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Essay/Term paper: Stats1

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USING STATISTICAL EVALUATION

FOR FUND PURCHASING

















In partial fulfillment of

the requirement for

MATH 2050

















ABSTRACT

Fund Purchasing Using Statistics

In the past few years many young people transiting into adulthood have found themselves victim to improper or no teachings on how to handle money, or how to build some kind of future funds. This trend has effected most young people. When talking about stocks and mutual funds, many individuals do not realize that statistics can play a major part in the selection of an asset for the future. This study was to show that statistics can be used to compare mutual funds, to what you want for a return. The mutual funds looked at were only in six sectors of the market.

















































TABLE OF CONTENTS







ABSTRACT

LIST OF TABLES AND GRAPHS. . . . . . ii

INTRODUCTION . . . . . . . 1

METHODS . . . . . . . . 3

RESULTS OF HOW STATISTICS CAN HELP

BUILD FOR THE FUTURE . . . . . 4

Importance of Saving For the Future . . . . . 4

Process of Evaluation . . . . . . . 4

CONCLUSIONS AND RECOMMENDATIONS . . . 13







LIST OF TABLES AND GRAPHS

Table A. Average, Range and Standard Deviation Comparison. . 4

Table 1. Returns for Conservative fund one and two . . . 7

Graph 1. Returns for Conservative fund one and two . . . 7

Table 2. Returns for Secure fund one and two . . . 8

Graph 2. Returns for Secure fund one and two . . . 8

Table 3. Returns for Moderate fund one and two . . . 9

Graph 3. Returns for Moderate fund one and two . . . 9

Table 4. Returns for Balanced fund one and two . . . 10

Graph 4. Returns for Balanced fund one and two . . . 10

Table 5. Returns for Ambitious fund one and two . . . 11

Graph 5. Returns for Ambitious fund one and two . . . 11

Table 6. Returns for Aggressive fund one and two . . . 12

Graph 6. Returns for Aggressive fund one and two . . . 12











INTRODUCTION

Potential purchases for building future wealth can be done with statistics. Individuals have many things to consider before they invest money, such as how much return they would like to have on a investment, how often they would like their money to double, and how much to invest. These factors help the individuals make an informed decision, about which investment would be best for them. This study was to compare the performance of two funds in six different sectors. Its main purpose was to look at how statistics can best be suited to do this. The six different sectors were selected; two funds were selected from each.



Sectors:

1. Conservative

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

C1 10.4 12.8 18.4 15.0 3.0 8.2 11.3 8.0 13.2 7.3 10.7

C2 10.9 14.0 24.2 15.9 2.5 8.7 13.7 10.2 17.9 8.0 11.6













2. Secure

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

S1 18.2 10.2 23.7 18.9 7.8 12.0 23.0 4.4 21.2 8.0 8.2

S2 16.3 9.3 27.8 19.1 0.5 12.8 15.3 1.4 27.9 2.7 13.1



3. Moderate

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

M1 14.5 10.0 29.7 23.2 11.6 16.0 19.7 0.8 29.5 7.6 7.5

M2 21.9 14.4 27.2 17.6 6.4 15.7 28.2 4.5 27.6 6.6 4.5





4. Balanced

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

B1 29.2 9.2 24.7 17.3 2.3 21.8 22.8 1.4 20.8 7.7 7.5

B2 21.5 8.9 23.2 13.2 7.8 12.7 24.8 2.3 25.6 9.2 11.9







5. Ambitious

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

A1 36.2 6.3 32.4 11.8 2.9 14.7 22.9 3.5 38.6 10.8 15.8

A2 27.3 2.6 33.5 14.7 3.4 15.1 32.8 -6.1 24.1 13.8 25.2







6. Aggressive

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

G1 23.7 7.6 33.4 25.8 5.5 13.3 28.6 6.9 51.5 4.0 -4.1

G2 22.3 0.3 38.3 19.7 6.0 14.1 37.0 -2.1 57.6 6.4 -1.2





METHODS

The methods used were the average, range, and the standard deviation associated with each fund. Assuming that the distribution for each fund was normal, the z-tables were then used to calculate the percentage of time the return was above the designated return goal for each fund.

RESULTS OF HOW USING STATISTICS CAN HELP BUILD FOR THE FUTURE.

Importance of Saving For the Future

The importance of saving early, is that the extra time allows your assets to build before they are needed. An example of this is an investment of $16,000.00 before the age of 27 properly managed with a 15 % return yearly, could net an individual approximately $750,000.00 at the retirement age of 62 years old. Whereas a 40 year old individual saving $2,000.00 a year properly managed with a 15 % return until the age of 62, will net approximately $500,000.00. Approximately 65 % of all retired persons retire with an annual income of less than $20,000.00 (Money 1997). This is one good reason for starting at an early age and to be able to enjoy your retirement. With inflation at approximately 3 % a year and increasing the dollar will be worth less tomorrow than today.

