorded the lowest sum of expense ratio which was 25.69. This shows that the small cap share category spends more than the other types of mutual funds. 1.6 Assets recorded by the shares categories The table below shows the sum of assets recorded by the shares categories against the risk level. Table 3: Sum of Assets Risk Total Average 111952.5 High 31594.4 Low 142743.9 Grand Total 286290.8 The shares category with low risk had the highest sum of assets (142743.9) followed by the shares category with average risk (111952.5) and shares category with high risk recorded the least sum of assets (31594.4). This indicates that the mutual fund types with low risks performed better than those with high risks. Figure 4: A Pie Chart Showing Shares Categories and Their 2013 Return Small cap shares category recorded the highest percentage of returns in 2013 followed by large cap shares category. Mid cap shares category recorded the least returns in the year 2013. Small cap shares are therefore the best option to consider in share investment plans of the company and individuals. 1.7 Mutual funds and fees payment 97 of the mutual funds categories do not pay fees while the remaining 24 pay fees as shown below. Figure 5: Line graph of mutual funds types against fees payment 1.8 4.9 Performance during the worst quarter Another aspect of the study was finding out the performance of the mutual funds types during their worst quarter. Table 4: The performance of the mutual funds types during their worst quarter Category Total large cap -736.8 mid cap -366.6 small cap -1131.5 Grand Total -2234.9 The performance of the small cap mutual funds type was the worst recording a deficit of 1131.5. The performance of the large cap mutual funds type followed with a deficit of 736.8 while the mid cap mutual funds type recorded an average deficit of 366.6 during their worst quarter. This shows that during recession the easier option to venture into is mid cap for such periods. 1.9 Inferential Statistics 1.1 T-Tests for 2013 Returns Statistical tests were carried out to test 2013 returns. The H1is that mutual funds will be more viable when invested on short term basis. The null hypothesis (H0) is that mutual funds will be not be more viable when invested on short term basis. Separate-Variances T Test for the Difference Between Two Means (Assumes unequal population variances) Hypothesized Difference 0 Level of Significance 0.05 Population 1 Sample Sample Size 97 Sample Mean 42.60515464 Sample Standard Deviation 13.5483 Population 2 Sample Sample Size 24 Sample Mean 42.6875 Sample Standard Deviation 10.9817 Intermediate Calculations Numerator of Degrees of Freedom 47.8482 Denominator of Degrees of Freedom 1.1351 Total Degrees of Freedom 42.1528 Degrees of Freedom 42 Standard Error 2.6301 Difference in Sample Means -0.082345361 Separate-Variance t Test Statistic -0.0313 Lower-Tail Test   Lower Critical Value -1.6820 p-Value 0.4876 Do not reject the null hypothesis   At 0.05 significant level, the decision rule is: Reject H0 if Tstat 0.4876.Do not reject H0 if -1.6820 ≤Tstat≤ 0.4876. The t statistic is -0.0313 which is within the range of -1.6820 ≤Tstat≤ 0.4876 hence the null hypothesis is not rejected implying that there is no enough evidence to show that short term investment of mutual funds is most viable. Separate-Variances t Test for the Difference Between Two Means (assumes unequal population variances) Data Hypothesized Difference 0 Level of Significance 0.05 Population 1 Sample   Sample Size 97 Sample Mean 12.41340206 Sample Standard Deviation 6.5031 Population 2 Sample   Sample Size 24 Sample Mean 13.36666667 Sample Standard Deviation 5.5605 Intermediate Calculations Calculations Area Numerator of Degrees of Freedom 2.9731 Pop. 1 Sample Variance 42.2897 Denominator of Degrees of Freedom 0.0741 Pop. 2 Sample Variance 30.9188 Total Degrees of Freedom 40.1009 Pop. 1 Sample Var./Sample Size 0.4360 Degrees of Freedom 40 Pop. 2 Sample Var./Sample Size 1.2883 Standard Error 1.3131 For one-tailed tests: Difference in Sample Means -0.953264605 TDIST value 0.2360 Separate-Variance t Test Statistic -0.7260 1-TDIST value 0.7640 Lower-Tail Test   Lower Critical Value -1.6839 p-Value 0.2360 Do not reject the null hypothesis   The t-statistic is -0.7260 which falls above the lower critical value and the below the p-value. The implication is that the null hypothesis is not rejected. Intermediate Calculations Numerator of Degrees of Freedom 32.0635 Denominator of Degrees of Freedom 0.9794 Total Degrees of Freedom 32.7381 Degrees of Freedom 32 Standard Error 2.3796 Difference in Sample Means -0.75725945 Separate-Variance t Test Statistic -0.3182 Lower-Tail Test   Lower Critical Value -1.6939 p-Value 0.3762 Do not reject the null hypothesis   There was no sufficient evidence from the t statistic (-0.3182) to prove that 5-year returns are best for mutual fund investment. Significance of average returns at different risk levels and time This was estimated through ANOVA test. The 2013 return data in this case is shown in the table below Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 60 2903 48.38333 128.1773 Column 2 19 877.7 46.19474 170.6205 Column 3 42 1376.5 32.77381 84.24686 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 6307.55 2 3153.775 26.41624 3.31E-10 3.07309 Within Groups 14087.75 118 119.3877 Total 20395.3 120         In this data, it is hypothesized that Ho: µ1= µ2= µ3 and Ha claiming that at least one of the mean is different from the others at various risk levels. In this case µ1: average mutual fund shares at low risk,µ2: average risk and µ3: high risk. From the data, Fcrit=F0.05, 2, 118= 3.07309. in other words, Ho is rejected when Fcalc>3.07309 and not rejected when Fcalc ≤ 3.07309. From the ANOVA data, Fcalc =26.41624>3.07309. At the 95% confidence interval, Ho is rejected because Fcalc =26.41624>3.07309. Therefore, there is significant difference of the average returns on mutual funds at low, average and high risk at the 2013 return period. The values for 5-yr returns Anova: Single Factor ANOVA Source of Variation SS df MS F P-value F crit Between Groups 3249.257 2 1624.629 23.63981 2.32E-09 3.07309 Within Groups 8109.464 118 68.72427 Total 11358.72 120         From the data, Fcalc (23.6398)>F crit (3.07309) meaning that the null hypothesis is rejected providing evidence that supports a significant difference in the average of mutual funds returns at various levels of risk in the 5-year return period. Similar results are obtained for 3-year return period where F (40.74342) >F crit (3.07309) an indicator that the null hypothesis is rejected an implication that there is a significant difference between the mean returns at low, average and high risk for the 5-year period 6.0 General Conclusion The best types of shares to invest in are the mutual funds in the small cap category. This is because the analysis indicates that the small cap category had the highest number of shares. The next recommended type of share is the large cap shares because this category closely followed the small cap category. The least recommendable type of share is the mid cap category because the analysis indicates that this type had the least shares. In regard to the performance of assets based on their growth, the small cam mutual fund type is the best objective in driving the business. In addition, in regard to the best quarter performance and year-interval performance, the small cap shares category recorded the highest sum of best quarter return whose value was 1915.5 followed closely by large cap shares category (1001.9). Mid cap shares category recorded the least return during its best quarter (580.6) compared to the large cap shares category and the small cap shares category. From the analysis, small cap shares are therefore the best option to consider in share investment plans of the company and individuals. 7.0 Implications The statistical analysis provides a comparative analysis of proportion of investments of funds invested in various kinds of stocks, namely large cap, mid cap and small cap stocks. In addition, statistical analysis of the portfolio is important in understanding the variability of returns from the mutual funds when compared to previous year. Provided that the statistical analysis the report recommends that the most reasonable investment choice for clients is small cap shares as per the statistical analysis. 7.0 Bibliography Gadhi K & Perumal R, 2016, Performance of Selected Bank Mutual Fund Schemes Impact in Investors’ Decision Making, International Journal of Advanced Research in Management and Social Sciences, 5(3), pp:361-370. Jagongo A & Mutswenje V, 2014, A Survey of the Factors Influencing Investment Decisions: The Case of Individual Investors at the NSE, International Journal of Humanities and Social Science, 4(4), pp: 92-102. Joshi J, 2013, Mutual Funds: An investment option from investors’ point of view, IBMRD'sJournal of Management and Research, 2(1), pp: 124-134. Krishnan R & Booker D, 2002, Investors’ use of Analysts’ recommendations, Behavioral Research in Accounting, 14(1). Mohit G & Navdeep A, 2009, Mutual Fund Portfolio Creation Using Industry Concentration, Tura: ICFAI University. Read More