Process of Evaluation

To find funds with high gains or losses, determine the average, range and standard deviation of each fund. The results are in the following Table:

Table 1. Average and Standard Deviation Comparison

AVG

% STD Range

S & P 16.15 11.38 34.80

CMI 14.28 8.29 27.60

C1 10.75 4.16 15.40

C2 12.50 5.70 21.70

S1 14.15 6.97 19.30

S2 13.30 9.50 27.40

M1 15.43 8.80 28.90

M2 12.50 21.70 23.70

B1 14.97 9.20 27.80

B2 14.64 7.50 23.30

A1 17.80 12.30 35.70

A2 16.94 12.40 39.60

G1 17.83 15.50 55.60

G2 18.03 18.40 59.70



A person wanting a 15 % annual return would take into consideration what funds averaged 15 % and over. The average will not guarantee that you will make the 15 % every year, it is only reflects how well you will do in the good and the bad years combined. The return for the S & P over the same time period was an average of 16.15 % with a range of 34.8 and a STD of 11.38. The Capitol Market Index was an average of 14.28 % with a range of 27.6 and a STD of 8.29. By removing any funds with an average that fell below the Standards & Poor"s, and Capitol Market Index, this would narrow it down to funds that did

as well as the market or better. The funds that fit this requirement are M1, A1, A2, B1, G1, and G2.

We now would want to look at the range and STD. Data varies dramatically, one range almost 60 points. In this data set the riskier funds have a greater range of values, since the ranges may have been caused by an isolated year that was good or bad. By removing any funds with a high range and standard deviation we can narrow the selection down to M1, A1, and A2. By reading the prospectus for these funds, will help to narrow it down even further.

The Z tables can now be used, but it must first be calculated. The equation to use for calculating the Z is:

Xi - X / STD = Z

By calculating the Z, and assuming a normal distribution, the Z tables are used to find the percentage of time the funds fell below 15 %. The following calculations are for the remaining funds:

M1: 15“15.43 / 8.8 = Z = -.05

Table percentage is 48.01%

A1: 15-17.80 / 12.3 = Z = -.31

Table percentage is 37.83 %

A2: 15-16.94. / 12.4 = Z = -.24

Table percentage is 40.52 %

The given calculations show that the return on the selected funds, returned less than 15 % at least 37.83 % of the time.

Data Calculations Results

Table 1. Returns for Conservative fund one and two

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

C1 10.4 12.8 18.4 15.0 3.0 8.2 11.3 8.0 13.2 7.3 10.7

C2 10.9 14.0 24.2 15.9 2.5 8.7 13.7 10.2 17.9 8.0 11.6

AVG STD RANGE

C1 10.75 4.16 15.40

C2 12.50 5.70 21.70





Graph 1. Returns for Conservative fund one and two

















Table 2. Returns for Secure fund one and two



1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

S1 18.2 10.2 23.7 18.9 7.8 12.0 23.0 4.4 21.2 8.0 8.2

S2 16.3 9.3 27.8 19.1 0.5 12.8 15.3 1.4 27.9 2.7 13.1

AVG STD RANGE

S1 14.15 6.97 19.30

S2 13.30 9.50 27.40







Graph 2. Returns for Secure fund one and two





Table 3. Returns for Moderate fund one and two

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

M1 14.5 10.0 29.7 23.2 11.6 16.0 19.7 0.8 29.5 7.6 7.5

M2 21.9 14.4 27.2 17.6 6.4 15.7 28.2 4.5 27.6 6.6 4.5

AVG STD RANGE

M1 15.43 8.87 28.90

M2 12.50 21.70 23.70









Graph 3. Returns for Moderate fund one and two











Table 4. Returns for Balanced fund one and two



1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

B1 29.2 9.2 24.7 17.3 2.3 21.8 22.8 1.4 20.8 7.7 7.5

B2 21.5 8.9 23.2 13.2 7.8 12.7 24.8 2.3 25.6 9.2 11.9

AVG STD RANGE

B1 14.97 9.20 27.80

B2 14.64 7.50 23.30





Graph 4. Returns for Balanced fund one and two







Table 5. Returns for Ambitious fund one and two

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

A1 36.2 6.3 32.4 11.8 2.9 14.7 22.9 3.5 38.6 10.8 15.8

A2 27.3 2.6 33.5 14.7 3.4 15.1 32.8 -6.1 24.1 13.8 25.2

AVG STD RANGE

A1 17.80 12.30 35.70

A2 16.94 12.40 39.60





Graph 5. Returns for Ambitious fund one and two













Table 6. Returns for Aggressive fund one and two

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

G1 23.7 7.6 33.4 25.8 5.5 13.3 28.6 6.9 51.5 4.0 -4.1

G2 22.3 0.3 38.3 19.7 6.0 14.1 37.0 -2.1 57.6 6.4 -1.2

AVG STD RANGE

G1 17.83 15.5 55.6

G2 18.03 18.4 59.7







Graph 6. Returns for Aggressive fund one and two





CONCLUSIONS AND RECOMMENDATIONS

The percentages from the calculations show that of the funds selected, only three from the original 12 would meet the requirement of 15 % percent a year. It also showed that they would fail to meet the expected return, at least 37.83% of the time sometimes more. The overall return should be up to the individual and to ensure continual growth of a portfolio, a person should meet the expected return at least 80 % of the time. By evaluating each fund using some of these methods will help a person make an informed decision. The use of statistics can help evaluate overall performance of funds. This in turn will help you make more informed decisions with your investments, to build the future that you want. Always remember to pay yourself something first, and control your money, don"t let your money control you.



 

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